diff options
Diffstat (limited to 'unsupported')
122 files changed, 31341 insertions, 0 deletions
diff --git a/unsupported/CMakeLists.txt b/unsupported/CMakeLists.txt new file mode 100644 index 000000000..4fef40a86 --- /dev/null +++ b/unsupported/CMakeLists.txt @@ -0,0 +1,7 @@ +add_subdirectory(Eigen) +add_subdirectory(doc EXCLUDE_FROM_ALL) +if(EIGEN_LEAVE_TEST_IN_ALL_TARGET) + add_subdirectory(test) # can't do EXCLUDE_FROM_ALL here, breaks CTest +else() + add_subdirectory(test EXCLUDE_FROM_ALL) +endif() diff --git a/unsupported/Eigen/AdolcForward b/unsupported/Eigen/AdolcForward new file mode 100644 index 000000000..b96f9450e --- /dev/null +++ b/unsupported/Eigen/AdolcForward @@ -0,0 +1,156 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_ADLOC_FORWARD +#define EIGEN_ADLOC_FORWARD + +//-------------------------------------------------------------------------------- +// +// This file provides support for adolc's adouble type in forward mode. +// ADOL-C is a C++ automatic differentiation library, +// see https://projects.coin-or.org/ADOL-C for more information. +// +// Note that the maximal number of directions is controlled by +// the preprocessor token NUMBER_DIRECTIONS. The default is 2. +// +//-------------------------------------------------------------------------------- + +#define ADOLC_TAPELESS +#ifndef NUMBER_DIRECTIONS +# define NUMBER_DIRECTIONS 2 +#endif +#include <adolc/adouble.h> + +// adolc defines some very stupid macros: +#if defined(malloc) +# undef malloc +#endif + +#if defined(calloc) +# undef calloc +#endif + +#if defined(realloc) +# undef realloc +#endif + +#include <Eigen/Core> + +namespace Eigen { + +/** \ingroup Unsupported_modules + * \defgroup AdolcForward_Module Adolc forward module + * This module provides support for adolc's adouble type in forward mode. + * ADOL-C is a C++ automatic differentiation library, + * see https://projects.coin-or.org/ADOL-C for more information. + * It mainly consists in: + * - a struct Eigen::NumTraits<adtl::adouble> specialization + * - overloads of internal::* math function for adtl::adouble type. + * + * Note that the maximal number of directions is controlled by + * the preprocessor token NUMBER_DIRECTIONS. The default is 2. + * + * \code + * #include <unsupported/Eigen/AdolcSupport> + * \endcode + */ + //@{ + +} // namespace Eigen + +// Eigen's require a few additional functions which must be defined in the same namespace +// than the custom scalar type own namespace +namespace adtl { + +inline const adouble& conj(const adouble& x) { return x; } +inline const adouble& real(const adouble& x) { return x; } +inline adouble imag(const adouble&) { return 0.; } +inline adouble abs(const adouble& x) { return fabs(x); } +inline adouble abs2(const adouble& x) { return x*x; } + +} + +namespace Eigen { + +template<> struct NumTraits<adtl::adouble> + : NumTraits<double> +{ + typedef adtl::adouble Real; + typedef adtl::adouble NonInteger; + typedef adtl::adouble Nested; + enum { + IsComplex = 0, + IsInteger = 0, + IsSigned = 1, + RequireInitialization = 1, + ReadCost = 1, + AddCost = 1, + MulCost = 1 + }; +}; + +template<typename Functor> class AdolcForwardJacobian : public Functor +{ + typedef adtl::adouble ActiveScalar; +public: + + AdolcForwardJacobian() : Functor() {} + AdolcForwardJacobian(const Functor& f) : Functor(f) {} + + // forward constructors + template<typename T0> + AdolcForwardJacobian(const T0& a0) : Functor(a0) {} + template<typename T0, typename T1> + AdolcForwardJacobian(const T0& a0, const T1& a1) : Functor(a0, a1) {} + template<typename T0, typename T1, typename T2> + AdolcForwardJacobian(const T0& a0, const T1& a1, const T1& a2) : Functor(a0, a1, a2) {} + + typedef typename Functor::InputType InputType; + typedef typename Functor::ValueType ValueType; + typedef typename Functor::JacobianType JacobianType; + + typedef Matrix<ActiveScalar, InputType::SizeAtCompileTime, 1> ActiveInput; + typedef Matrix<ActiveScalar, ValueType::SizeAtCompileTime, 1> ActiveValue; + + void operator() (const InputType& x, ValueType* v, JacobianType* _jac) const + { + eigen_assert(v!=0); + if (!_jac) + { + Functor::operator()(x, v); + return; + } + + JacobianType& jac = *_jac; + + ActiveInput ax = x.template cast<ActiveScalar>(); + ActiveValue av(jac.rows()); + + for (int j=0; j<jac.cols(); j++) + for (int i=0; i<jac.cols(); i++) + ax[i].setADValue(j, i==j ? 1 : 0); + + Functor::operator()(ax, &av); + + for (int i=0; i<jac.rows(); i++) + { + (*v)[i] = av[i].getValue(); + for (int j=0; j<jac.cols(); j++) + jac.coeffRef(i,j) = av[i].getADValue(j); + } + } +protected: + +}; + +//@} + +} + +#endif // EIGEN_ADLOC_FORWARD diff --git a/unsupported/Eigen/AlignedVector3 b/unsupported/Eigen/AlignedVector3 new file mode 100644 index 000000000..8ad0eb477 --- /dev/null +++ b/unsupported/Eigen/AlignedVector3 @@ -0,0 +1,189 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_ALIGNED_VECTOR3 +#define EIGEN_ALIGNED_VECTOR3 + +#include <Eigen/Geometry> + +namespace Eigen { + +/** \ingroup Unsupported_modules + * \defgroup AlignedVector3_Module Aligned vector3 module + * + * \code + * #include <unsupported/Eigen/AlignedVector3> + * \endcode + */ + //@{ + + +/** \class AlignedVector3 + * + * \brief A vectorization friendly 3D vector + * + * This class represents a 3D vector internally using a 4D vector + * such that vectorization can be seamlessly enabled. Of course, + * the same result can be achieved by directly using a 4D vector. + * This class makes this process simpler. + * + */ +// TODO specialize Cwise +template<typename _Scalar> class AlignedVector3; + +namespace internal { +template<typename _Scalar> struct traits<AlignedVector3<_Scalar> > + : traits<Matrix<_Scalar,3,1,0,4,1> > +{ +}; +} + +template<typename _Scalar> class AlignedVector3 + : public MatrixBase<AlignedVector3<_Scalar> > +{ + typedef Matrix<_Scalar,4,1> CoeffType; + CoeffType m_coeffs; + public: + + typedef MatrixBase<AlignedVector3<_Scalar> > Base; + EIGEN_DENSE_PUBLIC_INTERFACE(AlignedVector3) + using Base::operator*; + + inline Index rows() const { return 3; } + inline Index cols() const { return 1; } + + inline const Scalar& coeff(Index row, Index col) const + { return m_coeffs.coeff(row, col); } + + inline Scalar& coeffRef(Index row, Index col) + { return m_coeffs.coeffRef(row, col); } + + inline const Scalar& coeff(Index index) const + { return m_coeffs.coeff(index); } + + inline Scalar& coeffRef(Index index) + { return m_coeffs.coeffRef(index);} + + + inline AlignedVector3(const Scalar& x, const Scalar& y, const Scalar& z) + : m_coeffs(x, y, z, Scalar(0)) + {} + + inline AlignedVector3(const AlignedVector3& other) + : Base(), m_coeffs(other.m_coeffs) + {} + + template<typename XprType, int Size=XprType::SizeAtCompileTime> + struct generic_assign_selector {}; + + template<typename XprType> struct generic_assign_selector<XprType,4> + { + inline static void run(AlignedVector3& dest, const XprType& src) + { + dest.m_coeffs = src; + } + }; + + template<typename XprType> struct generic_assign_selector<XprType,3> + { + inline static void run(AlignedVector3& dest, const XprType& src) + { + dest.m_coeffs.template head<3>() = src; + dest.m_coeffs.w() = Scalar(0); + } + }; + + template<typename Derived> + inline explicit AlignedVector3(const MatrixBase<Derived>& other) + { + generic_assign_selector<Derived>::run(*this,other.derived()); + } + + inline AlignedVector3& operator=(const AlignedVector3& other) + { m_coeffs = other.m_coeffs; return *this; } + + + inline AlignedVector3 operator+(const AlignedVector3& other) const + { return AlignedVector3(m_coeffs + other.m_coeffs); } + + inline AlignedVector3& operator+=(const AlignedVector3& other) + { m_coeffs += other.m_coeffs; return *this; } + + inline AlignedVector3 operator-(const AlignedVector3& other) const + { return AlignedVector3(m_coeffs - other.m_coeffs); } + + inline AlignedVector3 operator-=(const AlignedVector3& other) + { m_coeffs -= other.m_coeffs; return *this; } + + inline AlignedVector3 operator*(const Scalar& s) const + { return AlignedVector3(m_coeffs * s); } + + inline friend AlignedVector3 operator*(const Scalar& s,const AlignedVector3& vec) + { return AlignedVector3(s * vec.m_coeffs); } + + inline AlignedVector3& operator*=(const Scalar& s) + { m_coeffs *= s; return *this; } + + inline AlignedVector3 operator/(const Scalar& s) const + { return AlignedVector3(m_coeffs / s); } + + inline AlignedVector3& operator/=(const Scalar& s) + { m_coeffs /= s; return *this; } + + inline Scalar dot(const AlignedVector3& other) const + { + eigen_assert(m_coeffs.w()==Scalar(0)); + eigen_assert(other.m_coeffs.w()==Scalar(0)); + return m_coeffs.dot(other.m_coeffs); + } + + inline void normalize() + { + m_coeffs /= norm(); + } + + inline AlignedVector3 normalized() + { + return AlignedVector3(m_coeffs / norm()); + } + + inline Scalar sum() const + { + eigen_assert(m_coeffs.w()==Scalar(0)); + return m_coeffs.sum(); + } + + inline Scalar squaredNorm() const + { + eigen_assert(m_coeffs.w()==Scalar(0)); + return m_coeffs.squaredNorm(); + } + + inline Scalar norm() const + { + return internal::sqrt(squaredNorm()); + } + + inline AlignedVector3 cross(const AlignedVector3& other) const + { + return AlignedVector3(m_coeffs.cross3(other.m_coeffs)); + } + + template<typename Derived> + inline bool isApprox(const MatrixBase<Derived>& other, RealScalar eps=NumTraits<Scalar>::dummy_precision()) const + { + return m_coeffs.template head<3>().isApprox(other,eps); + } +}; + +//@} + +} + +#endif // EIGEN_ALIGNED_VECTOR3 diff --git a/unsupported/Eigen/AutoDiff b/unsupported/Eigen/AutoDiff new file mode 100644 index 000000000..3c73b424e --- /dev/null +++ b/unsupported/Eigen/AutoDiff @@ -0,0 +1,40 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_AUTODIFF_MODULE +#define EIGEN_AUTODIFF_MODULE + +namespace Eigen { + +/** \ingroup Unsupported_modules + * \defgroup AutoDiff_Module Auto Diff module + * + * This module features forward automatic differentation via a simple + * templated scalar type wrapper AutoDiffScalar. + * + * Warning : this should NOT be confused with numerical differentiation, which + * is a different method and has its own module in Eigen : \ref NumericalDiff_Module. + * + * \code + * #include <unsupported/Eigen/AutoDiff> + * \endcode + */ +//@{ + +} + +#include "src/AutoDiff/AutoDiffScalar.h" +// #include "src/AutoDiff/AutoDiffVector.h" +#include "src/AutoDiff/AutoDiffJacobian.h" + +namespace Eigen { +//@} +} + +#endif // EIGEN_AUTODIFF_MODULE diff --git a/unsupported/Eigen/BVH b/unsupported/Eigen/BVH new file mode 100644 index 000000000..860a7dd89 --- /dev/null +++ b/unsupported/Eigen/BVH @@ -0,0 +1,95 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Ilya Baran <ibaran@mit.edu> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_BVH_MODULE_H +#define EIGEN_BVH_MODULE_H + +#include <Eigen/Core> +#include <Eigen/Geometry> +#include <Eigen/StdVector> +#include <algorithm> +#include <queue> + +namespace Eigen { + +/** \ingroup Unsupported_modules + * \defgroup BVH_Module BVH module + * \brief This module provides generic bounding volume hierarchy algorithms + * and reference tree implementations. + * + * + * \code + * #include <unsupported/Eigen/BVH> + * \endcode + * + * A bounding volume hierarchy (BVH) can accelerate many geometric queries. This module provides a generic implementation + * of the two basic algorithms over a BVH: intersection of a query object against all objects in the hierarchy and minimization + * of a function over the objects in the hierarchy. It also provides intersection and minimization over a cartesian product of + * two BVH's. A BVH accelerates intersection by using the fact that if a query object does not intersect a volume, then it cannot + * intersect any object contained in that volume. Similarly, a BVH accelerates minimization because the minimum of a function + * over a volume is no greater than the minimum of a function over any object contained in it. + * + * Some sample queries that can be written in terms of intersection are: + * - Determine all points where a ray intersects a triangle mesh + * - Given a set of points, determine which are contained in a query sphere + * - Given a set of spheres, determine which contain the query point + * - Given a set of disks, determine if any is completely contained in a query rectangle (represent each 2D disk as a point \f$(x,y,r)\f$ + * in 3D and represent the rectangle as a pyramid based on the original rectangle and shrinking in the \f$r\f$ direction) + * - Given a set of points, count how many pairs are \f$d\pm\epsilon\f$ apart (done by looking at the cartesian product of the set + * of points with itself) + * + * Some sample queries that can be written in terms of function minimization over a set of objects are: + * - Find the intersection between a ray and a triangle mesh closest to the ray origin (function is infinite off the ray) + * - Given a polyline and a query point, determine the closest point on the polyline to the query + * - Find the diameter of a point cloud (done by looking at the cartesian product and using negative distance as the function) + * - Determine how far two meshes are from colliding (this is also a cartesian product query) + * + * This implementation decouples the basic algorithms both from the type of hierarchy (and the types of the bounding volumes) and + * from the particulars of the query. To enable abstraction from the BVH, the BVH is required to implement a generic mechanism + * for traversal. To abstract from the query, the query is responsible for keeping track of results. + * + * To be used in the algorithms, a hierarchy must implement the following traversal mechanism (see KdBVH for a sample implementation): \code + typedef Volume //the type of bounding volume + typedef Object //the type of object in the hierarchy + typedef Index //a reference to a node in the hierarchy--typically an int or a pointer + typedef VolumeIterator //an iterator type over node children--returns Index + typedef ObjectIterator //an iterator over object (leaf) children--returns const Object & + Index getRootIndex() const //returns the index of the hierarchy root + const Volume &getVolume(Index index) const //returns the bounding volume of the node at given index + void getChildren(Index index, VolumeIterator &outVBegin, VolumeIterator &outVEnd, + ObjectIterator &outOBegin, ObjectIterator &outOEnd) const + //getChildren takes a node index and makes [outVBegin, outVEnd) range over its node children + //and [outOBegin, outOEnd) range over its object children + \endcode + * + * To use the hierarchy, call BVIntersect or BVMinimize, passing it a BVH (or two, for cartesian product) and a minimizer or intersector. + * For an intersection query on a single BVH, the intersector encapsulates the query and must provide two functions: + * \code + bool intersectVolume(const Volume &volume) //returns true if the query intersects the volume + bool intersectObject(const Object &object) //returns true if the intersection search should terminate immediately + \endcode + * The guarantee that BVIntersect provides is that intersectObject will be called on every object whose bounding volume + * intersects the query (but possibly on other objects too) unless the search is terminated prematurely. It is the + * responsibility of the intersectObject function to keep track of the results in whatever manner is appropriate. + * The cartesian product intersection and the BVMinimize queries are similar--see their individual documentation. + * + * The following is a simple but complete example for how to use the BVH to accelerate the search for a closest red-blue point pair: + * \include BVH_Example.cpp + * Output: \verbinclude BVH_Example.out + */ +} + +//@{ + +#include "src/BVH/BVAlgorithms.h" +#include "src/BVH/KdBVH.h" + +//@} + +#endif // EIGEN_BVH_MODULE_H diff --git a/unsupported/Eigen/CMakeLists.txt b/unsupported/Eigen/CMakeLists.txt new file mode 100644 index 000000000..e961e72c5 --- /dev/null +++ b/unsupported/Eigen/CMakeLists.txt @@ -0,0 +1,11 @@ +set(Eigen_HEADERS AdolcForward BVH IterativeSolvers MatrixFunctions MoreVectorization AutoDiff AlignedVector3 Polynomials + FFT NonLinearOptimization SparseExtra IterativeSolvers + NumericalDiff Skyline MPRealSupport OpenGLSupport KroneckerProduct Splines + ) + +install(FILES + ${Eigen_HEADERS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen COMPONENT Devel + ) + +add_subdirectory(src) diff --git a/unsupported/Eigen/FFT b/unsupported/Eigen/FFT new file mode 100644 index 000000000..d233c6d5f --- /dev/null +++ b/unsupported/Eigen/FFT @@ -0,0 +1,418 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Mark Borgerding mark a borgerding net +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_FFT_H +#define EIGEN_FFT_H + +#include <complex> +#include <vector> +#include <map> +#include <Eigen/Core> + + +/** \ingroup Unsupported_modules + * \defgroup FFT_Module Fast Fourier Transform module + * + * \code + * #include <unsupported/Eigen/FFT> + * \endcode + * + * This module provides Fast Fourier transformation, with a configurable backend + * implementation. + * + * The default implementation is based on kissfft. It is a small, free, and + * reasonably efficient default. + * + * There are currently two implementation backend: + * + * - fftw (http://www.fftw.org) : faster, GPL -- incompatible with Eigen in LGPL form, bigger code size. + * - MKL (http://en.wikipedia.org/wiki/Math_Kernel_Library) : fastest, commercial -- may be incompatible with Eigen in GPL form. + * + * \section FFTDesign Design + * + * The following design decisions were made concerning scaling and + * half-spectrum for real FFT. + * + * The intent is to facilitate generic programming and ease migrating code + * from Matlab/octave. + * We think the default behavior of Eigen/FFT should favor correctness and + * generality over speed. Of course, the caller should be able to "opt-out" from this + * behavior and get the speed increase if they want it. + * + * 1) %Scaling: + * Other libraries (FFTW,IMKL,KISSFFT) do not perform scaling, so there + * is a constant gain incurred after the forward&inverse transforms , so + * IFFT(FFT(x)) = Kx; this is done to avoid a vector-by-value multiply. + * The downside is that algorithms that worked correctly in Matlab/octave + * don't behave the same way once implemented in C++. + * + * How Eigen/FFT differs: invertible scaling is performed so IFFT( FFT(x) ) = x. + * + * 2) Real FFT half-spectrum + * Other libraries use only half the frequency spectrum (plus one extra + * sample for the Nyquist bin) for a real FFT, the other half is the + * conjugate-symmetric of the first half. This saves them a copy and some + * memory. The downside is the caller needs to have special logic for the + * number of bins in complex vs real. + * + * How Eigen/FFT differs: The full spectrum is returned from the forward + * transform. This facilitates generic template programming by obviating + * separate specializations for real vs complex. On the inverse + * transform, only half the spectrum is actually used if the output type is real. + */ + + +#ifdef EIGEN_FFTW_DEFAULT +// FFTW: faster, GPL -- incompatible with Eigen in LGPL form, bigger code size +# include <fftw3.h> +# include "src/FFT/ei_fftw_impl.h" + namespace Eigen { + //template <typename T> typedef struct internal::fftw_impl default_fft_impl; this does not work + template <typename T> struct default_fft_impl : public internal::fftw_impl<T> {}; + } +#elif defined EIGEN_MKL_DEFAULT +// TODO +// intel Math Kernel Library: fastest, commercial -- may be incompatible with Eigen in GPL form +# include "src/FFT/ei_imklfft_impl.h" + namespace Eigen { + template <typename T> struct default_fft_impl : public internal::imklfft_impl {}; + } +#else +// internal::kissfft_impl: small, free, reasonably efficient default, derived from kissfft +// +# include "src/FFT/ei_kissfft_impl.h" + namespace Eigen { + template <typename T> + struct default_fft_impl : public internal::kissfft_impl<T> {}; + } +#endif + +namespace Eigen { + + +// +template<typename T_SrcMat,typename T_FftIfc> struct fft_fwd_proxy; +template<typename T_SrcMat,typename T_FftIfc> struct fft_inv_proxy; + +namespace internal { +template<typename T_SrcMat,typename T_FftIfc> +struct traits< fft_fwd_proxy<T_SrcMat,T_FftIfc> > +{ + typedef typename T_SrcMat::PlainObject ReturnType; +}; +template<typename T_SrcMat,typename T_FftIfc> +struct traits< fft_inv_proxy<T_SrcMat,T_FftIfc> > +{ + typedef typename T_SrcMat::PlainObject ReturnType; +}; +} + +template<typename T_SrcMat,typename T_FftIfc> +struct fft_fwd_proxy + : public ReturnByValue<fft_fwd_proxy<T_SrcMat,T_FftIfc> > +{ + typedef DenseIndex Index; + + fft_fwd_proxy(const T_SrcMat& src,T_FftIfc & fft, Index nfft) : m_src(src),m_ifc(fft), m_nfft(nfft) {} + + template<typename T_DestMat> void evalTo(T_DestMat& dst) const; + + Index rows() const { return m_src.rows(); } + Index cols() const { return m_src.cols(); } +protected: + const T_SrcMat & m_src; + T_FftIfc & m_ifc; + Index m_nfft; +private: + fft_fwd_proxy& operator=(const fft_fwd_proxy&); +}; + +template<typename T_SrcMat,typename T_FftIfc> +struct fft_inv_proxy + : public ReturnByValue<fft_inv_proxy<T_SrcMat,T_FftIfc> > +{ + typedef DenseIndex Index; + + fft_inv_proxy(const T_SrcMat& src,T_FftIfc & fft, Index nfft) : m_src(src),m_ifc(fft), m_nfft(nfft) {} + + template<typename T_DestMat> void evalTo(T_DestMat& dst) const; + + Index rows() const { return m_src.rows(); } + Index cols() const { return m_src.cols(); } +protected: + const T_SrcMat & m_src; + T_FftIfc & m_ifc; + Index m_nfft; +private: + fft_inv_proxy& operator=(const fft_inv_proxy&); +}; + + +template <typename T_Scalar, + typename T_Impl=default_fft_impl<T_Scalar> > +class FFT +{ + public: + typedef T_Impl impl_type; + typedef DenseIndex Index; + typedef typename impl_type::Scalar Scalar; + typedef typename impl_type::Complex Complex; + + enum Flag { + Default=0, // goof proof + Unscaled=1, + HalfSpectrum=2, + // SomeOtherSpeedOptimization=4 + Speedy=32767 + }; + + FFT( const impl_type & impl=impl_type() , Flag flags=Default ) :m_impl(impl),m_flag(flags) { } + + inline + bool HasFlag(Flag f) const { return (m_flag & (int)f) == f;} + + inline + void SetFlag(Flag f) { m_flag |= (int)f;} + + inline + void ClearFlag(Flag f) { m_flag &= (~(int)f);} + + inline + void fwd( Complex * dst, const Scalar * src, Index nfft) + { + m_impl.fwd(dst,src,static_cast<int>(nfft)); + if ( HasFlag(HalfSpectrum) == false) + ReflectSpectrum(dst,nfft); + } + + inline + void fwd( Complex * dst, const Complex * src, Index nfft) + { + m_impl.fwd(dst,src,static_cast<int>(nfft)); + } + + /* + inline + void fwd2(Complex * dst, const Complex * src, int n0,int n1) + { + m_impl.fwd2(dst,src,n0,n1); + } + */ + + template <typename _Input> + inline + void fwd( std::vector<Complex> & dst, const std::vector<_Input> & src) + { + if ( NumTraits<_Input>::IsComplex == 0 && HasFlag(HalfSpectrum) ) + dst.resize( (src.size()>>1)+1); // half the bins + Nyquist bin + else + dst.resize(src.size()); + fwd(&dst[0],&src[0],src.size()); + } + + template<typename InputDerived, typename ComplexDerived> + inline + void fwd( MatrixBase<ComplexDerived> & dst, const MatrixBase<InputDerived> & src, Index nfft=-1) + { + typedef typename ComplexDerived::Scalar dst_type; + typedef typename InputDerived::Scalar src_type; + EIGEN_STATIC_ASSERT_VECTOR_ONLY(InputDerived) + EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived) + EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,InputDerived) // size at compile-time + EIGEN_STATIC_ASSERT((internal::is_same<dst_type, Complex>::value), + YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY) + EIGEN_STATIC_ASSERT(int(InputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit, + THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES) + + if (nfft<1) + nfft = src.size(); + + if ( NumTraits< src_type >::IsComplex == 0 && HasFlag(HalfSpectrum) ) + dst.derived().resize( (nfft>>1)+1); + else + dst.derived().resize(nfft); + + if ( src.innerStride() != 1 || src.size() < nfft ) { + Matrix<src_type,1,Dynamic> tmp; + if (src.size()<nfft) { + tmp.setZero(nfft); + tmp.block(0,0,src.size(),1 ) = src; + }else{ + tmp = src; + } + fwd( &dst[0],&tmp[0],nfft ); + }else{ + fwd( &dst[0],&src[0],nfft ); + } + } + + template<typename InputDerived> + inline + fft_fwd_proxy< MatrixBase<InputDerived>, FFT<T_Scalar,T_Impl> > + fwd( const MatrixBase<InputDerived> & src, Index nfft=-1) + { + return fft_fwd_proxy< MatrixBase<InputDerived> ,FFT<T_Scalar,T_Impl> >( src, *this,nfft ); + } + + template<typename InputDerived> + inline + fft_inv_proxy< MatrixBase<InputDerived>, FFT<T_Scalar,T_Impl> > + inv( const MatrixBase<InputDerived> & src, Index nfft=-1) + { + return fft_inv_proxy< MatrixBase<InputDerived> ,FFT<T_Scalar,T_Impl> >( src, *this,nfft ); + } + + inline + void inv( Complex * dst, const Complex * src, Index nfft) + { + m_impl.inv( dst,src,static_cast<int>(nfft) ); + if ( HasFlag( Unscaled ) == false) + scale(dst,Scalar(1./nfft),nfft); // scale the time series + } + + inline + void inv( Scalar * dst, const Complex * src, Index nfft) + { + m_impl.inv( dst,src,static_cast<int>(nfft) ); + if ( HasFlag( Unscaled ) == false) + scale(dst,Scalar(1./nfft),nfft); // scale the time series + } + + template<typename OutputDerived, typename ComplexDerived> + inline + void inv( MatrixBase<OutputDerived> & dst, const MatrixBase<ComplexDerived> & src, Index nfft=-1) + { + typedef typename ComplexDerived::Scalar src_type; + typedef typename OutputDerived::Scalar dst_type; + const bool realfft= (NumTraits<dst_type>::IsComplex == 0); + EIGEN_STATIC_ASSERT_VECTOR_ONLY(OutputDerived) + EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived) + EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,OutputDerived) // size at compile-time + EIGEN_STATIC_ASSERT((internal::is_same<src_type, Complex>::value), + YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY) + EIGEN_STATIC_ASSERT(int(OutputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit, + THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES) + + if (nfft<1) { //automatic FFT size determination + if ( realfft && HasFlag(HalfSpectrum) ) + nfft = 2*(src.size()-1); //assume even fft size + else + nfft = src.size(); + } + dst.derived().resize( nfft ); + + // check for nfft that does not fit the input data size + Index resize_input= ( realfft && HasFlag(HalfSpectrum) ) + ? ( (nfft/2+1) - src.size() ) + : ( nfft - src.size() ); + + if ( src.innerStride() != 1 || resize_input ) { + // if the vector is strided, then we need to copy it to a packed temporary + Matrix<src_type,1,Dynamic> tmp; + if ( resize_input ) { + size_t ncopy = (std::min)(src.size(),src.size() + resize_input); + tmp.setZero(src.size() + resize_input); + if ( realfft && HasFlag(HalfSpectrum) ) { + // pad at the Nyquist bin + tmp.head(ncopy) = src.head(ncopy); + tmp(ncopy-1) = real(tmp(ncopy-1)); // enforce real-only Nyquist bin + }else{ + size_t nhead,ntail; + nhead = 1+ncopy/2-1; // range [0:pi) + ntail = ncopy/2-1; // range (-pi:0) + tmp.head(nhead) = src.head(nhead); + tmp.tail(ntail) = src.tail(ntail); + if (resize_input<0) { //shrinking -- create the Nyquist bin as the average of the two bins that fold into it + tmp(nhead) = ( src(nfft/2) + src( src.size() - nfft/2 ) )*src_type(.5); + }else{ // expanding -- split the old Nyquist bin into two halves + tmp(nhead) = src(nhead) * src_type(.5); + tmp(tmp.size()-nhead) = tmp(nhead); + } + } + }else{ + tmp = src; + } + inv( &dst[0],&tmp[0], nfft); + }else{ + inv( &dst[0],&src[0], nfft); + } + } + + template <typename _Output> + inline + void inv( std::vector<_Output> & dst, const std::vector<Complex> & src,Index nfft=-1) + { + if (nfft<1) + nfft = ( NumTraits<_Output>::IsComplex == 0 && HasFlag(HalfSpectrum) ) ? 2*(src.size()-1) : src.size(); + dst.resize( nfft ); + inv( &dst[0],&src[0],nfft); + } + + + /* + // TODO: multi-dimensional FFTs + inline + void inv2(Complex * dst, const Complex * src, int n0,int n1) + { + m_impl.inv2(dst,src,n0,n1); + if ( HasFlag( Unscaled ) == false) + scale(dst,1./(n0*n1),n0*n1); + } + */ + + inline + impl_type & impl() {return m_impl;} + private: + + template <typename T_Data> + inline + void scale(T_Data * x,Scalar s,Index nx) + { +#if 1 + for (int k=0;k<nx;++k) + *x++ *= s; +#else + if ( ((ptrdiff_t)x) & 15 ) + Matrix<T_Data, Dynamic, 1>::Map(x,nx) *= s; + else + Matrix<T_Data, Dynamic, 1>::MapAligned(x,nx) *= s; + //Matrix<T_Data, Dynamic, Dynamic>::Map(x,nx) * s; +#endif + } + + inline + void ReflectSpectrum(Complex * freq, Index nfft) + { + // create the implicit right-half spectrum (conjugate-mirror of the left-half) + Index nhbins=(nfft>>1)+1; + for (Index k=nhbins;k < nfft; ++k ) + freq[k] = conj(freq[nfft-k]); + } + + impl_type m_impl; + int m_flag; +}; + +template<typename T_SrcMat,typename T_FftIfc> +template<typename T_DestMat> inline +void fft_fwd_proxy<T_SrcMat,T_FftIfc>::evalTo(T_DestMat& dst) const +{ + m_ifc.fwd( dst, m_src, m_nfft); +} + +template<typename T_SrcMat,typename T_FftIfc> +template<typename T_DestMat> inline +void fft_inv_proxy<T_SrcMat,T_FftIfc>::evalTo(T_DestMat& dst) const +{ + m_ifc.inv( dst, m_src, m_nfft); +} + +} +#endif +/* vim: set filetype=cpp et sw=2 ts=2 ai: */ diff --git a/unsupported/Eigen/IterativeSolvers b/unsupported/Eigen/IterativeSolvers new file mode 100644 index 000000000..6c6946d91 --- /dev/null +++ b/unsupported/Eigen/IterativeSolvers @@ -0,0 +1,40 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_ITERATIVE_SOLVERS_MODULE_H +#define EIGEN_ITERATIVE_SOLVERS_MODULE_H + +#include <Eigen/Sparse> + +/** \ingroup Unsupported_modules + * \defgroup IterativeSolvers_Module Iterative solvers module + * This module aims to provide various iterative linear and non linear solver algorithms. + * It currently provides: + * - a constrained conjugate gradient + * - a Householder GMRES implementation + * \code + * #include <unsupported/Eigen/IterativeSolvers> + * \endcode + */ +//@{ + +#include "../../Eigen/src/misc/Solve.h" +#include "../../Eigen/src/misc/SparseSolve.h" + +#include "src/IterativeSolvers/IterationController.h" +#include "src/IterativeSolvers/ConstrainedConjGrad.h" +#include "src/IterativeSolvers/IncompleteLU.h" +#include "../../Eigen/Jacobi" +#include "../../Eigen/Householder" +#include "src/IterativeSolvers/GMRES.h" +//#include "src/IterativeSolvers/SSORPreconditioner.h" + +//@} + +#endif // EIGEN_ITERATIVE_SOLVERS_MODULE_H diff --git a/unsupported/Eigen/KroneckerProduct b/unsupported/Eigen/KroneckerProduct new file mode 100644 index 000000000..796e386ad --- /dev/null +++ b/unsupported/Eigen/KroneckerProduct @@ -0,0 +1,26 @@ +#ifndef EIGEN_KRONECKER_PRODUCT_MODULE_H +#define EIGEN_KRONECKER_PRODUCT_MODULE_H + +#include "../../Eigen/Core" + +#include "../../Eigen/src/Core/util/DisableStupidWarnings.h" + +namespace Eigen { + +/** \ingroup Unsupported_modules + * \defgroup KroneckerProduct_Module KroneckerProduct module + * + * This module contains an experimental Kronecker product implementation. + * + * \code + * #include <Eigen/KroneckerProduct> + * \endcode + */ + +} // namespace Eigen + +#include "src/KroneckerProduct/KroneckerTensorProduct.h" + +#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_KRONECKER_PRODUCT_MODULE_H diff --git a/unsupported/Eigen/MPRealSupport b/unsupported/Eigen/MPRealSupport new file mode 100644 index 000000000..3895623fe --- /dev/null +++ b/unsupported/Eigen/MPRealSupport @@ -0,0 +1,148 @@ +// This file is part of a joint effort between Eigen, a lightweight C++ template library +// for linear algebra, and MPFR C++, a C++ interface to MPFR library (http://www.holoborodko.com/pavel/) +// +// Copyright (C) 2010 Pavel Holoborodko <pavel@holoborodko.com> +// Copyright (C) 2010 Konstantin Holoborodko <konstantin@holoborodko.com> +// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. +// +// Contributors: +// Brian Gladman, Helmut Jarausch, Fokko Beekhof, Ulrich Mutze, Heinz van Saanen, Pere Constans + +#ifndef EIGEN_MPREALSUPPORT_MODULE_H +#define EIGEN_MPREALSUPPORT_MODULE_H + +#include <ctime> +#include <mpreal.h> +#include <Eigen/Core> + +namespace Eigen { + + /** \ingroup Unsupported_modules + * \defgroup MPRealSupport_Module MPFRC++ Support module + * + * \code + * #include <Eigen/MPRealSupport> + * \endcode + * + * This module provides support for multi precision floating point numbers + * via the <a href="http://www.holoborodko.com/pavel/mpfr">MPFR C++</a> + * library which itself is built upon <a href="http://www.mpfr.org/">MPFR</a>/<a href="http://gmplib.org/">GMP</a>. + * + * You can find a copy of MPFR C++ that is known to be compatible in the unsupported/test/mpreal folder. + * + * Here is an example: + * +\code +#include <iostream> +#include <Eigen/MPRealSupport> +#include <Eigen/LU> +using namespace mpfr; +using namespace Eigen; +int main() +{ + // set precision to 256 bits (double has only 53 bits) + mpreal::set_default_prec(256); + // Declare matrix and vector types with multi-precision scalar type + typedef Matrix<mpreal,Dynamic,Dynamic> MatrixXmp; + typedef Matrix<mpreal,Dynamic,1> VectorXmp; + + MatrixXmp A = MatrixXmp::Random(100,100); + VectorXmp b = VectorXmp::Random(100); + + // Solve Ax=b using LU + VectorXmp x = A.lu().solve(b); + std::cout << "relative error: " << (A*x - b).norm() / b.norm() << std::endl; + return 0; +} +\endcode + * + */ + + template<> struct NumTraits<mpfr::mpreal> + : GenericNumTraits<mpfr::mpreal> + { + enum { + IsInteger = 0, + IsSigned = 1, + IsComplex = 0, + RequireInitialization = 1, + ReadCost = 10, + AddCost = 10, + MulCost = 40 + }; + + typedef mpfr::mpreal Real; + typedef mpfr::mpreal NonInteger; + + inline static mpfr::mpreal highest() { return mpfr::mpreal_max(mpfr::mpreal::get_default_prec()); } + inline static mpfr::mpreal lowest() { return -mpfr::mpreal_max(mpfr::mpreal::get_default_prec()); } + + inline static Real epsilon() + { + return mpfr::machine_epsilon(mpfr::mpreal::get_default_prec()); + } + inline static Real dummy_precision() + { + unsigned int weak_prec = ((mpfr::mpreal::get_default_prec()-1)*90)/100; + return mpfr::machine_epsilon(weak_prec); + } + }; + +namespace internal { + + template<> mpfr::mpreal random<mpfr::mpreal>() + { +#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0)) + static gmp_randstate_t state; + static bool isFirstTime = true; + + if(isFirstTime) + { + gmp_randinit_default(state); + gmp_randseed_ui(state,(unsigned)time(NULL)); + isFirstTime = false; + } + + return mpfr::urandom(state)*2-1; +#else + return mpfr::mpreal(random<double>()); +#endif + } + + template<> mpfr::mpreal random<mpfr::mpreal>(const mpfr::mpreal& a, const mpfr::mpreal& b) + { + return a + (b-a) * random<mpfr::mpreal>(); + } + + bool isMuchSmallerThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& prec) + { + return mpfr::abs(a) <= mpfr::abs(b) * prec; + } + + inline bool isApprox(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& prec) + { + return mpfr::abs(a - b) <= (mpfr::min)(mpfr::abs(a), mpfr::abs(b)) * prec; + } + + inline bool isApproxOrLessThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& prec) + { + return a <= b || isApprox(a, b, prec); + } + + template<> inline long double cast<mpfr::mpreal,long double>(const mpfr::mpreal& x) + { return x.toLDouble(); } + template<> inline double cast<mpfr::mpreal,double>(const mpfr::mpreal& x) + { return x.toDouble(); } + template<> inline long cast<mpfr::mpreal,long>(const mpfr::mpreal& x) + { return x.toLong(); } + template<> inline int cast<mpfr::mpreal,int>(const mpfr::mpreal& x) + { return int(x.toLong()); } + +} // end namespace internal +} + +#endif // EIGEN_MPREALSUPPORT_MODULE_H diff --git a/unsupported/Eigen/MatrixFunctions b/unsupported/Eigen/MatrixFunctions new file mode 100644 index 000000000..56ab71cd3 --- /dev/null +++ b/unsupported/Eigen/MatrixFunctions @@ -0,0 +1,380 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MATRIX_FUNCTIONS +#define EIGEN_MATRIX_FUNCTIONS + +#include <cfloat> +#include <list> +#include <functional> +#include <iterator> + +#include <Eigen/Core> +#include <Eigen/LU> +#include <Eigen/Eigenvalues> + +/** \ingroup Unsupported_modules + * \defgroup MatrixFunctions_Module Matrix functions module + * \brief This module aims to provide various methods for the computation of + * matrix functions. + * + * To use this module, add + * \code + * #include <unsupported/Eigen/MatrixFunctions> + * \endcode + * at the start of your source file. + * + * This module defines the following MatrixBase methods. + * - \ref matrixbase_cos "MatrixBase::cos()", for computing the matrix cosine + * - \ref matrixbase_cosh "MatrixBase::cosh()", for computing the matrix hyperbolic cosine + * - \ref matrixbase_exp "MatrixBase::exp()", for computing the matrix exponential + * - \ref matrixbase_log "MatrixBase::log()", for computing the matrix logarithm + * - \ref matrixbase_matrixfunction "MatrixBase::matrixFunction()", for computing general matrix functions + * - \ref matrixbase_sin "MatrixBase::sin()", for computing the matrix sine + * - \ref matrixbase_sinh "MatrixBase::sinh()", for computing the matrix hyperbolic sine + * - \ref matrixbase_sqrt "MatrixBase::sqrt()", for computing the matrix square root + * + * These methods are the main entry points to this module. + * + * %Matrix functions are defined as follows. Suppose that \f$ f \f$ + * is an entire function (that is, a function on the complex plane + * that is everywhere complex differentiable). Then its Taylor + * series + * \f[ f(0) + f'(0) x + \frac{f''(0)}{2} x^2 + \frac{f'''(0)}{3!} x^3 + \cdots \f] + * converges to \f$ f(x) \f$. In this case, we can define the matrix + * function by the same series: + * \f[ f(M) = f(0) + f'(0) M + \frac{f''(0)}{2} M^2 + \frac{f'''(0)}{3!} M^3 + \cdots \f] + * + */ + +#include "src/MatrixFunctions/MatrixExponential.h" +#include "src/MatrixFunctions/MatrixFunction.h" +#include "src/MatrixFunctions/MatrixSquareRoot.h" +#include "src/MatrixFunctions/MatrixLogarithm.h" + + + +/** +\page matrixbaseextra MatrixBase methods defined in the MatrixFunctions module +\ingroup MatrixFunctions_Module + +The remainder of the page documents the following MatrixBase methods +which are defined in the MatrixFunctions module. + + + +\section matrixbase_cos MatrixBase::cos() + +Compute the matrix cosine. + +\code +const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const +\endcode + +\param[in] M a square matrix. +\returns expression representing \f$ \cos(M) \f$. + +This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::cos(). + +\sa \ref matrixbase_sin "sin()" for an example. + + + +\section matrixbase_cosh MatrixBase::cosh() + +Compute the matrix hyberbolic cosine. + +\code +const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cosh() const +\endcode + +\param[in] M a square matrix. +\returns expression representing \f$ \cosh(M) \f$ + +This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::cosh(). + +\sa \ref matrixbase_sinh "sinh()" for an example. + + + +\section matrixbase_exp MatrixBase::exp() + +Compute the matrix exponential. + +\code +const MatrixExponentialReturnValue<Derived> MatrixBase<Derived>::exp() const +\endcode + +\param[in] M matrix whose exponential is to be computed. +\returns expression representing the matrix exponential of \p M. + +The matrix exponential of \f$ M \f$ is defined by +\f[ \exp(M) = \sum_{k=0}^\infty \frac{M^k}{k!}. \f] +The matrix exponential can be used to solve linear ordinary +differential equations: the solution of \f$ y' = My \f$ with the +initial condition \f$ y(0) = y_0 \f$ is given by +\f$ y(t) = \exp(M) y_0 \f$. + +The cost of the computation is approximately \f$ 20 n^3 \f$ for +matrices of size \f$ n \f$. The number 20 depends weakly on the +norm of the matrix. + +The matrix exponential is computed using the scaling-and-squaring +method combined with Padé approximation. The matrix is first +rescaled, then the exponential of the reduced matrix is computed +approximant, and then the rescaling is undone by repeated +squaring. The degree of the Padé approximant is chosen such +that the approximation error is less than the round-off +error. However, errors may accumulate during the squaring phase. + +Details of the algorithm can be found in: Nicholas J. Higham, "The +scaling and squaring method for the matrix exponential revisited," +<em>SIAM J. %Matrix Anal. Applic.</em>, <b>26</b>:1179–1193, +2005. + +Example: The following program checks that +\f[ \exp \left[ \begin{array}{ccc} + 0 & \frac14\pi & 0 \\ + -\frac14\pi & 0 & 0 \\ + 0 & 0 & 0 + \end{array} \right] = \left[ \begin{array}{ccc} + \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\ + \frac12\sqrt2 & \frac12\sqrt2 & 0 \\ + 0 & 0 & 1 + \end{array} \right]. \f] +This corresponds to a rotation of \f$ \frac14\pi \f$ radians around +the z-axis. + +\include MatrixExponential.cpp +Output: \verbinclude MatrixExponential.out + +\note \p M has to be a matrix of \c float, \c double, \c long double +\c complex<float>, \c complex<double>, or \c complex<long double> . + + +\section matrixbase_log MatrixBase::log() + +Compute the matrix logarithm. + +\code +const MatrixLogarithmReturnValue<Derived> MatrixBase<Derived>::log() const +\endcode + +\param[in] M invertible matrix whose logarithm is to be computed. +\returns expression representing the matrix logarithm root of \p M. + +The matrix logarithm of \f$ M \f$ is a matrix \f$ X \f$ such that +\f$ \exp(X) = M \f$ where exp denotes the matrix exponential. As for +the scalar logarithm, the equation \f$ \exp(X) = M \f$ may have +multiple solutions; this function returns a matrix whose eigenvalues +have imaginary part in the interval \f$ (-\pi,\pi] \f$. + +In the real case, the matrix \f$ M \f$ should be invertible and +it should have no eigenvalues which are real and negative (pairs of +complex conjugate eigenvalues are allowed). In the complex case, it +only needs to be invertible. + +This function computes the matrix logarithm using the Schur-Parlett +algorithm as implemented by MatrixBase::matrixFunction(). The +logarithm of an atomic block is computed by MatrixLogarithmAtomic, +which uses direct computation for 1-by-1 and 2-by-2 blocks and an +inverse scaling-and-squaring algorithm for bigger blocks, with the +square roots computed by MatrixBase::sqrt(). + +Details of the algorithm can be found in Section 11.6.2 of: +Nicholas J. Higham, +<em>Functions of Matrices: Theory and Computation</em>, +SIAM 2008. ISBN 978-0-898716-46-7. + +Example: The following program checks that +\f[ \log \left[ \begin{array}{ccc} + \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\ + \frac12\sqrt2 & \frac12\sqrt2 & 0 \\ + 0 & 0 & 1 + \end{array} \right] = \left[ \begin{array}{ccc} + 0 & \frac14\pi & 0 \\ + -\frac14\pi & 0 & 0 \\ + 0 & 0 & 0 + \end{array} \right]. \f] +This corresponds to a rotation of \f$ \frac14\pi \f$ radians around +the z-axis. This is the inverse of the example used in the +documentation of \ref matrixbase_exp "exp()". + +\include MatrixLogarithm.cpp +Output: \verbinclude MatrixLogarithm.out + +\note \p M has to be a matrix of \c float, \c double, \c long double +\c complex<float>, \c complex<double>, or \c complex<long double> . + +\sa MatrixBase::exp(), MatrixBase::matrixFunction(), + class MatrixLogarithmAtomic, MatrixBase::sqrt(). + + +\section matrixbase_matrixfunction MatrixBase::matrixFunction() + +Compute a matrix function. + +\code +const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::matrixFunction(typename internal::stem_function<typename internal::traits<Derived>::Scalar>::type f) const +\endcode + +\param[in] M argument of matrix function, should be a square matrix. +\param[in] f an entire function; \c f(x,n) should compute the n-th +derivative of f at x. +\returns expression representing \p f applied to \p M. + +Suppose that \p M is a matrix whose entries have type \c Scalar. +Then, the second argument, \p f, should be a function with prototype +\code +ComplexScalar f(ComplexScalar, int) +\endcode +where \c ComplexScalar = \c std::complex<Scalar> if \c Scalar is +real (e.g., \c float or \c double) and \c ComplexScalar = +\c Scalar if \c Scalar is complex. The return value of \c f(x,n) +should be \f$ f^{(n)}(x) \f$, the n-th derivative of f at x. + +This routine uses the algorithm described in: +Philip Davies and Nicholas J. Higham, +"A Schur-Parlett algorithm for computing matrix functions", +<em>SIAM J. %Matrix Anal. Applic.</em>, <b>25</b>:464–485, 2003. + +The actual work is done by the MatrixFunction class. + +Example: The following program checks that +\f[ \exp \left[ \begin{array}{ccc} + 0 & \frac14\pi & 0 \\ + -\frac14\pi & 0 & 0 \\ + 0 & 0 & 0 + \end{array} \right] = \left[ \begin{array}{ccc} + \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\ + \frac12\sqrt2 & \frac12\sqrt2 & 0 \\ + 0 & 0 & 1 + \end{array} \right]. \f] +This corresponds to a rotation of \f$ \frac14\pi \f$ radians around +the z-axis. This is the same example as used in the documentation +of \ref matrixbase_exp "exp()". + +\include MatrixFunction.cpp +Output: \verbinclude MatrixFunction.out + +Note that the function \c expfn is defined for complex numbers +\c x, even though the matrix \c A is over the reals. Instead of +\c expfn, we could also have used StdStemFunctions::exp: +\code +A.matrixFunction(StdStemFunctions<std::complex<double> >::exp, &B); +\endcode + + + +\section matrixbase_sin MatrixBase::sin() + +Compute the matrix sine. + +\code +const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const +\endcode + +\param[in] M a square matrix. +\returns expression representing \f$ \sin(M) \f$. + +This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::sin(). + +Example: \include MatrixSine.cpp +Output: \verbinclude MatrixSine.out + + + +\section matrixbase_sinh MatrixBase::sinh() + +Compute the matrix hyperbolic sine. + +\code +MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sinh() const +\endcode + +\param[in] M a square matrix. +\returns expression representing \f$ \sinh(M) \f$ + +This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::sinh(). + +Example: \include MatrixSinh.cpp +Output: \verbinclude MatrixSinh.out + + +\section matrixbase_sqrt MatrixBase::sqrt() + +Compute the matrix square root. + +\code +const MatrixSquareRootReturnValue<Derived> MatrixBase<Derived>::sqrt() const +\endcode + +\param[in] M invertible matrix whose square root is to be computed. +\returns expression representing the matrix square root of \p M. + +The matrix square root of \f$ M \f$ is the matrix \f$ M^{1/2} \f$ +whose square is the original matrix; so if \f$ S = M^{1/2} \f$ then +\f$ S^2 = M \f$. + +In the <b>real case</b>, the matrix \f$ M \f$ should be invertible and +it should have no eigenvalues which are real and negative (pairs of +complex conjugate eigenvalues are allowed). In that case, the matrix +has a square root which is also real, and this is the square root +computed by this function. + +The matrix square root is computed by first reducing the matrix to +quasi-triangular form with the real Schur decomposition. The square +root of the quasi-triangular matrix can then be computed directly. The +cost is approximately \f$ 25 n^3 \f$ real flops for the real Schur +decomposition and \f$ 3\frac13 n^3 \f$ real flops for the remainder +(though the computation time in practice is likely more than this +indicates). + +Details of the algorithm can be found in: Nicholas J. Highan, +"Computing real square roots of a real matrix", <em>Linear Algebra +Appl.</em>, 88/89:405–430, 1987. + +If the matrix is <b>positive-definite symmetric</b>, then the square +root is also positive-definite symmetric. In this case, it is best to +use SelfAdjointEigenSolver::operatorSqrt() to compute it. + +In the <b>complex case</b>, the matrix \f$ M \f$ should be invertible; +this is a restriction of the algorithm. The square root computed by +this algorithm is the one whose eigenvalues have an argument in the +interval \f$ (-\frac12\pi, \frac12\pi] \f$. This is the usual branch +cut. + +The computation is the same as in the real case, except that the +complex Schur decomposition is used to reduce the matrix to a +triangular matrix. The theoretical cost is the same. Details are in: +Åke Björck and Sven Hammarling, "A Schur method for the +square root of a matrix", <em>Linear Algebra Appl.</em>, +52/53:127–140, 1983. + +Example: The following program checks that the square root of +\f[ \left[ \begin{array}{cc} + \cos(\frac13\pi) & -\sin(\frac13\pi) \\ + \sin(\frac13\pi) & \cos(\frac13\pi) + \end{array} \right], \f] +corresponding to a rotation over 60 degrees, is a rotation over 30 degrees: +\f[ \left[ \begin{array}{cc} + \cos(\frac16\pi) & -\sin(\frac16\pi) \\ + \sin(\frac16\pi) & \cos(\frac16\pi) + \end{array} \right]. \f] + +\include MatrixSquareRoot.cpp +Output: \verbinclude MatrixSquareRoot.out + +\sa class RealSchur, class ComplexSchur, class MatrixSquareRoot, + SelfAdjointEigenSolver::operatorSqrt(). + +*/ + +#endif // EIGEN_MATRIX_FUNCTIONS + diff --git a/unsupported/Eigen/MoreVectorization b/unsupported/Eigen/MoreVectorization new file mode 100644 index 000000000..9f0a39f75 --- /dev/null +++ b/unsupported/Eigen/MoreVectorization @@ -0,0 +1,16 @@ +#ifndef EIGEN_MOREVECTORIZATION_MODULE_H +#define EIGEN_MOREVECTORIZATION_MODULE_H + +#include <Eigen/Core> + +namespace Eigen { + +/** \ingroup Unsupported_modules + * \defgroup MoreVectorization More vectorization module + */ + +} + +#include "src/MoreVectorization/MathFunctions.h" + +#endif // EIGEN_MOREVECTORIZATION_MODULE_H diff --git a/unsupported/Eigen/NonLinearOptimization b/unsupported/Eigen/NonLinearOptimization new file mode 100644 index 000000000..cf6ca58f8 --- /dev/null +++ b/unsupported/Eigen/NonLinearOptimization @@ -0,0 +1,134 @@ +// This file is part of Eugenio, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_NONLINEAROPTIMIZATION_MODULE +#define EIGEN_NONLINEAROPTIMIZATION_MODULE + +#include <vector> + +#include <Eigen/Core> +#include <Eigen/Jacobi> +#include <Eigen/QR> +#include <unsupported/Eigen/NumericalDiff> + +/** \ingroup Unsupported_modules + * \defgroup NonLinearOptimization_Module Non linear optimization module + * + * \code + * #include <unsupported/Eigen/NonLinearOptimization> + * \endcode + * + * This module provides implementation of two important algorithms in non linear + * optimization. In both cases, we consider a system of non linear functions. Of + * course, this should work, and even work very well if those functions are + * actually linear. But if this is so, you should probably better use other + * methods more fitted to this special case. + * + * One algorithm allows to find an extremum of such a system (Levenberg + * Marquardt algorithm) and the second one is used to find + * a zero for the system (Powell hybrid "dogleg" method). + * + * This code is a port of minpack (http://en.wikipedia.org/wiki/MINPACK). + * Minpack is a very famous, old, robust and well-reknown package, written in + * fortran. Those implementations have been carefully tuned, tested, and used + * for several decades. + * + * The original fortran code was automatically translated using f2c (http://en.wikipedia.org/wiki/F2c) in C, + * then c++, and then cleaned by several different authors. + * The last one of those cleanings being our starting point : + * http://devernay.free.fr/hacks/cminpack.html + * + * Finally, we ported this code to Eigen, creating classes and API + * coherent with Eigen. When possible, we switched to Eigen + * implementation, such as most linear algebra (vectors, matrices, stable norms). + * + * Doing so, we were very careful to check the tests we setup at the very + * beginning, which ensure that the same results are found. + * + * \section Tests Tests + * + * The tests are placed in the file unsupported/test/NonLinear.cpp. + * + * There are two kinds of tests : those that come from examples bundled with cminpack. + * They guaranty we get the same results as the original algorithms (value for 'x', + * for the number of evaluations of the function, and for the number of evaluations + * of the jacobian if ever). + * + * Other tests were added by myself at the very beginning of the + * process and check the results for levenberg-marquardt using the reference data + * on http://www.itl.nist.gov/div898/strd/nls/nls_main.shtml. Since then i've + * carefully checked that the same results were obtained when modifiying the + * code. Please note that we do not always get the exact same decimals as they do, + * but this is ok : they use 128bits float, and we do the tests using the C type 'double', + * which is 64 bits on most platforms (x86 and amd64, at least). + * I've performed those tests on several other implementations of levenberg-marquardt, and + * (c)minpack performs VERY well compared to those, both in accuracy and speed. + * + * The documentation for running the tests is on the wiki + * http://eigen.tuxfamily.org/index.php?title=Tests + * + * \section API API : overview of methods + * + * Both algorithms can use either the jacobian (provided by the user) or compute + * an approximation by themselves (actually using Eigen \ref NumericalDiff_Module). + * The part of API referring to the latter use 'NumericalDiff' in the method names + * (exemple: LevenbergMarquardt.minimizeNumericalDiff() ) + * + * The methods LevenbergMarquardt.lmder1()/lmdif1()/lmstr1() and + * HybridNonLinearSolver.hybrj1()/hybrd1() are specific methods from the original + * minpack package that you probably should NOT use until you are porting a code that + * was previously using minpack. They just define a 'simple' API with default values + * for some parameters. + * + * All algorithms are provided using Two APIs : + * - one where the user inits the algorithm, and uses '*OneStep()' as much as he wants : + * this way the caller have control over the steps + * - one where the user just calls a method (optimize() or solve()) which will + * handle the loop: init + loop until a stop condition is met. Those are provided for + * convenience. + * + * As an example, the method LevenbergMarquardt::minimize() is + * implemented as follow : + * \code + * Status LevenbergMarquardt<FunctorType,Scalar>::minimize(FVectorType &x, const int mode) + * { + * Status status = minimizeInit(x, mode); + * do { + * status = minimizeOneStep(x, mode); + * } while (status==Running); + * return status; + * } + * \endcode + * + * \section examples Examples + * + * The easiest way to understand how to use this module is by looking at the many examples in the file + * unsupported/test/NonLinearOptimization.cpp. + */ + +#ifndef EIGEN_PARSED_BY_DOXYGEN + +#include "src/NonLinearOptimization/qrsolv.h" +#include "src/NonLinearOptimization/r1updt.h" +#include "src/NonLinearOptimization/r1mpyq.h" +#include "src/NonLinearOptimization/rwupdt.h" +#include "src/NonLinearOptimization/fdjac1.h" +#include "src/NonLinearOptimization/lmpar.h" +#include "src/NonLinearOptimization/dogleg.h" +#include "src/NonLinearOptimization/covar.h" + +#include "src/NonLinearOptimization/chkder.h" + +#endif + +#include "src/NonLinearOptimization/HybridNonLinearSolver.h" +#include "src/NonLinearOptimization/LevenbergMarquardt.h" + + +#endif // EIGEN_NONLINEAROPTIMIZATION_MODULE diff --git a/unsupported/Eigen/NumericalDiff b/unsupported/Eigen/NumericalDiff new file mode 100644 index 000000000..b3480312d --- /dev/null +++ b/unsupported/Eigen/NumericalDiff @@ -0,0 +1,56 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_NUMERICALDIFF_MODULE +#define EIGEN_NUMERICALDIFF_MODULE + +#include <Eigen/Core> + +namespace Eigen { + +/** \ingroup Unsupported_modules + * \defgroup NumericalDiff_Module Numerical differentiation module + * + * \code + * #include <unsupported/Eigen/NumericalDiff> + * \endcode + * + * See http://en.wikipedia.org/wiki/Numerical_differentiation + * + * Warning : this should NOT be confused with automatic differentiation, which + * is a different method and has its own module in Eigen : \ref + * AutoDiff_Module. + * + * Currently only "Forward" and "Central" schemes are implemented. Those + * are basic methods, and there exist some more elaborated way of + * computing such approximates. They are implemented using both + * proprietary and free software, and usually requires linking to an + * external library. It is very easy for you to write a functor + * using such software, and the purpose is quite orthogonal to what we + * want to achieve with Eigen. + * + * This is why we will not provide wrappers for every great numerical + * differentiation software that exist, but should rather stick with those + * basic ones, that still are useful for testing. + * + * Also, the \ref NonLinearOptimization_Module needs this in order to + * provide full features compatibility with the original (c)minpack + * package. + * + */ +} + +//@{ + +#include "src/NumericalDiff/NumericalDiff.h" + +//@} + + +#endif // EIGEN_NUMERICALDIFF_MODULE diff --git a/unsupported/Eigen/OpenGLSupport b/unsupported/Eigen/OpenGLSupport new file mode 100644 index 000000000..e66a425f8 --- /dev/null +++ b/unsupported/Eigen/OpenGLSupport @@ -0,0 +1,317 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_OPENGL_MODULE +#define EIGEN_OPENGL_MODULE + +#include <Eigen/Geometry> +#include <GL/gl.h> + +namespace Eigen { + +/** \ingroup Unsupported_modules + * \defgroup OpenGLSUpport_Module OpenGL Support module + * + * This module provides wrapper functions for a couple of OpenGL functions + * which simplify the way to pass Eigen's object to openGL. + * Here is an exmaple: + * + * \code + * // You need to add path_to_eigen/unsupported to your include path. + * #include <Eigen/OpenGLSupport> + * // ... + * Vector3f x, y; + * Matrix3f rot; + * + * glVertex(y + x * rot); + * + * Quaternion q; + * glRotate(q); + * + * // ... + * \endcode + * + */ +//@{ + +#define EIGEN_GL_FUNC_DECLARATION(FUNC) \ +namespace internal { \ + template< typename XprType, \ + typename Scalar = typename XprType::Scalar, \ + int Rows = XprType::RowsAtCompileTime, \ + int Cols = XprType::ColsAtCompileTime, \ + bool IsGLCompatible = bool(XprType::Flags&LinearAccessBit) \ + && bool(XprType::Flags&DirectAccessBit) \ + && (XprType::IsVectorAtCompileTime || (XprType::Flags&RowMajorBit)==0)> \ + struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl); \ + \ + template<typename XprType, typename Scalar, int Rows, int Cols> \ + struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType,Scalar,Rows,Cols,false> { \ + inline static void run(const XprType& p) { \ + EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<typename plain_matrix_type_column_major<XprType>::type>::run(p); } \ + }; \ +} \ + \ +template<typename Derived> inline void FUNC(const Eigen::DenseBase<Derived>& p) { \ + EIGEN_CAT(EIGEN_CAT(internal::gl_,FUNC),_impl)<Derived>::run(p.derived()); \ +} + + +#define EIGEN_GL_FUNC_SPECIALIZATION_MAT(FUNC,SCALAR,ROWS,COLS,SUFFIX) \ +namespace internal { \ + template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, ROWS, COLS, true> { \ + inline static void run(const XprType& p) { FUNC##SUFFIX(p.data()); } \ + }; \ +} + + +#define EIGEN_GL_FUNC_SPECIALIZATION_VEC(FUNC,SCALAR,SIZE,SUFFIX) \ +namespace internal { \ + template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, SIZE, 1, true> { \ + inline static void run(const XprType& p) { FUNC##SUFFIX(p.data()); } \ + }; \ + template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, 1, SIZE, true> { \ + inline static void run(const XprType& p) { FUNC##SUFFIX(p.data()); } \ + }; \ +} + + +EIGEN_GL_FUNC_DECLARATION (glVertex) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,int, 2,2iv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,short, 2,2sv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,float, 2,2fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,double, 2,2dv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,int, 3,3iv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,short, 3,3sv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,float, 3,3fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,double, 3,3dv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,int, 4,4iv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,short, 4,4sv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,float, 4,4fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,double, 4,4dv) + +EIGEN_GL_FUNC_DECLARATION (glTexCoord) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,int, 2,2iv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,short, 2,2sv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,float, 2,2fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,double, 2,2dv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,int, 3,3iv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,short, 3,3sv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,float, 3,3fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,double, 3,3dv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,int, 4,4iv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,short, 4,4sv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,float, 4,4fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,double, 4,4dv) + +EIGEN_GL_FUNC_DECLARATION (glColor) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,int, 2,2iv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,short, 2,2sv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,float, 2,2fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,double, 2,2dv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,int, 3,3iv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,short, 3,3sv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,float, 3,3fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,double, 3,3dv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,int, 4,4iv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,short, 4,4sv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,float, 4,4fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,double, 4,4dv) + +EIGEN_GL_FUNC_DECLARATION (glNormal) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glNormal,int, 3,3iv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glNormal,short, 3,3sv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glNormal,float, 3,3fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glNormal,double, 3,3dv) + +inline void glScale2fv(const float* v) { glScalef(v[0], v[1], 1.f); } +inline void glScale2dv(const double* v) { glScaled(v[0], v[1], 1.0); } +inline void glScale3fv(const float* v) { glScalef(v[0], v[1], v[2]); } +inline void glScale3dv(const double* v) { glScaled(v[0], v[1], v[2]); } + +EIGEN_GL_FUNC_DECLARATION (glScale) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glScale,float, 2,2fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glScale,double, 2,2dv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glScale,float, 3,3fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glScale,double, 3,3dv) + +template<typename Scalar> void glScale(const UniformScaling<Scalar>& s) { glScale(Matrix<Scalar,3,1>::Constant(s.factor())); } + +inline void glTranslate2fv(const float* v) { glTranslatef(v[0], v[1], 0.f); } +inline void glTranslate2dv(const double* v) { glTranslated(v[0], v[1], 0.0); } +inline void glTranslate3fv(const float* v) { glTranslatef(v[0], v[1], v[2]); } +inline void glTranslate3dv(const double* v) { glTranslated(v[0], v[1], v[2]); } + +EIGEN_GL_FUNC_DECLARATION (glTranslate) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTranslate,float, 2,2fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTranslate,double, 2,2dv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTranslate,float, 3,3fv) +EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTranslate,double, 3,3dv) + +template<typename Scalar> void glTranslate(const Translation<Scalar,2>& t) { glTranslate(t.vector()); } +template<typename Scalar> void glTranslate(const Translation<Scalar,3>& t) { glTranslate(t.vector()); } + +EIGEN_GL_FUNC_DECLARATION (glMultMatrix) +EIGEN_GL_FUNC_SPECIALIZATION_MAT(glMultMatrix,float, 4,4,f) +EIGEN_GL_FUNC_SPECIALIZATION_MAT(glMultMatrix,double, 4,4,d) + +template<typename Scalar> void glMultMatrix(const Transform<Scalar,3,Affine>& t) { glMultMatrix(t.matrix()); } +template<typename Scalar> void glMultMatrix(const Transform<Scalar,3,Projective>& t) { glMultMatrix(t.matrix()); } +template<typename Scalar> void glMultMatrix(const Transform<Scalar,3,AffineCompact>& t) { glMultMatrix(Transform<Scalar,3,Affine>(t).matrix()); } + +EIGEN_GL_FUNC_DECLARATION (glLoadMatrix) +EIGEN_GL_FUNC_SPECIALIZATION_MAT(glLoadMatrix,float, 4,4,f) +EIGEN_GL_FUNC_SPECIALIZATION_MAT(glLoadMatrix,double, 4,4,d) + +template<typename Scalar> void glLoadMatrix(const Transform<Scalar,3,Affine>& t) { glLoadMatrix(t.matrix()); } +template<typename Scalar> void glLoadMatrix(const Transform<Scalar,3,Projective>& t) { glLoadMatrix(t.matrix()); } +template<typename Scalar> void glLoadMatrix(const Transform<Scalar,3,AffineCompact>& t) { glLoadMatrix(Transform<Scalar,3,Affine>(t).matrix()); } + +static void glRotate(const Rotation2D<float>& rot) +{ + glRotatef(rot.angle()*180.f/float(M_PI), 0.f, 0.f, 1.f); +} +static void glRotate(const Rotation2D<double>& rot) +{ + glRotated(rot.angle()*180.0/M_PI, 0.0, 0.0, 1.0); +} + +template<typename Derived> void glRotate(const RotationBase<Derived,3>& rot) +{ + Transform<typename Derived::Scalar,3,Projective> tr(rot); + glMultMatrix(tr.matrix()); +} + +#define EIGEN_GL_MAKE_CONST_const const +#define EIGEN_GL_MAKE_CONST__ +#define EIGEN_GL_EVAL(X) X + +#define EIGEN_GL_FUNC1_DECLARATION(FUNC,ARG1,CONST) \ +namespace internal { \ + template< typename XprType, \ + typename Scalar = typename XprType::Scalar, \ + int Rows = XprType::RowsAtCompileTime, \ + int Cols = XprType::ColsAtCompileTime, \ + bool IsGLCompatible = bool(XprType::Flags&LinearAccessBit) \ + && bool(XprType::Flags&DirectAccessBit) \ + && (XprType::IsVectorAtCompileTime || (XprType::Flags&RowMajorBit)==0)> \ + struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl); \ + \ + template<typename XprType, typename Scalar, int Rows, int Cols> \ + struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType,Scalar,Rows,Cols,false> { \ + inline static void run(ARG1 a,EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) XprType& p) { \ + EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<typename plain_matrix_type_column_major<XprType>::type>::run(a,p); } \ + }; \ +} \ + \ +template<typename Derived> inline void FUNC(ARG1 a,EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) Eigen::DenseBase<Derived>& p) { \ + EIGEN_CAT(EIGEN_CAT(internal::gl_,FUNC),_impl)<Derived>::run(a,p.derived()); \ +} + + +#define EIGEN_GL_FUNC1_SPECIALIZATION_MAT(FUNC,ARG1,CONST,SCALAR,ROWS,COLS,SUFFIX) \ +namespace internal { \ + template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, ROWS, COLS, true> { \ + inline static void run(ARG1 a, EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) XprType& p) { FUNC##SUFFIX(a,p.data()); } \ + }; \ +} + + +#define EIGEN_GL_FUNC1_SPECIALIZATION_VEC(FUNC,ARG1,CONST,SCALAR,SIZE,SUFFIX) \ +namespace internal { \ + template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, SIZE, 1, true> { \ + inline static void run(ARG1 a, EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) XprType& p) { FUNC##SUFFIX(a,p.data()); } \ + }; \ + template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, 1, SIZE, true> { \ + inline static void run(ARG1 a, EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) XprType& p) { FUNC##SUFFIX(a,p.data()); } \ + }; \ +} + +EIGEN_GL_FUNC1_DECLARATION (glGet,GLenum,_) +EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glGet,GLenum,_,float, 4,4,Floatv) +EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glGet,GLenum,_,double, 4,4,Doublev) + +// glUniform API + +#ifdef GL_VERSION_2_0 + +static void glUniform2fv_ei (GLint loc, const float* v) { glUniform2fv(loc,1,v); } +static void glUniform2iv_ei (GLint loc, const int* v) { glUniform2iv(loc,1,v); } + +static void glUniform3fv_ei (GLint loc, const float* v) { glUniform3fv(loc,1,v); } +static void glUniform3iv_ei (GLint loc, const int* v) { glUniform3iv(loc,1,v); } + +static void glUniform4fv_ei (GLint loc, const float* v) { glUniform4fv(loc,1,v); } +static void glUniform4iv_ei (GLint loc, const int* v) { glUniform4iv(loc,1,v); } + +static void glUniformMatrix2fv_ei (GLint loc, const float* v) { glUniformMatrix2fv(loc,1,false,v); } +static void glUniformMatrix3fv_ei (GLint loc, const float* v) { glUniformMatrix3fv(loc,1,false,v); } +static void glUniformMatrix4fv_ei (GLint loc, const float* v) { glUniformMatrix4fv(loc,1,false,v); } + + +EIGEN_GL_FUNC1_DECLARATION (glUniform,GLint,const) +EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,float, 2,2fv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,int, 2,2iv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,float, 3,3fv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,int, 3,3iv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,float, 4,4fv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,int, 4,4iv_ei) + +EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 2,2,Matrix2fv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 3,3,Matrix3fv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 4,4,Matrix4fv_ei) + +#endif + +#ifdef GL_VERSION_2_1 + +static void glUniformMatrix2x3fv_ei(GLint loc, const float* v) { glUniformMatrix2x3fv(loc,1,false,v); } +static void glUniformMatrix3x2fv_ei(GLint loc, const float* v) { glUniformMatrix3x2fv(loc,1,false,v); } +static void glUniformMatrix2x4fv_ei(GLint loc, const float* v) { glUniformMatrix2x4fv(loc,1,false,v); } +static void glUniformMatrix4x2fv_ei(GLint loc, const float* v) { glUniformMatrix4x2fv(loc,1,false,v); } +static void glUniformMatrix3x4fv_ei(GLint loc, const float* v) { glUniformMatrix3x4fv(loc,1,false,v); } +static void glUniformMatrix4x3fv_ei(GLint loc, const float* v) { glUniformMatrix4x3fv(loc,1,false,v); } + +EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 2,3,Matrix2x3fv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 3,2,Matrix3x2fv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 2,4,Matrix2x4fv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 4,2,Matrix4x2fv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 3,4,Matrix3x4fv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 4,3,Matrix4x3fv_ei) + +#endif + +#ifdef GL_VERSION_3_0 + +static void glUniform2uiv_ei (GLint loc, const unsigned int* v) { glUniform2uiv(loc,1,v); } +static void glUniform3uiv_ei (GLint loc, const unsigned int* v) { glUniform3uiv(loc,1,v); } +static void glUniform4uiv_ei (GLint loc, const unsigned int* v) { glUniform4uiv(loc,1,v); } + +EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,unsigned int, 2,2uiv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,unsigned int, 3,3uiv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,unsigned int, 4,4uiv_ei) + +#endif + +#ifdef GL_ARB_gpu_shader_fp64 +static void glUniform2dv_ei (GLint loc, const double* v) { glUniform2dv(loc,1,v); } +static void glUniform3dv_ei (GLint loc, const double* v) { glUniform3dv(loc,1,v); } +static void glUniform4dv_ei (GLint loc, const double* v) { glUniform4dv(loc,1,v); } + +EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,double, 2,2dv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,double, 3,3dv_ei) +EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,double, 4,4dv_ei) +#endif + + +//@} + +} + +#endif // EIGEN_OPENGL_MODULE diff --git a/unsupported/Eigen/Polynomials b/unsupported/Eigen/Polynomials new file mode 100644 index 000000000..fa58b006d --- /dev/null +++ b/unsupported/Eigen/Polynomials @@ -0,0 +1,133 @@ +#ifndef EIGEN_POLYNOMIALS_MODULE_H +#define EIGEN_POLYNOMIALS_MODULE_H + +#include <Eigen/Core> + +#include <Eigen/src/Core/util/DisableStupidWarnings.h> + +#include <Eigen/Eigenvalues> + +// Note that EIGEN_HIDE_HEAVY_CODE has to be defined per module +#if (defined EIGEN_EXTERN_INSTANTIATIONS) && (EIGEN_EXTERN_INSTANTIATIONS>=2) + #ifndef EIGEN_HIDE_HEAVY_CODE + #define EIGEN_HIDE_HEAVY_CODE + #endif +#elif defined EIGEN_HIDE_HEAVY_CODE + #undef EIGEN_HIDE_HEAVY_CODE +#endif + +/** \ingroup Unsupported_modules + * \defgroup Polynomials_Module Polynomials module + * + * + * + * \brief This module provides a QR based polynomial solver. + * + * To use this module, add + * \code + * #include <unsupported/Eigen/Polynomials> + * \endcode + * at the start of your source file. + */ + +#include "src/Polynomials/PolynomialUtils.h" +#include "src/Polynomials/Companion.h" +#include "src/Polynomials/PolynomialSolver.h" + +/** + \page polynomials Polynomials defines functions for dealing with polynomials + and a QR based polynomial solver. + \ingroup Polynomials_Module + + The remainder of the page documents first the functions for evaluating, computing + polynomials, computing estimates about polynomials and next the QR based polynomial + solver. + + \section polynomialUtils convenient functions to deal with polynomials + \subsection roots_to_monicPolynomial + The function + \code + void roots_to_monicPolynomial( const RootVector& rv, Polynomial& poly ) + \endcode + computes the coefficients \f$ a_i \f$ of + + \f$ p(x) = a_0 + a_{1}x + ... + a_{n-1}x^{n-1} + x^n \f$ + + where \f$ p \f$ is known through its roots i.e. \f$ p(x) = (x-r_1)(x-r_2)...(x-r_n) \f$. + + \subsection poly_eval + The function + \code + T poly_eval( const Polynomials& poly, const T& x ) + \endcode + evaluates a polynomial at a given point using stabilized Hörner method. + + The following code: first computes the coefficients in the monomial basis of the monic polynomial that has the provided roots; + then, it evaluates the computed polynomial, using a stabilized Hörner method. + + \include PolynomialUtils1.cpp + Output: \verbinclude PolynomialUtils1.out + + \subsection Cauchy bounds + The function + \code + Real cauchy_max_bound( const Polynomial& poly ) + \endcode + provides a maximum bound (the Cauchy one: \f$C(p)\f$) for the absolute value of a root of the given polynomial i.e. + \f$ \forall r_i \f$ root of \f$ p(x) = \sum_{k=0}^d a_k x^k \f$, + \f$ |r_i| \le C(p) = \sum_{k=0}^{d} \left | \frac{a_k}{a_d} \right | \f$ + The leading coefficient \f$ p \f$: should be non zero \f$a_d \neq 0\f$. + + + The function + \code + Real cauchy_min_bound( const Polynomial& poly ) + \endcode + provides a minimum bound (the Cauchy one: \f$c(p)\f$) for the absolute value of a non zero root of the given polynomial i.e. + \f$ \forall r_i \neq 0 \f$ root of \f$ p(x) = \sum_{k=0}^d a_k x^k \f$, + \f$ |r_i| \ge c(p) = \left( \sum_{k=0}^{d} \left | \frac{a_k}{a_0} \right | \right)^{-1} \f$ + + + + + \section QR polynomial solver class + Computes the complex roots of a polynomial by computing the eigenvalues of the associated companion matrix with the QR algorithm. + + The roots of \f$ p(x) = a_0 + a_1 x + a_2 x^2 + a_{3} x^3 + x^4 \f$ are the eigenvalues of + \f$ + \left [ + \begin{array}{cccc} + 0 & 0 & 0 & a_0 \\ + 1 & 0 & 0 & a_1 \\ + 0 & 1 & 0 & a_2 \\ + 0 & 0 & 1 & a_3 + \end{array} \right ] + \f$ + + However, the QR algorithm is not guaranteed to converge when there are several eigenvalues with same modulus. + + Therefore the current polynomial solver is guaranteed to provide a correct result only when the complex roots \f$r_1,r_2,...,r_d\f$ have distinct moduli i.e. + + \f$ \forall i,j \in [1;d],~ \| r_i \| \neq \| r_j \| \f$. + + With 32bit (float) floating types this problem shows up frequently. + However, almost always, correct accuracy is reached even in these cases for 64bit + (double) floating types and small polynomial degree (<20). + + \include PolynomialSolver1.cpp + + In the above example: + + -# a simple use of the polynomial solver is shown; + -# the accuracy problem with the QR algorithm is presented: a polynomial with almost conjugate roots is provided to the solver. + Those roots have almost same module therefore the QR algorithm failed to converge: the accuracy + of the last root is bad; + -# a simple way to circumvent the problem is shown: use doubles instead of floats. + + Output: \verbinclude PolynomialSolver1.out +*/ + +#include <Eigen/src/Core/util/ReenableStupidWarnings.h> + +#endif // EIGEN_POLYNOMIALS_MODULE_H +/* vim: set filetype=cpp et sw=2 ts=2 ai: */ diff --git a/unsupported/Eigen/Skyline b/unsupported/Eigen/Skyline new file mode 100644 index 000000000..c9823f358 --- /dev/null +++ b/unsupported/Eigen/Skyline @@ -0,0 +1,31 @@ +#ifndef EIGEN_SKYLINE_MODULE_H +#define EIGEN_SKYLINE_MODULE_H + + +#include "Eigen/Core" + +#include "Eigen/src/Core/util/DisableStupidWarnings.h" + +#include <map> +#include <cstdlib> +#include <cstring> +#include <algorithm> + +/** \ingroup Unsupported_modules + * \defgroup Skyline_Module Skyline module + * + * + * + * + */ + +#include "src/Skyline/SkylineUtil.h" +#include "src/Skyline/SkylineMatrixBase.h" +#include "src/Skyline/SkylineStorage.h" +#include "src/Skyline/SkylineMatrix.h" +#include "src/Skyline/SkylineInplaceLU.h" +#include "src/Skyline/SkylineProduct.h" + +#include "Eigen/src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_SKYLINE_MODULE_H diff --git a/unsupported/Eigen/SparseExtra b/unsupported/Eigen/SparseExtra new file mode 100644 index 000000000..340c34736 --- /dev/null +++ b/unsupported/Eigen/SparseExtra @@ -0,0 +1,47 @@ +#ifndef EIGEN_SPARSE_EXTRA_MODULE_H +#define EIGEN_SPARSE_EXTRA_MODULE_H + +#include "../../Eigen/Sparse" + +#include "../../Eigen/src/Core/util/DisableStupidWarnings.h" + +#include <vector> +#include <map> +#include <cstdlib> +#include <cstring> +#include <algorithm> +#include <fstream> +#include <sstream> + +#ifdef EIGEN_GOOGLEHASH_SUPPORT + #include <google/dense_hash_map> +#endif + +/** \ingroup Unsupported_modules + * \defgroup SparseExtra_Module SparseExtra module + * + * This module contains some experimental features extending the sparse module. + * + * \code + * #include <Eigen/SparseExtra> + * \endcode + */ + + +#include "../../Eigen/src/misc/Solve.h" +#include "../../Eigen/src/misc/SparseSolve.h" + +#include "src/SparseExtra/DynamicSparseMatrix.h" +#include "src/SparseExtra/BlockOfDynamicSparseMatrix.h" +#include "src/SparseExtra/RandomSetter.h" + +#include "src/SparseExtra/MarketIO.h" + +#if !defined(_WIN32) +#include <dirent.h> +#include "src/SparseExtra/MatrixMarketIterator.h" +#endif + +#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_SPARSE_EXTRA_MODULE_H diff --git a/unsupported/Eigen/Splines b/unsupported/Eigen/Splines new file mode 100644 index 000000000..801cec1a1 --- /dev/null +++ b/unsupported/Eigen/Splines @@ -0,0 +1,31 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPLINES_MODULE_H +#define EIGEN_SPLINES_MODULE_H + +namespace Eigen +{ +/** \ingroup Unsupported_modules + * \defgroup Splines_Module Spline and spline fitting module + * + * This module provides a simple multi-dimensional spline class while + * offering most basic functionality to fit a spline to point sets. + * + * \code + * #include <unsupported/Eigen/Splines> + * \endcode + */ +} + +#include "src/Splines/SplineFwd.h" +#include "src/Splines/Spline.h" +#include "src/Splines/SplineFitting.h" + +#endif // EIGEN_SPLINES_MODULE_H diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h b/unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h new file mode 100644 index 000000000..1a61e3367 --- /dev/null +++ b/unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h @@ -0,0 +1,83 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_AUTODIFF_JACOBIAN_H +#define EIGEN_AUTODIFF_JACOBIAN_H + +namespace Eigen +{ + +template<typename Functor> class AutoDiffJacobian : public Functor +{ +public: + AutoDiffJacobian() : Functor() {} + AutoDiffJacobian(const Functor& f) : Functor(f) {} + + // forward constructors + template<typename T0> + AutoDiffJacobian(const T0& a0) : Functor(a0) {} + template<typename T0, typename T1> + AutoDiffJacobian(const T0& a0, const T1& a1) : Functor(a0, a1) {} + template<typename T0, typename T1, typename T2> + AutoDiffJacobian(const T0& a0, const T1& a1, const T2& a2) : Functor(a0, a1, a2) {} + + enum { + InputsAtCompileTime = Functor::InputsAtCompileTime, + ValuesAtCompileTime = Functor::ValuesAtCompileTime + }; + + typedef typename Functor::InputType InputType; + typedef typename Functor::ValueType ValueType; + typedef typename Functor::JacobianType JacobianType; + typedef typename JacobianType::Scalar Scalar; + typedef typename JacobianType::Index Index; + + typedef Matrix<Scalar,InputsAtCompileTime,1> DerivativeType; + typedef AutoDiffScalar<DerivativeType> ActiveScalar; + + + typedef Matrix<ActiveScalar, InputsAtCompileTime, 1> ActiveInput; + typedef Matrix<ActiveScalar, ValuesAtCompileTime, 1> ActiveValue; + + void operator() (const InputType& x, ValueType* v, JacobianType* _jac=0) const + { + eigen_assert(v!=0); + if (!_jac) + { + Functor::operator()(x, v); + return; + } + + JacobianType& jac = *_jac; + + ActiveInput ax = x.template cast<ActiveScalar>(); + ActiveValue av(jac.rows()); + + if(InputsAtCompileTime==Dynamic) + for (Index j=0; j<jac.rows(); j++) + av[j].derivatives().resize(this->inputs()); + + for (Index i=0; i<jac.cols(); i++) + ax[i].derivatives() = DerivativeType::Unit(this->inputs(),i); + + Functor::operator()(ax, &av); + + for (Index i=0; i<jac.rows(); i++) + { + (*v)[i] = av[i].value(); + jac.row(i) = av[i].derivatives(); + } + } +protected: + +}; + +} + +#endif // EIGEN_AUTODIFF_JACOBIAN_H diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h new file mode 100644 index 000000000..b833df3c0 --- /dev/null +++ b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h @@ -0,0 +1,632 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_AUTODIFF_SCALAR_H +#define EIGEN_AUTODIFF_SCALAR_H + +namespace Eigen { + +namespace internal { + +template<typename A, typename B> +struct make_coherent_impl { + static void run(A&, B&) {} +}; + +// resize a to match b is a.size()==0, and conversely. +template<typename A, typename B> +void make_coherent(const A& a, const B&b) +{ + make_coherent_impl<A,B>::run(a.const_cast_derived(), b.const_cast_derived()); +} + +template<typename _DerType, bool Enable> struct auto_diff_special_op; + +} // end namespace internal + +/** \class AutoDiffScalar + * \brief A scalar type replacement with automatic differentation capability + * + * \param _DerType the vector type used to store/represent the derivatives. The base scalar type + * as well as the number of derivatives to compute are determined from this type. + * Typical choices include, e.g., \c Vector4f for 4 derivatives, or \c VectorXf + * if the number of derivatives is not known at compile time, and/or, the number + * of derivatives is large. + * Note that _DerType can also be a reference (e.g., \c VectorXf&) to wrap a + * existing vector into an AutoDiffScalar. + * Finally, _DerType can also be any Eigen compatible expression. + * + * This class represents a scalar value while tracking its respective derivatives using Eigen's expression + * template mechanism. + * + * It supports the following list of global math function: + * - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos, + * - internal::abs, internal::sqrt, internal::pow, internal::exp, internal::log, internal::sin, internal::cos, + * - internal::conj, internal::real, internal::imag, internal::abs2. + * + * AutoDiffScalar can be used as the scalar type of an Eigen::Matrix object. However, + * in that case, the expression template mechanism only occurs at the top Matrix level, + * while derivatives are computed right away. + * + */ + +template<typename _DerType> +class AutoDiffScalar + : public internal::auto_diff_special_op + <_DerType, !internal::is_same<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar, + typename NumTraits<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar>::Real>::value> +{ + public: + typedef internal::auto_diff_special_op + <_DerType, !internal::is_same<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar, + typename NumTraits<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar>::Real>::value> Base; + typedef typename internal::remove_all<_DerType>::type DerType; + typedef typename internal::traits<DerType>::Scalar Scalar; + typedef typename NumTraits<Scalar>::Real Real; + + using Base::operator+; + using Base::operator*; + + /** Default constructor without any initialization. */ + AutoDiffScalar() {} + + /** Constructs an active scalar from its \a value, + and initializes the \a nbDer derivatives such that it corresponds to the \a derNumber -th variable */ + AutoDiffScalar(const Scalar& value, int nbDer, int derNumber) + : m_value(value), m_derivatives(DerType::Zero(nbDer)) + { + m_derivatives.coeffRef(derNumber) = Scalar(1); + } + + /** Conversion from a scalar constant to an active scalar. + * The derivatives are set to zero. */ + /*explicit*/ AutoDiffScalar(const Real& value) + : m_value(value) + { + if(m_derivatives.size()>0) + m_derivatives.setZero(); + } + + /** Constructs an active scalar from its \a value and derivatives \a der */ + AutoDiffScalar(const Scalar& value, const DerType& der) + : m_value(value), m_derivatives(der) + {} + + template<typename OtherDerType> + AutoDiffScalar(const AutoDiffScalar<OtherDerType>& other) + : m_value(other.value()), m_derivatives(other.derivatives()) + {} + + friend std::ostream & operator << (std::ostream & s, const AutoDiffScalar& a) + { + return s << a.value(); + } + + AutoDiffScalar(const AutoDiffScalar& other) + : m_value(other.value()), m_derivatives(other.derivatives()) + {} + + template<typename OtherDerType> + inline AutoDiffScalar& operator=(const AutoDiffScalar<OtherDerType>& other) + { + m_value = other.value(); + m_derivatives = other.derivatives(); + return *this; + } + + inline AutoDiffScalar& operator=(const AutoDiffScalar& other) + { + m_value = other.value(); + m_derivatives = other.derivatives(); + return *this; + } + +// inline operator const Scalar& () const { return m_value; } +// inline operator Scalar& () { return m_value; } + + inline const Scalar& value() const { return m_value; } + inline Scalar& value() { return m_value; } + + inline const DerType& derivatives() const { return m_derivatives; } + inline DerType& derivatives() { return m_derivatives; } + + inline bool operator< (const Scalar& other) const { return m_value < other; } + inline bool operator<=(const Scalar& other) const { return m_value <= other; } + inline bool operator> (const Scalar& other) const { return m_value > other; } + inline bool operator>=(const Scalar& other) const { return m_value >= other; } + inline bool operator==(const Scalar& other) const { return m_value == other; } + inline bool operator!=(const Scalar& other) const { return m_value != other; } + + friend inline bool operator< (const Scalar& a, const AutoDiffScalar& b) { return a < b.value(); } + friend inline bool operator<=(const Scalar& a, const AutoDiffScalar& b) { return a <= b.value(); } + friend inline bool operator> (const Scalar& a, const AutoDiffScalar& b) { return a > b.value(); } + friend inline bool operator>=(const Scalar& a, const AutoDiffScalar& b) { return a >= b.value(); } + friend inline bool operator==(const Scalar& a, const AutoDiffScalar& b) { return a == b.value(); } + friend inline bool operator!=(const Scalar& a, const AutoDiffScalar& b) { return a != b.value(); } + + template<typename OtherDerType> inline bool operator< (const AutoDiffScalar<OtherDerType>& b) const { return m_value < b.value(); } + template<typename OtherDerType> inline bool operator<=(const AutoDiffScalar<OtherDerType>& b) const { return m_value <= b.value(); } + template<typename OtherDerType> inline bool operator> (const AutoDiffScalar<OtherDerType>& b) const { return m_value > b.value(); } + template<typename OtherDerType> inline bool operator>=(const AutoDiffScalar<OtherDerType>& b) const { return m_value >= b.value(); } + template<typename OtherDerType> inline bool operator==(const AutoDiffScalar<OtherDerType>& b) const { return m_value == b.value(); } + template<typename OtherDerType> inline bool operator!=(const AutoDiffScalar<OtherDerType>& b) const { return m_value != b.value(); } + + inline const AutoDiffScalar<DerType&> operator+(const Scalar& other) const + { + return AutoDiffScalar<DerType&>(m_value + other, m_derivatives); + } + + friend inline const AutoDiffScalar<DerType&> operator+(const Scalar& a, const AutoDiffScalar& b) + { + return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives()); + } + +// inline const AutoDiffScalar<DerType&> operator+(const Real& other) const +// { +// return AutoDiffScalar<DerType&>(m_value + other, m_derivatives); +// } + +// friend inline const AutoDiffScalar<DerType&> operator+(const Real& a, const AutoDiffScalar& b) +// { +// return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives()); +// } + + inline AutoDiffScalar& operator+=(const Scalar& other) + { + value() += other; + return *this; + } + + template<typename OtherDerType> + inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,const DerType,const typename internal::remove_all<OtherDerType>::type> > + operator+(const AutoDiffScalar<OtherDerType>& other) const + { + internal::make_coherent(m_derivatives, other.derivatives()); + return AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,const DerType,const typename internal::remove_all<OtherDerType>::type> >( + m_value + other.value(), + m_derivatives + other.derivatives()); + } + + template<typename OtherDerType> + inline AutoDiffScalar& + operator+=(const AutoDiffScalar<OtherDerType>& other) + { + (*this) = (*this) + other; + return *this; + } + + inline const AutoDiffScalar<DerType&> operator-(const Scalar& b) const + { + return AutoDiffScalar<DerType&>(m_value - b, m_derivatives); + } + + friend inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> > + operator-(const Scalar& a, const AutoDiffScalar& b) + { + return AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> > + (a - b.value(), -b.derivatives()); + } + + inline AutoDiffScalar& operator-=(const Scalar& other) + { + value() -= other; + return *this; + } + + template<typename OtherDerType> + inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>, const DerType,const typename internal::remove_all<OtherDerType>::type> > + operator-(const AutoDiffScalar<OtherDerType>& other) const + { + internal::make_coherent(m_derivatives, other.derivatives()); + return AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>, const DerType,const typename internal::remove_all<OtherDerType>::type> >( + m_value - other.value(), + m_derivatives - other.derivatives()); + } + + template<typename OtherDerType> + inline AutoDiffScalar& + operator-=(const AutoDiffScalar<OtherDerType>& other) + { + *this = *this - other; + return *this; + } + + inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> > + operator-() const + { + return AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >( + -m_value, + -m_derivatives); + } + + inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> > + operator*(const Scalar& other) const + { + return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >( + m_value * other, + (m_derivatives * other)); + } + + friend inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> > + operator*(const Scalar& other, const AutoDiffScalar& a) + { + return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >( + a.value() * other, + a.derivatives() * other); + } + +// inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type > +// operator*(const Real& other) const +// { +// return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >( +// m_value * other, +// (m_derivatives * other)); +// } +// +// friend inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type > +// operator*(const Real& other, const AutoDiffScalar& a) +// { +// return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >( +// a.value() * other, +// a.derivatives() * other); +// } + + inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> > + operator/(const Scalar& other) const + { + return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >( + m_value / other, + (m_derivatives * (Scalar(1)/other))); + } + + friend inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> > + operator/(const Scalar& other, const AutoDiffScalar& a) + { + return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >( + other / a.value(), + a.derivatives() * (Scalar(-other) / (a.value()*a.value()))); + } + +// inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type > +// operator/(const Real& other) const +// { +// return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >( +// m_value / other, +// (m_derivatives * (Real(1)/other))); +// } +// +// friend inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type > +// operator/(const Real& other, const AutoDiffScalar& a) +// { +// return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >( +// other / a.value(), +// a.derivatives() * (-Real(1)/other)); +// } + + template<typename OtherDerType> + inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, + const CwiseBinaryOp<internal::scalar_difference_op<Scalar>, + const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType>, + const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const typename internal::remove_all<OtherDerType>::type > > > > + operator/(const AutoDiffScalar<OtherDerType>& other) const + { + internal::make_coherent(m_derivatives, other.derivatives()); + return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, + const CwiseBinaryOp<internal::scalar_difference_op<Scalar>, + const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType>, + const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const typename internal::remove_all<OtherDerType>::type > > > >( + m_value / other.value(), + ((m_derivatives * other.value()) - (m_value * other.derivatives())) + * (Scalar(1)/(other.value()*other.value()))); + } + + template<typename OtherDerType> + inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>, + const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType>, + const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const typename internal::remove_all<OtherDerType>::type> > > + operator*(const AutoDiffScalar<OtherDerType>& other) const + { + internal::make_coherent(m_derivatives, other.derivatives()); + return AutoDiffScalar<const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, + const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType>, + const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const typename internal::remove_all<OtherDerType>::type > > >( + m_value * other.value(), + (m_derivatives * other.value()) + (m_value * other.derivatives())); + } + + inline AutoDiffScalar& operator*=(const Scalar& other) + { + *this = *this * other; + return *this; + } + + template<typename OtherDerType> + inline AutoDiffScalar& operator*=(const AutoDiffScalar<OtherDerType>& other) + { + *this = *this * other; + return *this; + } + + inline AutoDiffScalar& operator/=(const Scalar& other) + { + *this = *this / other; + return *this; + } + + template<typename OtherDerType> + inline AutoDiffScalar& operator/=(const AutoDiffScalar<OtherDerType>& other) + { + *this = *this / other; + return *this; + } + + protected: + Scalar m_value; + DerType m_derivatives; + +}; + +namespace internal { + +template<typename _DerType> +struct auto_diff_special_op<_DerType, true> +// : auto_diff_scalar_op<_DerType, typename NumTraits<Scalar>::Real, +// is_same<Scalar,typename NumTraits<Scalar>::Real>::value> +{ + typedef typename remove_all<_DerType>::type DerType; + typedef typename traits<DerType>::Scalar Scalar; + typedef typename NumTraits<Scalar>::Real Real; + +// typedef auto_diff_scalar_op<_DerType, typename NumTraits<Scalar>::Real, +// is_same<Scalar,typename NumTraits<Scalar>::Real>::value> Base; + +// using Base::operator+; +// using Base::operator+=; +// using Base::operator-; +// using Base::operator-=; +// using Base::operator*; +// using Base::operator*=; + + const AutoDiffScalar<_DerType>& derived() const { return *static_cast<const AutoDiffScalar<_DerType>*>(this); } + AutoDiffScalar<_DerType>& derived() { return *static_cast<AutoDiffScalar<_DerType>*>(this); } + + + inline const AutoDiffScalar<DerType&> operator+(const Real& other) const + { + return AutoDiffScalar<DerType&>(derived().value() + other, derived().derivatives()); + } + + friend inline const AutoDiffScalar<DerType&> operator+(const Real& a, const AutoDiffScalar<_DerType>& b) + { + return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives()); + } + + inline AutoDiffScalar<_DerType>& operator+=(const Real& other) + { + derived().value() += other; + return derived(); + } + + + inline const AutoDiffScalar<typename CwiseUnaryOp<scalar_multiple2_op<Scalar,Real>, DerType>::Type > + operator*(const Real& other) const + { + return AutoDiffScalar<typename CwiseUnaryOp<scalar_multiple2_op<Scalar,Real>, DerType>::Type >( + derived().value() * other, + derived().derivatives() * other); + } + + friend inline const AutoDiffScalar<typename CwiseUnaryOp<scalar_multiple2_op<Scalar,Real>, DerType>::Type > + operator*(const Real& other, const AutoDiffScalar<_DerType>& a) + { + return AutoDiffScalar<typename CwiseUnaryOp<scalar_multiple2_op<Scalar,Real>, DerType>::Type >( + a.value() * other, + a.derivatives() * other); + } + + inline AutoDiffScalar<_DerType>& operator*=(const Scalar& other) + { + *this = *this * other; + return derived(); + } +}; + +template<typename _DerType> +struct auto_diff_special_op<_DerType, false> +{ + void operator*() const; + void operator-() const; + void operator+() const; +}; + +template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols, typename B> +struct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>, B> { + typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A; + static void run(A& a, B& b) { + if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0)) + { + a.resize(b.size()); + a.setZero(); + } + } +}; + +template<typename A, typename B_Scalar, int B_Rows, int B_Cols, int B_Options, int B_MaxRows, int B_MaxCols> +struct make_coherent_impl<A, Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > { + typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B; + static void run(A& a, B& b) { + if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0)) + { + b.resize(a.size()); + b.setZero(); + } + } +}; + +template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols, + typename B_Scalar, int B_Rows, int B_Cols, int B_Options, int B_MaxRows, int B_MaxCols> +struct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>, + Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > { + typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A; + typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B; + static void run(A& a, B& b) { + if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0)) + { + a.resize(b.size()); + a.setZero(); + } + else if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0)) + { + b.resize(a.size()); + b.setZero(); + } + } +}; + +template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols> struct scalar_product_traits<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,A_Scalar> +{ + typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> ReturnType; +}; + +template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols> struct scalar_product_traits<A_Scalar, Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> > +{ + typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> ReturnType; +}; + +template<typename DerType> +struct scalar_product_traits<AutoDiffScalar<DerType>,typename DerType::Scalar> +{ + typedef AutoDiffScalar<DerType> ReturnType; +}; + +} // end namespace internal + +#define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \ + template<typename DerType> \ + inline const Eigen::AutoDiffScalar<Eigen::CwiseUnaryOp<Eigen::internal::scalar_multiple_op<typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar>, const typename Eigen::internal::remove_all<DerType>::type> > \ + FUNC(const Eigen::AutoDiffScalar<DerType>& x) { \ + using namespace Eigen; \ + typedef typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar Scalar; \ + typedef AutoDiffScalar<CwiseUnaryOp<Eigen::internal::scalar_multiple_op<Scalar>, const typename Eigen::internal::remove_all<DerType>::type> > ReturnType; \ + CODE; \ + } + +template<typename DerType> +inline const AutoDiffScalar<DerType>& conj(const AutoDiffScalar<DerType>& x) { return x; } +template<typename DerType> +inline const AutoDiffScalar<DerType>& real(const AutoDiffScalar<DerType>& x) { return x; } +template<typename DerType> +inline typename DerType::Scalar imag(const AutoDiffScalar<DerType>&) { return 0.; } +template<typename DerType, typename T> +inline AutoDiffScalar<DerType> (min)(const AutoDiffScalar<DerType>& x, const T& y) { return (x <= y ? x : y); } +template<typename DerType, typename T> +inline AutoDiffScalar<DerType> (max)(const AutoDiffScalar<DerType>& x, const T& y) { return (x >= y ? x : y); } +template<typename DerType, typename T> +inline AutoDiffScalar<DerType> (min)(const T& x, const AutoDiffScalar<DerType>& y) { return (x < y ? x : y); } +template<typename DerType, typename T> +inline AutoDiffScalar<DerType> (max)(const T& x, const AutoDiffScalar<DerType>& y) { return (x > y ? x : y); } + +#define sign(x) x >= 0 ? 1 : -1 // required for abs function below + +EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs, + using std::abs; + return ReturnType(abs(x.value()), x.derivatives() * (sign(x.value())));) + +EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs2, + using internal::abs2; + return ReturnType(abs2(x.value()), x.derivatives() * (Scalar(2)*x.value()));) + +EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sqrt, + using std::sqrt; + Scalar sqrtx = sqrt(x.value()); + return ReturnType(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));) + +EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cos, + using std::cos; + using std::sin; + return ReturnType(cos(x.value()), x.derivatives() * (-sin(x.value())));) + +EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sin, + using std::sin; + using std::cos; + return ReturnType(sin(x.value()),x.derivatives() * cos(x.value()));) + +EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(exp, + using std::exp; + Scalar expx = exp(x.value()); + return ReturnType(expx,x.derivatives() * expx);) + +EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(log, + using std::log; + return ReturnType(log(x.value()),x.derivatives() * (Scalar(1)/x.value()));) + +template<typename DerType> +inline const Eigen::AutoDiffScalar<Eigen::CwiseUnaryOp<Eigen::internal::scalar_multiple_op<typename Eigen::internal::traits<DerType>::Scalar>, const DerType> > +pow(const Eigen::AutoDiffScalar<DerType>& x, typename Eigen::internal::traits<DerType>::Scalar y) +{ + using namespace Eigen; + typedef typename Eigen::internal::traits<DerType>::Scalar Scalar; + return AutoDiffScalar<CwiseUnaryOp<Eigen::internal::scalar_multiple_op<Scalar>, const DerType> >( + std::pow(x.value(),y), + x.derivatives() * (y * std::pow(x.value(),y-1))); +} + + +template<typename DerTypeA,typename DerTypeB> +inline const AutoDiffScalar<Matrix<typename internal::traits<DerTypeA>::Scalar,Dynamic,1> > +atan2(const AutoDiffScalar<DerTypeA>& a, const AutoDiffScalar<DerTypeB>& b) +{ + using std::atan2; + using std::max; + typedef typename internal::traits<DerTypeA>::Scalar Scalar; + typedef AutoDiffScalar<Matrix<Scalar,Dynamic,1> > PlainADS; + PlainADS ret; + ret.value() = atan2(a.value(), b.value()); + + Scalar tmp2 = a.value() * a.value(); + Scalar tmp3 = b.value() * b.value(); + Scalar tmp4 = tmp3/(tmp2+tmp3); + + if (tmp4!=0) + ret.derivatives() = (a.derivatives() * b.value() - a.value() * b.derivatives()) * (tmp2+tmp3); + + return ret; +} + +EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(tan, + using std::tan; + using std::cos; + return ReturnType(tan(x.value()),x.derivatives() * (Scalar(1)/internal::abs2(cos(x.value()))));) + +EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(asin, + using std::sqrt; + using std::asin; + return ReturnType(asin(x.value()),x.derivatives() * (Scalar(1)/sqrt(1-internal::abs2(x.value()))));) + +EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(acos, + using std::sqrt; + using std::acos; + return ReturnType(acos(x.value()),x.derivatives() * (Scalar(-1)/sqrt(1-internal::abs2(x.value()))));) + +#undef EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY + +template<typename DerType> struct NumTraits<AutoDiffScalar<DerType> > + : NumTraits< typename NumTraits<typename DerType::Scalar>::Real > +{ + typedef AutoDiffScalar<Matrix<typename NumTraits<typename DerType::Scalar>::Real,DerType::RowsAtCompileTime,DerType::ColsAtCompileTime> > Real; + typedef AutoDiffScalar<DerType> NonInteger; + typedef AutoDiffScalar<DerType>& Nested; + enum{ + RequireInitialization = 1 + }; +}; + +} + +#endif // EIGEN_AUTODIFF_SCALAR_H diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffVector.h b/unsupported/Eigen/src/AutoDiff/AutoDiffVector.h new file mode 100644 index 000000000..0540add0a --- /dev/null +++ b/unsupported/Eigen/src/AutoDiff/AutoDiffVector.h @@ -0,0 +1,220 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_AUTODIFF_VECTOR_H +#define EIGEN_AUTODIFF_VECTOR_H + +namespace Eigen { + +/* \class AutoDiffScalar + * \brief A scalar type replacement with automatic differentation capability + * + * \param DerType the vector type used to store/represent the derivatives (e.g. Vector3f) + * + * This class represents a scalar value while tracking its respective derivatives. + * + * It supports the following list of global math function: + * - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos, + * - internal::abs, internal::sqrt, internal::pow, internal::exp, internal::log, internal::sin, internal::cos, + * - internal::conj, internal::real, internal::imag, internal::abs2. + * + * AutoDiffScalar can be used as the scalar type of an Eigen::Matrix object. However, + * in that case, the expression template mechanism only occurs at the top Matrix level, + * while derivatives are computed right away. + * + */ +template<typename ValueType, typename JacobianType> +class AutoDiffVector +{ + public: + //typedef typename internal::traits<ValueType>::Scalar Scalar; + typedef typename internal::traits<ValueType>::Scalar BaseScalar; + typedef AutoDiffScalar<Matrix<BaseScalar,JacobianType::RowsAtCompileTime,1> > ActiveScalar; + typedef ActiveScalar Scalar; + typedef AutoDiffScalar<typename JacobianType::ColXpr> CoeffType; + typedef typename JacobianType::Index Index; + + inline AutoDiffVector() {} + + inline AutoDiffVector(const ValueType& values) + : m_values(values) + { + m_jacobian.setZero(); + } + + + CoeffType operator[] (Index i) { return CoeffType(m_values[i], m_jacobian.col(i)); } + const CoeffType operator[] (Index i) const { return CoeffType(m_values[i], m_jacobian.col(i)); } + + CoeffType operator() (Index i) { return CoeffType(m_values[i], m_jacobian.col(i)); } + const CoeffType operator() (Index i) const { return CoeffType(m_values[i], m_jacobian.col(i)); } + + CoeffType coeffRef(Index i) { return CoeffType(m_values[i], m_jacobian.col(i)); } + const CoeffType coeffRef(Index i) const { return CoeffType(m_values[i], m_jacobian.col(i)); } + + Index size() const { return m_values.size(); } + + // FIXME here we could return an expression of the sum + Scalar sum() const { /*std::cerr << "sum \n\n";*/ /*std::cerr << m_jacobian.rowwise().sum() << "\n\n";*/ return Scalar(m_values.sum(), m_jacobian.rowwise().sum()); } + + + inline AutoDiffVector(const ValueType& values, const JacobianType& jac) + : m_values(values), m_jacobian(jac) + {} + + template<typename OtherValueType, typename OtherJacobianType> + inline AutoDiffVector(const AutoDiffVector<OtherValueType, OtherJacobianType>& other) + : m_values(other.values()), m_jacobian(other.jacobian()) + {} + + inline AutoDiffVector(const AutoDiffVector& other) + : m_values(other.values()), m_jacobian(other.jacobian()) + {} + + template<typename OtherValueType, typename OtherJacobianType> + inline AutoDiffVector& operator=(const AutoDiffVector<OtherValueType, OtherJacobianType>& other) + { + m_values = other.values(); + m_jacobian = other.jacobian(); + return *this; + } + + inline AutoDiffVector& operator=(const AutoDiffVector& other) + { + m_values = other.values(); + m_jacobian = other.jacobian(); + return *this; + } + + inline const ValueType& values() const { return m_values; } + inline ValueType& values() { return m_values; } + + inline const JacobianType& jacobian() const { return m_jacobian; } + inline JacobianType& jacobian() { return m_jacobian; } + + template<typename OtherValueType,typename OtherJacobianType> + inline const AutoDiffVector< + typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>,ValueType,OtherValueType>::Type, + typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>,JacobianType,OtherJacobianType>::Type > + operator+(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) const + { + return AutoDiffVector< + typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>,ValueType,OtherValueType>::Type, + typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>,JacobianType,OtherJacobianType>::Type >( + m_values + other.values(), + m_jacobian + other.jacobian()); + } + + template<typename OtherValueType, typename OtherJacobianType> + inline AutoDiffVector& + operator+=(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) + { + m_values += other.values(); + m_jacobian += other.jacobian(); + return *this; + } + + template<typename OtherValueType,typename OtherJacobianType> + inline const AutoDiffVector< + typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>,ValueType,OtherValueType>::Type, + typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>,JacobianType,OtherJacobianType>::Type > + operator-(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) const + { + return AutoDiffVector< + typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>,ValueType,OtherValueType>::Type, + typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>,JacobianType,OtherJacobianType>::Type >( + m_values - other.values(), + m_jacobian - other.jacobian()); + } + + template<typename OtherValueType, typename OtherJacobianType> + inline AutoDiffVector& + operator-=(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) + { + m_values -= other.values(); + m_jacobian -= other.jacobian(); + return *this; + } + + inline const AutoDiffVector< + typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, ValueType>::Type, + typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, JacobianType>::Type > + operator-() const + { + return AutoDiffVector< + typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, ValueType>::Type, + typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, JacobianType>::Type >( + -m_values, + -m_jacobian); + } + + inline const AutoDiffVector< + typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type, + typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type> + operator*(const BaseScalar& other) const + { + return AutoDiffVector< + typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type, + typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type >( + m_values * other, + m_jacobian * other); + } + + friend inline const AutoDiffVector< + typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type, + typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type > + operator*(const Scalar& other, const AutoDiffVector& v) + { + return AutoDiffVector< + typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type, + typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type >( + v.values() * other, + v.jacobian() * other); + } + +// template<typename OtherValueType,typename OtherJacobianType> +// inline const AutoDiffVector< +// CwiseBinaryOp<internal::scalar_multiple_op<Scalar>, ValueType, OtherValueType> +// CwiseBinaryOp<internal::scalar_sum_op<Scalar>, +// CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>, +// CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, OtherJacobianType> > > +// operator*(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) const +// { +// return AutoDiffVector< +// CwiseBinaryOp<internal::scalar_multiple_op<Scalar>, ValueType, OtherValueType> +// CwiseBinaryOp<internal::scalar_sum_op<Scalar>, +// CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>, +// CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, OtherJacobianType> > >( +// m_values.cwise() * other.values(), +// (m_jacobian * other.values()) + (m_values * other.jacobian())); +// } + + inline AutoDiffVector& operator*=(const Scalar& other) + { + m_values *= other; + m_jacobian *= other; + return *this; + } + + template<typename OtherValueType,typename OtherJacobianType> + inline AutoDiffVector& operator*=(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) + { + *this = *this * other; + return *this; + } + + protected: + ValueType m_values; + JacobianType m_jacobian; + +}; + +} + +#endif // EIGEN_AUTODIFF_VECTOR_H diff --git a/unsupported/Eigen/src/AutoDiff/CMakeLists.txt b/unsupported/Eigen/src/AutoDiff/CMakeLists.txt new file mode 100644 index 000000000..ad91fd9c4 --- /dev/null +++ b/unsupported/Eigen/src/AutoDiff/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_AutoDiff_SRCS "*.h") + +INSTALL(FILES + ${Eigen_AutoDiff_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/AutoDiff COMPONENT Devel + ) diff --git a/unsupported/Eigen/src/BVH/BVAlgorithms.h b/unsupported/Eigen/src/BVH/BVAlgorithms.h new file mode 100644 index 000000000..e5b51decb --- /dev/null +++ b/unsupported/Eigen/src/BVH/BVAlgorithms.h @@ -0,0 +1,293 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Ilya Baran <ibaran@mit.edu> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_BVALGORITHMS_H +#define EIGEN_BVALGORITHMS_H + +namespace Eigen { + +namespace internal { + +#ifndef EIGEN_PARSED_BY_DOXYGEN +template<typename BVH, typename Intersector> +bool intersect_helper(const BVH &tree, Intersector &intersector, typename BVH::Index root) +{ + typedef typename BVH::Index Index; + typedef typename BVH::VolumeIterator VolIter; + typedef typename BVH::ObjectIterator ObjIter; + + VolIter vBegin = VolIter(), vEnd = VolIter(); + ObjIter oBegin = ObjIter(), oEnd = ObjIter(); + + std::vector<Index> todo(1, root); + + while(!todo.empty()) { + tree.getChildren(todo.back(), vBegin, vEnd, oBegin, oEnd); + todo.pop_back(); + + for(; vBegin != vEnd; ++vBegin) //go through child volumes + if(intersector.intersectVolume(tree.getVolume(*vBegin))) + todo.push_back(*vBegin); + + for(; oBegin != oEnd; ++oBegin) //go through child objects + if(intersector.intersectObject(*oBegin)) + return true; //intersector said to stop query + } + return false; +} +#endif //not EIGEN_PARSED_BY_DOXYGEN + +template<typename Volume1, typename Object1, typename Object2, typename Intersector> +struct intersector_helper1 +{ + intersector_helper1(const Object2 &inStored, Intersector &in) : stored(inStored), intersector(in) {} + bool intersectVolume(const Volume1 &vol) { return intersector.intersectVolumeObject(vol, stored); } + bool intersectObject(const Object1 &obj) { return intersector.intersectObjectObject(obj, stored); } + Object2 stored; + Intersector &intersector; +private: + intersector_helper1& operator=(const intersector_helper1&); +}; + +template<typename Volume2, typename Object2, typename Object1, typename Intersector> +struct intersector_helper2 +{ + intersector_helper2(const Object1 &inStored, Intersector &in) : stored(inStored), intersector(in) {} + bool intersectVolume(const Volume2 &vol) { return intersector.intersectObjectVolume(stored, vol); } + bool intersectObject(const Object2 &obj) { return intersector.intersectObjectObject(stored, obj); } + Object1 stored; + Intersector &intersector; +private: + intersector_helper2& operator=(const intersector_helper2&); +}; + +} // end namespace internal + +/** Given a BVH, runs the query encapsulated by \a intersector. + * The Intersector type must provide the following members: \code + bool intersectVolume(const BVH::Volume &volume) //returns true if volume intersects the query + bool intersectObject(const BVH::Object &object) //returns true if the search should terminate immediately + \endcode + */ +template<typename BVH, typename Intersector> +void BVIntersect(const BVH &tree, Intersector &intersector) +{ + internal::intersect_helper(tree, intersector, tree.getRootIndex()); +} + +/** Given two BVH's, runs the query on their Cartesian product encapsulated by \a intersector. + * The Intersector type must provide the following members: \code + bool intersectVolumeVolume(const BVH1::Volume &v1, const BVH2::Volume &v2) //returns true if product of volumes intersects the query + bool intersectVolumeObject(const BVH1::Volume &v1, const BVH2::Object &o2) //returns true if the volume-object product intersects the query + bool intersectObjectVolume(const BVH1::Object &o1, const BVH2::Volume &v2) //returns true if the volume-object product intersects the query + bool intersectObjectObject(const BVH1::Object &o1, const BVH2::Object &o2) //returns true if the search should terminate immediately + \endcode + */ +template<typename BVH1, typename BVH2, typename Intersector> +void BVIntersect(const BVH1 &tree1, const BVH2 &tree2, Intersector &intersector) //TODO: tandem descent when it makes sense +{ + typedef typename BVH1::Index Index1; + typedef typename BVH2::Index Index2; + typedef internal::intersector_helper1<typename BVH1::Volume, typename BVH1::Object, typename BVH2::Object, Intersector> Helper1; + typedef internal::intersector_helper2<typename BVH2::Volume, typename BVH2::Object, typename BVH1::Object, Intersector> Helper2; + typedef typename BVH1::VolumeIterator VolIter1; + typedef typename BVH1::ObjectIterator ObjIter1; + typedef typename BVH2::VolumeIterator VolIter2; + typedef typename BVH2::ObjectIterator ObjIter2; + + VolIter1 vBegin1 = VolIter1(), vEnd1 = VolIter1(); + ObjIter1 oBegin1 = ObjIter1(), oEnd1 = ObjIter1(); + VolIter2 vBegin2 = VolIter2(), vEnd2 = VolIter2(), vCur2 = VolIter2(); + ObjIter2 oBegin2 = ObjIter2(), oEnd2 = ObjIter2(), oCur2 = ObjIter2(); + + std::vector<std::pair<Index1, Index2> > todo(1, std::make_pair(tree1.getRootIndex(), tree2.getRootIndex())); + + while(!todo.empty()) { + tree1.getChildren(todo.back().first, vBegin1, vEnd1, oBegin1, oEnd1); + tree2.getChildren(todo.back().second, vBegin2, vEnd2, oBegin2, oEnd2); + todo.pop_back(); + + for(; vBegin1 != vEnd1; ++vBegin1) { //go through child volumes of first tree + const typename BVH1::Volume &vol1 = tree1.getVolume(*vBegin1); + for(vCur2 = vBegin2; vCur2 != vEnd2; ++vCur2) { //go through child volumes of second tree + if(intersector.intersectVolumeVolume(vol1, tree2.getVolume(*vCur2))) + todo.push_back(std::make_pair(*vBegin1, *vCur2)); + } + + for(oCur2 = oBegin2; oCur2 != oEnd2; ++oCur2) {//go through child objects of second tree + Helper1 helper(*oCur2, intersector); + if(internal::intersect_helper(tree1, helper, *vBegin1)) + return; //intersector said to stop query + } + } + + for(; oBegin1 != oEnd1; ++oBegin1) { //go through child objects of first tree + for(vCur2 = vBegin2; vCur2 != vEnd2; ++vCur2) { //go through child volumes of second tree + Helper2 helper(*oBegin1, intersector); + if(internal::intersect_helper(tree2, helper, *vCur2)) + return; //intersector said to stop query + } + + for(oCur2 = oBegin2; oCur2 != oEnd2; ++oCur2) {//go through child objects of second tree + if(intersector.intersectObjectObject(*oBegin1, *oCur2)) + return; //intersector said to stop query + } + } + } +} + +namespace internal { + +#ifndef EIGEN_PARSED_BY_DOXYGEN +template<typename BVH, typename Minimizer> +typename Minimizer::Scalar minimize_helper(const BVH &tree, Minimizer &minimizer, typename BVH::Index root, typename Minimizer::Scalar minimum) +{ + typedef typename Minimizer::Scalar Scalar; + typedef typename BVH::Index Index; + typedef std::pair<Scalar, Index> QueueElement; //first element is priority + typedef typename BVH::VolumeIterator VolIter; + typedef typename BVH::ObjectIterator ObjIter; + + VolIter vBegin = VolIter(), vEnd = VolIter(); + ObjIter oBegin = ObjIter(), oEnd = ObjIter(); + std::priority_queue<QueueElement, std::vector<QueueElement>, std::greater<QueueElement> > todo; //smallest is at the top + + todo.push(std::make_pair(Scalar(), root)); + + while(!todo.empty()) { + tree.getChildren(todo.top().second, vBegin, vEnd, oBegin, oEnd); + todo.pop(); + + for(; oBegin != oEnd; ++oBegin) //go through child objects + minimum = (std::min)(minimum, minimizer.minimumOnObject(*oBegin)); + + for(; vBegin != vEnd; ++vBegin) { //go through child volumes + Scalar val = minimizer.minimumOnVolume(tree.getVolume(*vBegin)); + if(val < minimum) + todo.push(std::make_pair(val, *vBegin)); + } + } + + return minimum; +} +#endif //not EIGEN_PARSED_BY_DOXYGEN + + +template<typename Volume1, typename Object1, typename Object2, typename Minimizer> +struct minimizer_helper1 +{ + typedef typename Minimizer::Scalar Scalar; + minimizer_helper1(const Object2 &inStored, Minimizer &m) : stored(inStored), minimizer(m) {} + Scalar minimumOnVolume(const Volume1 &vol) { return minimizer.minimumOnVolumeObject(vol, stored); } + Scalar minimumOnObject(const Object1 &obj) { return minimizer.minimumOnObjectObject(obj, stored); } + Object2 stored; + Minimizer &minimizer; +private: + minimizer_helper1& operator=(const minimizer_helper1&) {} +}; + +template<typename Volume2, typename Object2, typename Object1, typename Minimizer> +struct minimizer_helper2 +{ + typedef typename Minimizer::Scalar Scalar; + minimizer_helper2(const Object1 &inStored, Minimizer &m) : stored(inStored), minimizer(m) {} + Scalar minimumOnVolume(const Volume2 &vol) { return minimizer.minimumOnObjectVolume(stored, vol); } + Scalar minimumOnObject(const Object2 &obj) { return minimizer.minimumOnObjectObject(stored, obj); } + Object1 stored; + Minimizer &minimizer; +private: + minimizer_helper2& operator=(const minimizer_helper2&); +}; + +} // end namespace internal + +/** Given a BVH, runs the query encapsulated by \a minimizer. + * \returns the minimum value. + * The Minimizer type must provide the following members: \code + typedef Scalar //the numeric type of what is being minimized--not necessarily the Scalar type of the BVH (if it has one) + Scalar minimumOnVolume(const BVH::Volume &volume) + Scalar minimumOnObject(const BVH::Object &object) + \endcode + */ +template<typename BVH, typename Minimizer> +typename Minimizer::Scalar BVMinimize(const BVH &tree, Minimizer &minimizer) +{ + return internal::minimize_helper(tree, minimizer, tree.getRootIndex(), (std::numeric_limits<typename Minimizer::Scalar>::max)()); +} + +/** Given two BVH's, runs the query on their cartesian product encapsulated by \a minimizer. + * \returns the minimum value. + * The Minimizer type must provide the following members: \code + typedef Scalar //the numeric type of what is being minimized--not necessarily the Scalar type of the BVH (if it has one) + Scalar minimumOnVolumeVolume(const BVH1::Volume &v1, const BVH2::Volume &v2) + Scalar minimumOnVolumeObject(const BVH1::Volume &v1, const BVH2::Object &o2) + Scalar minimumOnObjectVolume(const BVH1::Object &o1, const BVH2::Volume &v2) + Scalar minimumOnObjectObject(const BVH1::Object &o1, const BVH2::Object &o2) + \endcode + */ +template<typename BVH1, typename BVH2, typename Minimizer> +typename Minimizer::Scalar BVMinimize(const BVH1 &tree1, const BVH2 &tree2, Minimizer &minimizer) +{ + typedef typename Minimizer::Scalar Scalar; + typedef typename BVH1::Index Index1; + typedef typename BVH2::Index Index2; + typedef internal::minimizer_helper1<typename BVH1::Volume, typename BVH1::Object, typename BVH2::Object, Minimizer> Helper1; + typedef internal::minimizer_helper2<typename BVH2::Volume, typename BVH2::Object, typename BVH1::Object, Minimizer> Helper2; + typedef std::pair<Scalar, std::pair<Index1, Index2> > QueueElement; //first element is priority + typedef typename BVH1::VolumeIterator VolIter1; + typedef typename BVH1::ObjectIterator ObjIter1; + typedef typename BVH2::VolumeIterator VolIter2; + typedef typename BVH2::ObjectIterator ObjIter2; + + VolIter1 vBegin1 = VolIter1(), vEnd1 = VolIter1(); + ObjIter1 oBegin1 = ObjIter1(), oEnd1 = ObjIter1(); + VolIter2 vBegin2 = VolIter2(), vEnd2 = VolIter2(), vCur2 = VolIter2(); + ObjIter2 oBegin2 = ObjIter2(), oEnd2 = ObjIter2(), oCur2 = ObjIter2(); + std::priority_queue<QueueElement, std::vector<QueueElement>, std::greater<QueueElement> > todo; //smallest is at the top + + Scalar minimum = (std::numeric_limits<Scalar>::max)(); + todo.push(std::make_pair(Scalar(), std::make_pair(tree1.getRootIndex(), tree2.getRootIndex()))); + + while(!todo.empty()) { + tree1.getChildren(todo.top().second.first, vBegin1, vEnd1, oBegin1, oEnd1); + tree2.getChildren(todo.top().second.second, vBegin2, vEnd2, oBegin2, oEnd2); + todo.pop(); + + for(; oBegin1 != oEnd1; ++oBegin1) { //go through child objects of first tree + for(oCur2 = oBegin2; oCur2 != oEnd2; ++oCur2) {//go through child objects of second tree + minimum = (std::min)(minimum, minimizer.minimumOnObjectObject(*oBegin1, *oCur2)); + } + + for(vCur2 = vBegin2; vCur2 != vEnd2; ++vCur2) { //go through child volumes of second tree + Helper2 helper(*oBegin1, minimizer); + minimum = (std::min)(minimum, internal::minimize_helper(tree2, helper, *vCur2, minimum)); + } + } + + for(; vBegin1 != vEnd1; ++vBegin1) { //go through child volumes of first tree + const typename BVH1::Volume &vol1 = tree1.getVolume(*vBegin1); + + for(oCur2 = oBegin2; oCur2 != oEnd2; ++oCur2) {//go through child objects of second tree + Helper1 helper(*oCur2, minimizer); + minimum = (std::min)(minimum, internal::minimize_helper(tree1, helper, *vBegin1, minimum)); + } + + for(vCur2 = vBegin2; vCur2 != vEnd2; ++vCur2) { //go through child volumes of second tree + Scalar val = minimizer.minimumOnVolumeVolume(vol1, tree2.getVolume(*vCur2)); + if(val < minimum) + todo.push(std::make_pair(val, std::make_pair(*vBegin1, *vCur2))); + } + } + } + return minimum; +} + +} // end namespace Eigen + +#endif // EIGEN_BVALGORITHMS_H diff --git a/unsupported/Eigen/src/BVH/CMakeLists.txt b/unsupported/Eigen/src/BVH/CMakeLists.txt new file mode 100644 index 000000000..b377d865c --- /dev/null +++ b/unsupported/Eigen/src/BVH/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_BVH_SRCS "*.h") + +INSTALL(FILES + ${Eigen_BVH_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/BVH COMPONENT Devel + ) diff --git a/unsupported/Eigen/src/BVH/KdBVH.h b/unsupported/Eigen/src/BVH/KdBVH.h new file mode 100644 index 000000000..1b8d75865 --- /dev/null +++ b/unsupported/Eigen/src/BVH/KdBVH.h @@ -0,0 +1,222 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Ilya Baran <ibaran@mit.edu> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef KDBVH_H_INCLUDED +#define KDBVH_H_INCLUDED + +namespace Eigen { + +namespace internal { + +//internal pair class for the BVH--used instead of std::pair because of alignment +template<typename Scalar, int Dim> +struct vector_int_pair +{ +EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar, Dim) + typedef Matrix<Scalar, Dim, 1> VectorType; + + vector_int_pair(const VectorType &v, int i) : first(v), second(i) {} + + VectorType first; + int second; +}; + +//these templates help the tree initializer get the bounding boxes either from a provided +//iterator range or using bounding_box in a unified way +template<typename ObjectList, typename VolumeList, typename BoxIter> +struct get_boxes_helper { + void operator()(const ObjectList &objects, BoxIter boxBegin, BoxIter boxEnd, VolumeList &outBoxes) + { + outBoxes.insert(outBoxes.end(), boxBegin, boxEnd); + eigen_assert(outBoxes.size() == objects.size()); + } +}; + +template<typename ObjectList, typename VolumeList> +struct get_boxes_helper<ObjectList, VolumeList, int> { + void operator()(const ObjectList &objects, int, int, VolumeList &outBoxes) + { + outBoxes.reserve(objects.size()); + for(int i = 0; i < (int)objects.size(); ++i) + outBoxes.push_back(bounding_box(objects[i])); + } +}; + +} // end namespace internal + + +/** \class KdBVH + * \brief A simple bounding volume hierarchy based on AlignedBox + * + * \param _Scalar The underlying scalar type of the bounding boxes + * \param _Dim The dimension of the space in which the hierarchy lives + * \param _Object The object type that lives in the hierarchy. It must have value semantics. Either bounding_box(_Object) must + * be defined and return an AlignedBox<_Scalar, _Dim> or bounding boxes must be provided to the tree initializer. + * + * This class provides a simple (as opposed to optimized) implementation of a bounding volume hierarchy analogous to a Kd-tree. + * Given a sequence of objects, it computes their bounding boxes, constructs a Kd-tree of their centers + * and builds a BVH with the structure of that Kd-tree. When the elements of the tree are too expensive to be copied around, + * it is useful for _Object to be a pointer. + */ +template<typename _Scalar, int _Dim, typename _Object> class KdBVH +{ +public: + enum { Dim = _Dim }; + typedef _Object Object; + typedef std::vector<Object, aligned_allocator<Object> > ObjectList; + typedef _Scalar Scalar; + typedef AlignedBox<Scalar, Dim> Volume; + typedef std::vector<Volume, aligned_allocator<Volume> > VolumeList; + typedef int Index; + typedef const int *VolumeIterator; //the iterators are just pointers into the tree's vectors + typedef const Object *ObjectIterator; + + KdBVH() {} + + /** Given an iterator range over \a Object references, constructs the BVH. Requires that bounding_box(Object) return a Volume. */ + template<typename Iter> KdBVH(Iter begin, Iter end) { init(begin, end, 0, 0); } //int is recognized by init as not being an iterator type + + /** Given an iterator range over \a Object references and an iterator range over their bounding boxes, constructs the BVH */ + template<typename OIter, typename BIter> KdBVH(OIter begin, OIter end, BIter boxBegin, BIter boxEnd) { init(begin, end, boxBegin, boxEnd); } + + /** Given an iterator range over \a Object references, constructs the BVH, overwriting whatever is in there currently. + * Requires that bounding_box(Object) return a Volume. */ + template<typename Iter> void init(Iter begin, Iter end) { init(begin, end, 0, 0); } + + /** Given an iterator range over \a Object references and an iterator range over their bounding boxes, + * constructs the BVH, overwriting whatever is in there currently. */ + template<typename OIter, typename BIter> void init(OIter begin, OIter end, BIter boxBegin, BIter boxEnd) + { + objects.clear(); + boxes.clear(); + children.clear(); + + objects.insert(objects.end(), begin, end); + int n = static_cast<int>(objects.size()); + + if(n < 2) + return; //if we have at most one object, we don't need any internal nodes + + VolumeList objBoxes; + VIPairList objCenters; + + //compute the bounding boxes depending on BIter type + internal::get_boxes_helper<ObjectList, VolumeList, BIter>()(objects, boxBegin, boxEnd, objBoxes); + + objCenters.reserve(n); + boxes.reserve(n - 1); + children.reserve(2 * n - 2); + + for(int i = 0; i < n; ++i) + objCenters.push_back(VIPair(objBoxes[i].center(), i)); + + build(objCenters, 0, n, objBoxes, 0); //the recursive part of the algorithm + + ObjectList tmp(n); + tmp.swap(objects); + for(int i = 0; i < n; ++i) + objects[i] = tmp[objCenters[i].second]; + } + + /** \returns the index of the root of the hierarchy */ + inline Index getRootIndex() const { return (int)boxes.size() - 1; } + + /** Given an \a index of a node, on exit, \a outVBegin and \a outVEnd range over the indices of the volume children of the node + * and \a outOBegin and \a outOEnd range over the object children of the node */ + EIGEN_STRONG_INLINE void getChildren(Index index, VolumeIterator &outVBegin, VolumeIterator &outVEnd, + ObjectIterator &outOBegin, ObjectIterator &outOEnd) const + { //inlining this function should open lots of optimization opportunities to the compiler + if(index < 0) { + outVBegin = outVEnd; + if(!objects.empty()) + outOBegin = &(objects[0]); + outOEnd = outOBegin + objects.size(); //output all objects--necessary when the tree has only one object + return; + } + + int numBoxes = static_cast<int>(boxes.size()); + + int idx = index * 2; + if(children[idx + 1] < numBoxes) { //second index is always bigger + outVBegin = &(children[idx]); + outVEnd = outVBegin + 2; + outOBegin = outOEnd; + } + else if(children[idx] >= numBoxes) { //if both children are objects + outVBegin = outVEnd; + outOBegin = &(objects[children[idx] - numBoxes]); + outOEnd = outOBegin + 2; + } else { //if the first child is a volume and the second is an object + outVBegin = &(children[idx]); + outVEnd = outVBegin + 1; + outOBegin = &(objects[children[idx + 1] - numBoxes]); + outOEnd = outOBegin + 1; + } + } + + /** \returns the bounding box of the node at \a index */ + inline const Volume &getVolume(Index index) const + { + return boxes[index]; + } + +private: + typedef internal::vector_int_pair<Scalar, Dim> VIPair; + typedef std::vector<VIPair, aligned_allocator<VIPair> > VIPairList; + typedef Matrix<Scalar, Dim, 1> VectorType; + struct VectorComparator //compares vectors, or, more specificall, VIPairs along a particular dimension + { + VectorComparator(int inDim) : dim(inDim) {} + inline bool operator()(const VIPair &v1, const VIPair &v2) const { return v1.first[dim] < v2.first[dim]; } + int dim; + }; + + //Build the part of the tree between objects[from] and objects[to] (not including objects[to]). + //This routine partitions the objCenters in [from, to) along the dimension dim, recursively constructs + //the two halves, and adds their parent node. TODO: a cache-friendlier layout + void build(VIPairList &objCenters, int from, int to, const VolumeList &objBoxes, int dim) + { + eigen_assert(to - from > 1); + if(to - from == 2) { + boxes.push_back(objBoxes[objCenters[from].second].merged(objBoxes[objCenters[from + 1].second])); + children.push_back(from + (int)objects.size() - 1); //there are objects.size() - 1 tree nodes + children.push_back(from + (int)objects.size()); + } + else if(to - from == 3) { + int mid = from + 2; + std::nth_element(objCenters.begin() + from, objCenters.begin() + mid, + objCenters.begin() + to, VectorComparator(dim)); //partition + build(objCenters, from, mid, objBoxes, (dim + 1) % Dim); + int idx1 = (int)boxes.size() - 1; + boxes.push_back(boxes[idx1].merged(objBoxes[objCenters[mid].second])); + children.push_back(idx1); + children.push_back(mid + (int)objects.size() - 1); + } + else { + int mid = from + (to - from) / 2; + nth_element(objCenters.begin() + from, objCenters.begin() + mid, + objCenters.begin() + to, VectorComparator(dim)); //partition + build(objCenters, from, mid, objBoxes, (dim + 1) % Dim); + int idx1 = (int)boxes.size() - 1; + build(objCenters, mid, to, objBoxes, (dim + 1) % Dim); + int idx2 = (int)boxes.size() - 1; + boxes.push_back(boxes[idx1].merged(boxes[idx2])); + children.push_back(idx1); + children.push_back(idx2); + } + } + + std::vector<int> children; //children of x are children[2x] and children[2x+1], indices bigger than boxes.size() index into objects. + VolumeList boxes; + ObjectList objects; +}; + +} // end namespace Eigen + +#endif //KDBVH_H_INCLUDED diff --git a/unsupported/Eigen/src/CMakeLists.txt b/unsupported/Eigen/src/CMakeLists.txt new file mode 100644 index 000000000..f3180b52b --- /dev/null +++ b/unsupported/Eigen/src/CMakeLists.txt @@ -0,0 +1,13 @@ +ADD_SUBDIRECTORY(AutoDiff) +ADD_SUBDIRECTORY(BVH) +ADD_SUBDIRECTORY(FFT) +ADD_SUBDIRECTORY(IterativeSolvers) +ADD_SUBDIRECTORY(MatrixFunctions) +ADD_SUBDIRECTORY(MoreVectorization) +ADD_SUBDIRECTORY(NonLinearOptimization) +ADD_SUBDIRECTORY(NumericalDiff) +ADD_SUBDIRECTORY(Polynomials) +ADD_SUBDIRECTORY(Skyline) +ADD_SUBDIRECTORY(SparseExtra) +ADD_SUBDIRECTORY(KroneckerProduct) +ADD_SUBDIRECTORY(Splines) diff --git a/unsupported/Eigen/src/FFT/CMakeLists.txt b/unsupported/Eigen/src/FFT/CMakeLists.txt new file mode 100644 index 000000000..edcffcb18 --- /dev/null +++ b/unsupported/Eigen/src/FFT/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_FFT_SRCS "*.h") + +INSTALL(FILES + ${Eigen_FFT_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/FFT COMPONENT Devel + ) diff --git a/unsupported/Eigen/src/FFT/ei_fftw_impl.h b/unsupported/Eigen/src/FFT/ei_fftw_impl.h new file mode 100644 index 000000000..d49aa17f5 --- /dev/null +++ b/unsupported/Eigen/src/FFT/ei_fftw_impl.h @@ -0,0 +1,261 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Mark Borgerding mark a borgerding net +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +namespace Eigen { + +namespace internal { + + // FFTW uses non-const arguments + // so we must use ugly const_cast calls for all the args it uses + // + // This should be safe as long as + // 1. we use FFTW_ESTIMATE for all our planning + // see the FFTW docs section 4.3.2 "Planner Flags" + // 2. fftw_complex is compatible with std::complex + // This assumes std::complex<T> layout is array of size 2 with real,imag + template <typename T> + inline + T * fftw_cast(const T* p) + { + return const_cast<T*>( p); + } + + inline + fftw_complex * fftw_cast( const std::complex<double> * p) + { + return const_cast<fftw_complex*>( reinterpret_cast<const fftw_complex*>(p) ); + } + + inline + fftwf_complex * fftw_cast( const std::complex<float> * p) + { + return const_cast<fftwf_complex*>( reinterpret_cast<const fftwf_complex*>(p) ); + } + + inline + fftwl_complex * fftw_cast( const std::complex<long double> * p) + { + return const_cast<fftwl_complex*>( reinterpret_cast<const fftwl_complex*>(p) ); + } + + template <typename T> + struct fftw_plan {}; + + template <> + struct fftw_plan<float> + { + typedef float scalar_type; + typedef fftwf_complex complex_type; + fftwf_plan m_plan; + fftw_plan() :m_plan(NULL) {} + ~fftw_plan() {if (m_plan) fftwf_destroy_plan(m_plan);} + + inline + void fwd(complex_type * dst,complex_type * src,int nfft) { + if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftwf_execute_dft( m_plan, src,dst); + } + inline + void inv(complex_type * dst,complex_type * src,int nfft) { + if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftwf_execute_dft( m_plan, src,dst); + } + inline + void fwd(complex_type * dst,scalar_type * src,int nfft) { + if (m_plan==NULL) m_plan = fftwf_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftwf_execute_dft_r2c( m_plan,src,dst); + } + inline + void inv(scalar_type * dst,complex_type * src,int nfft) { + if (m_plan==NULL) + m_plan = fftwf_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftwf_execute_dft_c2r( m_plan, src,dst); + } + + inline + void fwd2( complex_type * dst,complex_type * src,int n0,int n1) { + if (m_plan==NULL) m_plan = fftwf_plan_dft_2d(n0,n1,src,dst,FFTW_FORWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftwf_execute_dft( m_plan, src,dst); + } + inline + void inv2( complex_type * dst,complex_type * src,int n0,int n1) { + if (m_plan==NULL) m_plan = fftwf_plan_dft_2d(n0,n1,src,dst,FFTW_BACKWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftwf_execute_dft( m_plan, src,dst); + } + + }; + template <> + struct fftw_plan<double> + { + typedef double scalar_type; + typedef fftw_complex complex_type; + ::fftw_plan m_plan; + fftw_plan() :m_plan(NULL) {} + ~fftw_plan() {if (m_plan) fftw_destroy_plan(m_plan);} + + inline + void fwd(complex_type * dst,complex_type * src,int nfft) { + if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftw_execute_dft( m_plan, src,dst); + } + inline + void inv(complex_type * dst,complex_type * src,int nfft) { + if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftw_execute_dft( m_plan, src,dst); + } + inline + void fwd(complex_type * dst,scalar_type * src,int nfft) { + if (m_plan==NULL) m_plan = fftw_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftw_execute_dft_r2c( m_plan,src,dst); + } + inline + void inv(scalar_type * dst,complex_type * src,int nfft) { + if (m_plan==NULL) + m_plan = fftw_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftw_execute_dft_c2r( m_plan, src,dst); + } + inline + void fwd2( complex_type * dst,complex_type * src,int n0,int n1) { + if (m_plan==NULL) m_plan = fftw_plan_dft_2d(n0,n1,src,dst,FFTW_FORWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftw_execute_dft( m_plan, src,dst); + } + inline + void inv2( complex_type * dst,complex_type * src,int n0,int n1) { + if (m_plan==NULL) m_plan = fftw_plan_dft_2d(n0,n1,src,dst,FFTW_BACKWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftw_execute_dft( m_plan, src,dst); + } + }; + template <> + struct fftw_plan<long double> + { + typedef long double scalar_type; + typedef fftwl_complex complex_type; + fftwl_plan m_plan; + fftw_plan() :m_plan(NULL) {} + ~fftw_plan() {if (m_plan) fftwl_destroy_plan(m_plan);} + + inline + void fwd(complex_type * dst,complex_type * src,int nfft) { + if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftwl_execute_dft( m_plan, src,dst); + } + inline + void inv(complex_type * dst,complex_type * src,int nfft) { + if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftwl_execute_dft( m_plan, src,dst); + } + inline + void fwd(complex_type * dst,scalar_type * src,int nfft) { + if (m_plan==NULL) m_plan = fftwl_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftwl_execute_dft_r2c( m_plan,src,dst); + } + inline + void inv(scalar_type * dst,complex_type * src,int nfft) { + if (m_plan==NULL) + m_plan = fftwl_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftwl_execute_dft_c2r( m_plan, src,dst); + } + inline + void fwd2( complex_type * dst,complex_type * src,int n0,int n1) { + if (m_plan==NULL) m_plan = fftwl_plan_dft_2d(n0,n1,src,dst,FFTW_FORWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftwl_execute_dft( m_plan, src,dst); + } + inline + void inv2( complex_type * dst,complex_type * src,int n0,int n1) { + if (m_plan==NULL) m_plan = fftwl_plan_dft_2d(n0,n1,src,dst,FFTW_BACKWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT); + fftwl_execute_dft( m_plan, src,dst); + } + }; + + template <typename _Scalar> + struct fftw_impl + { + typedef _Scalar Scalar; + typedef std::complex<Scalar> Complex; + + inline + void clear() + { + m_plans.clear(); + } + + // complex-to-complex forward FFT + inline + void fwd( Complex * dst,const Complex *src,int nfft) + { + get_plan(nfft,false,dst,src).fwd(fftw_cast(dst), fftw_cast(src),nfft ); + } + + // real-to-complex forward FFT + inline + void fwd( Complex * dst,const Scalar * src,int nfft) + { + get_plan(nfft,false,dst,src).fwd(fftw_cast(dst), fftw_cast(src) ,nfft); + } + + // 2-d complex-to-complex + inline + void fwd2(Complex * dst, const Complex * src, int n0,int n1) + { + get_plan(n0,n1,false,dst,src).fwd2(fftw_cast(dst), fftw_cast(src) ,n0,n1); + } + + // inverse complex-to-complex + inline + void inv(Complex * dst,const Complex *src,int nfft) + { + get_plan(nfft,true,dst,src).inv(fftw_cast(dst), fftw_cast(src),nfft ); + } + + // half-complex to scalar + inline + void inv( Scalar * dst,const Complex * src,int nfft) + { + get_plan(nfft,true,dst,src).inv(fftw_cast(dst), fftw_cast(src),nfft ); + } + + // 2-d complex-to-complex + inline + void inv2(Complex * dst, const Complex * src, int n0,int n1) + { + get_plan(n0,n1,true,dst,src).inv2(fftw_cast(dst), fftw_cast(src) ,n0,n1); + } + + + protected: + typedef fftw_plan<Scalar> PlanData; + + typedef std::map<int64_t,PlanData> PlanMap; + + PlanMap m_plans; + + inline + PlanData & get_plan(int nfft,bool inverse,void * dst,const void * src) + { + bool inplace = (dst==src); + bool aligned = ( (reinterpret_cast<size_t>(src)&15) | (reinterpret_cast<size_t>(dst)&15) ) == 0; + int64_t key = ( (nfft<<3 ) | (inverse<<2) | (inplace<<1) | aligned ) << 1; + return m_plans[key]; + } + + inline + PlanData & get_plan(int n0,int n1,bool inverse,void * dst,const void * src) + { + bool inplace = (dst==src); + bool aligned = ( (reinterpret_cast<size_t>(src)&15) | (reinterpret_cast<size_t>(dst)&15) ) == 0; + int64_t key = ( ( (((int64_t)n0) << 30)|(n1<<3 ) | (inverse<<2) | (inplace<<1) | aligned ) << 1 ) + 1; + return m_plans[key]; + } + }; + +} // end namespace internal + +} // end namespace Eigen + +/* vim: set filetype=cpp et sw=2 ts=2 ai: */ diff --git a/unsupported/Eigen/src/FFT/ei_kissfft_impl.h b/unsupported/Eigen/src/FFT/ei_kissfft_impl.h new file mode 100644 index 000000000..37f5af4c1 --- /dev/null +++ b/unsupported/Eigen/src/FFT/ei_kissfft_impl.h @@ -0,0 +1,418 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Mark Borgerding mark a borgerding net +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +namespace Eigen { + +namespace internal { + + // This FFT implementation was derived from kissfft http:sourceforge.net/projects/kissfft + // Copyright 2003-2009 Mark Borgerding + +template <typename _Scalar> +struct kiss_cpx_fft +{ + typedef _Scalar Scalar; + typedef std::complex<Scalar> Complex; + std::vector<Complex> m_twiddles; + std::vector<int> m_stageRadix; + std::vector<int> m_stageRemainder; + std::vector<Complex> m_scratchBuf; + bool m_inverse; + + inline + void make_twiddles(int nfft,bool inverse) + { + m_inverse = inverse; + m_twiddles.resize(nfft); + Scalar phinc = (inverse?2:-2)* acos( (Scalar) -1) / nfft; + for (int i=0;i<nfft;++i) + m_twiddles[i] = exp( Complex(0,i*phinc) ); + } + + void factorize(int nfft) + { + //start factoring out 4's, then 2's, then 3,5,7,9,... + int n= nfft; + int p=4; + do { + while (n % p) { + switch (p) { + case 4: p = 2; break; + case 2: p = 3; break; + default: p += 2; break; + } + if (p*p>n) + p=n;// impossible to have a factor > sqrt(n) + } + n /= p; + m_stageRadix.push_back(p); + m_stageRemainder.push_back(n); + if ( p > 5 ) + m_scratchBuf.resize(p); // scratchbuf will be needed in bfly_generic + }while(n>1); + } + + template <typename _Src> + inline + void work( int stage,Complex * xout, const _Src * xin, size_t fstride,size_t in_stride) + { + int p = m_stageRadix[stage]; + int m = m_stageRemainder[stage]; + Complex * Fout_beg = xout; + Complex * Fout_end = xout + p*m; + + if (m>1) { + do{ + // recursive call: + // DFT of size m*p performed by doing + // p instances of smaller DFTs of size m, + // each one takes a decimated version of the input + work(stage+1, xout , xin, fstride*p,in_stride); + xin += fstride*in_stride; + }while( (xout += m) != Fout_end ); + }else{ + do{ + *xout = *xin; + xin += fstride*in_stride; + }while(++xout != Fout_end ); + } + xout=Fout_beg; + + // recombine the p smaller DFTs + switch (p) { + case 2: bfly2(xout,fstride,m); break; + case 3: bfly3(xout,fstride,m); break; + case 4: bfly4(xout,fstride,m); break; + case 5: bfly5(xout,fstride,m); break; + default: bfly_generic(xout,fstride,m,p); break; + } + } + + inline + void bfly2( Complex * Fout, const size_t fstride, int m) + { + for (int k=0;k<m;++k) { + Complex t = Fout[m+k] * m_twiddles[k*fstride]; + Fout[m+k] = Fout[k] - t; + Fout[k] += t; + } + } + + inline + void bfly4( Complex * Fout, const size_t fstride, const size_t m) + { + Complex scratch[6]; + int negative_if_inverse = m_inverse * -2 +1; + for (size_t k=0;k<m;++k) { + scratch[0] = Fout[k+m] * m_twiddles[k*fstride]; + scratch[1] = Fout[k+2*m] * m_twiddles[k*fstride*2]; + scratch[2] = Fout[k+3*m] * m_twiddles[k*fstride*3]; + scratch[5] = Fout[k] - scratch[1]; + + Fout[k] += scratch[1]; + scratch[3] = scratch[0] + scratch[2]; + scratch[4] = scratch[0] - scratch[2]; + scratch[4] = Complex( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse ); + + Fout[k+2*m] = Fout[k] - scratch[3]; + Fout[k] += scratch[3]; + Fout[k+m] = scratch[5] + scratch[4]; + Fout[k+3*m] = scratch[5] - scratch[4]; + } + } + + inline + void bfly3( Complex * Fout, const size_t fstride, const size_t m) + { + size_t k=m; + const size_t m2 = 2*m; + Complex *tw1,*tw2; + Complex scratch[5]; + Complex epi3; + epi3 = m_twiddles[fstride*m]; + + tw1=tw2=&m_twiddles[0]; + + do{ + scratch[1]=Fout[m] * *tw1; + scratch[2]=Fout[m2] * *tw2; + + scratch[3]=scratch[1]+scratch[2]; + scratch[0]=scratch[1]-scratch[2]; + tw1 += fstride; + tw2 += fstride*2; + Fout[m] = Complex( Fout->real() - Scalar(.5)*scratch[3].real() , Fout->imag() - Scalar(.5)*scratch[3].imag() ); + scratch[0] *= epi3.imag(); + *Fout += scratch[3]; + Fout[m2] = Complex( Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() ); + Fout[m] += Complex( -scratch[0].imag(),scratch[0].real() ); + ++Fout; + }while(--k); + } + + inline + void bfly5( Complex * Fout, const size_t fstride, const size_t m) + { + Complex *Fout0,*Fout1,*Fout2,*Fout3,*Fout4; + size_t u; + Complex scratch[13]; + Complex * twiddles = &m_twiddles[0]; + Complex *tw; + Complex ya,yb; + ya = twiddles[fstride*m]; + yb = twiddles[fstride*2*m]; + + Fout0=Fout; + Fout1=Fout0+m; + Fout2=Fout0+2*m; + Fout3=Fout0+3*m; + Fout4=Fout0+4*m; + + tw=twiddles; + for ( u=0; u<m; ++u ) { + scratch[0] = *Fout0; + + scratch[1] = *Fout1 * tw[u*fstride]; + scratch[2] = *Fout2 * tw[2*u*fstride]; + scratch[3] = *Fout3 * tw[3*u*fstride]; + scratch[4] = *Fout4 * tw[4*u*fstride]; + + scratch[7] = scratch[1] + scratch[4]; + scratch[10] = scratch[1] - scratch[4]; + scratch[8] = scratch[2] + scratch[3]; + scratch[9] = scratch[2] - scratch[3]; + + *Fout0 += scratch[7]; + *Fout0 += scratch[8]; + + scratch[5] = scratch[0] + Complex( + (scratch[7].real()*ya.real() ) + (scratch[8].real() *yb.real() ), + (scratch[7].imag()*ya.real()) + (scratch[8].imag()*yb.real()) + ); + + scratch[6] = Complex( + (scratch[10].imag()*ya.imag()) + (scratch[9].imag()*yb.imag()), + -(scratch[10].real()*ya.imag()) - (scratch[9].real()*yb.imag()) + ); + + *Fout1 = scratch[5] - scratch[6]; + *Fout4 = scratch[5] + scratch[6]; + + scratch[11] = scratch[0] + + Complex( + (scratch[7].real()*yb.real()) + (scratch[8].real()*ya.real()), + (scratch[7].imag()*yb.real()) + (scratch[8].imag()*ya.real()) + ); + + scratch[12] = Complex( + -(scratch[10].imag()*yb.imag()) + (scratch[9].imag()*ya.imag()), + (scratch[10].real()*yb.imag()) - (scratch[9].real()*ya.imag()) + ); + + *Fout2=scratch[11]+scratch[12]; + *Fout3=scratch[11]-scratch[12]; + + ++Fout0;++Fout1;++Fout2;++Fout3;++Fout4; + } + } + + /* perform the butterfly for one stage of a mixed radix FFT */ + inline + void bfly_generic( + Complex * Fout, + const size_t fstride, + int m, + int p + ) + { + int u,k,q1,q; + Complex * twiddles = &m_twiddles[0]; + Complex t; + int Norig = static_cast<int>(m_twiddles.size()); + Complex * scratchbuf = &m_scratchBuf[0]; + + for ( u=0; u<m; ++u ) { + k=u; + for ( q1=0 ; q1<p ; ++q1 ) { + scratchbuf[q1] = Fout[ k ]; + k += m; + } + + k=u; + for ( q1=0 ; q1<p ; ++q1 ) { + int twidx=0; + Fout[ k ] = scratchbuf[0]; + for (q=1;q<p;++q ) { + twidx += static_cast<int>(fstride) * k; + if (twidx>=Norig) twidx-=Norig; + t=scratchbuf[q] * twiddles[twidx]; + Fout[ k ] += t; + } + k += m; + } + } + } +}; + +template <typename _Scalar> +struct kissfft_impl +{ + typedef _Scalar Scalar; + typedef std::complex<Scalar> Complex; + + void clear() + { + m_plans.clear(); + m_realTwiddles.clear(); + } + + inline + void fwd( Complex * dst,const Complex *src,int nfft) + { + get_plan(nfft,false).work(0, dst, src, 1,1); + } + + inline + void fwd2( Complex * dst,const Complex *src,int n0,int n1) + { + EIGEN_UNUSED_VARIABLE(dst); + EIGEN_UNUSED_VARIABLE(src); + EIGEN_UNUSED_VARIABLE(n0); + EIGEN_UNUSED_VARIABLE(n1); + } + + inline + void inv2( Complex * dst,const Complex *src,int n0,int n1) + { + EIGEN_UNUSED_VARIABLE(dst); + EIGEN_UNUSED_VARIABLE(src); + EIGEN_UNUSED_VARIABLE(n0); + EIGEN_UNUSED_VARIABLE(n1); + } + + // real-to-complex forward FFT + // perform two FFTs of src even and src odd + // then twiddle to recombine them into the half-spectrum format + // then fill in the conjugate symmetric half + inline + void fwd( Complex * dst,const Scalar * src,int nfft) + { + if ( nfft&3 ) { + // use generic mode for odd + m_tmpBuf1.resize(nfft); + get_plan(nfft,false).work(0, &m_tmpBuf1[0], src, 1,1); + std::copy(m_tmpBuf1.begin(),m_tmpBuf1.begin()+(nfft>>1)+1,dst ); + }else{ + int ncfft = nfft>>1; + int ncfft2 = nfft>>2; + Complex * rtw = real_twiddles(ncfft2); + + // use optimized mode for even real + fwd( dst, reinterpret_cast<const Complex*> (src), ncfft); + Complex dc = dst[0].real() + dst[0].imag(); + Complex nyquist = dst[0].real() - dst[0].imag(); + int k; + for ( k=1;k <= ncfft2 ; ++k ) { + Complex fpk = dst[k]; + Complex fpnk = conj(dst[ncfft-k]); + Complex f1k = fpk + fpnk; + Complex f2k = fpk - fpnk; + Complex tw= f2k * rtw[k-1]; + dst[k] = (f1k + tw) * Scalar(.5); + dst[ncfft-k] = conj(f1k -tw)*Scalar(.5); + } + dst[0] = dc; + dst[ncfft] = nyquist; + } + } + + // inverse complex-to-complex + inline + void inv(Complex * dst,const Complex *src,int nfft) + { + get_plan(nfft,true).work(0, dst, src, 1,1); + } + + // half-complex to scalar + inline + void inv( Scalar * dst,const Complex * src,int nfft) + { + if (nfft&3) { + m_tmpBuf1.resize(nfft); + m_tmpBuf2.resize(nfft); + std::copy(src,src+(nfft>>1)+1,m_tmpBuf1.begin() ); + for (int k=1;k<(nfft>>1)+1;++k) + m_tmpBuf1[nfft-k] = conj(m_tmpBuf1[k]); + inv(&m_tmpBuf2[0],&m_tmpBuf1[0],nfft); + for (int k=0;k<nfft;++k) + dst[k] = m_tmpBuf2[k].real(); + }else{ + // optimized version for multiple of 4 + int ncfft = nfft>>1; + int ncfft2 = nfft>>2; + Complex * rtw = real_twiddles(ncfft2); + m_tmpBuf1.resize(ncfft); + m_tmpBuf1[0] = Complex( src[0].real() + src[ncfft].real(), src[0].real() - src[ncfft].real() ); + for (int k = 1; k <= ncfft / 2; ++k) { + Complex fk = src[k]; + Complex fnkc = conj(src[ncfft-k]); + Complex fek = fk + fnkc; + Complex tmp = fk - fnkc; + Complex fok = tmp * conj(rtw[k-1]); + m_tmpBuf1[k] = fek + fok; + m_tmpBuf1[ncfft-k] = conj(fek - fok); + } + get_plan(ncfft,true).work(0, reinterpret_cast<Complex*>(dst), &m_tmpBuf1[0], 1,1); + } + } + + protected: + typedef kiss_cpx_fft<Scalar> PlanData; + typedef std::map<int,PlanData> PlanMap; + + PlanMap m_plans; + std::map<int, std::vector<Complex> > m_realTwiddles; + std::vector<Complex> m_tmpBuf1; + std::vector<Complex> m_tmpBuf2; + + inline + int PlanKey(int nfft, bool isinverse) const { return (nfft<<1) | int(isinverse); } + + inline + PlanData & get_plan(int nfft, bool inverse) + { + // TODO look for PlanKey(nfft, ! inverse) and conjugate the twiddles + PlanData & pd = m_plans[ PlanKey(nfft,inverse) ]; + if ( pd.m_twiddles.size() == 0 ) { + pd.make_twiddles(nfft,inverse); + pd.factorize(nfft); + } + return pd; + } + + inline + Complex * real_twiddles(int ncfft2) + { + std::vector<Complex> & twidref = m_realTwiddles[ncfft2];// creates new if not there + if ( (int)twidref.size() != ncfft2 ) { + twidref.resize(ncfft2); + int ncfft= ncfft2<<1; + Scalar pi = acos( Scalar(-1) ); + for (int k=1;k<=ncfft2;++k) + twidref[k-1] = exp( Complex(0,-pi * (Scalar(k) / ncfft + Scalar(.5)) ) ); + } + return &twidref[0]; + } +}; + +} // end namespace internal + +} // end namespace Eigen + +/* vim: set filetype=cpp et sw=2 ts=2 ai: */ diff --git a/unsupported/Eigen/src/IterativeSolvers/CMakeLists.txt b/unsupported/Eigen/src/IterativeSolvers/CMakeLists.txt new file mode 100644 index 000000000..7986afc5e --- /dev/null +++ b/unsupported/Eigen/src/IterativeSolvers/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_IterativeSolvers_SRCS "*.h") + +INSTALL(FILES + ${Eigen_IterativeSolvers_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/IterativeSolvers COMPONENT Devel + ) diff --git a/unsupported/Eigen/src/IterativeSolvers/ConstrainedConjGrad.h b/unsupported/Eigen/src/IterativeSolvers/ConstrainedConjGrad.h new file mode 100644 index 000000000..b83bf7aef --- /dev/null +++ b/unsupported/Eigen/src/IterativeSolvers/ConstrainedConjGrad.h @@ -0,0 +1,189 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* NOTE The functions of this file have been adapted from the GMM++ library */ + +//======================================================================== +// +// Copyright (C) 2002-2007 Yves Renard +// +// This file is a part of GETFEM++ +// +// Getfem++ is free software; you can redistribute it and/or modify +// it under the terms of the GNU Lesser General Public License as +// published by the Free Software Foundation; version 2.1 of the License. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU Lesser General Public License for more details. +// You should have received a copy of the GNU Lesser General Public +// License along with this program; if not, write to the Free Software +// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, +// USA. +// +//======================================================================== + +#include "../../../../Eigen/src/Core/util/NonMPL2.h" + +#ifndef EIGEN_CONSTRAINEDCG_H +#define EIGEN_CONSTRAINEDCG_H + +#include <Eigen/Core> + +namespace Eigen { + +namespace internal { + +/** \ingroup IterativeSolvers_Module + * Compute the pseudo inverse of the non-square matrix C such that + * \f$ CINV = (C * C^T)^{-1} * C \f$ based on a conjugate gradient method. + * + * This function is internally used by constrained_cg. + */ +template <typename CMatrix, typename CINVMatrix> +void pseudo_inverse(const CMatrix &C, CINVMatrix &CINV) +{ + // optimisable : copie de la ligne, precalcul de C * trans(C). + typedef typename CMatrix::Scalar Scalar; + typedef typename CMatrix::Index Index; + // FIXME use sparse vectors ? + typedef Matrix<Scalar,Dynamic,1> TmpVec; + + Index rows = C.rows(), cols = C.cols(); + + TmpVec d(rows), e(rows), l(cols), p(rows), q(rows), r(rows); + Scalar rho, rho_1, alpha; + d.setZero(); + + CINV.startFill(); // FIXME estimate the number of non-zeros + for (Index i = 0; i < rows; ++i) + { + d[i] = 1.0; + rho = 1.0; + e.setZero(); + r = d; + p = d; + + while (rho >= 1e-38) + { /* conjugate gradient to compute e */ + /* which is the i-th row of inv(C * trans(C)) */ + l = C.transpose() * p; + q = C * l; + alpha = rho / p.dot(q); + e += alpha * p; + r += -alpha * q; + rho_1 = rho; + rho = r.dot(r); + p = (rho/rho_1) * p + r; + } + + l = C.transpose() * e; // l is the i-th row of CINV + // FIXME add a generic "prune/filter" expression for both dense and sparse object to sparse + for (Index j=0; j<l.size(); ++j) + if (l[j]<1e-15) + CINV.fill(i,j) = l[j]; + + d[i] = 0.0; + } + CINV.endFill(); +} + + + +/** \ingroup IterativeSolvers_Module + * Constrained conjugate gradient + * + * Computes the minimum of \f$ 1/2((Ax).x) - bx \f$ under the contraint \f$ Cx \le f \f$ + */ +template<typename TMatrix, typename CMatrix, + typename VectorX, typename VectorB, typename VectorF> +void constrained_cg(const TMatrix& A, const CMatrix& C, VectorX& x, + const VectorB& b, const VectorF& f, IterationController &iter) +{ + typedef typename TMatrix::Scalar Scalar; + typedef typename TMatrix::Index Index; + typedef Matrix<Scalar,Dynamic,1> TmpVec; + + Scalar rho = 1.0, rho_1, lambda, gamma; + Index xSize = x.size(); + TmpVec p(xSize), q(xSize), q2(xSize), + r(xSize), old_z(xSize), z(xSize), + memox(xSize); + std::vector<bool> satured(C.rows()); + p.setZero(); + iter.setRhsNorm(sqrt(b.dot(b))); // gael vect_sp(PS, b, b) + if (iter.rhsNorm() == 0.0) iter.setRhsNorm(1.0); + + SparseMatrix<Scalar,RowMajor> CINV(C.rows(), C.cols()); + pseudo_inverse(C, CINV); + + while(true) + { + // computation of residual + old_z = z; + memox = x; + r = b; + r += A * -x; + z = r; + bool transition = false; + for (Index i = 0; i < C.rows(); ++i) + { + Scalar al = C.row(i).dot(x) - f.coeff(i); + if (al >= -1.0E-15) + { + if (!satured[i]) + { + satured[i] = true; + transition = true; + } + Scalar bb = CINV.row(i).dot(z); + if (bb > 0.0) + // FIXME: we should allow that: z += -bb * C.row(i); + for (typename CMatrix::InnerIterator it(C,i); it; ++it) + z.coeffRef(it.index()) -= bb*it.value(); + } + else + satured[i] = false; + } + + // descent direction + rho_1 = rho; + rho = r.dot(z); + + if (iter.finished(rho)) break; + + if (iter.noiseLevel() > 0 && transition) std::cerr << "CCG: transition\n"; + if (transition || iter.first()) gamma = 0.0; + else gamma = (std::max)(0.0, (rho - old_z.dot(z)) / rho_1); + p = z + gamma*p; + + ++iter; + // one dimensionnal optimization + q = A * p; + lambda = rho / q.dot(p); + for (Index i = 0; i < C.rows(); ++i) + { + if (!satured[i]) + { + Scalar bb = C.row(i).dot(p) - f[i]; + if (bb > 0.0) + lambda = (std::min)(lambda, (f.coeff(i)-C.row(i).dot(x)) / bb); + } + } + x += lambda * p; + memox -= x; + } +} + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_CONSTRAINEDCG_H diff --git a/unsupported/Eigen/src/IterativeSolvers/GMRES.h b/unsupported/Eigen/src/IterativeSolvers/GMRES.h new file mode 100644 index 000000000..34e67db82 --- /dev/null +++ b/unsupported/Eigen/src/IterativeSolvers/GMRES.h @@ -0,0 +1,379 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr> +// Copyright (C) 2012 Kolja Brix <brix@igpm.rwth-aaachen.de> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_GMRES_H +#define EIGEN_GMRES_H + +namespace Eigen { + +namespace internal { + +/** + * Generalized Minimal Residual Algorithm based on the + * Arnoldi algorithm implemented with Householder reflections. + * + * Parameters: + * \param mat matrix of linear system of equations + * \param Rhs right hand side vector of linear system of equations + * \param x on input: initial guess, on output: solution + * \param precond preconditioner used + * \param iters on input: maximum number of iterations to perform + * on output: number of iterations performed + * \param restart number of iterations for a restart + * \param tol_error on input: residual tolerance + * on output: residuum achieved + * + * \sa IterativeMethods::bicgstab() + * + * + * For references, please see: + * + * Saad, Y. and Schultz, M. H. + * GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems. + * SIAM J.Sci.Stat.Comp. 7, 1986, pp. 856 - 869. + * + * Saad, Y. + * Iterative Methods for Sparse Linear Systems. + * Society for Industrial and Applied Mathematics, Philadelphia, 2003. + * + * Walker, H. F. + * Implementations of the GMRES method. + * Comput.Phys.Comm. 53, 1989, pp. 311 - 320. + * + * Walker, H. F. + * Implementation of the GMRES Method using Householder Transformations. + * SIAM J.Sci.Stat.Comp. 9, 1988, pp. 152 - 163. + * + */ +template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner> +bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Preconditioner & precond, + int &iters, const int &restart, typename Dest::RealScalar & tol_error) { + + using std::sqrt; + using std::abs; + + typedef typename Dest::RealScalar RealScalar; + typedef typename Dest::Scalar Scalar; + typedef Matrix < RealScalar, Dynamic, 1 > RealVectorType; + typedef Matrix < Scalar, Dynamic, 1 > VectorType; + typedef Matrix < Scalar, Dynamic, Dynamic > FMatrixType; + + RealScalar tol = tol_error; + const int maxIters = iters; + iters = 0; + + const int m = mat.rows(); + + VectorType p0 = rhs - mat*x; + VectorType r0 = precond.solve(p0); +// RealScalar r0_sqnorm = r0.squaredNorm(); + + VectorType w = VectorType::Zero(restart + 1); + + FMatrixType H = FMatrixType::Zero(m, restart + 1); + VectorType tau = VectorType::Zero(restart + 1); + std::vector < JacobiRotation < Scalar > > G(restart); + + // generate first Householder vector + VectorType e; + RealScalar beta; + r0.makeHouseholder(e, tau.coeffRef(0), beta); + w(0)=(Scalar) beta; + H.bottomLeftCorner(m - 1, 1) = e; + + for (int k = 1; k <= restart; ++k) { + + ++iters; + + VectorType v = VectorType::Unit(m, k - 1), workspace(m); + + // apply Householder reflections H_{1} ... H_{k-1} to v + for (int i = k - 1; i >= 0; --i) { + v.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data()); + } + + // apply matrix M to v: v = mat * v; + VectorType t=mat*v; + v=precond.solve(t); + + // apply Householder reflections H_{k-1} ... H_{1} to v + for (int i = 0; i < k; ++i) { + v.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data()); + } + + if (v.tail(m - k).norm() != 0.0) { + + if (k <= restart) { + + // generate new Householder vector + VectorType e(m - k - 1); + RealScalar beta; + v.tail(m - k).makeHouseholder(e, tau.coeffRef(k), beta); + H.col(k).tail(m - k - 1) = e; + + // apply Householder reflection H_{k} to v + v.tail(m - k).applyHouseholderOnTheLeft(H.col(k).tail(m - k - 1), tau.coeffRef(k), workspace.data()); + + } + } + + if (k > 1) { + for (int i = 0; i < k - 1; ++i) { + // apply old Givens rotations to v + v.applyOnTheLeft(i, i + 1, G[i].adjoint()); + } + } + + if (k<m && v(k) != (Scalar) 0) { + // determine next Givens rotation + G[k - 1].makeGivens(v(k - 1), v(k)); + + // apply Givens rotation to v and w + v.applyOnTheLeft(k - 1, k, G[k - 1].adjoint()); + w.applyOnTheLeft(k - 1, k, G[k - 1].adjoint()); + + } + + // insert coefficients into upper matrix triangle + H.col(k - 1).head(k) = v.head(k); + + bool stop=(k==m || abs(w(k)) < tol || iters == maxIters); + + if (stop || k == restart) { + + // solve upper triangular system + VectorType y = w.head(k); + H.topLeftCorner(k, k).template triangularView < Eigen::Upper > ().solveInPlace(y); + + // use Horner-like scheme to calculate solution vector + VectorType x_new = y(k - 1) * VectorType::Unit(m, k - 1); + + // apply Householder reflection H_{k} to x_new + x_new.tail(m - k + 1).applyHouseholderOnTheLeft(H.col(k - 1).tail(m - k), tau.coeffRef(k - 1), workspace.data()); + + for (int i = k - 2; i >= 0; --i) { + x_new += y(i) * VectorType::Unit(m, i); + // apply Householder reflection H_{i} to x_new + x_new.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data()); + } + + x += x_new; + + if (stop) { + return true; + } else { + k=0; + + // reset data for a restart r0 = rhs - mat * x; + VectorType p0=mat*x; + VectorType p1=precond.solve(p0); + r0 = rhs - p1; +// r0_sqnorm = r0.squaredNorm(); + w = VectorType::Zero(restart + 1); + H = FMatrixType::Zero(m, restart + 1); + tau = VectorType::Zero(restart + 1); + + // generate first Householder vector + RealScalar beta; + r0.makeHouseholder(e, tau.coeffRef(0), beta); + w(0)=(Scalar) beta; + H.bottomLeftCorner(m - 1, 1) = e; + + } + + } + + + + } + + return false; + +} + +} + +template< typename _MatrixType, + typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> > +class GMRES; + +namespace internal { + +template< typename _MatrixType, typename _Preconditioner> +struct traits<GMRES<_MatrixType,_Preconditioner> > +{ + typedef _MatrixType MatrixType; + typedef _Preconditioner Preconditioner; +}; + +} + +/** \ingroup IterativeLinearSolvers_Module + * \brief A GMRES solver for sparse square problems + * + * This class allows to solve for A.x = b sparse linear problems using a generalized minimal + * residual method. The vectors x and b can be either dense or sparse. + * + * \tparam _MatrixType the type of the sparse matrix A, can be a dense or a sparse matrix. + * \tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner + * + * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations() + * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations + * and NumTraits<Scalar>::epsilon() for the tolerance. + * + * This class can be used as the direct solver classes. Here is a typical usage example: + * \code + * int n = 10000; + * VectorXd x(n), b(n); + * SparseMatrix<double> A(n,n); + * // fill A and b + * GMRES<SparseMatrix<double> > solver(A); + * x = solver.solve(b); + * std::cout << "#iterations: " << solver.iterations() << std::endl; + * std::cout << "estimated error: " << solver.error() << std::endl; + * // update b, and solve again + * x = solver.solve(b); + * \endcode + * + * By default the iterations start with x=0 as an initial guess of the solution. + * One can control the start using the solveWithGuess() method. Here is a step by + * step execution example starting with a random guess and printing the evolution + * of the estimated error: + * * \code + * x = VectorXd::Random(n); + * solver.setMaxIterations(1); + * int i = 0; + * do { + * x = solver.solveWithGuess(b,x); + * std::cout << i << " : " << solver.error() << std::endl; + * ++i; + * } while (solver.info()!=Success && i<100); + * \endcode + * Note that such a step by step excution is slightly slower. + * + * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner + */ +template< typename _MatrixType, typename _Preconditioner> +class GMRES : public IterativeSolverBase<GMRES<_MatrixType,_Preconditioner> > +{ + typedef IterativeSolverBase<GMRES> Base; + using Base::mp_matrix; + using Base::m_error; + using Base::m_iterations; + using Base::m_info; + using Base::m_isInitialized; + +private: + int m_restart; + +public: + typedef _MatrixType MatrixType; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::Index Index; + typedef typename MatrixType::RealScalar RealScalar; + typedef _Preconditioner Preconditioner; + +public: + + /** Default constructor. */ + GMRES() : Base(), m_restart(30) {} + + /** Initialize the solver with matrix \a A for further \c Ax=b solving. + * + * This constructor is a shortcut for the default constructor followed + * by a call to compute(). + * + * \warning this class stores a reference to the matrix A as well as some + * precomputed values that depend on it. Therefore, if \a A is changed + * this class becomes invalid. Call compute() to update it with the new + * matrix A, or modify a copy of A. + */ + GMRES(const MatrixType& A) : Base(A), m_restart(30) {} + + ~GMRES() {} + + /** Get the number of iterations after that a restart is performed. + */ + int get_restart() { return m_restart; } + + /** Set the number of iterations after that a restart is performed. + * \param restart number of iterations for a restarti, default is 30. + */ + void set_restart(const int restart) { m_restart=restart; } + + /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A + * \a x0 as an initial solution. + * + * \sa compute() + */ + template<typename Rhs,typename Guess> + inline const internal::solve_retval_with_guess<GMRES, Rhs, Guess> + solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const + { + eigen_assert(m_isInitialized && "GMRES is not initialized."); + eigen_assert(Base::rows()==b.rows() + && "GMRES::solve(): invalid number of rows of the right hand side matrix b"); + return internal::solve_retval_with_guess + <GMRES, Rhs, Guess>(*this, b.derived(), x0); + } + + /** \internal */ + template<typename Rhs,typename Dest> + void _solveWithGuess(const Rhs& b, Dest& x) const + { + bool failed = false; + for(int j=0; j<b.cols(); ++j) + { + m_iterations = Base::maxIterations(); + m_error = Base::m_tolerance; + + typename Dest::ColXpr xj(x,j); + if(!internal::gmres(*mp_matrix, b.col(j), xj, Base::m_preconditioner, m_iterations, m_restart, m_error)) + failed = true; + } + m_info = failed ? NumericalIssue + : m_error <= Base::m_tolerance ? Success + : NoConvergence; + m_isInitialized = true; + } + + /** \internal */ + template<typename Rhs,typename Dest> + void _solve(const Rhs& b, Dest& x) const + { + x.setZero(); + _solveWithGuess(b,x); + } + +protected: + +}; + + +namespace internal { + + template<typename _MatrixType, typename _Preconditioner, typename Rhs> +struct solve_retval<GMRES<_MatrixType, _Preconditioner>, Rhs> + : solve_retval_base<GMRES<_MatrixType, _Preconditioner>, Rhs> +{ + typedef GMRES<_MatrixType, _Preconditioner> Dec; + EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) + + template<typename Dest> void evalTo(Dest& dst) const + { + dec()._solve(rhs(),dst); + } +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_GMRES_H diff --git a/unsupported/Eigen/src/IterativeSolvers/IncompleteLU.h b/unsupported/Eigen/src/IterativeSolvers/IncompleteLU.h new file mode 100644 index 000000000..67e780181 --- /dev/null +++ b/unsupported/Eigen/src/IterativeSolvers/IncompleteLU.h @@ -0,0 +1,113 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_INCOMPLETE_LU_H +#define EIGEN_INCOMPLETE_LU_H + +namespace Eigen { + +template <typename _Scalar> +class IncompleteLU +{ + typedef _Scalar Scalar; + typedef Matrix<Scalar,Dynamic,1> Vector; + typedef typename Vector::Index Index; + typedef SparseMatrix<Scalar,RowMajor> FactorType; + + public: + typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType; + + IncompleteLU() : m_isInitialized(false) {} + + template<typename MatrixType> + IncompleteLU(const MatrixType& mat) : m_isInitialized(false) + { + compute(mat); + } + + Index rows() const { return m_lu.rows(); } + Index cols() const { return m_lu.cols(); } + + template<typename MatrixType> + IncompleteLU& compute(const MatrixType& mat) + { + m_lu = mat; + int size = mat.cols(); + Vector diag(size); + for(int i=0; i<size; ++i) + { + typename FactorType::InnerIterator k_it(m_lu,i); + for(; k_it && k_it.index()<i; ++k_it) + { + int k = k_it.index(); + k_it.valueRef() /= diag(k); + + typename FactorType::InnerIterator j_it(k_it); + typename FactorType::InnerIterator kj_it(m_lu, k); + while(kj_it && kj_it.index()<=k) ++kj_it; + for(++j_it; j_it; ) + { + if(kj_it.index()==j_it.index()) + { + j_it.valueRef() -= k_it.value() * kj_it.value(); + ++j_it; + ++kj_it; + } + else if(kj_it.index()<j_it.index()) ++kj_it; + else ++j_it; + } + } + if(k_it && k_it.index()==i) diag(i) = k_it.value(); + else diag(i) = 1; + } + m_isInitialized = true; + return *this; + } + + template<typename Rhs, typename Dest> + void _solve(const Rhs& b, Dest& x) const + { + x = m_lu.template triangularView<UnitLower>().solve(b); + x = m_lu.template triangularView<Upper>().solve(x); + } + + template<typename Rhs> inline const internal::solve_retval<IncompleteLU, Rhs> + solve(const MatrixBase<Rhs>& b) const + { + eigen_assert(m_isInitialized && "IncompleteLU is not initialized."); + eigen_assert(cols()==b.rows() + && "IncompleteLU::solve(): invalid number of rows of the right hand side matrix b"); + return internal::solve_retval<IncompleteLU, Rhs>(*this, b.derived()); + } + + protected: + FactorType m_lu; + bool m_isInitialized; +}; + +namespace internal { + +template<typename _MatrixType, typename Rhs> +struct solve_retval<IncompleteLU<_MatrixType>, Rhs> + : solve_retval_base<IncompleteLU<_MatrixType>, Rhs> +{ + typedef IncompleteLU<_MatrixType> Dec; + EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) + + template<typename Dest> void evalTo(Dest& dst) const + { + dec()._solve(rhs(),dst); + } +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_INCOMPLETE_LU_H diff --git a/unsupported/Eigen/src/IterativeSolvers/IterationController.h b/unsupported/Eigen/src/IterativeSolvers/IterationController.h new file mode 100644 index 000000000..aaf46d544 --- /dev/null +++ b/unsupported/Eigen/src/IterativeSolvers/IterationController.h @@ -0,0 +1,157 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* NOTE The class IterationController has been adapted from the iteration + * class of the GMM++ and ITL libraries. + */ + +//======================================================================= +// Copyright (C) 1997-2001 +// Authors: Andrew Lumsdaine <lums@osl.iu.edu> +// Lie-Quan Lee <llee@osl.iu.edu> +// +// This file is part of the Iterative Template Library +// +// You should have received a copy of the License Agreement for the +// Iterative Template Library along with the software; see the +// file LICENSE. +// +// Permission to modify the code and to distribute modified code is +// granted, provided the text of this NOTICE is retained, a notice that +// the code was modified is included with the above COPYRIGHT NOTICE and +// with the COPYRIGHT NOTICE in the LICENSE file, and that the LICENSE +// file is distributed with the modified code. +// +// LICENSOR MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR IMPLIED. +// By way of example, but not limitation, Licensor MAKES NO +// REPRESENTATIONS OR WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY +// PARTICULAR PURPOSE OR THAT THE USE OF THE LICENSED SOFTWARE COMPONENTS +// OR DOCUMENTATION WILL NOT INFRINGE ANY PATENTS, COPYRIGHTS, TRADEMARKS +// OR OTHER RIGHTS. +//======================================================================= + +//======================================================================== +// +// Copyright (C) 2002-2007 Yves Renard +// +// This file is a part of GETFEM++ +// +// Getfem++ is free software; you can redistribute it and/or modify +// it under the terms of the GNU Lesser General Public License as +// published by the Free Software Foundation; version 2.1 of the License. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU Lesser General Public License for more details. +// You should have received a copy of the GNU Lesser General Public +// License along with this program; if not, write to the Free Software +// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, +// USA. +// +//======================================================================== + +#include "../../../../Eigen/src/Core/util/NonMPL2.h" + +#ifndef EIGEN_ITERATION_CONTROLLER_H +#define EIGEN_ITERATION_CONTROLLER_H + +namespace Eigen { + +/** \ingroup IterativeSolvers_Module + * \class IterationController + * + * \brief Controls the iterations of the iterative solvers + * + * This class has been adapted from the iteration class of GMM++ and ITL libraries. + * + */ +class IterationController +{ + protected : + double m_rhsn; ///< Right hand side norm + size_t m_maxiter; ///< Max. number of iterations + int m_noise; ///< if noise > 0 iterations are printed + double m_resmax; ///< maximum residual + double m_resminreach, m_resadd; + size_t m_nit; ///< iteration number + double m_res; ///< last computed residual + bool m_written; + void (*m_callback)(const IterationController&); + public : + + void init() + { + m_nit = 0; m_res = 0.0; m_written = false; + m_resminreach = 1E50; m_resadd = 0.0; + m_callback = 0; + } + + IterationController(double r = 1.0E-8, int noi = 0, size_t mit = size_t(-1)) + : m_rhsn(1.0), m_maxiter(mit), m_noise(noi), m_resmax(r) { init(); } + + void operator ++(int) { m_nit++; m_written = false; m_resadd += m_res; } + void operator ++() { (*this)++; } + + bool first() { return m_nit == 0; } + + /* get/set the "noisyness" (verbosity) of the solvers */ + int noiseLevel() const { return m_noise; } + void setNoiseLevel(int n) { m_noise = n; } + void reduceNoiseLevel() { if (m_noise > 0) m_noise--; } + + double maxResidual() const { return m_resmax; } + void setMaxResidual(double r) { m_resmax = r; } + + double residual() const { return m_res; } + + /* change the user-definable callback, called after each iteration */ + void setCallback(void (*t)(const IterationController&)) + { + m_callback = t; + } + + size_t iteration() const { return m_nit; } + void setIteration(size_t i) { m_nit = i; } + + size_t maxIterarions() const { return m_maxiter; } + void setMaxIterations(size_t i) { m_maxiter = i; } + + double rhsNorm() const { return m_rhsn; } + void setRhsNorm(double r) { m_rhsn = r; } + + bool converged() const { return m_res <= m_rhsn * m_resmax; } + bool converged(double nr) + { + m_res = internal::abs(nr); + m_resminreach = (std::min)(m_resminreach, m_res); + return converged(); + } + template<typename VectorType> bool converged(const VectorType &v) + { return converged(v.squaredNorm()); } + + bool finished(double nr) + { + if (m_callback) m_callback(*this); + if (m_noise > 0 && !m_written) + { + converged(nr); + m_written = true; + } + return (m_nit >= m_maxiter || converged(nr)); + } + template <typename VectorType> + bool finished(const MatrixBase<VectorType> &v) + { return finished(double(v.squaredNorm())); } + +}; + +} // end namespace Eigen + +#endif // EIGEN_ITERATION_CONTROLLER_H diff --git a/unsupported/Eigen/src/IterativeSolvers/Scaling.h b/unsupported/Eigen/src/IterativeSolvers/Scaling.h new file mode 100644 index 000000000..fdef0aca3 --- /dev/null +++ b/unsupported/Eigen/src/IterativeSolvers/Scaling.h @@ -0,0 +1,185 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Desire NUENTSA WAKAM <desire.nuentsa_wakam@inria.fr +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SCALING_H +#define EIGEN_SCALING_H +/** + * \ingroup IterativeSolvers_Module + * \brief iterative scaling algorithm to equilibrate rows and column norms in matrices + * + * This class can be used as a preprocessing tool to accelerate the convergence of iterative methods + * + * This feature is useful to limit the pivoting amount during LU/ILU factorization + * The scaling strategy as presented here preserves the symmetry of the problem + * NOTE It is assumed that the matrix does not have empty row or column, + * + * Example with key steps + * \code + * VectorXd x(n), b(n); + * SparseMatrix<double> A; + * // fill A and b; + * Scaling<SparseMatrix<double> > scal; + * // Compute the left and right scaling vectors. The matrix is equilibrated at output + * scal.computeRef(A); + * // Scale the right hand side + * b = scal.LeftScaling().cwiseProduct(b); + * // Now, solve the equilibrated linear system with any available solver + * + * // Scale back the computed solution + * x = scal.RightScaling().cwiseProduct(x); + * \endcode + * + * \tparam _MatrixType the type of the matrix. It should be a real square sparsematrix + * + * References : D. Ruiz and B. Ucar, A Symmetry Preserving Algorithm for Matrix Scaling, INRIA Research report RR-7552 + * + * \sa \ref IncompleteLUT + */ +using std::abs; +using namespace Eigen; +template<typename _MatrixType> +class Scaling +{ + public: + typedef _MatrixType MatrixType; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::Index Index; + + public: + Scaling() { init(); } + + Scaling(const MatrixType& matrix) + { + init(); + compute(matrix); + } + + ~Scaling() { } + + /** + * Compute the left and right diagonal matrices to scale the input matrix @p mat + * + * FIXME This algorithm will be modified such that the diagonal elements are permuted on the diagonal. + * + * \sa LeftScaling() RightScaling() + */ + void compute (const MatrixType& mat) + { + int m = mat.rows(); + int n = mat.cols(); + assert((m>0 && m == n) && "Please give a non - empty matrix"); + m_left.resize(m); + m_right.resize(n); + m_left.setOnes(); + m_right.setOnes(); + m_matrix = mat; + VectorXd Dr, Dc, DrRes, DcRes; // Temporary Left and right scaling vectors + Dr.resize(m); Dc.resize(n); + DrRes.resize(m); DcRes.resize(n); + double EpsRow = 1.0, EpsCol = 1.0; + int its = 0; + do + { // Iterate until the infinite norm of each row and column is approximately 1 + // Get the maximum value in each row and column + Dr.setZero(); Dc.setZero(); + for (int k=0; k<m_matrix.outerSize(); ++k) + { + for (typename MatrixType::InnerIterator it(m_matrix, k); it; ++it) + { + if ( Dr(it.row()) < abs(it.value()) ) + Dr(it.row()) = abs(it.value()); + + if ( Dc(it.col()) < abs(it.value()) ) + Dc(it.col()) = abs(it.value()); + } + } + for (int i = 0; i < m; ++i) + { + Dr(i) = std::sqrt(Dr(i)); + Dc(i) = std::sqrt(Dc(i)); + } + // Save the scaling factors + for (int i = 0; i < m; ++i) + { + m_left(i) /= Dr(i); + m_right(i) /= Dc(i); + } + // Scale the rows and the columns of the matrix + DrRes.setZero(); DcRes.setZero(); + for (int k=0; k<m_matrix.outerSize(); ++k) + { + for (typename MatrixType::InnerIterator it(m_matrix, k); it; ++it) + { + it.valueRef() = it.value()/( Dr(it.row()) * Dc(it.col()) ); + // Accumulate the norms of the row and column vectors + if ( DrRes(it.row()) < abs(it.value()) ) + DrRes(it.row()) = abs(it.value()); + + if ( DcRes(it.col()) < abs(it.value()) ) + DcRes(it.col()) = abs(it.value()); + } + } + DrRes.array() = (1-DrRes.array()).abs(); + EpsRow = DrRes.maxCoeff(); + DcRes.array() = (1-DcRes.array()).abs(); + EpsCol = DcRes.maxCoeff(); + its++; + }while ( (EpsRow >m_tol || EpsCol > m_tol) && (its < m_maxits) ); + m_isInitialized = true; + } + /** Compute the left and right vectors to scale the vectors + * the input matrix is scaled with the computed vectors at output + * + * \sa compute() + */ + void computeRef (MatrixType& mat) + { + compute (mat); + mat = m_matrix; + } + /** Get the vector to scale the rows of the matrix + */ + VectorXd& LeftScaling() + { + return m_left; + } + + /** Get the vector to scale the columns of the matrix + */ + VectorXd& RightScaling() + { + return m_right; + } + + /** Set the tolerance for the convergence of the iterative scaling algorithm + */ + void setTolerance(double tol) + { + m_tol = tol; + } + + protected: + + void init() + { + m_tol = 1e-10; + m_maxits = 5; + m_isInitialized = false; + } + + MatrixType m_matrix; + mutable ComputationInfo m_info; + bool m_isInitialized; + VectorXd m_left; // Left scaling vector + VectorXd m_right; // m_right scaling vector + double m_tol; + int m_maxits; // Maximum number of iterations allowed +}; + +#endif
\ No newline at end of file diff --git a/unsupported/Eigen/src/KroneckerProduct/CMakeLists.txt b/unsupported/Eigen/src/KroneckerProduct/CMakeLists.txt new file mode 100644 index 000000000..4daefebee --- /dev/null +++ b/unsupported/Eigen/src/KroneckerProduct/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_KroneckerProduct_SRCS "*.h") + +INSTALL(FILES + ${Eigen_KroneckerProduct_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/KroneckerProduct COMPONENT Devel + ) diff --git a/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h b/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h new file mode 100644 index 000000000..84fd72fc6 --- /dev/null +++ b/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h @@ -0,0 +1,157 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de> +// Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + + +#ifndef KRONECKER_TENSOR_PRODUCT_H +#define KRONECKER_TENSOR_PRODUCT_H + + +namespace Eigen { + +namespace internal { + +/*! + * Kronecker tensor product helper function for dense matrices + * + * \param A Dense matrix A + * \param B Dense matrix B + * \param AB_ Kronecker tensor product of A and B + */ +template<typename Derived_A, typename Derived_B, typename Derived_AB> +void kroneckerProduct_full(const Derived_A& A, const Derived_B& B, Derived_AB & AB) +{ + const unsigned int Ar = A.rows(), + Ac = A.cols(), + Br = B.rows(), + Bc = B.cols(); + for (unsigned int i=0; i<Ar; ++i) + for (unsigned int j=0; j<Ac; ++j) + AB.block(i*Br,j*Bc,Br,Bc) = A(i,j)*B; +} + + +/*! + * Kronecker tensor product helper function for matrices, where at least one is sparse + * + * \param A Matrix A + * \param B Matrix B + * \param AB_ Kronecker tensor product of A and B + */ +template<typename Derived_A, typename Derived_B, typename Derived_AB> +void kroneckerProduct_sparse(const Derived_A &A, const Derived_B &B, Derived_AB &AB) +{ + const unsigned int Ar = A.rows(), + Ac = A.cols(), + Br = B.rows(), + Bc = B.cols(); + AB.resize(Ar*Br,Ac*Bc); + AB.resizeNonZeros(0); + AB.reserve(A.nonZeros()*B.nonZeros()); + + for (int kA=0; kA<A.outerSize(); ++kA) + { + for (int kB=0; kB<B.outerSize(); ++kB) + { + for (typename Derived_A::InnerIterator itA(A,kA); itA; ++itA) + { + for (typename Derived_B::InnerIterator itB(B,kB); itB; ++itB) + { + const unsigned int iA = itA.row(), + jA = itA.col(), + iB = itB.row(), + jB = itB.col(), + i = iA*Br + iB, + j = jA*Bc + jB; + AB.insert(i,j) = itA.value() * itB.value(); + } + } + } + } +} + +} // end namespace internal + + + +/*! + * Computes Kronecker tensor product of two dense matrices + * + * \param a Dense matrix a + * \param b Dense matrix b + * \param c Kronecker tensor product of a and b + */ +template<typename A,typename B,typename CScalar,int CRows,int CCols, int COptions, int CMaxRows, int CMaxCols> +void kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b, Matrix<CScalar,CRows,CCols,COptions,CMaxRows,CMaxCols>& c) +{ + c.resize(a.rows()*b.rows(),a.cols()*b.cols()); + internal::kroneckerProduct_full(a.derived(), b.derived(), c); +} + +/*! + * Computes Kronecker tensor product of two dense matrices + * + * Remark: this function uses the const cast hack and has been + * implemented to make the function call possible, where the + * output matrix is a submatrix, e.g. + * kroneckerProduct(A,B,AB.block(2,5,6,6)); + * + * \param a Dense matrix a + * \param b Dense matrix b + * \param c Kronecker tensor product of a and b + */ +template<typename A,typename B,typename C> +void kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b, MatrixBase<C> const & c_) +{ + MatrixBase<C>& c = const_cast<MatrixBase<C>& >(c_); + internal::kroneckerProduct_full(a.derived(), b.derived(), c.derived()); +} + +/*! + * Computes Kronecker tensor product of a dense and a sparse matrix + * + * \param a Dense matrix a + * \param b Sparse matrix b + * \param c Kronecker tensor product of a and b + */ +template<typename A,typename B,typename C> +void kroneckerProduct(const MatrixBase<A>& a, const SparseMatrixBase<B>& b, SparseMatrixBase<C>& c) +{ + internal::kroneckerProduct_sparse(a.derived(), b.derived(), c.derived()); +} + +/*! + * Computes Kronecker tensor product of a sparse and a dense matrix + * + * \param a Sparse matrix a + * \param b Dense matrix b + * \param c Kronecker tensor product of a and b + */ +template<typename A,typename B,typename C> +void kroneckerProduct(const SparseMatrixBase<A>& a, const MatrixBase<B>& b, SparseMatrixBase<C>& c) +{ + internal::kroneckerProduct_sparse(a.derived(), b.derived(), c.derived()); +} + +/*! + * Computes Kronecker tensor product of two sparse matrices + * + * \param a Sparse matrix a + * \param b Sparse matrix b + * \param c Kronecker tensor product of a and b + */ +template<typename A,typename B,typename C> +void kroneckerProduct(const SparseMatrixBase<A>& a, const SparseMatrixBase<B>& b, SparseMatrixBase<C>& c) +{ + internal::kroneckerProduct_sparse(a.derived(), b.derived(), c.derived()); +} + +} // end namespace Eigen + +#endif // KRONECKER_TENSOR_PRODUCT_H diff --git a/unsupported/Eigen/src/MatrixFunctions/CMakeLists.txt b/unsupported/Eigen/src/MatrixFunctions/CMakeLists.txt new file mode 100644 index 000000000..cdde64d2c --- /dev/null +++ b/unsupported/Eigen/src/MatrixFunctions/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_MatrixFunctions_SRCS "*.h") + +INSTALL(FILES + ${Eigen_MatrixFunctions_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/MatrixFunctions COMPONENT Devel + ) diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h new file mode 100644 index 000000000..642916764 --- /dev/null +++ b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h @@ -0,0 +1,454 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009, 2010 Jitse Niesen <jitse@maths.leeds.ac.uk> +// Copyright (C) 2011 Chen-Pang He <jdh8@ms63.hinet.net> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MATRIX_EXPONENTIAL +#define EIGEN_MATRIX_EXPONENTIAL + +#include "StemFunction.h" + +namespace Eigen { + +#if defined(_MSC_VER) || defined(__FreeBSD__) + template <typename Scalar> Scalar log2(Scalar v) { using std::log; return log(v)/log(Scalar(2)); } +#endif + + +/** \ingroup MatrixFunctions_Module + * \brief Class for computing the matrix exponential. + * \tparam MatrixType type of the argument of the exponential, + * expected to be an instantiation of the Matrix class template. + */ +template <typename MatrixType> +class MatrixExponential { + + public: + + /** \brief Constructor. + * + * The class stores a reference to \p M, so it should not be + * changed (or destroyed) before compute() is called. + * + * \param[in] M matrix whose exponential is to be computed. + */ + MatrixExponential(const MatrixType &M); + + /** \brief Computes the matrix exponential. + * + * \param[out] result the matrix exponential of \p M in the constructor. + */ + template <typename ResultType> + void compute(ResultType &result); + + private: + + // Prevent copying + MatrixExponential(const MatrixExponential&); + MatrixExponential& operator=(const MatrixExponential&); + + /** \brief Compute the (3,3)-Padé approximant to the exponential. + * + * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé + * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$. + * + * \param[in] A Argument of matrix exponential + */ + void pade3(const MatrixType &A); + + /** \brief Compute the (5,5)-Padé approximant to the exponential. + * + * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé + * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$. + * + * \param[in] A Argument of matrix exponential + */ + void pade5(const MatrixType &A); + + /** \brief Compute the (7,7)-Padé approximant to the exponential. + * + * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé + * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$. + * + * \param[in] A Argument of matrix exponential + */ + void pade7(const MatrixType &A); + + /** \brief Compute the (9,9)-Padé approximant to the exponential. + * + * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé + * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$. + * + * \param[in] A Argument of matrix exponential + */ + void pade9(const MatrixType &A); + + /** \brief Compute the (13,13)-Padé approximant to the exponential. + * + * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé + * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$. + * + * \param[in] A Argument of matrix exponential + */ + void pade13(const MatrixType &A); + + /** \brief Compute the (17,17)-Padé approximant to the exponential. + * + * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé + * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$. + * + * This function activates only if your long double is double-double or quadruple. + * + * \param[in] A Argument of matrix exponential + */ + void pade17(const MatrixType &A); + + /** \brief Compute Padé approximant to the exponential. + * + * Computes \c m_U, \c m_V and \c m_squarings such that + * \f$ (V+U)(V-U)^{-1} \f$ is a Padé of + * \f$ \exp(2^{-\mbox{squarings}}M) \f$ around \f$ M = 0 \f$. The + * degree of the Padé approximant and the value of + * squarings are chosen such that the approximation error is no + * more than the round-off error. + * + * The argument of this function should correspond with the (real + * part of) the entries of \c m_M. It is used to select the + * correct implementation using overloading. + */ + void computeUV(double); + + /** \brief Compute Padé approximant to the exponential. + * + * \sa computeUV(double); + */ + void computeUV(float); + + /** \brief Compute Padé approximant to the exponential. + * + * \sa computeUV(double); + */ + void computeUV(long double); + + typedef typename internal::traits<MatrixType>::Scalar Scalar; + typedef typename NumTraits<Scalar>::Real RealScalar; + typedef typename std::complex<RealScalar> ComplexScalar; + + /** \brief Reference to matrix whose exponential is to be computed. */ + typename internal::nested<MatrixType>::type m_M; + + /** \brief Odd-degree terms in numerator of Padé approximant. */ + MatrixType m_U; + + /** \brief Even-degree terms in numerator of Padé approximant. */ + MatrixType m_V; + + /** \brief Used for temporary storage. */ + MatrixType m_tmp1; + + /** \brief Used for temporary storage. */ + MatrixType m_tmp2; + + /** \brief Identity matrix of the same size as \c m_M. */ + MatrixType m_Id; + + /** \brief Number of squarings required in the last step. */ + int m_squarings; + + /** \brief L1 norm of m_M. */ + RealScalar m_l1norm; +}; + +template <typename MatrixType> +MatrixExponential<MatrixType>::MatrixExponential(const MatrixType &M) : + m_M(M), + m_U(M.rows(),M.cols()), + m_V(M.rows(),M.cols()), + m_tmp1(M.rows(),M.cols()), + m_tmp2(M.rows(),M.cols()), + m_Id(MatrixType::Identity(M.rows(), M.cols())), + m_squarings(0), + m_l1norm(M.cwiseAbs().colwise().sum().maxCoeff()) +{ + /* empty body */ +} + +template <typename MatrixType> +template <typename ResultType> +void MatrixExponential<MatrixType>::compute(ResultType &result) +{ +#if LDBL_MANT_DIG > 112 // rarely happens + if(sizeof(RealScalar) > 14) { + result = m_M.matrixFunction(StdStemFunctions<ComplexScalar>::exp); + return; + } +#endif + computeUV(RealScalar()); + m_tmp1 = m_U + m_V; // numerator of Pade approximant + m_tmp2 = -m_U + m_V; // denominator of Pade approximant + result = m_tmp2.partialPivLu().solve(m_tmp1); + for (int i=0; i<m_squarings; i++) + result *= result; // undo scaling by repeated squaring +} + +template <typename MatrixType> +EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade3(const MatrixType &A) +{ + const RealScalar b[] = {120., 60., 12., 1.}; + m_tmp1.noalias() = A * A; + m_tmp2 = b[3]*m_tmp1 + b[1]*m_Id; + m_U.noalias() = A * m_tmp2; + m_V = b[2]*m_tmp1 + b[0]*m_Id; +} + +template <typename MatrixType> +EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade5(const MatrixType &A) +{ + const RealScalar b[] = {30240., 15120., 3360., 420., 30., 1.}; + MatrixType A2 = A * A; + m_tmp1.noalias() = A2 * A2; + m_tmp2 = b[5]*m_tmp1 + b[3]*A2 + b[1]*m_Id; + m_U.noalias() = A * m_tmp2; + m_V = b[4]*m_tmp1 + b[2]*A2 + b[0]*m_Id; +} + +template <typename MatrixType> +EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade7(const MatrixType &A) +{ + const RealScalar b[] = {17297280., 8648640., 1995840., 277200., 25200., 1512., 56., 1.}; + MatrixType A2 = A * A; + MatrixType A4 = A2 * A2; + m_tmp1.noalias() = A4 * A2; + m_tmp2 = b[7]*m_tmp1 + b[5]*A4 + b[3]*A2 + b[1]*m_Id; + m_U.noalias() = A * m_tmp2; + m_V = b[6]*m_tmp1 + b[4]*A4 + b[2]*A2 + b[0]*m_Id; +} + +template <typename MatrixType> +EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade9(const MatrixType &A) +{ + const RealScalar b[] = {17643225600., 8821612800., 2075673600., 302702400., 30270240., + 2162160., 110880., 3960., 90., 1.}; + MatrixType A2 = A * A; + MatrixType A4 = A2 * A2; + MatrixType A6 = A4 * A2; + m_tmp1.noalias() = A6 * A2; + m_tmp2 = b[9]*m_tmp1 + b[7]*A6 + b[5]*A4 + b[3]*A2 + b[1]*m_Id; + m_U.noalias() = A * m_tmp2; + m_V = b[8]*m_tmp1 + b[6]*A6 + b[4]*A4 + b[2]*A2 + b[0]*m_Id; +} + +template <typename MatrixType> +EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade13(const MatrixType &A) +{ + const RealScalar b[] = {64764752532480000., 32382376266240000., 7771770303897600., + 1187353796428800., 129060195264000., 10559470521600., 670442572800., + 33522128640., 1323241920., 40840800., 960960., 16380., 182., 1.}; + MatrixType A2 = A * A; + MatrixType A4 = A2 * A2; + m_tmp1.noalias() = A4 * A2; + m_V = b[13]*m_tmp1 + b[11]*A4 + b[9]*A2; // used for temporary storage + m_tmp2.noalias() = m_tmp1 * m_V; + m_tmp2 += b[7]*m_tmp1 + b[5]*A4 + b[3]*A2 + b[1]*m_Id; + m_U.noalias() = A * m_tmp2; + m_tmp2 = b[12]*m_tmp1 + b[10]*A4 + b[8]*A2; + m_V.noalias() = m_tmp1 * m_tmp2; + m_V += b[6]*m_tmp1 + b[4]*A4 + b[2]*A2 + b[0]*m_Id; +} + +#if LDBL_MANT_DIG > 64 +template <typename MatrixType> +EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade17(const MatrixType &A) +{ + const RealScalar b[] = {830034394580628357120000.L, 415017197290314178560000.L, + 100610229646136770560000.L, 15720348382208870400000.L, + 1774878043152614400000.L, 153822763739893248000.L, 10608466464820224000.L, + 595373117923584000.L, 27563570274240000.L, 1060137318240000.L, + 33924394183680.L, 899510451840.L, 19554575040.L, 341863200.L, 4651200.L, + 46512.L, 306.L, 1.L}; + MatrixType A2 = A * A; + MatrixType A4 = A2 * A2; + MatrixType A6 = A4 * A2; + m_tmp1.noalias() = A4 * A4; + m_V = b[17]*m_tmp1 + b[15]*A6 + b[13]*A4 + b[11]*A2; // used for temporary storage + m_tmp2.noalias() = m_tmp1 * m_V; + m_tmp2 += b[9]*m_tmp1 + b[7]*A6 + b[5]*A4 + b[3]*A2 + b[1]*m_Id; + m_U.noalias() = A * m_tmp2; + m_tmp2 = b[16]*m_tmp1 + b[14]*A6 + b[12]*A4 + b[10]*A2; + m_V.noalias() = m_tmp1 * m_tmp2; + m_V += b[8]*m_tmp1 + b[6]*A6 + b[4]*A4 + b[2]*A2 + b[0]*m_Id; +} +#endif + +template <typename MatrixType> +void MatrixExponential<MatrixType>::computeUV(float) +{ + using std::max; + using std::pow; + using std::ceil; + if (m_l1norm < 4.258730016922831e-001) { + pade3(m_M); + } else if (m_l1norm < 1.880152677804762e+000) { + pade5(m_M); + } else { + const float maxnorm = 3.925724783138660f; + m_squarings = (max)(0, (int)ceil(log2(m_l1norm / maxnorm))); + MatrixType A = m_M / pow(Scalar(2), m_squarings); + pade7(A); + } +} + +template <typename MatrixType> +void MatrixExponential<MatrixType>::computeUV(double) +{ + using std::max; + using std::pow; + using std::ceil; + if (m_l1norm < 1.495585217958292e-002) { + pade3(m_M); + } else if (m_l1norm < 2.539398330063230e-001) { + pade5(m_M); + } else if (m_l1norm < 9.504178996162932e-001) { + pade7(m_M); + } else if (m_l1norm < 2.097847961257068e+000) { + pade9(m_M); + } else { + const double maxnorm = 5.371920351148152; + m_squarings = (max)(0, (int)ceil(log2(m_l1norm / maxnorm))); + MatrixType A = m_M / pow(Scalar(2), m_squarings); + pade13(A); + } +} + +template <typename MatrixType> +void MatrixExponential<MatrixType>::computeUV(long double) +{ + using std::max; + using std::pow; + using std::ceil; +#if LDBL_MANT_DIG == 53 // double precision + computeUV(double()); +#elif LDBL_MANT_DIG <= 64 // extended precision + if (m_l1norm < 4.1968497232266989671e-003L) { + pade3(m_M); + } else if (m_l1norm < 1.1848116734693823091e-001L) { + pade5(m_M); + } else if (m_l1norm < 5.5170388480686700274e-001L) { + pade7(m_M); + } else if (m_l1norm < 1.3759868875587845383e+000L) { + pade9(m_M); + } else { + const long double maxnorm = 4.0246098906697353063L; + m_squarings = (max)(0, (int)ceil(log2(m_l1norm / maxnorm))); + MatrixType A = m_M / pow(Scalar(2), m_squarings); + pade13(A); + } +#elif LDBL_MANT_DIG <= 106 // double-double + if (m_l1norm < 3.2787892205607026992947488108213e-005L) { + pade3(m_M); + } else if (m_l1norm < 6.4467025060072760084130906076332e-003L) { + pade5(m_M); + } else if (m_l1norm < 6.8988028496595374751374122881143e-002L) { + pade7(m_M); + } else if (m_l1norm < 2.7339737518502231741495857201670e-001L) { + pade9(m_M); + } else if (m_l1norm < 1.3203382096514474905666448850278e+000L) { + pade13(m_M); + } else { + const long double maxnorm = 3.2579440895405400856599663723517L; + m_squarings = (max)(0, (int)ceil(log2(m_l1norm / maxnorm))); + MatrixType A = m_M / pow(Scalar(2), m_squarings); + pade17(A); + } +#elif LDBL_MANT_DIG <= 112 // quadruple precison + if (m_l1norm < 1.639394610288918690547467954466970e-005L) { + pade3(m_M); + } else if (m_l1norm < 4.253237712165275566025884344433009e-003L) { + pade5(m_M); + } else if (m_l1norm < 5.125804063165764409885122032933142e-002L) { + pade7(m_M); + } else if (m_l1norm < 2.170000765161155195453205651889853e-001L) { + pade9(m_M); + } else if (m_l1norm < 1.125358383453143065081397882891878e+000L) { + pade13(m_M); + } else { + const long double maxnorm = 2.884233277829519311757165057717815L; + m_squarings = (max)(0, (int)ceil(log2(m_l1norm / maxnorm))); + MatrixType A = m_M / pow(Scalar(2), m_squarings); + pade17(A); + } +#else + // this case should be handled in compute() + eigen_assert(false && "Bug in MatrixExponential"); +#endif // LDBL_MANT_DIG +} + +/** \ingroup MatrixFunctions_Module + * + * \brief Proxy for the matrix exponential of some matrix (expression). + * + * \tparam Derived Type of the argument to the matrix exponential. + * + * This class holds the argument to the matrix exponential until it + * is assigned or evaluated for some other reason (so the argument + * should not be changed in the meantime). It is the return type of + * MatrixBase::exp() and most of the time this is the only way it is + * used. + */ +template<typename Derived> struct MatrixExponentialReturnValue +: public ReturnByValue<MatrixExponentialReturnValue<Derived> > +{ + typedef typename Derived::Index Index; + public: + /** \brief Constructor. + * + * \param[in] src %Matrix (expression) forming the argument of the + * matrix exponential. + */ + MatrixExponentialReturnValue(const Derived& src) : m_src(src) { } + + /** \brief Compute the matrix exponential. + * + * \param[out] result the matrix exponential of \p src in the + * constructor. + */ + template <typename ResultType> + inline void evalTo(ResultType& result) const + { + const typename Derived::PlainObject srcEvaluated = m_src.eval(); + MatrixExponential<typename Derived::PlainObject> me(srcEvaluated); + me.compute(result); + } + + Index rows() const { return m_src.rows(); } + Index cols() const { return m_src.cols(); } + + protected: + const Derived& m_src; + private: + MatrixExponentialReturnValue& operator=(const MatrixExponentialReturnValue&); +}; + +namespace internal { +template<typename Derived> +struct traits<MatrixExponentialReturnValue<Derived> > +{ + typedef typename Derived::PlainObject ReturnType; +}; +} + +template <typename Derived> +const MatrixExponentialReturnValue<Derived> MatrixBase<Derived>::exp() const +{ + eigen_assert(rows() == cols()); + return MatrixExponentialReturnValue<Derived>(derived()); +} + +} // end namespace Eigen + +#endif // EIGEN_MATRIX_EXPONENTIAL diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h new file mode 100644 index 000000000..c57ca87ed --- /dev/null +++ b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h @@ -0,0 +1,590 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009-2011 Jitse Niesen <jitse@maths.leeds.ac.uk> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MATRIX_FUNCTION +#define EIGEN_MATRIX_FUNCTION + +#include "StemFunction.h" +#include "MatrixFunctionAtomic.h" + + +namespace Eigen { + +/** \ingroup MatrixFunctions_Module + * \brief Class for computing matrix functions. + * \tparam MatrixType type of the argument of the matrix function, + * expected to be an instantiation of the Matrix class template. + * \tparam AtomicType type for computing matrix function of atomic blocks. + * \tparam IsComplex used internally to select correct specialization. + * + * This class implements the Schur-Parlett algorithm for computing matrix functions. The spectrum of the + * matrix is divided in clustered of eigenvalues that lies close together. This class delegates the + * computation of the matrix function on every block corresponding to these clusters to an object of type + * \p AtomicType and uses these results to compute the matrix function of the whole matrix. The class + * \p AtomicType should have a \p compute() member function for computing the matrix function of a block. + * + * \sa class MatrixFunctionAtomic, class MatrixLogarithmAtomic + */ +template <typename MatrixType, + typename AtomicType, + int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex> +class MatrixFunction +{ + public: + + /** \brief Constructor. + * + * \param[in] A argument of matrix function, should be a square matrix. + * \param[in] atomic class for computing matrix function of atomic blocks. + * + * The class stores references to \p A and \p atomic, so they should not be + * changed (or destroyed) before compute() is called. + */ + MatrixFunction(const MatrixType& A, AtomicType& atomic); + + /** \brief Compute the matrix function. + * + * \param[out] result the function \p f applied to \p A, as + * specified in the constructor. + * + * See MatrixBase::matrixFunction() for details on how this computation + * is implemented. + */ + template <typename ResultType> + void compute(ResultType &result); +}; + + +/** \internal \ingroup MatrixFunctions_Module + * \brief Partial specialization of MatrixFunction for real matrices + */ +template <typename MatrixType, typename AtomicType> +class MatrixFunction<MatrixType, AtomicType, 0> +{ + private: + + typedef internal::traits<MatrixType> Traits; + typedef typename Traits::Scalar Scalar; + static const int Rows = Traits::RowsAtCompileTime; + static const int Cols = Traits::ColsAtCompileTime; + static const int Options = MatrixType::Options; + static const int MaxRows = Traits::MaxRowsAtCompileTime; + static const int MaxCols = Traits::MaxColsAtCompileTime; + + typedef std::complex<Scalar> ComplexScalar; + typedef Matrix<ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols> ComplexMatrix; + + public: + + /** \brief Constructor. + * + * \param[in] A argument of matrix function, should be a square matrix. + * \param[in] atomic class for computing matrix function of atomic blocks. + */ + MatrixFunction(const MatrixType& A, AtomicType& atomic) : m_A(A), m_atomic(atomic) { } + + /** \brief Compute the matrix function. + * + * \param[out] result the function \p f applied to \p A, as + * specified in the constructor. + * + * This function converts the real matrix \c A to a complex matrix, + * uses MatrixFunction<MatrixType,1> and then converts the result back to + * a real matrix. + */ + template <typename ResultType> + void compute(ResultType& result) + { + ComplexMatrix CA = m_A.template cast<ComplexScalar>(); + ComplexMatrix Cresult; + MatrixFunction<ComplexMatrix, AtomicType> mf(CA, m_atomic); + mf.compute(Cresult); + result = Cresult.real(); + } + + private: + typename internal::nested<MatrixType>::type m_A; /**< \brief Reference to argument of matrix function. */ + AtomicType& m_atomic; /**< \brief Class for computing matrix function of atomic blocks. */ + + MatrixFunction& operator=(const MatrixFunction&); +}; + + +/** \internal \ingroup MatrixFunctions_Module + * \brief Partial specialization of MatrixFunction for complex matrices + */ +template <typename MatrixType, typename AtomicType> +class MatrixFunction<MatrixType, AtomicType, 1> +{ + private: + + typedef internal::traits<MatrixType> Traits; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::Index Index; + static const int RowsAtCompileTime = Traits::RowsAtCompileTime; + static const int ColsAtCompileTime = Traits::ColsAtCompileTime; + static const int Options = MatrixType::Options; + typedef typename NumTraits<Scalar>::Real RealScalar; + typedef Matrix<Scalar, Traits::RowsAtCompileTime, 1> VectorType; + typedef Matrix<Index, Traits::RowsAtCompileTime, 1> IntVectorType; + typedef Matrix<Index, Dynamic, 1> DynamicIntVectorType; + typedef std::list<Scalar> Cluster; + typedef std::list<Cluster> ListOfClusters; + typedef Matrix<Scalar, Dynamic, Dynamic, Options, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType; + + public: + + MatrixFunction(const MatrixType& A, AtomicType& atomic); + template <typename ResultType> void compute(ResultType& result); + + private: + + void computeSchurDecomposition(); + void partitionEigenvalues(); + typename ListOfClusters::iterator findCluster(Scalar key); + void computeClusterSize(); + void computeBlockStart(); + void constructPermutation(); + void permuteSchur(); + void swapEntriesInSchur(Index index); + void computeBlockAtomic(); + Block<MatrixType> block(MatrixType& A, Index i, Index j); + void computeOffDiagonal(); + DynMatrixType solveTriangularSylvester(const DynMatrixType& A, const DynMatrixType& B, const DynMatrixType& C); + + typename internal::nested<MatrixType>::type m_A; /**< \brief Reference to argument of matrix function. */ + AtomicType& m_atomic; /**< \brief Class for computing matrix function of atomic blocks. */ + MatrixType m_T; /**< \brief Triangular part of Schur decomposition */ + MatrixType m_U; /**< \brief Unitary part of Schur decomposition */ + MatrixType m_fT; /**< \brief %Matrix function applied to #m_T */ + ListOfClusters m_clusters; /**< \brief Partition of eigenvalues into clusters of ei'vals "close" to each other */ + DynamicIntVectorType m_eivalToCluster; /**< \brief m_eivalToCluster[i] = j means i-th ei'val is in j-th cluster */ + DynamicIntVectorType m_clusterSize; /**< \brief Number of eigenvalues in each clusters */ + DynamicIntVectorType m_blockStart; /**< \brief Row index at which block corresponding to i-th cluster starts */ + IntVectorType m_permutation; /**< \brief Permutation which groups ei'vals in the same cluster together */ + + /** \brief Maximum distance allowed between eigenvalues to be considered "close". + * + * This is morally a \c static \c const \c Scalar, but only + * integers can be static constant class members in C++. The + * separation constant is set to 0.1, a value taken from the + * paper by Davies and Higham. */ + static const RealScalar separation() { return static_cast<RealScalar>(0.1); } + + MatrixFunction& operator=(const MatrixFunction&); +}; + +/** \brief Constructor. + * + * \param[in] A argument of matrix function, should be a square matrix. + * \param[in] atomic class for computing matrix function of atomic blocks. + */ +template <typename MatrixType, typename AtomicType> +MatrixFunction<MatrixType,AtomicType,1>::MatrixFunction(const MatrixType& A, AtomicType& atomic) + : m_A(A), m_atomic(atomic) +{ + /* empty body */ +} + +/** \brief Compute the matrix function. + * + * \param[out] result the function \p f applied to \p A, as + * specified in the constructor. + */ +template <typename MatrixType, typename AtomicType> +template <typename ResultType> +void MatrixFunction<MatrixType,AtomicType,1>::compute(ResultType& result) +{ + computeSchurDecomposition(); + partitionEigenvalues(); + computeClusterSize(); + computeBlockStart(); + constructPermutation(); + permuteSchur(); + computeBlockAtomic(); + computeOffDiagonal(); + result = m_U * m_fT * m_U.adjoint(); +} + +/** \brief Store the Schur decomposition of #m_A in #m_T and #m_U */ +template <typename MatrixType, typename AtomicType> +void MatrixFunction<MatrixType,AtomicType,1>::computeSchurDecomposition() +{ + const ComplexSchur<MatrixType> schurOfA(m_A); + m_T = schurOfA.matrixT(); + m_U = schurOfA.matrixU(); +} + +/** \brief Partition eigenvalues in clusters of ei'vals close to each other + * + * This function computes #m_clusters. This is a partition of the + * eigenvalues of #m_T in clusters, such that + * # Any eigenvalue in a certain cluster is at most separation() away + * from another eigenvalue in the same cluster. + * # The distance between two eigenvalues in different clusters is + * more than separation(). + * The implementation follows Algorithm 4.1 in the paper of Davies + * and Higham. + */ +template <typename MatrixType, typename AtomicType> +void MatrixFunction<MatrixType,AtomicType,1>::partitionEigenvalues() +{ + const Index rows = m_T.rows(); + VectorType diag = m_T.diagonal(); // contains eigenvalues of A + + for (Index i=0; i<rows; ++i) { + // Find set containing diag(i), adding a new set if necessary + typename ListOfClusters::iterator qi = findCluster(diag(i)); + if (qi == m_clusters.end()) { + Cluster l; + l.push_back(diag(i)); + m_clusters.push_back(l); + qi = m_clusters.end(); + --qi; + } + + // Look for other element to add to the set + for (Index j=i+1; j<rows; ++j) { + if (internal::abs(diag(j) - diag(i)) <= separation() && std::find(qi->begin(), qi->end(), diag(j)) == qi->end()) { + typename ListOfClusters::iterator qj = findCluster(diag(j)); + if (qj == m_clusters.end()) { + qi->push_back(diag(j)); + } else { + qi->insert(qi->end(), qj->begin(), qj->end()); + m_clusters.erase(qj); + } + } + } + } +} + +/** \brief Find cluster in #m_clusters containing some value + * \param[in] key Value to find + * \returns Iterator to cluster containing \c key, or + * \c m_clusters.end() if no cluster in m_clusters contains \c key. + */ +template <typename MatrixType, typename AtomicType> +typename MatrixFunction<MatrixType,AtomicType,1>::ListOfClusters::iterator MatrixFunction<MatrixType,AtomicType,1>::findCluster(Scalar key) +{ + typename Cluster::iterator j; + for (typename ListOfClusters::iterator i = m_clusters.begin(); i != m_clusters.end(); ++i) { + j = std::find(i->begin(), i->end(), key); + if (j != i->end()) + return i; + } + return m_clusters.end(); +} + +/** \brief Compute #m_clusterSize and #m_eivalToCluster using #m_clusters */ +template <typename MatrixType, typename AtomicType> +void MatrixFunction<MatrixType,AtomicType,1>::computeClusterSize() +{ + const Index rows = m_T.rows(); + VectorType diag = m_T.diagonal(); + const Index numClusters = static_cast<Index>(m_clusters.size()); + + m_clusterSize.setZero(numClusters); + m_eivalToCluster.resize(rows); + Index clusterIndex = 0; + for (typename ListOfClusters::const_iterator cluster = m_clusters.begin(); cluster != m_clusters.end(); ++cluster) { + for (Index i = 0; i < diag.rows(); ++i) { + if (std::find(cluster->begin(), cluster->end(), diag(i)) != cluster->end()) { + ++m_clusterSize[clusterIndex]; + m_eivalToCluster[i] = clusterIndex; + } + } + ++clusterIndex; + } +} + +/** \brief Compute #m_blockStart using #m_clusterSize */ +template <typename MatrixType, typename AtomicType> +void MatrixFunction<MatrixType,AtomicType,1>::computeBlockStart() +{ + m_blockStart.resize(m_clusterSize.rows()); + m_blockStart(0) = 0; + for (Index i = 1; i < m_clusterSize.rows(); i++) { + m_blockStart(i) = m_blockStart(i-1) + m_clusterSize(i-1); + } +} + +/** \brief Compute #m_permutation using #m_eivalToCluster and #m_blockStart */ +template <typename MatrixType, typename AtomicType> +void MatrixFunction<MatrixType,AtomicType,1>::constructPermutation() +{ + DynamicIntVectorType indexNextEntry = m_blockStart; + m_permutation.resize(m_T.rows()); + for (Index i = 0; i < m_T.rows(); i++) { + Index cluster = m_eivalToCluster[i]; + m_permutation[i] = indexNextEntry[cluster]; + ++indexNextEntry[cluster]; + } +} + +/** \brief Permute Schur decomposition in #m_U and #m_T according to #m_permutation */ +template <typename MatrixType, typename AtomicType> +void MatrixFunction<MatrixType,AtomicType,1>::permuteSchur() +{ + IntVectorType p = m_permutation; + for (Index i = 0; i < p.rows() - 1; i++) { + Index j; + for (j = i; j < p.rows(); j++) { + if (p(j) == i) break; + } + eigen_assert(p(j) == i); + for (Index k = j-1; k >= i; k--) { + swapEntriesInSchur(k); + std::swap(p.coeffRef(k), p.coeffRef(k+1)); + } + } +} + +/** \brief Swap rows \a index and \a index+1 in Schur decomposition in #m_U and #m_T */ +template <typename MatrixType, typename AtomicType> +void MatrixFunction<MatrixType,AtomicType,1>::swapEntriesInSchur(Index index) +{ + JacobiRotation<Scalar> rotation; + rotation.makeGivens(m_T(index, index+1), m_T(index+1, index+1) - m_T(index, index)); + m_T.applyOnTheLeft(index, index+1, rotation.adjoint()); + m_T.applyOnTheRight(index, index+1, rotation); + m_U.applyOnTheRight(index, index+1, rotation); +} + +/** \brief Compute block diagonal part of #m_fT. + * + * This routine computes the matrix function applied to the block diagonal part of #m_T, with the blocking + * given by #m_blockStart. The matrix function of each diagonal block is computed by #m_atomic. The + * off-diagonal parts of #m_fT are set to zero. + */ +template <typename MatrixType, typename AtomicType> +void MatrixFunction<MatrixType,AtomicType,1>::computeBlockAtomic() +{ + m_fT.resize(m_T.rows(), m_T.cols()); + m_fT.setZero(); + for (Index i = 0; i < m_clusterSize.rows(); ++i) { + block(m_fT, i, i) = m_atomic.compute(block(m_T, i, i)); + } +} + +/** \brief Return block of matrix according to blocking given by #m_blockStart */ +template <typename MatrixType, typename AtomicType> +Block<MatrixType> MatrixFunction<MatrixType,AtomicType,1>::block(MatrixType& A, Index i, Index j) +{ + return A.block(m_blockStart(i), m_blockStart(j), m_clusterSize(i), m_clusterSize(j)); +} + +/** \brief Compute part of #m_fT above block diagonal. + * + * This routine assumes that the block diagonal part of #m_fT (which + * equals the matrix function applied to #m_T) has already been computed and computes + * the part above the block diagonal. The part below the diagonal is + * zero, because #m_T is upper triangular. + */ +template <typename MatrixType, typename AtomicType> +void MatrixFunction<MatrixType,AtomicType,1>::computeOffDiagonal() +{ + for (Index diagIndex = 1; diagIndex < m_clusterSize.rows(); diagIndex++) { + for (Index blockIndex = 0; blockIndex < m_clusterSize.rows() - diagIndex; blockIndex++) { + // compute (blockIndex, blockIndex+diagIndex) block + DynMatrixType A = block(m_T, blockIndex, blockIndex); + DynMatrixType B = -block(m_T, blockIndex+diagIndex, blockIndex+diagIndex); + DynMatrixType C = block(m_fT, blockIndex, blockIndex) * block(m_T, blockIndex, blockIndex+diagIndex); + C -= block(m_T, blockIndex, blockIndex+diagIndex) * block(m_fT, blockIndex+diagIndex, blockIndex+diagIndex); + for (Index k = blockIndex + 1; k < blockIndex + diagIndex; k++) { + C += block(m_fT, blockIndex, k) * block(m_T, k, blockIndex+diagIndex); + C -= block(m_T, blockIndex, k) * block(m_fT, k, blockIndex+diagIndex); + } + block(m_fT, blockIndex, blockIndex+diagIndex) = solveTriangularSylvester(A, B, C); + } + } +} + +/** \brief Solve a triangular Sylvester equation AX + XB = C + * + * \param[in] A the matrix A; should be square and upper triangular + * \param[in] B the matrix B; should be square and upper triangular + * \param[in] C the matrix C; should have correct size. + * + * \returns the solution X. + * + * If A is m-by-m and B is n-by-n, then both C and X are m-by-n. + * The (i,j)-th component of the Sylvester equation is + * \f[ + * \sum_{k=i}^m A_{ik} X_{kj} + \sum_{k=1}^j X_{ik} B_{kj} = C_{ij}. + * \f] + * This can be re-arranged to yield: + * \f[ + * X_{ij} = \frac{1}{A_{ii} + B_{jj}} \Bigl( C_{ij} + * - \sum_{k=i+1}^m A_{ik} X_{kj} - \sum_{k=1}^{j-1} X_{ik} B_{kj} \Bigr). + * \f] + * It is assumed that A and B are such that the numerator is never + * zero (otherwise the Sylvester equation does not have a unique + * solution). In that case, these equations can be evaluated in the + * order \f$ i=m,\ldots,1 \f$ and \f$ j=1,\ldots,n \f$. + */ +template <typename MatrixType, typename AtomicType> +typename MatrixFunction<MatrixType,AtomicType,1>::DynMatrixType MatrixFunction<MatrixType,AtomicType,1>::solveTriangularSylvester( + const DynMatrixType& A, + const DynMatrixType& B, + const DynMatrixType& C) +{ + eigen_assert(A.rows() == A.cols()); + eigen_assert(A.isUpperTriangular()); + eigen_assert(B.rows() == B.cols()); + eigen_assert(B.isUpperTriangular()); + eigen_assert(C.rows() == A.rows()); + eigen_assert(C.cols() == B.rows()); + + Index m = A.rows(); + Index n = B.rows(); + DynMatrixType X(m, n); + + for (Index i = m - 1; i >= 0; --i) { + for (Index j = 0; j < n; ++j) { + + // Compute AX = \sum_{k=i+1}^m A_{ik} X_{kj} + Scalar AX; + if (i == m - 1) { + AX = 0; + } else { + Matrix<Scalar,1,1> AXmatrix = A.row(i).tail(m-1-i) * X.col(j).tail(m-1-i); + AX = AXmatrix(0,0); + } + + // Compute XB = \sum_{k=1}^{j-1} X_{ik} B_{kj} + Scalar XB; + if (j == 0) { + XB = 0; + } else { + Matrix<Scalar,1,1> XBmatrix = X.row(i).head(j) * B.col(j).head(j); + XB = XBmatrix(0,0); + } + + X(i,j) = (C(i,j) - AX - XB) / (A(i,i) + B(j,j)); + } + } + return X; +} + +/** \ingroup MatrixFunctions_Module + * + * \brief Proxy for the matrix function of some matrix (expression). + * + * \tparam Derived Type of the argument to the matrix function. + * + * This class holds the argument to the matrix function until it is + * assigned or evaluated for some other reason (so the argument + * should not be changed in the meantime). It is the return type of + * matrixBase::matrixFunction() and related functions and most of the + * time this is the only way it is used. + */ +template<typename Derived> class MatrixFunctionReturnValue +: public ReturnByValue<MatrixFunctionReturnValue<Derived> > +{ + public: + + typedef typename Derived::Scalar Scalar; + typedef typename Derived::Index Index; + typedef typename internal::stem_function<Scalar>::type StemFunction; + + /** \brief Constructor. + * + * \param[in] A %Matrix (expression) forming the argument of the + * matrix function. + * \param[in] f Stem function for matrix function under consideration. + */ + MatrixFunctionReturnValue(const Derived& A, StemFunction f) : m_A(A), m_f(f) { } + + /** \brief Compute the matrix function. + * + * \param[out] result \p f applied to \p A, where \p f and \p A + * are as in the constructor. + */ + template <typename ResultType> + inline void evalTo(ResultType& result) const + { + typedef typename Derived::PlainObject PlainObject; + typedef internal::traits<PlainObject> Traits; + static const int RowsAtCompileTime = Traits::RowsAtCompileTime; + static const int ColsAtCompileTime = Traits::ColsAtCompileTime; + static const int Options = PlainObject::Options; + typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar; + typedef Matrix<ComplexScalar, Dynamic, Dynamic, Options, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType; + typedef MatrixFunctionAtomic<DynMatrixType> AtomicType; + AtomicType atomic(m_f); + + const PlainObject Aevaluated = m_A.eval(); + MatrixFunction<PlainObject, AtomicType> mf(Aevaluated, atomic); + mf.compute(result); + } + + Index rows() const { return m_A.rows(); } + Index cols() const { return m_A.cols(); } + + private: + typename internal::nested<Derived>::type m_A; + StemFunction *m_f; + + MatrixFunctionReturnValue& operator=(const MatrixFunctionReturnValue&); +}; + +namespace internal { +template<typename Derived> +struct traits<MatrixFunctionReturnValue<Derived> > +{ + typedef typename Derived::PlainObject ReturnType; +}; +} + + +/********** MatrixBase methods **********/ + + +template <typename Derived> +const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::matrixFunction(typename internal::stem_function<typename internal::traits<Derived>::Scalar>::type f) const +{ + eigen_assert(rows() == cols()); + return MatrixFunctionReturnValue<Derived>(derived(), f); +} + +template <typename Derived> +const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const +{ + eigen_assert(rows() == cols()); + typedef typename internal::stem_function<Scalar>::ComplexScalar ComplexScalar; + return MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::sin); +} + +template <typename Derived> +const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const +{ + eigen_assert(rows() == cols()); + typedef typename internal::stem_function<Scalar>::ComplexScalar ComplexScalar; + return MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::cos); +} + +template <typename Derived> +const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sinh() const +{ + eigen_assert(rows() == cols()); + typedef typename internal::stem_function<Scalar>::ComplexScalar ComplexScalar; + return MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::sinh); +} + +template <typename Derived> +const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cosh() const +{ + eigen_assert(rows() == cols()); + typedef typename internal::stem_function<Scalar>::ComplexScalar ComplexScalar; + return MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::cosh); +} + +} // end namespace Eigen + +#endif // EIGEN_MATRIX_FUNCTION diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixFunctionAtomic.h b/unsupported/Eigen/src/MatrixFunctions/MatrixFunctionAtomic.h new file mode 100644 index 000000000..efe332c48 --- /dev/null +++ b/unsupported/Eigen/src/MatrixFunctions/MatrixFunctionAtomic.h @@ -0,0 +1,131 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MATRIX_FUNCTION_ATOMIC +#define EIGEN_MATRIX_FUNCTION_ATOMIC + +namespace Eigen { + +/** \ingroup MatrixFunctions_Module + * \class MatrixFunctionAtomic + * \brief Helper class for computing matrix functions of atomic matrices. + * + * \internal + * Here, an atomic matrix is a triangular matrix whose diagonal + * entries are close to each other. + */ +template <typename MatrixType> +class MatrixFunctionAtomic +{ + public: + + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::Index Index; + typedef typename NumTraits<Scalar>::Real RealScalar; + typedef typename internal::stem_function<Scalar>::type StemFunction; + typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; + + /** \brief Constructor + * \param[in] f matrix function to compute. + */ + MatrixFunctionAtomic(StemFunction f) : m_f(f) { } + + /** \brief Compute matrix function of atomic matrix + * \param[in] A argument of matrix function, should be upper triangular and atomic + * \returns f(A), the matrix function evaluated at the given matrix + */ + MatrixType compute(const MatrixType& A); + + private: + + // Prevent copying + MatrixFunctionAtomic(const MatrixFunctionAtomic&); + MatrixFunctionAtomic& operator=(const MatrixFunctionAtomic&); + + void computeMu(); + bool taylorConverged(Index s, const MatrixType& F, const MatrixType& Fincr, const MatrixType& P); + + /** \brief Pointer to scalar function */ + StemFunction* m_f; + + /** \brief Size of matrix function */ + Index m_Arows; + + /** \brief Mean of eigenvalues */ + Scalar m_avgEival; + + /** \brief Argument shifted by mean of eigenvalues */ + MatrixType m_Ashifted; + + /** \brief Constant used to determine whether Taylor series has converged */ + RealScalar m_mu; +}; + +template <typename MatrixType> +MatrixType MatrixFunctionAtomic<MatrixType>::compute(const MatrixType& A) +{ + // TODO: Use that A is upper triangular + m_Arows = A.rows(); + m_avgEival = A.trace() / Scalar(RealScalar(m_Arows)); + m_Ashifted = A - m_avgEival * MatrixType::Identity(m_Arows, m_Arows); + computeMu(); + MatrixType F = m_f(m_avgEival, 0) * MatrixType::Identity(m_Arows, m_Arows); + MatrixType P = m_Ashifted; + MatrixType Fincr; + for (Index s = 1; s < 1.1 * m_Arows + 10; s++) { // upper limit is fairly arbitrary + Fincr = m_f(m_avgEival, static_cast<int>(s)) * P; + F += Fincr; + P = Scalar(RealScalar(1.0/(s + 1))) * P * m_Ashifted; + if (taylorConverged(s, F, Fincr, P)) { + return F; + } + } + eigen_assert("Taylor series does not converge" && 0); + return F; +} + +/** \brief Compute \c m_mu. */ +template <typename MatrixType> +void MatrixFunctionAtomic<MatrixType>::computeMu() +{ + const MatrixType N = MatrixType::Identity(m_Arows, m_Arows) - m_Ashifted; + VectorType e = VectorType::Ones(m_Arows); + N.template triangularView<Upper>().solveInPlace(e); + m_mu = e.cwiseAbs().maxCoeff(); +} + +/** \brief Determine whether Taylor series has converged */ +template <typename MatrixType> +bool MatrixFunctionAtomic<MatrixType>::taylorConverged(Index s, const MatrixType& F, + const MatrixType& Fincr, const MatrixType& P) +{ + const Index n = F.rows(); + const RealScalar F_norm = F.cwiseAbs().rowwise().sum().maxCoeff(); + const RealScalar Fincr_norm = Fincr.cwiseAbs().rowwise().sum().maxCoeff(); + if (Fincr_norm < NumTraits<Scalar>::epsilon() * F_norm) { + RealScalar delta = 0; + RealScalar rfactorial = 1; + for (Index r = 0; r < n; r++) { + RealScalar mx = 0; + for (Index i = 0; i < n; i++) + mx = (std::max)(mx, std::abs(m_f(m_Ashifted(i, i) + m_avgEival, static_cast<int>(s+r)))); + if (r != 0) + rfactorial *= RealScalar(r); + delta = (std::max)(delta, mx / rfactorial); + } + const RealScalar P_norm = P.cwiseAbs().rowwise().sum().maxCoeff(); + if (m_mu * delta * P_norm < NumTraits<Scalar>::epsilon() * F_norm) + return true; + } + return false; +} + +} // end namespace Eigen + +#endif // EIGEN_MATRIX_FUNCTION_ATOMIC diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h b/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h new file mode 100644 index 000000000..3a50514b9 --- /dev/null +++ b/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h @@ -0,0 +1,495 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Jitse Niesen <jitse@maths.leeds.ac.uk> +// Copyright (C) 2011 Chen-Pang He <jdh8@ms63.hinet.net> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MATRIX_LOGARITHM +#define EIGEN_MATRIX_LOGARITHM + +#ifndef M_PI +#define M_PI 3.141592653589793238462643383279503L +#endif + +namespace Eigen { + +/** \ingroup MatrixFunctions_Module + * \class MatrixLogarithmAtomic + * \brief Helper class for computing matrix logarithm of atomic matrices. + * + * \internal + * Here, an atomic matrix is a triangular matrix whose diagonal + * entries are close to each other. + * + * \sa class MatrixFunctionAtomic, MatrixBase::log() + */ +template <typename MatrixType> +class MatrixLogarithmAtomic +{ +public: + + typedef typename MatrixType::Scalar Scalar; + // typedef typename MatrixType::Index Index; + typedef typename NumTraits<Scalar>::Real RealScalar; + // typedef typename internal::stem_function<Scalar>::type StemFunction; + // typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; + + /** \brief Constructor. */ + MatrixLogarithmAtomic() { } + + /** \brief Compute matrix logarithm of atomic matrix + * \param[in] A argument of matrix logarithm, should be upper triangular and atomic + * \returns The logarithm of \p A. + */ + MatrixType compute(const MatrixType& A); + +private: + + void compute2x2(const MatrixType& A, MatrixType& result); + void computeBig(const MatrixType& A, MatrixType& result); + static Scalar atanh(Scalar x); + int getPadeDegree(float normTminusI); + int getPadeDegree(double normTminusI); + int getPadeDegree(long double normTminusI); + void computePade(MatrixType& result, const MatrixType& T, int degree); + void computePade3(MatrixType& result, const MatrixType& T); + void computePade4(MatrixType& result, const MatrixType& T); + void computePade5(MatrixType& result, const MatrixType& T); + void computePade6(MatrixType& result, const MatrixType& T); + void computePade7(MatrixType& result, const MatrixType& T); + void computePade8(MatrixType& result, const MatrixType& T); + void computePade9(MatrixType& result, const MatrixType& T); + void computePade10(MatrixType& result, const MatrixType& T); + void computePade11(MatrixType& result, const MatrixType& T); + + static const int minPadeDegree = 3; + static const int maxPadeDegree = std::numeric_limits<RealScalar>::digits<= 24? 5: // single precision + std::numeric_limits<RealScalar>::digits<= 53? 7: // double precision + std::numeric_limits<RealScalar>::digits<= 64? 8: // extended precision + std::numeric_limits<RealScalar>::digits<=106? 10: 11; // double-double or quadruple precision + + // Prevent copying + MatrixLogarithmAtomic(const MatrixLogarithmAtomic&); + MatrixLogarithmAtomic& operator=(const MatrixLogarithmAtomic&); +}; + +/** \brief Compute logarithm of triangular matrix with clustered eigenvalues. */ +template <typename MatrixType> +MatrixType MatrixLogarithmAtomic<MatrixType>::compute(const MatrixType& A) +{ + using std::log; + MatrixType result(A.rows(), A.rows()); + if (A.rows() == 1) + result(0,0) = log(A(0,0)); + else if (A.rows() == 2) + compute2x2(A, result); + else + computeBig(A, result); + return result; +} + +/** \brief Compute atanh (inverse hyperbolic tangent). */ +template <typename MatrixType> +typename MatrixType::Scalar MatrixLogarithmAtomic<MatrixType>::atanh(typename MatrixType::Scalar x) +{ + using std::abs; + using std::sqrt; + if (abs(x) > sqrt(NumTraits<Scalar>::epsilon())) + return Scalar(0.5) * log((Scalar(1) + x) / (Scalar(1) - x)); + else + return x + x*x*x / Scalar(3); +} + +/** \brief Compute logarithm of 2x2 triangular matrix. */ +template <typename MatrixType> +void MatrixLogarithmAtomic<MatrixType>::compute2x2(const MatrixType& A, MatrixType& result) +{ + using std::abs; + using std::ceil; + using std::imag; + using std::log; + + Scalar logA00 = log(A(0,0)); + Scalar logA11 = log(A(1,1)); + + result(0,0) = logA00; + result(1,0) = Scalar(0); + result(1,1) = logA11; + + if (A(0,0) == A(1,1)) { + result(0,1) = A(0,1) / A(0,0); + } else if ((abs(A(0,0)) < 0.5*abs(A(1,1))) || (abs(A(0,0)) > 2*abs(A(1,1)))) { + result(0,1) = A(0,1) * (logA11 - logA00) / (A(1,1) - A(0,0)); + } else { + // computation in previous branch is inaccurate if A(1,1) \approx A(0,0) + int unwindingNumber = static_cast<int>(ceil((imag(logA11 - logA00) - M_PI) / (2*M_PI))); + Scalar z = (A(1,1) - A(0,0)) / (A(1,1) + A(0,0)); + result(0,1) = A(0,1) * (Scalar(2) * atanh(z) + Scalar(0,2*M_PI*unwindingNumber)) / (A(1,1) - A(0,0)); + } +} + +/** \brief Compute logarithm of triangular matrices with size > 2. + * \details This uses a inverse scale-and-square algorithm. */ +template <typename MatrixType> +void MatrixLogarithmAtomic<MatrixType>::computeBig(const MatrixType& A, MatrixType& result) +{ + int numberOfSquareRoots = 0; + int numberOfExtraSquareRoots = 0; + int degree; + MatrixType T = A; + const RealScalar maxNormForPade = maxPadeDegree<= 5? 5.3149729967117310e-1: // single precision + maxPadeDegree<= 7? 2.6429608311114350e-1: // double precision + maxPadeDegree<= 8? 2.32777776523703892094e-1L: // extended precision + maxPadeDegree<=10? 1.05026503471351080481093652651105e-1L: // double-double + 1.1880960220216759245467951592883642e-1L; // quadruple precision + + while (true) { + RealScalar normTminusI = (T - MatrixType::Identity(T.rows(), T.rows())).cwiseAbs().colwise().sum().maxCoeff(); + if (normTminusI < maxNormForPade) { + degree = getPadeDegree(normTminusI); + int degree2 = getPadeDegree(normTminusI / RealScalar(2)); + if ((degree - degree2 <= 1) || (numberOfExtraSquareRoots == 1)) + break; + ++numberOfExtraSquareRoots; + } + MatrixType sqrtT; + MatrixSquareRootTriangular<MatrixType>(T).compute(sqrtT); + T = sqrtT; + ++numberOfSquareRoots; + } + + computePade(result, T, degree); + result *= pow(RealScalar(2), numberOfSquareRoots); +} + +/* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = float) */ +template <typename MatrixType> +int MatrixLogarithmAtomic<MatrixType>::getPadeDegree(float normTminusI) +{ + const float maxNormForPade[] = { 2.5111573934555054e-1 /* degree = 3 */ , 4.0535837411880493e-1, + 5.3149729967117310e-1 }; + for (int degree = 3; degree <= maxPadeDegree; ++degree) + if (normTminusI <= maxNormForPade[degree - minPadeDegree]) + return degree; + assert(false); // this line should never be reached +} + +/* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = double) */ +template <typename MatrixType> +int MatrixLogarithmAtomic<MatrixType>::getPadeDegree(double normTminusI) +{ + const double maxNormForPade[] = { 1.6206284795015624e-2 /* degree = 3 */ , 5.3873532631381171e-2, + 1.1352802267628681e-1, 1.8662860613541288e-1, 2.642960831111435e-1 }; + for (int degree = 3; degree <= maxPadeDegree; ++degree) + if (normTminusI <= maxNormForPade[degree - minPadeDegree]) + return degree; + assert(false); // this line should never be reached +} + +/* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = long double) */ +template <typename MatrixType> +int MatrixLogarithmAtomic<MatrixType>::getPadeDegree(long double normTminusI) +{ +#if LDBL_MANT_DIG == 53 // double precision + const double maxNormForPade[] = { 1.6206284795015624e-2 /* degree = 3 */ , 5.3873532631381171e-2, + 1.1352802267628681e-1, 1.8662860613541288e-1, 2.642960831111435e-1 }; +#elif LDBL_MANT_DIG <= 64 // extended precision + const double maxNormForPade[] = { 5.48256690357782863103e-3 /* degree = 3 */, 2.34559162387971167321e-2, + 5.84603923897347449857e-2, 1.08486423756725170223e-1, 1.68385767881294446649e-1, + 2.32777776523703892094e-1 }; +#elif LDBL_MANT_DIG <= 106 // double-double + const double maxNormForPade[] = { 8.58970550342939562202529664318890e-5 /* degree = 3 */, + 9.34074328446359654039446552677759e-4, 4.26117194647672175773064114582860e-3, + 1.21546224740281848743149666560464e-2, 2.61100544998339436713088248557444e-2, + 4.66170074627052749243018566390567e-2, 7.32585144444135027565872014932387e-2, + 1.05026503471351080481093652651105e-1 }; +#else // quadruple precision + const double maxNormForPade[] = { 4.7419931187193005048501568167858103e-5 /* degree = 3 */, + 5.8853168473544560470387769480192666e-4, 2.9216120366601315391789493628113520e-3, + 8.8415758124319434347116734705174308e-3, 1.9850836029449446668518049562565291e-2, + 3.6688019729653446926585242192447447e-2, 5.9290962294020186998954055264528393e-2, + 8.6998436081634343903250580992127677e-2, 1.1880960220216759245467951592883642e-1 }; +#endif + for (int degree = 3; degree <= maxPadeDegree; ++degree) + if (normTminusI <= maxNormForPade[degree - minPadeDegree]) + return degree; + assert(false); // this line should never be reached +} + +/* \brief Compute Pade approximation to matrix logarithm */ +template <typename MatrixType> +void MatrixLogarithmAtomic<MatrixType>::computePade(MatrixType& result, const MatrixType& T, int degree) +{ + switch (degree) { + case 3: computePade3(result, T); break; + case 4: computePade4(result, T); break; + case 5: computePade5(result, T); break; + case 6: computePade6(result, T); break; + case 7: computePade7(result, T); break; + case 8: computePade8(result, T); break; + case 9: computePade9(result, T); break; + case 10: computePade10(result, T); break; + case 11: computePade11(result, T); break; + default: assert(false); // should never happen + } +} + +template <typename MatrixType> +void MatrixLogarithmAtomic<MatrixType>::computePade3(MatrixType& result, const MatrixType& T) +{ + const int degree = 3; + const RealScalar nodes[] = { 0.1127016653792583114820734600217600L, 0.5000000000000000000000000000000000L, + 0.8872983346207416885179265399782400L }; + const RealScalar weights[] = { 0.2777777777777777777777777777777778L, 0.4444444444444444444444444444444444L, + 0.2777777777777777777777777777777778L }; + assert(degree <= maxPadeDegree); + MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); + result.setZero(T.rows(), T.rows()); + for (int k = 0; k < degree; ++k) + result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) + .template triangularView<Upper>().solve(TminusI); +} + +template <typename MatrixType> +void MatrixLogarithmAtomic<MatrixType>::computePade4(MatrixType& result, const MatrixType& T) +{ + const int degree = 4; + const RealScalar nodes[] = { 0.0694318442029737123880267555535953L, 0.3300094782075718675986671204483777L, + 0.6699905217924281324013328795516223L, 0.9305681557970262876119732444464048L }; + const RealScalar weights[] = { 0.1739274225687269286865319746109997L, 0.3260725774312730713134680253890003L, + 0.3260725774312730713134680253890003L, 0.1739274225687269286865319746109997L }; + assert(degree <= maxPadeDegree); + MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); + result.setZero(T.rows(), T.rows()); + for (int k = 0; k < degree; ++k) + result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) + .template triangularView<Upper>().solve(TminusI); +} + +template <typename MatrixType> +void MatrixLogarithmAtomic<MatrixType>::computePade5(MatrixType& result, const MatrixType& T) +{ + const int degree = 5; + const RealScalar nodes[] = { 0.0469100770306680036011865608503035L, 0.2307653449471584544818427896498956L, + 0.5000000000000000000000000000000000L, 0.7692346550528415455181572103501044L, + 0.9530899229693319963988134391496965L }; + const RealScalar weights[] = { 0.1184634425280945437571320203599587L, 0.2393143352496832340206457574178191L, + 0.2844444444444444444444444444444444L, 0.2393143352496832340206457574178191L, + 0.1184634425280945437571320203599587L }; + assert(degree <= maxPadeDegree); + MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); + result.setZero(T.rows(), T.rows()); + for (int k = 0; k < degree; ++k) + result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) + .template triangularView<Upper>().solve(TminusI); +} + +template <typename MatrixType> +void MatrixLogarithmAtomic<MatrixType>::computePade6(MatrixType& result, const MatrixType& T) +{ + const int degree = 6; + const RealScalar nodes[] = { 0.0337652428984239860938492227530027L, 0.1693953067668677431693002024900473L, + 0.3806904069584015456847491391596440L, 0.6193095930415984543152508608403560L, + 0.8306046932331322568306997975099527L, 0.9662347571015760139061507772469973L }; + const RealScalar weights[] = { 0.0856622461895851725201480710863665L, 0.1803807865240693037849167569188581L, + 0.2339569672863455236949351719947755L, 0.2339569672863455236949351719947755L, + 0.1803807865240693037849167569188581L, 0.0856622461895851725201480710863665L }; + assert(degree <= maxPadeDegree); + MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); + result.setZero(T.rows(), T.rows()); + for (int k = 0; k < degree; ++k) + result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) + .template triangularView<Upper>().solve(TminusI); +} + +template <typename MatrixType> +void MatrixLogarithmAtomic<MatrixType>::computePade7(MatrixType& result, const MatrixType& T) +{ + const int degree = 7; + const RealScalar nodes[] = { 0.0254460438286207377369051579760744L, 0.1292344072003027800680676133596058L, + 0.2970774243113014165466967939615193L, 0.5000000000000000000000000000000000L, + 0.7029225756886985834533032060384807L, 0.8707655927996972199319323866403942L, + 0.9745539561713792622630948420239256L }; + const RealScalar weights[] = { 0.0647424830844348466353057163395410L, 0.1398526957446383339507338857118898L, + 0.1909150252525594724751848877444876L, 0.2089795918367346938775510204081633L, + 0.1909150252525594724751848877444876L, 0.1398526957446383339507338857118898L, + 0.0647424830844348466353057163395410L }; + assert(degree <= maxPadeDegree); + MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); + result.setZero(T.rows(), T.rows()); + for (int k = 0; k < degree; ++k) + result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) + .template triangularView<Upper>().solve(TminusI); +} + +template <typename MatrixType> +void MatrixLogarithmAtomic<MatrixType>::computePade8(MatrixType& result, const MatrixType& T) +{ + const int degree = 8; + const RealScalar nodes[] = { 0.0198550717512318841582195657152635L, 0.1016667612931866302042230317620848L, + 0.2372337950418355070911304754053768L, 0.4082826787521750975302619288199080L, + 0.5917173212478249024697380711800920L, 0.7627662049581644929088695245946232L, + 0.8983332387068133697957769682379152L, 0.9801449282487681158417804342847365L }; + const RealScalar weights[] = { 0.0506142681451881295762656771549811L, 0.1111905172266872352721779972131204L, + 0.1568533229389436436689811009933007L, 0.1813418916891809914825752246385978L, + 0.1813418916891809914825752246385978L, 0.1568533229389436436689811009933007L, + 0.1111905172266872352721779972131204L, 0.0506142681451881295762656771549811L }; + assert(degree <= maxPadeDegree); + MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); + result.setZero(T.rows(), T.rows()); + for (int k = 0; k < degree; ++k) + result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) + .template triangularView<Upper>().solve(TminusI); +} + +template <typename MatrixType> +void MatrixLogarithmAtomic<MatrixType>::computePade9(MatrixType& result, const MatrixType& T) +{ + const int degree = 9; + const RealScalar nodes[] = { 0.0159198802461869550822118985481636L, 0.0819844463366821028502851059651326L, + 0.1933142836497048013456489803292629L, 0.3378732882980955354807309926783317L, + 0.5000000000000000000000000000000000L, 0.6621267117019044645192690073216683L, + 0.8066857163502951986543510196707371L, 0.9180155536633178971497148940348674L, + 0.9840801197538130449177881014518364L }; + const RealScalar weights[] = { 0.0406371941807872059859460790552618L, 0.0903240803474287020292360156214564L, + 0.1303053482014677311593714347093164L, 0.1561735385200014200343152032922218L, + 0.1651196775006298815822625346434870L, 0.1561735385200014200343152032922218L, + 0.1303053482014677311593714347093164L, 0.0903240803474287020292360156214564L, + 0.0406371941807872059859460790552618L }; + assert(degree <= maxPadeDegree); + MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); + result.setZero(T.rows(), T.rows()); + for (int k = 0; k < degree; ++k) + result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) + .template triangularView<Upper>().solve(TminusI); +} + +template <typename MatrixType> +void MatrixLogarithmAtomic<MatrixType>::computePade10(MatrixType& result, const MatrixType& T) +{ + const int degree = 10; + const RealScalar nodes[] = { 0.0130467357414141399610179939577740L, 0.0674683166555077446339516557882535L, + 0.1602952158504877968828363174425632L, 0.2833023029353764046003670284171079L, + 0.4255628305091843945575869994351400L, 0.5744371694908156054424130005648600L, + 0.7166976970646235953996329715828921L, 0.8397047841495122031171636825574368L, + 0.9325316833444922553660483442117465L, 0.9869532642585858600389820060422260L }; + const RealScalar weights[] = { 0.0333356721543440687967844049466659L, 0.0747256745752902965728881698288487L, + 0.1095431812579910219977674671140816L, 0.1346333596549981775456134607847347L, + 0.1477621123573764350869464973256692L, 0.1477621123573764350869464973256692L, + 0.1346333596549981775456134607847347L, 0.1095431812579910219977674671140816L, + 0.0747256745752902965728881698288487L, 0.0333356721543440687967844049466659L }; + assert(degree <= maxPadeDegree); + MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); + result.setZero(T.rows(), T.rows()); + for (int k = 0; k < degree; ++k) + result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) + .template triangularView<Upper>().solve(TminusI); +} + +template <typename MatrixType> +void MatrixLogarithmAtomic<MatrixType>::computePade11(MatrixType& result, const MatrixType& T) +{ + const int degree = 11; + const RealScalar nodes[] = { 0.0108856709269715035980309994385713L, 0.0564687001159523504624211153480364L, + 0.1349239972129753379532918739844233L, 0.2404519353965940920371371652706952L, + 0.3652284220238275138342340072995692L, 0.5000000000000000000000000000000000L, + 0.6347715779761724861657659927004308L, 0.7595480646034059079628628347293048L, + 0.8650760027870246620467081260155767L, 0.9435312998840476495375788846519636L, + 0.9891143290730284964019690005614287L }; + const RealScalar weights[] = { 0.0278342835580868332413768602212743L, 0.0627901847324523123173471496119701L, + 0.0931451054638671257130488207158280L, 0.1165968822959952399592618524215876L, + 0.1314022722551233310903444349452546L, 0.1364625433889503153572417641681711L, + 0.1314022722551233310903444349452546L, 0.1165968822959952399592618524215876L, + 0.0931451054638671257130488207158280L, 0.0627901847324523123173471496119701L, + 0.0278342835580868332413768602212743L }; + assert(degree <= maxPadeDegree); + MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); + result.setZero(T.rows(), T.rows()); + for (int k = 0; k < degree; ++k) + result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) + .template triangularView<Upper>().solve(TminusI); +} + +/** \ingroup MatrixFunctions_Module + * + * \brief Proxy for the matrix logarithm of some matrix (expression). + * + * \tparam Derived Type of the argument to the matrix function. + * + * This class holds the argument to the matrix function until it is + * assigned or evaluated for some other reason (so the argument + * should not be changed in the meantime). It is the return type of + * matrixBase::matrixLogarithm() and most of the time this is the + * only way it is used. + */ +template<typename Derived> class MatrixLogarithmReturnValue +: public ReturnByValue<MatrixLogarithmReturnValue<Derived> > +{ +public: + + typedef typename Derived::Scalar Scalar; + typedef typename Derived::Index Index; + + /** \brief Constructor. + * + * \param[in] A %Matrix (expression) forming the argument of the matrix logarithm. + */ + MatrixLogarithmReturnValue(const Derived& A) : m_A(A) { } + + /** \brief Compute the matrix logarithm. + * + * \param[out] result Logarithm of \p A, where \A is as specified in the constructor. + */ + template <typename ResultType> + inline void evalTo(ResultType& result) const + { + typedef typename Derived::PlainObject PlainObject; + typedef internal::traits<PlainObject> Traits; + static const int RowsAtCompileTime = Traits::RowsAtCompileTime; + static const int ColsAtCompileTime = Traits::ColsAtCompileTime; + static const int Options = PlainObject::Options; + typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar; + typedef Matrix<ComplexScalar, Dynamic, Dynamic, Options, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType; + typedef MatrixLogarithmAtomic<DynMatrixType> AtomicType; + AtomicType atomic; + + const PlainObject Aevaluated = m_A.eval(); + MatrixFunction<PlainObject, AtomicType> mf(Aevaluated, atomic); + mf.compute(result); + } + + Index rows() const { return m_A.rows(); } + Index cols() const { return m_A.cols(); } + +private: + typename internal::nested<Derived>::type m_A; + + MatrixLogarithmReturnValue& operator=(const MatrixLogarithmReturnValue&); +}; + +namespace internal { + template<typename Derived> + struct traits<MatrixLogarithmReturnValue<Derived> > + { + typedef typename Derived::PlainObject ReturnType; + }; +} + + +/********** MatrixBase method **********/ + + +template <typename Derived> +const MatrixLogarithmReturnValue<Derived> MatrixBase<Derived>::log() const +{ + eigen_assert(rows() == cols()); + return MatrixLogarithmReturnValue<Derived>(derived()); +} + +} // end namespace Eigen + +#endif // EIGEN_MATRIX_LOGARITHM diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h b/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h new file mode 100644 index 000000000..10319fa17 --- /dev/null +++ b/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h @@ -0,0 +1,484 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Jitse Niesen <jitse@maths.leeds.ac.uk> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MATRIX_SQUARE_ROOT +#define EIGEN_MATRIX_SQUARE_ROOT + +namespace Eigen { + +/** \ingroup MatrixFunctions_Module + * \brief Class for computing matrix square roots of upper quasi-triangular matrices. + * \tparam MatrixType type of the argument of the matrix square root, + * expected to be an instantiation of the Matrix class template. + * + * This class computes the square root of the upper quasi-triangular + * matrix stored in the upper Hessenberg part of the matrix passed to + * the constructor. + * + * \sa MatrixSquareRoot, MatrixSquareRootTriangular + */ +template <typename MatrixType> +class MatrixSquareRootQuasiTriangular +{ + public: + + /** \brief Constructor. + * + * \param[in] A upper quasi-triangular matrix whose square root + * is to be computed. + * + * The class stores a reference to \p A, so it should not be + * changed (or destroyed) before compute() is called. + */ + MatrixSquareRootQuasiTriangular(const MatrixType& A) + : m_A(A) + { + eigen_assert(A.rows() == A.cols()); + } + + /** \brief Compute the matrix square root + * + * \param[out] result square root of \p A, as specified in the constructor. + * + * Only the upper Hessenberg part of \p result is updated, the + * rest is not touched. See MatrixBase::sqrt() for details on + * how this computation is implemented. + */ + template <typename ResultType> void compute(ResultType &result); + + private: + typedef typename MatrixType::Index Index; + typedef typename MatrixType::Scalar Scalar; + + void computeDiagonalPartOfSqrt(MatrixType& sqrtT, const MatrixType& T); + void computeOffDiagonalPartOfSqrt(MatrixType& sqrtT, const MatrixType& T); + void compute2x2diagonalBlock(MatrixType& sqrtT, const MatrixType& T, typename MatrixType::Index i); + void compute1x1offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, + typename MatrixType::Index i, typename MatrixType::Index j); + void compute1x2offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, + typename MatrixType::Index i, typename MatrixType::Index j); + void compute2x1offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, + typename MatrixType::Index i, typename MatrixType::Index j); + void compute2x2offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, + typename MatrixType::Index i, typename MatrixType::Index j); + + template <typename SmallMatrixType> + static void solveAuxiliaryEquation(SmallMatrixType& X, const SmallMatrixType& A, + const SmallMatrixType& B, const SmallMatrixType& C); + + const MatrixType& m_A; +}; + +template <typename MatrixType> +template <typename ResultType> +void MatrixSquareRootQuasiTriangular<MatrixType>::compute(ResultType &result) +{ + // Compute Schur decomposition of m_A + const RealSchur<MatrixType> schurOfA(m_A); + const MatrixType& T = schurOfA.matrixT(); + const MatrixType& U = schurOfA.matrixU(); + + // Compute square root of T + MatrixType sqrtT = MatrixType::Zero(m_A.rows(), m_A.rows()); + computeDiagonalPartOfSqrt(sqrtT, T); + computeOffDiagonalPartOfSqrt(sqrtT, T); + + // Compute square root of m_A + result = U * sqrtT * U.adjoint(); +} + +// pre: T is quasi-upper-triangular and sqrtT is a zero matrix of the same size +// post: the diagonal blocks of sqrtT are the square roots of the diagonal blocks of T +template <typename MatrixType> +void MatrixSquareRootQuasiTriangular<MatrixType>::computeDiagonalPartOfSqrt(MatrixType& sqrtT, + const MatrixType& T) +{ + const Index size = m_A.rows(); + for (Index i = 0; i < size; i++) { + if (i == size - 1 || T.coeff(i+1, i) == 0) { + eigen_assert(T(i,i) > 0); + sqrtT.coeffRef(i,i) = internal::sqrt(T.coeff(i,i)); + } + else { + compute2x2diagonalBlock(sqrtT, T, i); + ++i; + } + } +} + +// pre: T is quasi-upper-triangular and diagonal blocks of sqrtT are square root of diagonal blocks of T. +// post: sqrtT is the square root of T. +template <typename MatrixType> +void MatrixSquareRootQuasiTriangular<MatrixType>::computeOffDiagonalPartOfSqrt(MatrixType& sqrtT, + const MatrixType& T) +{ + const Index size = m_A.rows(); + for (Index j = 1; j < size; j++) { + if (T.coeff(j, j-1) != 0) // if T(j-1:j, j-1:j) is a 2-by-2 block + continue; + for (Index i = j-1; i >= 0; i--) { + if (i > 0 && T.coeff(i, i-1) != 0) // if T(i-1:i, i-1:i) is a 2-by-2 block + continue; + bool iBlockIs2x2 = (i < size - 1) && (T.coeff(i+1, i) != 0); + bool jBlockIs2x2 = (j < size - 1) && (T.coeff(j+1, j) != 0); + if (iBlockIs2x2 && jBlockIs2x2) + compute2x2offDiagonalBlock(sqrtT, T, i, j); + else if (iBlockIs2x2 && !jBlockIs2x2) + compute2x1offDiagonalBlock(sqrtT, T, i, j); + else if (!iBlockIs2x2 && jBlockIs2x2) + compute1x2offDiagonalBlock(sqrtT, T, i, j); + else if (!iBlockIs2x2 && !jBlockIs2x2) + compute1x1offDiagonalBlock(sqrtT, T, i, j); + } + } +} + +// pre: T.block(i,i,2,2) has complex conjugate eigenvalues +// post: sqrtT.block(i,i,2,2) is square root of T.block(i,i,2,2) +template <typename MatrixType> +void MatrixSquareRootQuasiTriangular<MatrixType> + ::compute2x2diagonalBlock(MatrixType& sqrtT, const MatrixType& T, typename MatrixType::Index i) +{ + // TODO: This case (2-by-2 blocks with complex conjugate eigenvalues) is probably hidden somewhere + // in EigenSolver. If we expose it, we could call it directly from here. + Matrix<Scalar,2,2> block = T.template block<2,2>(i,i); + EigenSolver<Matrix<Scalar,2,2> > es(block); + sqrtT.template block<2,2>(i,i) + = (es.eigenvectors() * es.eigenvalues().cwiseSqrt().asDiagonal() * es.eigenvectors().inverse()).real(); +} + +// pre: block structure of T is such that (i,j) is a 1x1 block, +// all blocks of sqrtT to left of and below (i,j) are correct +// post: sqrtT(i,j) has the correct value +template <typename MatrixType> +void MatrixSquareRootQuasiTriangular<MatrixType> + ::compute1x1offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, + typename MatrixType::Index i, typename MatrixType::Index j) +{ + Scalar tmp = (sqrtT.row(i).segment(i+1,j-i-1) * sqrtT.col(j).segment(i+1,j-i-1)).value(); + sqrtT.coeffRef(i,j) = (T.coeff(i,j) - tmp) / (sqrtT.coeff(i,i) + sqrtT.coeff(j,j)); +} + +// similar to compute1x1offDiagonalBlock() +template <typename MatrixType> +void MatrixSquareRootQuasiTriangular<MatrixType> + ::compute1x2offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, + typename MatrixType::Index i, typename MatrixType::Index j) +{ + Matrix<Scalar,1,2> rhs = T.template block<1,2>(i,j); + if (j-i > 1) + rhs -= sqrtT.block(i, i+1, 1, j-i-1) * sqrtT.block(i+1, j, j-i-1, 2); + Matrix<Scalar,2,2> A = sqrtT.coeff(i,i) * Matrix<Scalar,2,2>::Identity(); + A += sqrtT.template block<2,2>(j,j).transpose(); + sqrtT.template block<1,2>(i,j).transpose() = A.fullPivLu().solve(rhs.transpose()); +} + +// similar to compute1x1offDiagonalBlock() +template <typename MatrixType> +void MatrixSquareRootQuasiTriangular<MatrixType> + ::compute2x1offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, + typename MatrixType::Index i, typename MatrixType::Index j) +{ + Matrix<Scalar,2,1> rhs = T.template block<2,1>(i,j); + if (j-i > 2) + rhs -= sqrtT.block(i, i+2, 2, j-i-2) * sqrtT.block(i+2, j, j-i-2, 1); + Matrix<Scalar,2,2> A = sqrtT.coeff(j,j) * Matrix<Scalar,2,2>::Identity(); + A += sqrtT.template block<2,2>(i,i); + sqrtT.template block<2,1>(i,j) = A.fullPivLu().solve(rhs); +} + +// similar to compute1x1offDiagonalBlock() +template <typename MatrixType> +void MatrixSquareRootQuasiTriangular<MatrixType> + ::compute2x2offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, + typename MatrixType::Index i, typename MatrixType::Index j) +{ + Matrix<Scalar,2,2> A = sqrtT.template block<2,2>(i,i); + Matrix<Scalar,2,2> B = sqrtT.template block<2,2>(j,j); + Matrix<Scalar,2,2> C = T.template block<2,2>(i,j); + if (j-i > 2) + C -= sqrtT.block(i, i+2, 2, j-i-2) * sqrtT.block(i+2, j, j-i-2, 2); + Matrix<Scalar,2,2> X; + solveAuxiliaryEquation(X, A, B, C); + sqrtT.template block<2,2>(i,j) = X; +} + +// solves the equation A X + X B = C where all matrices are 2-by-2 +template <typename MatrixType> +template <typename SmallMatrixType> +void MatrixSquareRootQuasiTriangular<MatrixType> + ::solveAuxiliaryEquation(SmallMatrixType& X, const SmallMatrixType& A, + const SmallMatrixType& B, const SmallMatrixType& C) +{ + EIGEN_STATIC_ASSERT((internal::is_same<SmallMatrixType, Matrix<Scalar,2,2> >::value), + EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT); + + Matrix<Scalar,4,4> coeffMatrix = Matrix<Scalar,4,4>::Zero(); + coeffMatrix.coeffRef(0,0) = A.coeff(0,0) + B.coeff(0,0); + coeffMatrix.coeffRef(1,1) = A.coeff(0,0) + B.coeff(1,1); + coeffMatrix.coeffRef(2,2) = A.coeff(1,1) + B.coeff(0,0); + coeffMatrix.coeffRef(3,3) = A.coeff(1,1) + B.coeff(1,1); + coeffMatrix.coeffRef(0,1) = B.coeff(1,0); + coeffMatrix.coeffRef(0,2) = A.coeff(0,1); + coeffMatrix.coeffRef(1,0) = B.coeff(0,1); + coeffMatrix.coeffRef(1,3) = A.coeff(0,1); + coeffMatrix.coeffRef(2,0) = A.coeff(1,0); + coeffMatrix.coeffRef(2,3) = B.coeff(1,0); + coeffMatrix.coeffRef(3,1) = A.coeff(1,0); + coeffMatrix.coeffRef(3,2) = B.coeff(0,1); + + Matrix<Scalar,4,1> rhs; + rhs.coeffRef(0) = C.coeff(0,0); + rhs.coeffRef(1) = C.coeff(0,1); + rhs.coeffRef(2) = C.coeff(1,0); + rhs.coeffRef(3) = C.coeff(1,1); + + Matrix<Scalar,4,1> result; + result = coeffMatrix.fullPivLu().solve(rhs); + + X.coeffRef(0,0) = result.coeff(0); + X.coeffRef(0,1) = result.coeff(1); + X.coeffRef(1,0) = result.coeff(2); + X.coeffRef(1,1) = result.coeff(3); +} + + +/** \ingroup MatrixFunctions_Module + * \brief Class for computing matrix square roots of upper triangular matrices. + * \tparam MatrixType type of the argument of the matrix square root, + * expected to be an instantiation of the Matrix class template. + * + * This class computes the square root of the upper triangular matrix + * stored in the upper triangular part (including the diagonal) of + * the matrix passed to the constructor. + * + * \sa MatrixSquareRoot, MatrixSquareRootQuasiTriangular + */ +template <typename MatrixType> +class MatrixSquareRootTriangular +{ + public: + MatrixSquareRootTriangular(const MatrixType& A) + : m_A(A) + { + eigen_assert(A.rows() == A.cols()); + } + + /** \brief Compute the matrix square root + * + * \param[out] result square root of \p A, as specified in the constructor. + * + * Only the upper triangular part (including the diagonal) of + * \p result is updated, the rest is not touched. See + * MatrixBase::sqrt() for details on how this computation is + * implemented. + */ + template <typename ResultType> void compute(ResultType &result); + + private: + const MatrixType& m_A; +}; + +template <typename MatrixType> +template <typename ResultType> +void MatrixSquareRootTriangular<MatrixType>::compute(ResultType &result) +{ + // Compute Schur decomposition of m_A + const ComplexSchur<MatrixType> schurOfA(m_A); + const MatrixType& T = schurOfA.matrixT(); + const MatrixType& U = schurOfA.matrixU(); + + // Compute square root of T and store it in upper triangular part of result + // This uses that the square root of triangular matrices can be computed directly. + result.resize(m_A.rows(), m_A.cols()); + typedef typename MatrixType::Index Index; + for (Index i = 0; i < m_A.rows(); i++) { + result.coeffRef(i,i) = internal::sqrt(T.coeff(i,i)); + } + for (Index j = 1; j < m_A.cols(); j++) { + for (Index i = j-1; i >= 0; i--) { + typedef typename MatrixType::Scalar Scalar; + // if i = j-1, then segment has length 0 so tmp = 0 + Scalar tmp = (result.row(i).segment(i+1,j-i-1) * result.col(j).segment(i+1,j-i-1)).value(); + // denominator may be zero if original matrix is singular + result.coeffRef(i,j) = (T.coeff(i,j) - tmp) / (result.coeff(i,i) + result.coeff(j,j)); + } + } + + // Compute square root of m_A as U * result * U.adjoint() + MatrixType tmp; + tmp.noalias() = U * result.template triangularView<Upper>(); + result.noalias() = tmp * U.adjoint(); +} + + +/** \ingroup MatrixFunctions_Module + * \brief Class for computing matrix square roots of general matrices. + * \tparam MatrixType type of the argument of the matrix square root, + * expected to be an instantiation of the Matrix class template. + * + * \sa MatrixSquareRootTriangular, MatrixSquareRootQuasiTriangular, MatrixBase::sqrt() + */ +template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex> +class MatrixSquareRoot +{ + public: + + /** \brief Constructor. + * + * \param[in] A matrix whose square root is to be computed. + * + * The class stores a reference to \p A, so it should not be + * changed (or destroyed) before compute() is called. + */ + MatrixSquareRoot(const MatrixType& A); + + /** \brief Compute the matrix square root + * + * \param[out] result square root of \p A, as specified in the constructor. + * + * See MatrixBase::sqrt() for details on how this computation is + * implemented. + */ + template <typename ResultType> void compute(ResultType &result); +}; + + +// ********** Partial specialization for real matrices ********** + +template <typename MatrixType> +class MatrixSquareRoot<MatrixType, 0> +{ + public: + + MatrixSquareRoot(const MatrixType& A) + : m_A(A) + { + eigen_assert(A.rows() == A.cols()); + } + + template <typename ResultType> void compute(ResultType &result) + { + // Compute Schur decomposition of m_A + const RealSchur<MatrixType> schurOfA(m_A); + const MatrixType& T = schurOfA.matrixT(); + const MatrixType& U = schurOfA.matrixU(); + + // Compute square root of T + MatrixSquareRootQuasiTriangular<MatrixType> tmp(T); + MatrixType sqrtT = MatrixType::Zero(m_A.rows(), m_A.rows()); + tmp.compute(sqrtT); + + // Compute square root of m_A + result = U * sqrtT * U.adjoint(); + } + + private: + const MatrixType& m_A; +}; + + +// ********** Partial specialization for complex matrices ********** + +template <typename MatrixType> +class MatrixSquareRoot<MatrixType, 1> +{ + public: + + MatrixSquareRoot(const MatrixType& A) + : m_A(A) + { + eigen_assert(A.rows() == A.cols()); + } + + template <typename ResultType> void compute(ResultType &result) + { + // Compute Schur decomposition of m_A + const ComplexSchur<MatrixType> schurOfA(m_A); + const MatrixType& T = schurOfA.matrixT(); + const MatrixType& U = schurOfA.matrixU(); + + // Compute square root of T + MatrixSquareRootTriangular<MatrixType> tmp(T); + MatrixType sqrtT = MatrixType::Zero(m_A.rows(), m_A.rows()); + tmp.compute(sqrtT); + + // Compute square root of m_A + result = U * sqrtT * U.adjoint(); + } + + private: + const MatrixType& m_A; +}; + + +/** \ingroup MatrixFunctions_Module + * + * \brief Proxy for the matrix square root of some matrix (expression). + * + * \tparam Derived Type of the argument to the matrix square root. + * + * This class holds the argument to the matrix square root until it + * is assigned or evaluated for some other reason (so the argument + * should not be changed in the meantime). It is the return type of + * MatrixBase::sqrt() and most of the time this is the only way it is + * used. + */ +template<typename Derived> class MatrixSquareRootReturnValue +: public ReturnByValue<MatrixSquareRootReturnValue<Derived> > +{ + typedef typename Derived::Index Index; + public: + /** \brief Constructor. + * + * \param[in] src %Matrix (expression) forming the argument of the + * matrix square root. + */ + MatrixSquareRootReturnValue(const Derived& src) : m_src(src) { } + + /** \brief Compute the matrix square root. + * + * \param[out] result the matrix square root of \p src in the + * constructor. + */ + template <typename ResultType> + inline void evalTo(ResultType& result) const + { + const typename Derived::PlainObject srcEvaluated = m_src.eval(); + MatrixSquareRoot<typename Derived::PlainObject> me(srcEvaluated); + me.compute(result); + } + + Index rows() const { return m_src.rows(); } + Index cols() const { return m_src.cols(); } + + protected: + const Derived& m_src; + private: + MatrixSquareRootReturnValue& operator=(const MatrixSquareRootReturnValue&); +}; + +namespace internal { +template<typename Derived> +struct traits<MatrixSquareRootReturnValue<Derived> > +{ + typedef typename Derived::PlainObject ReturnType; +}; +} + +template <typename Derived> +const MatrixSquareRootReturnValue<Derived> MatrixBase<Derived>::sqrt() const +{ + eigen_assert(rows() == cols()); + return MatrixSquareRootReturnValue<Derived>(derived()); +} + +} // end namespace Eigen + +#endif // EIGEN_MATRIX_FUNCTION diff --git a/unsupported/Eigen/src/MatrixFunctions/StemFunction.h b/unsupported/Eigen/src/MatrixFunctions/StemFunction.h new file mode 100644 index 000000000..724e55c1d --- /dev/null +++ b/unsupported/Eigen/src/MatrixFunctions/StemFunction.h @@ -0,0 +1,105 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_STEM_FUNCTION +#define EIGEN_STEM_FUNCTION + +namespace Eigen { + +/** \ingroup MatrixFunctions_Module + * \brief Stem functions corresponding to standard mathematical functions. + */ +template <typename Scalar> +class StdStemFunctions +{ + public: + + /** \brief The exponential function (and its derivatives). */ + static Scalar exp(Scalar x, int) + { + return std::exp(x); + } + + /** \brief Cosine (and its derivatives). */ + static Scalar cos(Scalar x, int n) + { + Scalar res; + switch (n % 4) { + case 0: + res = std::cos(x); + break; + case 1: + res = -std::sin(x); + break; + case 2: + res = -std::cos(x); + break; + case 3: + res = std::sin(x); + break; + } + return res; + } + + /** \brief Sine (and its derivatives). */ + static Scalar sin(Scalar x, int n) + { + Scalar res; + switch (n % 4) { + case 0: + res = std::sin(x); + break; + case 1: + res = std::cos(x); + break; + case 2: + res = -std::sin(x); + break; + case 3: + res = -std::cos(x); + break; + } + return res; + } + + /** \brief Hyperbolic cosine (and its derivatives). */ + static Scalar cosh(Scalar x, int n) + { + Scalar res; + switch (n % 2) { + case 0: + res = std::cosh(x); + break; + case 1: + res = std::sinh(x); + break; + } + return res; + } + + /** \brief Hyperbolic sine (and its derivatives). */ + static Scalar sinh(Scalar x, int n) + { + Scalar res; + switch (n % 2) { + case 0: + res = std::sinh(x); + break; + case 1: + res = std::cosh(x); + break; + } + return res; + } + +}; // end of class StdStemFunctions + +} // end namespace Eigen + +#endif // EIGEN_STEM_FUNCTION diff --git a/unsupported/Eigen/src/MoreVectorization/CMakeLists.txt b/unsupported/Eigen/src/MoreVectorization/CMakeLists.txt new file mode 100644 index 000000000..1b887cc8e --- /dev/null +++ b/unsupported/Eigen/src/MoreVectorization/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_MoreVectorization_SRCS "*.h") + +INSTALL(FILES + ${Eigen_MoreVectorization_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/MoreVectorization COMPONENT Devel + ) diff --git a/unsupported/Eigen/src/MoreVectorization/MathFunctions.h b/unsupported/Eigen/src/MoreVectorization/MathFunctions.h new file mode 100644 index 000000000..63cb28dea --- /dev/null +++ b/unsupported/Eigen/src/MoreVectorization/MathFunctions.h @@ -0,0 +1,95 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Rohit Garg <rpg.314@gmail.com> +// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H +#define EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H + +namespace Eigen { + +namespace internal { + +/** \internal \returns the arcsin of \a a (coeff-wise) */ +template<typename Packet> inline static Packet pasin(Packet a) { return std::asin(a); } + +#ifdef EIGEN_VECTORIZE_SSE + +template<> EIGEN_DONT_INLINE Packet4f pasin(Packet4f x) +{ + _EIGEN_DECLARE_CONST_Packet4f(half, 0.5); + _EIGEN_DECLARE_CONST_Packet4f(minus_half, -0.5); + _EIGEN_DECLARE_CONST_Packet4f(3half, 1.5); + + _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000); + + _EIGEN_DECLARE_CONST_Packet4f(pi, 3.141592654); + _EIGEN_DECLARE_CONST_Packet4f(pi_over_2, 3.141592654*0.5); + + _EIGEN_DECLARE_CONST_Packet4f(asin1, 4.2163199048E-2); + _EIGEN_DECLARE_CONST_Packet4f(asin2, 2.4181311049E-2); + _EIGEN_DECLARE_CONST_Packet4f(asin3, 4.5470025998E-2); + _EIGEN_DECLARE_CONST_Packet4f(asin4, 7.4953002686E-2); + _EIGEN_DECLARE_CONST_Packet4f(asin5, 1.6666752422E-1); + + Packet4f a = pabs(x);//got the absolute value + + Packet4f sign_bit= _mm_and_ps(x, p4f_sign_mask);//extracted the sign bit + + Packet4f z1,z2;//will need them during computation + + +//will compute the two branches for asin +//so first compare with half + + Packet4f branch_mask= _mm_cmpgt_ps(a, p4f_half);//this is to select which branch to take +//both will be taken, and finally results will be merged +//the branch for values >0.5 + + { +//the core series expansion + z1=pmadd(p4f_minus_half,a,p4f_half); + Packet4f x1=psqrt(z1); + Packet4f s1=pmadd(p4f_asin1, z1, p4f_asin2); + Packet4f s2=pmadd(s1, z1, p4f_asin3); + Packet4f s3=pmadd(s2,z1, p4f_asin4); + Packet4f s4=pmadd(s3,z1, p4f_asin5); + Packet4f temp=pmul(s4,z1);//not really a madd but a mul by z so that the next term can be a madd + z1=pmadd(temp,x1,x1); + z1=padd(z1,z1); + z1=psub(p4f_pi_over_2,z1); + } + + { +//the core series expansion + Packet4f x2=a; + z2=pmul(x2,x2); + Packet4f s1=pmadd(p4f_asin1, z2, p4f_asin2); + Packet4f s2=pmadd(s1, z2, p4f_asin3); + Packet4f s3=pmadd(s2,z2, p4f_asin4); + Packet4f s4=pmadd(s3,z2, p4f_asin5); + Packet4f temp=pmul(s4,z2);//not really a madd but a mul by z so that the next term can be a madd + z2=pmadd(temp,x2,x2); + } + +/* select the correct result from the two branch evaluations */ + z1 = _mm_and_ps(branch_mask, z1); + z2 = _mm_andnot_ps(branch_mask, z2); + Packet4f z = _mm_or_ps(z1,z2); + +/* update the sign */ + return _mm_xor_ps(z, sign_bit); +} + +#endif // EIGEN_VECTORIZE_SSE + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H diff --git a/unsupported/Eigen/src/NonLinearOptimization/CMakeLists.txt b/unsupported/Eigen/src/NonLinearOptimization/CMakeLists.txt new file mode 100644 index 000000000..9322ddadf --- /dev/null +++ b/unsupported/Eigen/src/NonLinearOptimization/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_NonLinearOptimization_SRCS "*.h") + +INSTALL(FILES + ${Eigen_NonLinearOptimization_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/NonLinearOptimization COMPONENT Devel + ) diff --git a/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h b/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h new file mode 100644 index 000000000..d9ce4eab6 --- /dev/null +++ b/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h @@ -0,0 +1,596 @@ +// -*- coding: utf-8 +// vim: set fileencoding=utf-8 + +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_HYBRIDNONLINEARSOLVER_H +#define EIGEN_HYBRIDNONLINEARSOLVER_H + +namespace Eigen { + +namespace HybridNonLinearSolverSpace { + enum Status { + Running = -1, + ImproperInputParameters = 0, + RelativeErrorTooSmall = 1, + TooManyFunctionEvaluation = 2, + TolTooSmall = 3, + NotMakingProgressJacobian = 4, + NotMakingProgressIterations = 5, + UserAsked = 6 + }; +} + +/** + * \ingroup NonLinearOptimization_Module + * \brief Finds a zero of a system of n + * nonlinear functions in n variables by a modification of the Powell + * hybrid method ("dogleg"). + * + * The user must provide a subroutine which calculates the + * functions. The Jacobian is either provided by the user, or approximated + * using a forward-difference method. + * + */ +template<typename FunctorType, typename Scalar=double> +class HybridNonLinearSolver +{ +public: + typedef DenseIndex Index; + + HybridNonLinearSolver(FunctorType &_functor) + : functor(_functor) { nfev=njev=iter = 0; fnorm= 0.; useExternalScaling=false;} + + struct Parameters { + Parameters() + : factor(Scalar(100.)) + , maxfev(1000) + , xtol(internal::sqrt(NumTraits<Scalar>::epsilon())) + , nb_of_subdiagonals(-1) + , nb_of_superdiagonals(-1) + , epsfcn(Scalar(0.)) {} + Scalar factor; + Index maxfev; // maximum number of function evaluation + Scalar xtol; + Index nb_of_subdiagonals; + Index nb_of_superdiagonals; + Scalar epsfcn; + }; + typedef Matrix< Scalar, Dynamic, 1 > FVectorType; + typedef Matrix< Scalar, Dynamic, Dynamic > JacobianType; + /* TODO: if eigen provides a triangular storage, use it here */ + typedef Matrix< Scalar, Dynamic, Dynamic > UpperTriangularType; + + HybridNonLinearSolverSpace::Status hybrj1( + FVectorType &x, + const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon()) + ); + + HybridNonLinearSolverSpace::Status solveInit(FVectorType &x); + HybridNonLinearSolverSpace::Status solveOneStep(FVectorType &x); + HybridNonLinearSolverSpace::Status solve(FVectorType &x); + + HybridNonLinearSolverSpace::Status hybrd1( + FVectorType &x, + const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon()) + ); + + HybridNonLinearSolverSpace::Status solveNumericalDiffInit(FVectorType &x); + HybridNonLinearSolverSpace::Status solveNumericalDiffOneStep(FVectorType &x); + HybridNonLinearSolverSpace::Status solveNumericalDiff(FVectorType &x); + + void resetParameters(void) { parameters = Parameters(); } + Parameters parameters; + FVectorType fvec, qtf, diag; + JacobianType fjac; + UpperTriangularType R; + Index nfev; + Index njev; + Index iter; + Scalar fnorm; + bool useExternalScaling; +private: + FunctorType &functor; + Index n; + Scalar sum; + bool sing; + Scalar temp; + Scalar delta; + bool jeval; + Index ncsuc; + Scalar ratio; + Scalar pnorm, xnorm, fnorm1; + Index nslow1, nslow2; + Index ncfail; + Scalar actred, prered; + FVectorType wa1, wa2, wa3, wa4; + + HybridNonLinearSolver& operator=(const HybridNonLinearSolver&); +}; + + + +template<typename FunctorType, typename Scalar> +HybridNonLinearSolverSpace::Status +HybridNonLinearSolver<FunctorType,Scalar>::hybrj1( + FVectorType &x, + const Scalar tol + ) +{ + n = x.size(); + + /* check the input parameters for errors. */ + if (n <= 0 || tol < 0.) + return HybridNonLinearSolverSpace::ImproperInputParameters; + + resetParameters(); + parameters.maxfev = 100*(n+1); + parameters.xtol = tol; + diag.setConstant(n, 1.); + useExternalScaling = true; + return solve(x); +} + +template<typename FunctorType, typename Scalar> +HybridNonLinearSolverSpace::Status +HybridNonLinearSolver<FunctorType,Scalar>::solveInit(FVectorType &x) +{ + n = x.size(); + + wa1.resize(n); wa2.resize(n); wa3.resize(n); wa4.resize(n); + fvec.resize(n); + qtf.resize(n); + fjac.resize(n, n); + if (!useExternalScaling) + diag.resize(n); + assert( (!useExternalScaling || diag.size()==n) || "When useExternalScaling is set, the caller must provide a valid 'diag'"); + + /* Function Body */ + nfev = 0; + njev = 0; + + /* check the input parameters for errors. */ + if (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0. ) + return HybridNonLinearSolverSpace::ImproperInputParameters; + if (useExternalScaling) + for (Index j = 0; j < n; ++j) + if (diag[j] <= 0.) + return HybridNonLinearSolverSpace::ImproperInputParameters; + + /* evaluate the function at the starting point */ + /* and calculate its norm. */ + nfev = 1; + if ( functor(x, fvec) < 0) + return HybridNonLinearSolverSpace::UserAsked; + fnorm = fvec.stableNorm(); + + /* initialize iteration counter and monitors. */ + iter = 1; + ncsuc = 0; + ncfail = 0; + nslow1 = 0; + nslow2 = 0; + + return HybridNonLinearSolverSpace::Running; +} + +template<typename FunctorType, typename Scalar> +HybridNonLinearSolverSpace::Status +HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType &x) +{ + assert(x.size()==n); // check the caller is not cheating us + + Index j; + std::vector<JacobiRotation<Scalar> > v_givens(n), w_givens(n); + + jeval = true; + + /* calculate the jacobian matrix. */ + if ( functor.df(x, fjac) < 0) + return HybridNonLinearSolverSpace::UserAsked; + ++njev; + + wa2 = fjac.colwise().blueNorm(); + + /* on the first iteration and if external scaling is not used, scale according */ + /* to the norms of the columns of the initial jacobian. */ + if (iter == 1) { + if (!useExternalScaling) + for (j = 0; j < n; ++j) + diag[j] = (wa2[j]==0.) ? 1. : wa2[j]; + + /* on the first iteration, calculate the norm of the scaled x */ + /* and initialize the step bound delta. */ + xnorm = diag.cwiseProduct(x).stableNorm(); + delta = parameters.factor * xnorm; + if (delta == 0.) + delta = parameters.factor; + } + + /* compute the qr factorization of the jacobian. */ + HouseholderQR<JacobianType> qrfac(fjac); // no pivoting: + + /* copy the triangular factor of the qr factorization into r. */ + R = qrfac.matrixQR(); + + /* accumulate the orthogonal factor in fjac. */ + fjac = qrfac.householderQ(); + + /* form (q transpose)*fvec and store in qtf. */ + qtf = fjac.transpose() * fvec; + + /* rescale if necessary. */ + if (!useExternalScaling) + diag = diag.cwiseMax(wa2); + + while (true) { + /* determine the direction p. */ + internal::dogleg<Scalar>(R, diag, qtf, delta, wa1); + + /* store the direction p and x + p. calculate the norm of p. */ + wa1 = -wa1; + wa2 = x + wa1; + pnorm = diag.cwiseProduct(wa1).stableNorm(); + + /* on the first iteration, adjust the initial step bound. */ + if (iter == 1) + delta = (std::min)(delta,pnorm); + + /* evaluate the function at x + p and calculate its norm. */ + if ( functor(wa2, wa4) < 0) + return HybridNonLinearSolverSpace::UserAsked; + ++nfev; + fnorm1 = wa4.stableNorm(); + + /* compute the scaled actual reduction. */ + actred = -1.; + if (fnorm1 < fnorm) /* Computing 2nd power */ + actred = 1. - internal::abs2(fnorm1 / fnorm); + + /* compute the scaled predicted reduction. */ + wa3 = R.template triangularView<Upper>()*wa1 + qtf; + temp = wa3.stableNorm(); + prered = 0.; + if (temp < fnorm) /* Computing 2nd power */ + prered = 1. - internal::abs2(temp / fnorm); + + /* compute the ratio of the actual to the predicted reduction. */ + ratio = 0.; + if (prered > 0.) + ratio = actred / prered; + + /* update the step bound. */ + if (ratio < Scalar(.1)) { + ncsuc = 0; + ++ncfail; + delta = Scalar(.5) * delta; + } else { + ncfail = 0; + ++ncsuc; + if (ratio >= Scalar(.5) || ncsuc > 1) + delta = (std::max)(delta, pnorm / Scalar(.5)); + if (internal::abs(ratio - 1.) <= Scalar(.1)) { + delta = pnorm / Scalar(.5); + } + } + + /* test for successful iteration. */ + if (ratio >= Scalar(1e-4)) { + /* successful iteration. update x, fvec, and their norms. */ + x = wa2; + wa2 = diag.cwiseProduct(x); + fvec = wa4; + xnorm = wa2.stableNorm(); + fnorm = fnorm1; + ++iter; + } + + /* determine the progress of the iteration. */ + ++nslow1; + if (actred >= Scalar(.001)) + nslow1 = 0; + if (jeval) + ++nslow2; + if (actred >= Scalar(.1)) + nslow2 = 0; + + /* test for convergence. */ + if (delta <= parameters.xtol * xnorm || fnorm == 0.) + return HybridNonLinearSolverSpace::RelativeErrorTooSmall; + + /* tests for termination and stringent tolerances. */ + if (nfev >= parameters.maxfev) + return HybridNonLinearSolverSpace::TooManyFunctionEvaluation; + if (Scalar(.1) * (std::max)(Scalar(.1) * delta, pnorm) <= NumTraits<Scalar>::epsilon() * xnorm) + return HybridNonLinearSolverSpace::TolTooSmall; + if (nslow2 == 5) + return HybridNonLinearSolverSpace::NotMakingProgressJacobian; + if (nslow1 == 10) + return HybridNonLinearSolverSpace::NotMakingProgressIterations; + + /* criterion for recalculating jacobian. */ + if (ncfail == 2) + break; // leave inner loop and go for the next outer loop iteration + + /* calculate the rank one modification to the jacobian */ + /* and update qtf if necessary. */ + wa1 = diag.cwiseProduct( diag.cwiseProduct(wa1)/pnorm ); + wa2 = fjac.transpose() * wa4; + if (ratio >= Scalar(1e-4)) + qtf = wa2; + wa2 = (wa2-wa3)/pnorm; + + /* compute the qr factorization of the updated jacobian. */ + internal::r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing); + internal::r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens); + internal::r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens); + + jeval = false; + } + return HybridNonLinearSolverSpace::Running; +} + +template<typename FunctorType, typename Scalar> +HybridNonLinearSolverSpace::Status +HybridNonLinearSolver<FunctorType,Scalar>::solve(FVectorType &x) +{ + HybridNonLinearSolverSpace::Status status = solveInit(x); + if (status==HybridNonLinearSolverSpace::ImproperInputParameters) + return status; + while (status==HybridNonLinearSolverSpace::Running) + status = solveOneStep(x); + return status; +} + + + +template<typename FunctorType, typename Scalar> +HybridNonLinearSolverSpace::Status +HybridNonLinearSolver<FunctorType,Scalar>::hybrd1( + FVectorType &x, + const Scalar tol + ) +{ + n = x.size(); + + /* check the input parameters for errors. */ + if (n <= 0 || tol < 0.) + return HybridNonLinearSolverSpace::ImproperInputParameters; + + resetParameters(); + parameters.maxfev = 200*(n+1); + parameters.xtol = tol; + + diag.setConstant(n, 1.); + useExternalScaling = true; + return solveNumericalDiff(x); +} + +template<typename FunctorType, typename Scalar> +HybridNonLinearSolverSpace::Status +HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffInit(FVectorType &x) +{ + n = x.size(); + + if (parameters.nb_of_subdiagonals<0) parameters.nb_of_subdiagonals= n-1; + if (parameters.nb_of_superdiagonals<0) parameters.nb_of_superdiagonals= n-1; + + wa1.resize(n); wa2.resize(n); wa3.resize(n); wa4.resize(n); + qtf.resize(n); + fjac.resize(n, n); + fvec.resize(n); + if (!useExternalScaling) + diag.resize(n); + assert( (!useExternalScaling || diag.size()==n) || "When useExternalScaling is set, the caller must provide a valid 'diag'"); + + /* Function Body */ + nfev = 0; + njev = 0; + + /* check the input parameters for errors. */ + if (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.nb_of_subdiagonals< 0 || parameters.nb_of_superdiagonals< 0 || parameters.factor <= 0. ) + return HybridNonLinearSolverSpace::ImproperInputParameters; + if (useExternalScaling) + for (Index j = 0; j < n; ++j) + if (diag[j] <= 0.) + return HybridNonLinearSolverSpace::ImproperInputParameters; + + /* evaluate the function at the starting point */ + /* and calculate its norm. */ + nfev = 1; + if ( functor(x, fvec) < 0) + return HybridNonLinearSolverSpace::UserAsked; + fnorm = fvec.stableNorm(); + + /* initialize iteration counter and monitors. */ + iter = 1; + ncsuc = 0; + ncfail = 0; + nslow1 = 0; + nslow2 = 0; + + return HybridNonLinearSolverSpace::Running; +} + +template<typename FunctorType, typename Scalar> +HybridNonLinearSolverSpace::Status +HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType &x) +{ + assert(x.size()==n); // check the caller is not cheating us + + Index j; + std::vector<JacobiRotation<Scalar> > v_givens(n), w_givens(n); + + jeval = true; + if (parameters.nb_of_subdiagonals<0) parameters.nb_of_subdiagonals= n-1; + if (parameters.nb_of_superdiagonals<0) parameters.nb_of_superdiagonals= n-1; + + /* calculate the jacobian matrix. */ + if (internal::fdjac1(functor, x, fvec, fjac, parameters.nb_of_subdiagonals, parameters.nb_of_superdiagonals, parameters.epsfcn) <0) + return HybridNonLinearSolverSpace::UserAsked; + nfev += (std::min)(parameters.nb_of_subdiagonals+parameters.nb_of_superdiagonals+ 1, n); + + wa2 = fjac.colwise().blueNorm(); + + /* on the first iteration and if external scaling is not used, scale according */ + /* to the norms of the columns of the initial jacobian. */ + if (iter == 1) { + if (!useExternalScaling) + for (j = 0; j < n; ++j) + diag[j] = (wa2[j]==0.) ? 1. : wa2[j]; + + /* on the first iteration, calculate the norm of the scaled x */ + /* and initialize the step bound delta. */ + xnorm = diag.cwiseProduct(x).stableNorm(); + delta = parameters.factor * xnorm; + if (delta == 0.) + delta = parameters.factor; + } + + /* compute the qr factorization of the jacobian. */ + HouseholderQR<JacobianType> qrfac(fjac); // no pivoting: + + /* copy the triangular factor of the qr factorization into r. */ + R = qrfac.matrixQR(); + + /* accumulate the orthogonal factor in fjac. */ + fjac = qrfac.householderQ(); + + /* form (q transpose)*fvec and store in qtf. */ + qtf = fjac.transpose() * fvec; + + /* rescale if necessary. */ + if (!useExternalScaling) + diag = diag.cwiseMax(wa2); + + while (true) { + /* determine the direction p. */ + internal::dogleg<Scalar>(R, diag, qtf, delta, wa1); + + /* store the direction p and x + p. calculate the norm of p. */ + wa1 = -wa1; + wa2 = x + wa1; + pnorm = diag.cwiseProduct(wa1).stableNorm(); + + /* on the first iteration, adjust the initial step bound. */ + if (iter == 1) + delta = (std::min)(delta,pnorm); + + /* evaluate the function at x + p and calculate its norm. */ + if ( functor(wa2, wa4) < 0) + return HybridNonLinearSolverSpace::UserAsked; + ++nfev; + fnorm1 = wa4.stableNorm(); + + /* compute the scaled actual reduction. */ + actred = -1.; + if (fnorm1 < fnorm) /* Computing 2nd power */ + actred = 1. - internal::abs2(fnorm1 / fnorm); + + /* compute the scaled predicted reduction. */ + wa3 = R.template triangularView<Upper>()*wa1 + qtf; + temp = wa3.stableNorm(); + prered = 0.; + if (temp < fnorm) /* Computing 2nd power */ + prered = 1. - internal::abs2(temp / fnorm); + + /* compute the ratio of the actual to the predicted reduction. */ + ratio = 0.; + if (prered > 0.) + ratio = actred / prered; + + /* update the step bound. */ + if (ratio < Scalar(.1)) { + ncsuc = 0; + ++ncfail; + delta = Scalar(.5) * delta; + } else { + ncfail = 0; + ++ncsuc; + if (ratio >= Scalar(.5) || ncsuc > 1) + delta = (std::max)(delta, pnorm / Scalar(.5)); + if (internal::abs(ratio - 1.) <= Scalar(.1)) { + delta = pnorm / Scalar(.5); + } + } + + /* test for successful iteration. */ + if (ratio >= Scalar(1e-4)) { + /* successful iteration. update x, fvec, and their norms. */ + x = wa2; + wa2 = diag.cwiseProduct(x); + fvec = wa4; + xnorm = wa2.stableNorm(); + fnorm = fnorm1; + ++iter; + } + + /* determine the progress of the iteration. */ + ++nslow1; + if (actred >= Scalar(.001)) + nslow1 = 0; + if (jeval) + ++nslow2; + if (actred >= Scalar(.1)) + nslow2 = 0; + + /* test for convergence. */ + if (delta <= parameters.xtol * xnorm || fnorm == 0.) + return HybridNonLinearSolverSpace::RelativeErrorTooSmall; + + /* tests for termination and stringent tolerances. */ + if (nfev >= parameters.maxfev) + return HybridNonLinearSolverSpace::TooManyFunctionEvaluation; + if (Scalar(.1) * (std::max)(Scalar(.1) * delta, pnorm) <= NumTraits<Scalar>::epsilon() * xnorm) + return HybridNonLinearSolverSpace::TolTooSmall; + if (nslow2 == 5) + return HybridNonLinearSolverSpace::NotMakingProgressJacobian; + if (nslow1 == 10) + return HybridNonLinearSolverSpace::NotMakingProgressIterations; + + /* criterion for recalculating jacobian. */ + if (ncfail == 2) + break; // leave inner loop and go for the next outer loop iteration + + /* calculate the rank one modification to the jacobian */ + /* and update qtf if necessary. */ + wa1 = diag.cwiseProduct( diag.cwiseProduct(wa1)/pnorm ); + wa2 = fjac.transpose() * wa4; + if (ratio >= Scalar(1e-4)) + qtf = wa2; + wa2 = (wa2-wa3)/pnorm; + + /* compute the qr factorization of the updated jacobian. */ + internal::r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing); + internal::r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens); + internal::r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens); + + jeval = false; + } + return HybridNonLinearSolverSpace::Running; +} + +template<typename FunctorType, typename Scalar> +HybridNonLinearSolverSpace::Status +HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiff(FVectorType &x) +{ + HybridNonLinearSolverSpace::Status status = solveNumericalDiffInit(x); + if (status==HybridNonLinearSolverSpace::ImproperInputParameters) + return status; + while (status==HybridNonLinearSolverSpace::Running) + status = solveNumericalDiffOneStep(x); + return status; +} + +} // end namespace Eigen + +#endif // EIGEN_HYBRIDNONLINEARSOLVER_H + +//vim: ai ts=4 sts=4 et sw=4 diff --git a/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h b/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h new file mode 100644 index 000000000..075faeeb0 --- /dev/null +++ b/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h @@ -0,0 +1,644 @@ +// -*- coding: utf-8 +// vim: set fileencoding=utf-8 + +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_LEVENBERGMARQUARDT__H +#define EIGEN_LEVENBERGMARQUARDT__H + +namespace Eigen { + +namespace LevenbergMarquardtSpace { + enum Status { + NotStarted = -2, + Running = -1, + ImproperInputParameters = 0, + RelativeReductionTooSmall = 1, + RelativeErrorTooSmall = 2, + RelativeErrorAndReductionTooSmall = 3, + CosinusTooSmall = 4, + TooManyFunctionEvaluation = 5, + FtolTooSmall = 6, + XtolTooSmall = 7, + GtolTooSmall = 8, + UserAsked = 9 + }; +} + + + +/** + * \ingroup NonLinearOptimization_Module + * \brief Performs non linear optimization over a non-linear function, + * using a variant of the Levenberg Marquardt algorithm. + * + * Check wikipedia for more information. + * http://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm + */ +template<typename FunctorType, typename Scalar=double> +class LevenbergMarquardt +{ +public: + LevenbergMarquardt(FunctorType &_functor) + : functor(_functor) { nfev = njev = iter = 0; fnorm = gnorm = 0.; useExternalScaling=false; } + + typedef DenseIndex Index; + + struct Parameters { + Parameters() + : factor(Scalar(100.)) + , maxfev(400) + , ftol(internal::sqrt(NumTraits<Scalar>::epsilon())) + , xtol(internal::sqrt(NumTraits<Scalar>::epsilon())) + , gtol(Scalar(0.)) + , epsfcn(Scalar(0.)) {} + Scalar factor; + Index maxfev; // maximum number of function evaluation + Scalar ftol; + Scalar xtol; + Scalar gtol; + Scalar epsfcn; + }; + + typedef Matrix< Scalar, Dynamic, 1 > FVectorType; + typedef Matrix< Scalar, Dynamic, Dynamic > JacobianType; + + LevenbergMarquardtSpace::Status lmder1( + FVectorType &x, + const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon()) + ); + + LevenbergMarquardtSpace::Status minimize(FVectorType &x); + LevenbergMarquardtSpace::Status minimizeInit(FVectorType &x); + LevenbergMarquardtSpace::Status minimizeOneStep(FVectorType &x); + + static LevenbergMarquardtSpace::Status lmdif1( + FunctorType &functor, + FVectorType &x, + Index *nfev, + const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon()) + ); + + LevenbergMarquardtSpace::Status lmstr1( + FVectorType &x, + const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon()) + ); + + LevenbergMarquardtSpace::Status minimizeOptimumStorage(FVectorType &x); + LevenbergMarquardtSpace::Status minimizeOptimumStorageInit(FVectorType &x); + LevenbergMarquardtSpace::Status minimizeOptimumStorageOneStep(FVectorType &x); + + void resetParameters(void) { parameters = Parameters(); } + + Parameters parameters; + FVectorType fvec, qtf, diag; + JacobianType fjac; + PermutationMatrix<Dynamic,Dynamic> permutation; + Index nfev; + Index njev; + Index iter; + Scalar fnorm, gnorm; + bool useExternalScaling; + + Scalar lm_param(void) { return par; } +private: + FunctorType &functor; + Index n; + Index m; + FVectorType wa1, wa2, wa3, wa4; + + Scalar par, sum; + Scalar temp, temp1, temp2; + Scalar delta; + Scalar ratio; + Scalar pnorm, xnorm, fnorm1, actred, dirder, prered; + + LevenbergMarquardt& operator=(const LevenbergMarquardt&); +}; + +template<typename FunctorType, typename Scalar> +LevenbergMarquardtSpace::Status +LevenbergMarquardt<FunctorType,Scalar>::lmder1( + FVectorType &x, + const Scalar tol + ) +{ + n = x.size(); + m = functor.values(); + + /* check the input parameters for errors. */ + if (n <= 0 || m < n || tol < 0.) + return LevenbergMarquardtSpace::ImproperInputParameters; + + resetParameters(); + parameters.ftol = tol; + parameters.xtol = tol; + parameters.maxfev = 100*(n+1); + + return minimize(x); +} + + +template<typename FunctorType, typename Scalar> +LevenbergMarquardtSpace::Status +LevenbergMarquardt<FunctorType,Scalar>::minimize(FVectorType &x) +{ + LevenbergMarquardtSpace::Status status = minimizeInit(x); + if (status==LevenbergMarquardtSpace::ImproperInputParameters) + return status; + do { + status = minimizeOneStep(x); + } while (status==LevenbergMarquardtSpace::Running); + return status; +} + +template<typename FunctorType, typename Scalar> +LevenbergMarquardtSpace::Status +LevenbergMarquardt<FunctorType,Scalar>::minimizeInit(FVectorType &x) +{ + n = x.size(); + m = functor.values(); + + wa1.resize(n); wa2.resize(n); wa3.resize(n); + wa4.resize(m); + fvec.resize(m); + fjac.resize(m, n); + if (!useExternalScaling) + diag.resize(n); + assert( (!useExternalScaling || diag.size()==n) || "When useExternalScaling is set, the caller must provide a valid 'diag'"); + qtf.resize(n); + + /* Function Body */ + nfev = 0; + njev = 0; + + /* check the input parameters for errors. */ + if (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.) + return LevenbergMarquardtSpace::ImproperInputParameters; + + if (useExternalScaling) + for (Index j = 0; j < n; ++j) + if (diag[j] <= 0.) + return LevenbergMarquardtSpace::ImproperInputParameters; + + /* evaluate the function at the starting point */ + /* and calculate its norm. */ + nfev = 1; + if ( functor(x, fvec) < 0) + return LevenbergMarquardtSpace::UserAsked; + fnorm = fvec.stableNorm(); + + /* initialize levenberg-marquardt parameter and iteration counter. */ + par = 0.; + iter = 1; + + return LevenbergMarquardtSpace::NotStarted; +} + +template<typename FunctorType, typename Scalar> +LevenbergMarquardtSpace::Status +LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x) +{ + assert(x.size()==n); // check the caller is not cheating us + + /* calculate the jacobian matrix. */ + Index df_ret = functor.df(x, fjac); + if (df_ret<0) + return LevenbergMarquardtSpace::UserAsked; + if (df_ret>0) + // numerical diff, we evaluated the function df_ret times + nfev += df_ret; + else njev++; + + /* compute the qr factorization of the jacobian. */ + wa2 = fjac.colwise().blueNorm(); + ColPivHouseholderQR<JacobianType> qrfac(fjac); + fjac = qrfac.matrixQR(); + permutation = qrfac.colsPermutation(); + + /* on the first iteration and if external scaling is not used, scale according */ + /* to the norms of the columns of the initial jacobian. */ + if (iter == 1) { + if (!useExternalScaling) + for (Index j = 0; j < n; ++j) + diag[j] = (wa2[j]==0.)? 1. : wa2[j]; + + /* on the first iteration, calculate the norm of the scaled x */ + /* and initialize the step bound delta. */ + xnorm = diag.cwiseProduct(x).stableNorm(); + delta = parameters.factor * xnorm; + if (delta == 0.) + delta = parameters.factor; + } + + /* form (q transpose)*fvec and store the first n components in */ + /* qtf. */ + wa4 = fvec; + wa4.applyOnTheLeft(qrfac.householderQ().adjoint()); + qtf = wa4.head(n); + + /* compute the norm of the scaled gradient. */ + gnorm = 0.; + if (fnorm != 0.) + for (Index j = 0; j < n; ++j) + if (wa2[permutation.indices()[j]] != 0.) + gnorm = (std::max)(gnorm, internal::abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]])); + + /* test for convergence of the gradient norm. */ + if (gnorm <= parameters.gtol) + return LevenbergMarquardtSpace::CosinusTooSmall; + + /* rescale if necessary. */ + if (!useExternalScaling) + diag = diag.cwiseMax(wa2); + + do { + + /* determine the levenberg-marquardt parameter. */ + internal::lmpar2<Scalar>(qrfac, diag, qtf, delta, par, wa1); + + /* store the direction p and x + p. calculate the norm of p. */ + wa1 = -wa1; + wa2 = x + wa1; + pnorm = diag.cwiseProduct(wa1).stableNorm(); + + /* on the first iteration, adjust the initial step bound. */ + if (iter == 1) + delta = (std::min)(delta,pnorm); + + /* evaluate the function at x + p and calculate its norm. */ + if ( functor(wa2, wa4) < 0) + return LevenbergMarquardtSpace::UserAsked; + ++nfev; + fnorm1 = wa4.stableNorm(); + + /* compute the scaled actual reduction. */ + actred = -1.; + if (Scalar(.1) * fnorm1 < fnorm) + actred = 1. - internal::abs2(fnorm1 / fnorm); + + /* compute the scaled predicted reduction and */ + /* the scaled directional derivative. */ + wa3 = fjac.template triangularView<Upper>() * (qrfac.colsPermutation().inverse() *wa1); + temp1 = internal::abs2(wa3.stableNorm() / fnorm); + temp2 = internal::abs2(internal::sqrt(par) * pnorm / fnorm); + prered = temp1 + temp2 / Scalar(.5); + dirder = -(temp1 + temp2); + + /* compute the ratio of the actual to the predicted */ + /* reduction. */ + ratio = 0.; + if (prered != 0.) + ratio = actred / prered; + + /* update the step bound. */ + if (ratio <= Scalar(.25)) { + if (actred >= 0.) + temp = Scalar(.5); + if (actred < 0.) + temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred); + if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1)) + temp = Scalar(.1); + /* Computing MIN */ + delta = temp * (std::min)(delta, pnorm / Scalar(.1)); + par /= temp; + } else if (!(par != 0. && ratio < Scalar(.75))) { + delta = pnorm / Scalar(.5); + par = Scalar(.5) * par; + } + + /* test for successful iteration. */ + if (ratio >= Scalar(1e-4)) { + /* successful iteration. update x, fvec, and their norms. */ + x = wa2; + wa2 = diag.cwiseProduct(x); + fvec = wa4; + xnorm = wa2.stableNorm(); + fnorm = fnorm1; + ++iter; + } + + /* tests for convergence. */ + if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm) + return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall; + if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.) + return LevenbergMarquardtSpace::RelativeReductionTooSmall; + if (delta <= parameters.xtol * xnorm) + return LevenbergMarquardtSpace::RelativeErrorTooSmall; + + /* tests for termination and stringent tolerances. */ + if (nfev >= parameters.maxfev) + return LevenbergMarquardtSpace::TooManyFunctionEvaluation; + if (internal::abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.) + return LevenbergMarquardtSpace::FtolTooSmall; + if (delta <= NumTraits<Scalar>::epsilon() * xnorm) + return LevenbergMarquardtSpace::XtolTooSmall; + if (gnorm <= NumTraits<Scalar>::epsilon()) + return LevenbergMarquardtSpace::GtolTooSmall; + + } while (ratio < Scalar(1e-4)); + + return LevenbergMarquardtSpace::Running; +} + +template<typename FunctorType, typename Scalar> +LevenbergMarquardtSpace::Status +LevenbergMarquardt<FunctorType,Scalar>::lmstr1( + FVectorType &x, + const Scalar tol + ) +{ + n = x.size(); + m = functor.values(); + + /* check the input parameters for errors. */ + if (n <= 0 || m < n || tol < 0.) + return LevenbergMarquardtSpace::ImproperInputParameters; + + resetParameters(); + parameters.ftol = tol; + parameters.xtol = tol; + parameters.maxfev = 100*(n+1); + + return minimizeOptimumStorage(x); +} + +template<typename FunctorType, typename Scalar> +LevenbergMarquardtSpace::Status +LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageInit(FVectorType &x) +{ + n = x.size(); + m = functor.values(); + + wa1.resize(n); wa2.resize(n); wa3.resize(n); + wa4.resize(m); + fvec.resize(m); + // Only R is stored in fjac. Q is only used to compute 'qtf', which is + // Q.transpose()*rhs. qtf will be updated using givens rotation, + // instead of storing them in Q. + // The purpose it to only use a nxn matrix, instead of mxn here, so + // that we can handle cases where m>>n : + fjac.resize(n, n); + if (!useExternalScaling) + diag.resize(n); + assert( (!useExternalScaling || diag.size()==n) || "When useExternalScaling is set, the caller must provide a valid 'diag'"); + qtf.resize(n); + + /* Function Body */ + nfev = 0; + njev = 0; + + /* check the input parameters for errors. */ + if (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.) + return LevenbergMarquardtSpace::ImproperInputParameters; + + if (useExternalScaling) + for (Index j = 0; j < n; ++j) + if (diag[j] <= 0.) + return LevenbergMarquardtSpace::ImproperInputParameters; + + /* evaluate the function at the starting point */ + /* and calculate its norm. */ + nfev = 1; + if ( functor(x, fvec) < 0) + return LevenbergMarquardtSpace::UserAsked; + fnorm = fvec.stableNorm(); + + /* initialize levenberg-marquardt parameter and iteration counter. */ + par = 0.; + iter = 1; + + return LevenbergMarquardtSpace::NotStarted; +} + + +template<typename FunctorType, typename Scalar> +LevenbergMarquardtSpace::Status +LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorType &x) +{ + assert(x.size()==n); // check the caller is not cheating us + + Index i, j; + bool sing; + + /* compute the qr factorization of the jacobian matrix */ + /* calculated one row at a time, while simultaneously */ + /* forming (q transpose)*fvec and storing the first */ + /* n components in qtf. */ + qtf.fill(0.); + fjac.fill(0.); + Index rownb = 2; + for (i = 0; i < m; ++i) { + if (functor.df(x, wa3, rownb) < 0) return LevenbergMarquardtSpace::UserAsked; + internal::rwupdt<Scalar>(fjac, wa3, qtf, fvec[i]); + ++rownb; + } + ++njev; + + /* if the jacobian is rank deficient, call qrfac to */ + /* reorder its columns and update the components of qtf. */ + sing = false; + for (j = 0; j < n; ++j) { + if (fjac(j,j) == 0.) + sing = true; + wa2[j] = fjac.col(j).head(j).stableNorm(); + } + permutation.setIdentity(n); + if (sing) { + wa2 = fjac.colwise().blueNorm(); + // TODO We have no unit test covering this code path, do not modify + // until it is carefully tested + ColPivHouseholderQR<JacobianType> qrfac(fjac); + fjac = qrfac.matrixQR(); + wa1 = fjac.diagonal(); + fjac.diagonal() = qrfac.hCoeffs(); + permutation = qrfac.colsPermutation(); + // TODO : avoid this: + for(Index ii=0; ii< fjac.cols(); ii++) fjac.col(ii).segment(ii+1, fjac.rows()-ii-1) *= fjac(ii,ii); // rescale vectors + + for (j = 0; j < n; ++j) { + if (fjac(j,j) != 0.) { + sum = 0.; + for (i = j; i < n; ++i) + sum += fjac(i,j) * qtf[i]; + temp = -sum / fjac(j,j); + for (i = j; i < n; ++i) + qtf[i] += fjac(i,j) * temp; + } + fjac(j,j) = wa1[j]; + } + } + + /* on the first iteration and if external scaling is not used, scale according */ + /* to the norms of the columns of the initial jacobian. */ + if (iter == 1) { + if (!useExternalScaling) + for (j = 0; j < n; ++j) + diag[j] = (wa2[j]==0.)? 1. : wa2[j]; + + /* on the first iteration, calculate the norm of the scaled x */ + /* and initialize the step bound delta. */ + xnorm = diag.cwiseProduct(x).stableNorm(); + delta = parameters.factor * xnorm; + if (delta == 0.) + delta = parameters.factor; + } + + /* compute the norm of the scaled gradient. */ + gnorm = 0.; + if (fnorm != 0.) + for (j = 0; j < n; ++j) + if (wa2[permutation.indices()[j]] != 0.) + gnorm = (std::max)(gnorm, internal::abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]])); + + /* test for convergence of the gradient norm. */ + if (gnorm <= parameters.gtol) + return LevenbergMarquardtSpace::CosinusTooSmall; + + /* rescale if necessary. */ + if (!useExternalScaling) + diag = diag.cwiseMax(wa2); + + do { + + /* determine the levenberg-marquardt parameter. */ + internal::lmpar<Scalar>(fjac, permutation.indices(), diag, qtf, delta, par, wa1); + + /* store the direction p and x + p. calculate the norm of p. */ + wa1 = -wa1; + wa2 = x + wa1; + pnorm = diag.cwiseProduct(wa1).stableNorm(); + + /* on the first iteration, adjust the initial step bound. */ + if (iter == 1) + delta = (std::min)(delta,pnorm); + + /* evaluate the function at x + p and calculate its norm. */ + if ( functor(wa2, wa4) < 0) + return LevenbergMarquardtSpace::UserAsked; + ++nfev; + fnorm1 = wa4.stableNorm(); + + /* compute the scaled actual reduction. */ + actred = -1.; + if (Scalar(.1) * fnorm1 < fnorm) + actred = 1. - internal::abs2(fnorm1 / fnorm); + + /* compute the scaled predicted reduction and */ + /* the scaled directional derivative. */ + wa3 = fjac.topLeftCorner(n,n).template triangularView<Upper>() * (permutation.inverse() * wa1); + temp1 = internal::abs2(wa3.stableNorm() / fnorm); + temp2 = internal::abs2(internal::sqrt(par) * pnorm / fnorm); + prered = temp1 + temp2 / Scalar(.5); + dirder = -(temp1 + temp2); + + /* compute the ratio of the actual to the predicted */ + /* reduction. */ + ratio = 0.; + if (prered != 0.) + ratio = actred / prered; + + /* update the step bound. */ + if (ratio <= Scalar(.25)) { + if (actred >= 0.) + temp = Scalar(.5); + if (actred < 0.) + temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred); + if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1)) + temp = Scalar(.1); + /* Computing MIN */ + delta = temp * (std::min)(delta, pnorm / Scalar(.1)); + par /= temp; + } else if (!(par != 0. && ratio < Scalar(.75))) { + delta = pnorm / Scalar(.5); + par = Scalar(.5) * par; + } + + /* test for successful iteration. */ + if (ratio >= Scalar(1e-4)) { + /* successful iteration. update x, fvec, and their norms. */ + x = wa2; + wa2 = diag.cwiseProduct(x); + fvec = wa4; + xnorm = wa2.stableNorm(); + fnorm = fnorm1; + ++iter; + } + + /* tests for convergence. */ + if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm) + return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall; + if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.) + return LevenbergMarquardtSpace::RelativeReductionTooSmall; + if (delta <= parameters.xtol * xnorm) + return LevenbergMarquardtSpace::RelativeErrorTooSmall; + + /* tests for termination and stringent tolerances. */ + if (nfev >= parameters.maxfev) + return LevenbergMarquardtSpace::TooManyFunctionEvaluation; + if (internal::abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.) + return LevenbergMarquardtSpace::FtolTooSmall; + if (delta <= NumTraits<Scalar>::epsilon() * xnorm) + return LevenbergMarquardtSpace::XtolTooSmall; + if (gnorm <= NumTraits<Scalar>::epsilon()) + return LevenbergMarquardtSpace::GtolTooSmall; + + } while (ratio < Scalar(1e-4)); + + return LevenbergMarquardtSpace::Running; +} + +template<typename FunctorType, typename Scalar> +LevenbergMarquardtSpace::Status +LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorage(FVectorType &x) +{ + LevenbergMarquardtSpace::Status status = minimizeOptimumStorageInit(x); + if (status==LevenbergMarquardtSpace::ImproperInputParameters) + return status; + do { + status = minimizeOptimumStorageOneStep(x); + } while (status==LevenbergMarquardtSpace::Running); + return status; +} + +template<typename FunctorType, typename Scalar> +LevenbergMarquardtSpace::Status +LevenbergMarquardt<FunctorType,Scalar>::lmdif1( + FunctorType &functor, + FVectorType &x, + Index *nfev, + const Scalar tol + ) +{ + Index n = x.size(); + Index m = functor.values(); + + /* check the input parameters for errors. */ + if (n <= 0 || m < n || tol < 0.) + return LevenbergMarquardtSpace::ImproperInputParameters; + + NumericalDiff<FunctorType> numDiff(functor); + // embedded LevenbergMarquardt + LevenbergMarquardt<NumericalDiff<FunctorType>, Scalar > lm(numDiff); + lm.parameters.ftol = tol; + lm.parameters.xtol = tol; + lm.parameters.maxfev = 200*(n+1); + + LevenbergMarquardtSpace::Status info = LevenbergMarquardtSpace::Status(lm.minimize(x)); + if (nfev) + * nfev = lm.nfev; + return info; +} + +} // end namespace Eigen + +#endif // EIGEN_LEVENBERGMARQUARDT__H + +//vim: ai ts=4 sts=4 et sw=4 diff --git a/unsupported/Eigen/src/NonLinearOptimization/chkder.h b/unsupported/Eigen/src/NonLinearOptimization/chkder.h new file mode 100644 index 000000000..ad37c5029 --- /dev/null +++ b/unsupported/Eigen/src/NonLinearOptimization/chkder.h @@ -0,0 +1,62 @@ +#define chkder_log10e 0.43429448190325182765 +#define chkder_factor 100. + +namespace Eigen { + +namespace internal { + +template<typename Scalar> +void chkder( + const Matrix< Scalar, Dynamic, 1 > &x, + const Matrix< Scalar, Dynamic, 1 > &fvec, + const Matrix< Scalar, Dynamic, Dynamic > &fjac, + Matrix< Scalar, Dynamic, 1 > &xp, + const Matrix< Scalar, Dynamic, 1 > &fvecp, + int mode, + Matrix< Scalar, Dynamic, 1 > &err + ) +{ + typedef DenseIndex Index; + + const Scalar eps = sqrt(NumTraits<Scalar>::epsilon()); + const Scalar epsf = chkder_factor * NumTraits<Scalar>::epsilon(); + const Scalar epslog = chkder_log10e * log(eps); + Scalar temp; + + const Index m = fvec.size(), n = x.size(); + + if (mode != 2) { + /* mode = 1. */ + xp.resize(n); + for (Index j = 0; j < n; ++j) { + temp = eps * abs(x[j]); + if (temp == 0.) + temp = eps; + xp[j] = x[j] + temp; + } + } + else { + /* mode = 2. */ + err.setZero(m); + for (Index j = 0; j < n; ++j) { + temp = abs(x[j]); + if (temp == 0.) + temp = 1.; + err += temp * fjac.col(j); + } + for (Index i = 0; i < m; ++i) { + temp = 1.; + if (fvec[i] != 0. && fvecp[i] != 0. && abs(fvecp[i] - fvec[i]) >= epsf * abs(fvec[i])) + temp = eps * abs((fvecp[i] - fvec[i]) / eps - err[i]) / (abs(fvec[i]) + abs(fvecp[i])); + err[i] = 1.; + if (temp > NumTraits<Scalar>::epsilon() && temp < eps) + err[i] = (chkder_log10e * log(temp) - epslog) / epslog; + if (temp >= eps) + err[i] = 0.; + } + } +} + +} // end namespace internal + +} // end namespace Eigen diff --git a/unsupported/Eigen/src/NonLinearOptimization/covar.h b/unsupported/Eigen/src/NonLinearOptimization/covar.h new file mode 100644 index 000000000..c73a09645 --- /dev/null +++ b/unsupported/Eigen/src/NonLinearOptimization/covar.h @@ -0,0 +1,69 @@ +namespace Eigen { + +namespace internal { + +template <typename Scalar> +void covar( + Matrix< Scalar, Dynamic, Dynamic > &r, + const VectorXi &ipvt, + Scalar tol = sqrt(NumTraits<Scalar>::epsilon()) ) +{ + typedef DenseIndex Index; + + /* Local variables */ + Index i, j, k, l, ii, jj; + bool sing; + Scalar temp; + + /* Function Body */ + const Index n = r.cols(); + const Scalar tolr = tol * abs(r(0,0)); + Matrix< Scalar, Dynamic, 1 > wa(n); + assert(ipvt.size()==n); + + /* form the inverse of r in the full upper triangle of r. */ + l = -1; + for (k = 0; k < n; ++k) + if (abs(r(k,k)) > tolr) { + r(k,k) = 1. / r(k,k); + for (j = 0; j <= k-1; ++j) { + temp = r(k,k) * r(j,k); + r(j,k) = 0.; + r.col(k).head(j+1) -= r.col(j).head(j+1) * temp; + } + l = k; + } + + /* form the full upper triangle of the inverse of (r transpose)*r */ + /* in the full upper triangle of r. */ + for (k = 0; k <= l; ++k) { + for (j = 0; j <= k-1; ++j) + r.col(j).head(j+1) += r.col(k).head(j+1) * r(j,k); + r.col(k).head(k+1) *= r(k,k); + } + + /* form the full lower triangle of the covariance matrix */ + /* in the strict lower triangle of r and in wa. */ + for (j = 0; j < n; ++j) { + jj = ipvt[j]; + sing = j > l; + for (i = 0; i <= j; ++i) { + if (sing) + r(i,j) = 0.; + ii = ipvt[i]; + if (ii > jj) + r(ii,jj) = r(i,j); + if (ii < jj) + r(jj,ii) = r(i,j); + } + wa[jj] = r(j,j); + } + + /* symmetrize the covariance matrix in r. */ + r.topLeftCorner(n,n).template triangularView<StrictlyUpper>() = r.topLeftCorner(n,n).transpose(); + r.diagonal() = wa; +} + +} // end namespace internal + +} // end namespace Eigen diff --git a/unsupported/Eigen/src/NonLinearOptimization/dogleg.h b/unsupported/Eigen/src/NonLinearOptimization/dogleg.h new file mode 100644 index 000000000..4fbc98bfc --- /dev/null +++ b/unsupported/Eigen/src/NonLinearOptimization/dogleg.h @@ -0,0 +1,104 @@ +namespace Eigen { + +namespace internal { + +template <typename Scalar> +void dogleg( + const Matrix< Scalar, Dynamic, Dynamic > &qrfac, + const Matrix< Scalar, Dynamic, 1 > &diag, + const Matrix< Scalar, Dynamic, 1 > &qtb, + Scalar delta, + Matrix< Scalar, Dynamic, 1 > &x) +{ + typedef DenseIndex Index; + + /* Local variables */ + Index i, j; + Scalar sum, temp, alpha, bnorm; + Scalar gnorm, qnorm; + Scalar sgnorm; + + /* Function Body */ + const Scalar epsmch = NumTraits<Scalar>::epsilon(); + const Index n = qrfac.cols(); + assert(n==qtb.size()); + assert(n==x.size()); + assert(n==diag.size()); + Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n); + + /* first, calculate the gauss-newton direction. */ + for (j = n-1; j >=0; --j) { + temp = qrfac(j,j); + if (temp == 0.) { + temp = epsmch * qrfac.col(j).head(j+1).maxCoeff(); + if (temp == 0.) + temp = epsmch; + } + if (j==n-1) + x[j] = qtb[j] / temp; + else + x[j] = (qtb[j] - qrfac.row(j).tail(n-j-1).dot(x.tail(n-j-1))) / temp; + } + + /* test whether the gauss-newton direction is acceptable. */ + qnorm = diag.cwiseProduct(x).stableNorm(); + if (qnorm <= delta) + return; + + // TODO : this path is not tested by Eigen unit tests + + /* the gauss-newton direction is not acceptable. */ + /* next, calculate the scaled gradient direction. */ + + wa1.fill(0.); + for (j = 0; j < n; ++j) { + wa1.tail(n-j) += qrfac.row(j).tail(n-j) * qtb[j]; + wa1[j] /= diag[j]; + } + + /* calculate the norm of the scaled gradient and test for */ + /* the special case in which the scaled gradient is zero. */ + gnorm = wa1.stableNorm(); + sgnorm = 0.; + alpha = delta / qnorm; + if (gnorm == 0.) + goto algo_end; + + /* calculate the point along the scaled gradient */ + /* at which the quadratic is minimized. */ + wa1.array() /= (diag*gnorm).array(); + // TODO : once unit tests cover this part,: + // wa2 = qrfac.template triangularView<Upper>() * wa1; + for (j = 0; j < n; ++j) { + sum = 0.; + for (i = j; i < n; ++i) { + sum += qrfac(j,i) * wa1[i]; + } + wa2[j] = sum; + } + temp = wa2.stableNorm(); + sgnorm = gnorm / temp / temp; + + /* test whether the scaled gradient direction is acceptable. */ + alpha = 0.; + if (sgnorm >= delta) + goto algo_end; + + /* the scaled gradient direction is not acceptable. */ + /* finally, calculate the point along the dogleg */ + /* at which the quadratic is minimized. */ + bnorm = qtb.stableNorm(); + temp = bnorm / gnorm * (bnorm / qnorm) * (sgnorm / delta); + temp = temp - delta / qnorm * abs2(sgnorm / delta) + sqrt(abs2(temp - delta / qnorm) + (1.-abs2(delta / qnorm)) * (1.-abs2(sgnorm / delta))); + alpha = delta / qnorm * (1. - abs2(sgnorm / delta)) / temp; +algo_end: + + /* form appropriate convex combination of the gauss-newton */ + /* direction and the scaled gradient direction. */ + temp = (1.-alpha) * (std::min)(sgnorm,delta); + x = temp * wa1 + alpha * x; +} + +} // end namespace internal + +} // end namespace Eigen diff --git a/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h b/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h new file mode 100644 index 000000000..1cabe69ae --- /dev/null +++ b/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h @@ -0,0 +1,76 @@ +namespace Eigen { + +namespace internal { + +template<typename FunctorType, typename Scalar> +DenseIndex fdjac1( + const FunctorType &Functor, + Matrix< Scalar, Dynamic, 1 > &x, + Matrix< Scalar, Dynamic, 1 > &fvec, + Matrix< Scalar, Dynamic, Dynamic > &fjac, + DenseIndex ml, DenseIndex mu, + Scalar epsfcn) +{ + typedef DenseIndex Index; + + /* Local variables */ + Scalar h; + Index j, k; + Scalar eps, temp; + Index msum; + int iflag; + Index start, length; + + /* Function Body */ + const Scalar epsmch = NumTraits<Scalar>::epsilon(); + const Index n = x.size(); + assert(fvec.size()==n); + Matrix< Scalar, Dynamic, 1 > wa1(n); + Matrix< Scalar, Dynamic, 1 > wa2(n); + + eps = sqrt((std::max)(epsfcn,epsmch)); + msum = ml + mu + 1; + if (msum >= n) { + /* computation of dense approximate jacobian. */ + for (j = 0; j < n; ++j) { + temp = x[j]; + h = eps * abs(temp); + if (h == 0.) + h = eps; + x[j] = temp + h; + iflag = Functor(x, wa1); + if (iflag < 0) + return iflag; + x[j] = temp; + fjac.col(j) = (wa1-fvec)/h; + } + + }else { + /* computation of banded approximate jacobian. */ + for (k = 0; k < msum; ++k) { + for (j = k; (msum<0) ? (j>n): (j<n); j += msum) { + wa2[j] = x[j]; + h = eps * abs(wa2[j]); + if (h == 0.) h = eps; + x[j] = wa2[j] + h; + } + iflag = Functor(x, wa1); + if (iflag < 0) + return iflag; + for (j = k; (msum<0) ? (j>n): (j<n); j += msum) { + x[j] = wa2[j]; + h = eps * abs(wa2[j]); + if (h == 0.) h = eps; + fjac.col(j).setZero(); + start = std::max<Index>(0,j-mu); + length = (std::min)(n-1, j+ml) - start + 1; + fjac.col(j).segment(start, length) = ( wa1.segment(start, length)-fvec.segment(start, length))/h; + } + } + } + return 0; +} + +} // end namespace internal + +} // end namespace Eigen diff --git a/unsupported/Eigen/src/NonLinearOptimization/lmpar.h b/unsupported/Eigen/src/NonLinearOptimization/lmpar.h new file mode 100644 index 000000000..cc1ca530f --- /dev/null +++ b/unsupported/Eigen/src/NonLinearOptimization/lmpar.h @@ -0,0 +1,294 @@ +namespace Eigen { + +namespace internal { + +template <typename Scalar> +void lmpar( + Matrix< Scalar, Dynamic, Dynamic > &r, + const VectorXi &ipvt, + const Matrix< Scalar, Dynamic, 1 > &diag, + const Matrix< Scalar, Dynamic, 1 > &qtb, + Scalar delta, + Scalar &par, + Matrix< Scalar, Dynamic, 1 > &x) +{ + typedef DenseIndex Index; + + /* Local variables */ + Index i, j, l; + Scalar fp; + Scalar parc, parl; + Index iter; + Scalar temp, paru; + Scalar gnorm; + Scalar dxnorm; + + + /* Function Body */ + const Scalar dwarf = std::numeric_limits<Scalar>::min(); + const Index n = r.cols(); + assert(n==diag.size()); + assert(n==qtb.size()); + assert(n==x.size()); + + Matrix< Scalar, Dynamic, 1 > wa1, wa2; + + /* compute and store in x the gauss-newton direction. if the */ + /* jacobian is rank-deficient, obtain a least squares solution. */ + Index nsing = n-1; + wa1 = qtb; + for (j = 0; j < n; ++j) { + if (r(j,j) == 0. && nsing == n-1) + nsing = j - 1; + if (nsing < n-1) + wa1[j] = 0.; + } + for (j = nsing; j>=0; --j) { + wa1[j] /= r(j,j); + temp = wa1[j]; + for (i = 0; i < j ; ++i) + wa1[i] -= r(i,j) * temp; + } + + for (j = 0; j < n; ++j) + x[ipvt[j]] = wa1[j]; + + /* initialize the iteration counter. */ + /* evaluate the function at the origin, and test */ + /* for acceptance of the gauss-newton direction. */ + iter = 0; + wa2 = diag.cwiseProduct(x); + dxnorm = wa2.blueNorm(); + fp = dxnorm - delta; + if (fp <= Scalar(0.1) * delta) { + par = 0; + return; + } + + /* if the jacobian is not rank deficient, the newton */ + /* step provides a lower bound, parl, for the zero of */ + /* the function. otherwise set this bound to zero. */ + parl = 0.; + if (nsing >= n-1) { + for (j = 0; j < n; ++j) { + l = ipvt[j]; + wa1[j] = diag[l] * (wa2[l] / dxnorm); + } + // it's actually a triangularView.solveInplace(), though in a weird + // way: + for (j = 0; j < n; ++j) { + Scalar sum = 0.; + for (i = 0; i < j; ++i) + sum += r(i,j) * wa1[i]; + wa1[j] = (wa1[j] - sum) / r(j,j); + } + temp = wa1.blueNorm(); + parl = fp / delta / temp / temp; + } + + /* calculate an upper bound, paru, for the zero of the function. */ + for (j = 0; j < n; ++j) + wa1[j] = r.col(j).head(j+1).dot(qtb.head(j+1)) / diag[ipvt[j]]; + + gnorm = wa1.stableNorm(); + paru = gnorm / delta; + if (paru == 0.) + paru = dwarf / (std::min)(delta,Scalar(0.1)); + + /* if the input par lies outside of the interval (parl,paru), */ + /* set par to the closer endpoint. */ + par = (std::max)(par,parl); + par = (std::min)(par,paru); + if (par == 0.) + par = gnorm / dxnorm; + + /* beginning of an iteration. */ + while (true) { + ++iter; + + /* evaluate the function at the current value of par. */ + if (par == 0.) + par = (std::max)(dwarf,Scalar(.001) * paru); /* Computing MAX */ + wa1 = sqrt(par)* diag; + + Matrix< Scalar, Dynamic, 1 > sdiag(n); + qrsolv<Scalar>(r, ipvt, wa1, qtb, x, sdiag); + + wa2 = diag.cwiseProduct(x); + dxnorm = wa2.blueNorm(); + temp = fp; + fp = dxnorm - delta; + + /* if the function is small enough, accept the current value */ + /* of par. also test for the exceptional cases where parl */ + /* is zero or the number of iterations has reached 10. */ + if (abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10) + break; + + /* compute the newton correction. */ + for (j = 0; j < n; ++j) { + l = ipvt[j]; + wa1[j] = diag[l] * (wa2[l] / dxnorm); + } + for (j = 0; j < n; ++j) { + wa1[j] /= sdiag[j]; + temp = wa1[j]; + for (i = j+1; i < n; ++i) + wa1[i] -= r(i,j) * temp; + } + temp = wa1.blueNorm(); + parc = fp / delta / temp / temp; + + /* depending on the sign of the function, update parl or paru. */ + if (fp > 0.) + parl = (std::max)(parl,par); + if (fp < 0.) + paru = (std::min)(paru,par); + + /* compute an improved estimate for par. */ + /* Computing MAX */ + par = (std::max)(parl,par+parc); + + /* end of an iteration. */ + } + + /* termination. */ + if (iter == 0) + par = 0.; + return; +} + +template <typename Scalar> +void lmpar2( + const ColPivHouseholderQR<Matrix< Scalar, Dynamic, Dynamic> > &qr, + const Matrix< Scalar, Dynamic, 1 > &diag, + const Matrix< Scalar, Dynamic, 1 > &qtb, + Scalar delta, + Scalar &par, + Matrix< Scalar, Dynamic, 1 > &x) + +{ + typedef DenseIndex Index; + + /* Local variables */ + Index j; + Scalar fp; + Scalar parc, parl; + Index iter; + Scalar temp, paru; + Scalar gnorm; + Scalar dxnorm; + + + /* Function Body */ + const Scalar dwarf = std::numeric_limits<Scalar>::min(); + const Index n = qr.matrixQR().cols(); + assert(n==diag.size()); + assert(n==qtb.size()); + + Matrix< Scalar, Dynamic, 1 > wa1, wa2; + + /* compute and store in x the gauss-newton direction. if the */ + /* jacobian is rank-deficient, obtain a least squares solution. */ + +// const Index rank = qr.nonzeroPivots(); // exactly double(0.) + const Index rank = qr.rank(); // use a threshold + wa1 = qtb; + wa1.tail(n-rank).setZero(); + qr.matrixQR().topLeftCorner(rank, rank).template triangularView<Upper>().solveInPlace(wa1.head(rank)); + + x = qr.colsPermutation()*wa1; + + /* initialize the iteration counter. */ + /* evaluate the function at the origin, and test */ + /* for acceptance of the gauss-newton direction. */ + iter = 0; + wa2 = diag.cwiseProduct(x); + dxnorm = wa2.blueNorm(); + fp = dxnorm - delta; + if (fp <= Scalar(0.1) * delta) { + par = 0; + return; + } + + /* if the jacobian is not rank deficient, the newton */ + /* step provides a lower bound, parl, for the zero of */ + /* the function. otherwise set this bound to zero. */ + parl = 0.; + if (rank==n) { + wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2)/dxnorm; + qr.matrixQR().topLeftCorner(n, n).transpose().template triangularView<Lower>().solveInPlace(wa1); + temp = wa1.blueNorm(); + parl = fp / delta / temp / temp; + } + + /* calculate an upper bound, paru, for the zero of the function. */ + for (j = 0; j < n; ++j) + wa1[j] = qr.matrixQR().col(j).head(j+1).dot(qtb.head(j+1)) / diag[qr.colsPermutation().indices()(j)]; + + gnorm = wa1.stableNorm(); + paru = gnorm / delta; + if (paru == 0.) + paru = dwarf / (std::min)(delta,Scalar(0.1)); + + /* if the input par lies outside of the interval (parl,paru), */ + /* set par to the closer endpoint. */ + par = (std::max)(par,parl); + par = (std::min)(par,paru); + if (par == 0.) + par = gnorm / dxnorm; + + /* beginning of an iteration. */ + Matrix< Scalar, Dynamic, Dynamic > s = qr.matrixQR(); + while (true) { + ++iter; + + /* evaluate the function at the current value of par. */ + if (par == 0.) + par = (std::max)(dwarf,Scalar(.001) * paru); /* Computing MAX */ + wa1 = sqrt(par)* diag; + + Matrix< Scalar, Dynamic, 1 > sdiag(n); + qrsolv<Scalar>(s, qr.colsPermutation().indices(), wa1, qtb, x, sdiag); + + wa2 = diag.cwiseProduct(x); + dxnorm = wa2.blueNorm(); + temp = fp; + fp = dxnorm - delta; + + /* if the function is small enough, accept the current value */ + /* of par. also test for the exceptional cases where parl */ + /* is zero or the number of iterations has reached 10. */ + if (abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10) + break; + + /* compute the newton correction. */ + wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2/dxnorm); + // we could almost use this here, but the diagonal is outside qr, in sdiag[] + // qr.matrixQR().topLeftCorner(n, n).transpose().template triangularView<Lower>().solveInPlace(wa1); + for (j = 0; j < n; ++j) { + wa1[j] /= sdiag[j]; + temp = wa1[j]; + for (Index i = j+1; i < n; ++i) + wa1[i] -= s(i,j) * temp; + } + temp = wa1.blueNorm(); + parc = fp / delta / temp / temp; + + /* depending on the sign of the function, update parl or paru. */ + if (fp > 0.) + parl = (std::max)(parl,par); + if (fp < 0.) + paru = (std::min)(paru,par); + + /* compute an improved estimate for par. */ + par = (std::max)(parl,par+parc); + } + if (iter == 0) + par = 0.; + return; +} + +} // end namespace internal + +} // end namespace Eigen diff --git a/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h b/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h new file mode 100644 index 000000000..feafd62a8 --- /dev/null +++ b/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h @@ -0,0 +1,91 @@ +namespace Eigen { + +namespace internal { + +// TODO : once qrsolv2 is removed, use ColPivHouseholderQR or PermutationMatrix instead of ipvt +template <typename Scalar> +void qrsolv( + Matrix< Scalar, Dynamic, Dynamic > &s, + // TODO : use a PermutationMatrix once lmpar is no more: + const VectorXi &ipvt, + const Matrix< Scalar, Dynamic, 1 > &diag, + const Matrix< Scalar, Dynamic, 1 > &qtb, + Matrix< Scalar, Dynamic, 1 > &x, + Matrix< Scalar, Dynamic, 1 > &sdiag) + +{ + typedef DenseIndex Index; + + /* Local variables */ + Index i, j, k, l; + Scalar temp; + Index n = s.cols(); + Matrix< Scalar, Dynamic, 1 > wa(n); + JacobiRotation<Scalar> givens; + + /* Function Body */ + // the following will only change the lower triangular part of s, including + // the diagonal, though the diagonal is restored afterward + + /* copy r and (q transpose)*b to preserve input and initialize s. */ + /* in particular, save the diagonal elements of r in x. */ + x = s.diagonal(); + wa = qtb; + + s.topLeftCorner(n,n).template triangularView<StrictlyLower>() = s.topLeftCorner(n,n).transpose(); + + /* eliminate the diagonal matrix d using a givens rotation. */ + for (j = 0; j < n; ++j) { + + /* prepare the row of d to be eliminated, locating the */ + /* diagonal element using p from the qr factorization. */ + l = ipvt[j]; + if (diag[l] == 0.) + break; + sdiag.tail(n-j).setZero(); + sdiag[j] = diag[l]; + + /* the transformations to eliminate the row of d */ + /* modify only a single element of (q transpose)*b */ + /* beyond the first n, which is initially zero. */ + Scalar qtbpj = 0.; + for (k = j; k < n; ++k) { + /* determine a givens rotation which eliminates the */ + /* appropriate element in the current row of d. */ + givens.makeGivens(-s(k,k), sdiag[k]); + + /* compute the modified diagonal element of r and */ + /* the modified element of ((q transpose)*b,0). */ + s(k,k) = givens.c() * s(k,k) + givens.s() * sdiag[k]; + temp = givens.c() * wa[k] + givens.s() * qtbpj; + qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj; + wa[k] = temp; + + /* accumulate the tranformation in the row of s. */ + for (i = k+1; i<n; ++i) { + temp = givens.c() * s(i,k) + givens.s() * sdiag[i]; + sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i]; + s(i,k) = temp; + } + } + } + + /* solve the triangular system for z. if the system is */ + /* singular, then obtain a least squares solution. */ + Index nsing; + for(nsing=0; nsing<n && sdiag[nsing]!=0; nsing++) {} + + wa.tail(n-nsing).setZero(); + s.topLeftCorner(nsing, nsing).transpose().template triangularView<Upper>().solveInPlace(wa.head(nsing)); + + // restore + sdiag = s.diagonal(); + s.diagonal() = x; + + /* permute the components of z back to components of x. */ + for (j = 0; j < n; ++j) x[ipvt[j]] = wa[j]; +} + +} // end namespace internal + +} // end namespace Eigen diff --git a/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h b/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h new file mode 100644 index 000000000..36ff700e9 --- /dev/null +++ b/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h @@ -0,0 +1,30 @@ +namespace Eigen { + +namespace internal { + +// TODO : move this to GivensQR once there's such a thing in Eigen + +template <typename Scalar> +void r1mpyq(DenseIndex m, DenseIndex n, Scalar *a, const std::vector<JacobiRotation<Scalar> > &v_givens, const std::vector<JacobiRotation<Scalar> > &w_givens) +{ + typedef DenseIndex Index; + + /* apply the first set of givens rotations to a. */ + for (Index j = n-2; j>=0; --j) + for (Index i = 0; i<m; ++i) { + Scalar temp = v_givens[j].c() * a[i+m*j] - v_givens[j].s() * a[i+m*(n-1)]; + a[i+m*(n-1)] = v_givens[j].s() * a[i+m*j] + v_givens[j].c() * a[i+m*(n-1)]; + a[i+m*j] = temp; + } + /* apply the second set of givens rotations to a. */ + for (Index j = 0; j<n-1; ++j) + for (Index i = 0; i<m; ++i) { + Scalar temp = w_givens[j].c() * a[i+m*j] + w_givens[j].s() * a[i+m*(n-1)]; + a[i+m*(n-1)] = -w_givens[j].s() * a[i+m*j] + w_givens[j].c() * a[i+m*(n-1)]; + a[i+m*j] = temp; + } +} + +} // end namespace internal + +} // end namespace Eigen diff --git a/unsupported/Eigen/src/NonLinearOptimization/r1updt.h b/unsupported/Eigen/src/NonLinearOptimization/r1updt.h new file mode 100644 index 000000000..55fae5ae8 --- /dev/null +++ b/unsupported/Eigen/src/NonLinearOptimization/r1updt.h @@ -0,0 +1,99 @@ +namespace Eigen { + +namespace internal { + +template <typename Scalar> +void r1updt( + Matrix< Scalar, Dynamic, Dynamic > &s, + const Matrix< Scalar, Dynamic, 1> &u, + std::vector<JacobiRotation<Scalar> > &v_givens, + std::vector<JacobiRotation<Scalar> > &w_givens, + Matrix< Scalar, Dynamic, 1> &v, + Matrix< Scalar, Dynamic, 1> &w, + bool *sing) +{ + typedef DenseIndex Index; + const JacobiRotation<Scalar> IdentityRotation = JacobiRotation<Scalar>(1,0); + + /* Local variables */ + const Index m = s.rows(); + const Index n = s.cols(); + Index i, j=1; + Scalar temp; + JacobiRotation<Scalar> givens; + + // r1updt had a broader usecase, but we dont use it here. And, more + // importantly, we can not test it. + assert(m==n); + assert(u.size()==m); + assert(v.size()==n); + assert(w.size()==n); + + /* move the nontrivial part of the last column of s into w. */ + w[n-1] = s(n-1,n-1); + + /* rotate the vector v into a multiple of the n-th unit vector */ + /* in such a way that a spike is introduced into w. */ + for (j=n-2; j>=0; --j) { + w[j] = 0.; + if (v[j] != 0.) { + /* determine a givens rotation which eliminates the */ + /* j-th element of v. */ + givens.makeGivens(-v[n-1], v[j]); + + /* apply the transformation to v and store the information */ + /* necessary to recover the givens rotation. */ + v[n-1] = givens.s() * v[j] + givens.c() * v[n-1]; + v_givens[j] = givens; + + /* apply the transformation to s and extend the spike in w. */ + for (i = j; i < m; ++i) { + temp = givens.c() * s(j,i) - givens.s() * w[i]; + w[i] = givens.s() * s(j,i) + givens.c() * w[i]; + s(j,i) = temp; + } + } else + v_givens[j] = IdentityRotation; + } + + /* add the spike from the rank 1 update to w. */ + w += v[n-1] * u; + + /* eliminate the spike. */ + *sing = false; + for (j = 0; j < n-1; ++j) { + if (w[j] != 0.) { + /* determine a givens rotation which eliminates the */ + /* j-th element of the spike. */ + givens.makeGivens(-s(j,j), w[j]); + + /* apply the transformation to s and reduce the spike in w. */ + for (i = j; i < m; ++i) { + temp = givens.c() * s(j,i) + givens.s() * w[i]; + w[i] = -givens.s() * s(j,i) + givens.c() * w[i]; + s(j,i) = temp; + } + + /* store the information necessary to recover the */ + /* givens rotation. */ + w_givens[j] = givens; + } else + v_givens[j] = IdentityRotation; + + /* test for zero diagonal elements in the output s. */ + if (s(j,j) == 0.) { + *sing = true; + } + } + /* move w back into the last column of the output s. */ + s(n-1,n-1) = w[n-1]; + + if (s(j,j) == 0.) { + *sing = true; + } + return; +} + +} // end namespace internal + +} // end namespace Eigen diff --git a/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h b/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h new file mode 100644 index 000000000..9ce079e22 --- /dev/null +++ b/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h @@ -0,0 +1,49 @@ +namespace Eigen { + +namespace internal { + +template <typename Scalar> +void rwupdt( + Matrix< Scalar, Dynamic, Dynamic > &r, + const Matrix< Scalar, Dynamic, 1> &w, + Matrix< Scalar, Dynamic, 1> &b, + Scalar alpha) +{ + typedef DenseIndex Index; + + const Index n = r.cols(); + assert(r.rows()>=n); + std::vector<JacobiRotation<Scalar> > givens(n); + + /* Local variables */ + Scalar temp, rowj; + + /* Function Body */ + for (Index j = 0; j < n; ++j) { + rowj = w[j]; + + /* apply the previous transformations to */ + /* r(i,j), i=0,1,...,j-1, and to w(j). */ + for (Index i = 0; i < j; ++i) { + temp = givens[i].c() * r(i,j) + givens[i].s() * rowj; + rowj = -givens[i].s() * r(i,j) + givens[i].c() * rowj; + r(i,j) = temp; + } + + /* determine a givens rotation which eliminates w(j). */ + givens[j].makeGivens(-r(j,j), rowj); + + if (rowj == 0.) + continue; // givens[j] is identity + + /* apply the current transformation to r(j,j), b(j), and alpha. */ + r(j,j) = givens[j].c() * r(j,j) + givens[j].s() * rowj; + temp = givens[j].c() * b[j] + givens[j].s() * alpha; + alpha = -givens[j].s() * b[j] + givens[j].c() * alpha; + b[j] = temp; + } +} + +} // end namespace internal + +} // end namespace Eigen diff --git a/unsupported/Eigen/src/NumericalDiff/CMakeLists.txt b/unsupported/Eigen/src/NumericalDiff/CMakeLists.txt new file mode 100644 index 000000000..1199aca2f --- /dev/null +++ b/unsupported/Eigen/src/NumericalDiff/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_NumericalDiff_SRCS "*.h") + +INSTALL(FILES + ${Eigen_NumericalDiff_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/NumericalDiff COMPONENT Devel + ) diff --git a/unsupported/Eigen/src/NumericalDiff/NumericalDiff.h b/unsupported/Eigen/src/NumericalDiff/NumericalDiff.h new file mode 100644 index 000000000..d848cb407 --- /dev/null +++ b/unsupported/Eigen/src/NumericalDiff/NumericalDiff.h @@ -0,0 +1,128 @@ +// -*- coding: utf-8 +// vim: set fileencoding=utf-8 + +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_NUMERICAL_DIFF_H +#define EIGEN_NUMERICAL_DIFF_H + +namespace Eigen { + +enum NumericalDiffMode { + Forward, + Central +}; + + +/** + * This class allows you to add a method df() to your functor, which will + * use numerical differentiation to compute an approximate of the + * derivative for the functor. Of course, if you have an analytical form + * for the derivative, you should rather implement df() by yourself. + * + * More information on + * http://en.wikipedia.org/wiki/Numerical_differentiation + * + * Currently only "Forward" and "Central" scheme are implemented. + */ +template<typename _Functor, NumericalDiffMode mode=Forward> +class NumericalDiff : public _Functor +{ +public: + typedef _Functor Functor; + typedef typename Functor::Scalar Scalar; + typedef typename Functor::InputType InputType; + typedef typename Functor::ValueType ValueType; + typedef typename Functor::JacobianType JacobianType; + + NumericalDiff(Scalar _epsfcn=0.) : Functor(), epsfcn(_epsfcn) {} + NumericalDiff(const Functor& f, Scalar _epsfcn=0.) : Functor(f), epsfcn(_epsfcn) {} + + // forward constructors + template<typename T0> + NumericalDiff(const T0& a0) : Functor(a0), epsfcn(0) {} + template<typename T0, typename T1> + NumericalDiff(const T0& a0, const T1& a1) : Functor(a0, a1), epsfcn(0) {} + template<typename T0, typename T1, typename T2> + NumericalDiff(const T0& a0, const T1& a1, const T2& a2) : Functor(a0, a1, a2), epsfcn(0) {} + + enum { + InputsAtCompileTime = Functor::InputsAtCompileTime, + ValuesAtCompileTime = Functor::ValuesAtCompileTime + }; + + /** + * return the number of evaluation of functor + */ + int df(const InputType& _x, JacobianType &jac) const + { + /* Local variables */ + Scalar h; + int nfev=0; + const typename InputType::Index n = _x.size(); + const Scalar eps = internal::sqrt(((std::max)(epsfcn,NumTraits<Scalar>::epsilon() ))); + ValueType val1, val2; + InputType x = _x; + // TODO : we should do this only if the size is not already known + val1.resize(Functor::values()); + val2.resize(Functor::values()); + + // initialization + switch(mode) { + case Forward: + // compute f(x) + Functor::operator()(x, val1); nfev++; + break; + case Central: + // do nothing + break; + default: + assert(false); + }; + + // Function Body + for (int j = 0; j < n; ++j) { + h = eps * internal::abs(x[j]); + if (h == 0.) { + h = eps; + } + switch(mode) { + case Forward: + x[j] += h; + Functor::operator()(x, val2); + nfev++; + x[j] = _x[j]; + jac.col(j) = (val2-val1)/h; + break; + case Central: + x[j] += h; + Functor::operator()(x, val2); nfev++; + x[j] -= 2*h; + Functor::operator()(x, val1); nfev++; + x[j] = _x[j]; + jac.col(j) = (val2-val1)/(2*h); + break; + default: + assert(false); + }; + } + return nfev; + } +private: + Scalar epsfcn; + + NumericalDiff& operator=(const NumericalDiff&); +}; + +} // end namespace Eigen + +//vim: ai ts=4 sts=4 et sw=4 +#endif // EIGEN_NUMERICAL_DIFF_H + diff --git a/unsupported/Eigen/src/Polynomials/CMakeLists.txt b/unsupported/Eigen/src/Polynomials/CMakeLists.txt new file mode 100644 index 000000000..51f13f3cb --- /dev/null +++ b/unsupported/Eigen/src/Polynomials/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_Polynomials_SRCS "*.h") + +INSTALL(FILES + ${Eigen_Polynomials_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/Polynomials COMPONENT Devel + ) diff --git a/unsupported/Eigen/src/Polynomials/Companion.h b/unsupported/Eigen/src/Polynomials/Companion.h new file mode 100644 index 000000000..4badd9d58 --- /dev/null +++ b/unsupported/Eigen/src/Polynomials/Companion.h @@ -0,0 +1,275 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_COMPANION_H +#define EIGEN_COMPANION_H + +// This file requires the user to include +// * Eigen/Core +// * Eigen/src/PolynomialSolver.h + +namespace Eigen { + +namespace internal { + +#ifndef EIGEN_PARSED_BY_DOXYGEN + +template <typename T> +T radix(){ return 2; } + +template <typename T> +T radix2(){ return radix<T>()*radix<T>(); } + +template<int Size> +struct decrement_if_fixed_size +{ + enum { + ret = (Size == Dynamic) ? Dynamic : Size-1 }; +}; + +#endif + +template< typename _Scalar, int _Deg > +class companion +{ + public: + EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Deg==Dynamic ? Dynamic : _Deg) + + enum { + Deg = _Deg, + Deg_1=decrement_if_fixed_size<Deg>::ret + }; + + typedef _Scalar Scalar; + typedef typename NumTraits<Scalar>::Real RealScalar; + typedef Matrix<Scalar, Deg, 1> RightColumn; + //typedef DiagonalMatrix< Scalar, Deg_1, Deg_1 > BottomLeftDiagonal; + typedef Matrix<Scalar, Deg_1, 1> BottomLeftDiagonal; + + typedef Matrix<Scalar, Deg, Deg> DenseCompanionMatrixType; + typedef Matrix< Scalar, _Deg, Deg_1 > LeftBlock; + typedef Matrix< Scalar, Deg_1, Deg_1 > BottomLeftBlock; + typedef Matrix< Scalar, 1, Deg_1 > LeftBlockFirstRow; + + typedef DenseIndex Index; + + public: + EIGEN_STRONG_INLINE const _Scalar operator()(Index row, Index col ) const + { + if( m_bl_diag.rows() > col ) + { + if( 0 < row ){ return m_bl_diag[col]; } + else{ return 0; } + } + else{ return m_monic[row]; } + } + + public: + template<typename VectorType> + void setPolynomial( const VectorType& poly ) + { + const Index deg = poly.size()-1; + m_monic = -1/poly[deg] * poly.head(deg); + //m_bl_diag.setIdentity( deg-1 ); + m_bl_diag.setOnes(deg-1); + } + + template<typename VectorType> + companion( const VectorType& poly ){ + setPolynomial( poly ); } + + public: + DenseCompanionMatrixType denseMatrix() const + { + const Index deg = m_monic.size(); + const Index deg_1 = deg-1; + DenseCompanionMatrixType companion(deg,deg); + companion << + ( LeftBlock(deg,deg_1) + << LeftBlockFirstRow::Zero(1,deg_1), + BottomLeftBlock::Identity(deg-1,deg-1)*m_bl_diag.asDiagonal() ).finished() + , m_monic; + return companion; + } + + + + protected: + /** Helper function for the balancing algorithm. + * \returns true if the row and the column, having colNorm and rowNorm + * as norms, are balanced, false otherwise. + * colB and rowB are repectively the multipliers for + * the column and the row in order to balance them. + * */ + bool balanced( Scalar colNorm, Scalar rowNorm, + bool& isBalanced, Scalar& colB, Scalar& rowB ); + + /** Helper function for the balancing algorithm. + * \returns true if the row and the column, having colNorm and rowNorm + * as norms, are balanced, false otherwise. + * colB and rowB are repectively the multipliers for + * the column and the row in order to balance them. + * */ + bool balancedR( Scalar colNorm, Scalar rowNorm, + bool& isBalanced, Scalar& colB, Scalar& rowB ); + + public: + /** + * Balancing algorithm from B. N. PARLETT and C. REINSCH (1969) + * "Balancing a matrix for calculation of eigenvalues and eigenvectors" + * adapted to the case of companion matrices. + * A matrix with non zero row and non zero column is balanced + * for a certain norm if the i-th row and the i-th column + * have same norm for all i. + */ + void balance(); + + protected: + RightColumn m_monic; + BottomLeftDiagonal m_bl_diag; +}; + + + +template< typename _Scalar, int _Deg > +inline +bool companion<_Scalar,_Deg>::balanced( Scalar colNorm, Scalar rowNorm, + bool& isBalanced, Scalar& colB, Scalar& rowB ) +{ + if( Scalar(0) == colNorm || Scalar(0) == rowNorm ){ return true; } + else + { + //To find the balancing coefficients, if the radix is 2, + //one finds \f$ \sigma \f$ such that + // \f$ 2^{2\sigma-1} < rowNorm / colNorm \le 2^{2\sigma+1} \f$ + // then the balancing coefficient for the row is \f$ 1/2^{\sigma} \f$ + // and the balancing coefficient for the column is \f$ 2^{\sigma} \f$ + rowB = rowNorm / radix<Scalar>(); + colB = Scalar(1); + const Scalar s = colNorm + rowNorm; + + while (colNorm < rowB) + { + colB *= radix<Scalar>(); + colNorm *= radix2<Scalar>(); + } + + rowB = rowNorm * radix<Scalar>(); + + while (colNorm >= rowB) + { + colB /= radix<Scalar>(); + colNorm /= radix2<Scalar>(); + } + + //This line is used to avoid insubstantial balancing + if ((rowNorm + colNorm) < Scalar(0.95) * s * colB) + { + isBalanced = false; + rowB = Scalar(1) / colB; + return false; + } + else{ + return true; } + } +} + +template< typename _Scalar, int _Deg > +inline +bool companion<_Scalar,_Deg>::balancedR( Scalar colNorm, Scalar rowNorm, + bool& isBalanced, Scalar& colB, Scalar& rowB ) +{ + if( Scalar(0) == colNorm || Scalar(0) == rowNorm ){ return true; } + else + { + /** + * Set the norm of the column and the row to the geometric mean + * of the row and column norm + */ + const _Scalar q = colNorm/rowNorm; + if( !isApprox( q, _Scalar(1) ) ) + { + rowB = sqrt( colNorm/rowNorm ); + colB = Scalar(1)/rowB; + + isBalanced = false; + return false; + } + else{ + return true; } + } +} + + +template< typename _Scalar, int _Deg > +void companion<_Scalar,_Deg>::balance() +{ + EIGEN_STATIC_ASSERT( Deg == Dynamic || 1 < Deg, YOU_MADE_A_PROGRAMMING_MISTAKE ); + const Index deg = m_monic.size(); + const Index deg_1 = deg-1; + + bool hasConverged=false; + while( !hasConverged ) + { + hasConverged = true; + Scalar colNorm,rowNorm; + Scalar colB,rowB; + + //First row, first column excluding the diagonal + //============================================== + colNorm = abs(m_bl_diag[0]); + rowNorm = abs(m_monic[0]); + + //Compute balancing of the row and the column + if( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) ) + { + m_bl_diag[0] *= colB; + m_monic[0] *= rowB; + } + + //Middle rows and columns excluding the diagonal + //============================================== + for( Index i=1; i<deg_1; ++i ) + { + // column norm, excluding the diagonal + colNorm = abs(m_bl_diag[i]); + + // row norm, excluding the diagonal + rowNorm = abs(m_bl_diag[i-1]) + abs(m_monic[i]); + + //Compute balancing of the row and the column + if( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) ) + { + m_bl_diag[i] *= colB; + m_bl_diag[i-1] *= rowB; + m_monic[i] *= rowB; + } + } + + //Last row, last column excluding the diagonal + //============================================ + const Index ebl = m_bl_diag.size()-1; + VectorBlock<RightColumn,Deg_1> headMonic( m_monic, 0, deg_1 ); + colNorm = headMonic.array().abs().sum(); + rowNorm = abs( m_bl_diag[ebl] ); + + //Compute balancing of the row and the column + if( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) ) + { + headMonic *= colB; + m_bl_diag[ebl] *= rowB; + } + } +} + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_COMPANION_H diff --git a/unsupported/Eigen/src/Polynomials/PolynomialSolver.h b/unsupported/Eigen/src/Polynomials/PolynomialSolver.h new file mode 100644 index 000000000..70b873dbc --- /dev/null +++ b/unsupported/Eigen/src/Polynomials/PolynomialSolver.h @@ -0,0 +1,386 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_POLYNOMIAL_SOLVER_H +#define EIGEN_POLYNOMIAL_SOLVER_H + +namespace Eigen { + +/** \ingroup Polynomials_Module + * \class PolynomialSolverBase. + * + * \brief Defined to be inherited by polynomial solvers: it provides + * convenient methods such as + * - real roots, + * - greatest, smallest complex roots, + * - real roots with greatest, smallest absolute real value, + * - greatest, smallest real roots. + * + * It stores the set of roots as a vector of complexes. + * + */ +template< typename _Scalar, int _Deg > +class PolynomialSolverBase +{ + public: + EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Deg==Dynamic ? Dynamic : _Deg) + + typedef _Scalar Scalar; + typedef typename NumTraits<Scalar>::Real RealScalar; + typedef std::complex<RealScalar> RootType; + typedef Matrix<RootType,_Deg,1> RootsType; + + typedef DenseIndex Index; + + protected: + template< typename OtherPolynomial > + inline void setPolynomial( const OtherPolynomial& poly ){ + m_roots.resize(poly.size()); } + + public: + template< typename OtherPolynomial > + inline PolynomialSolverBase( const OtherPolynomial& poly ){ + setPolynomial( poly() ); } + + inline PolynomialSolverBase(){} + + public: + /** \returns the complex roots of the polynomial */ + inline const RootsType& roots() const { return m_roots; } + + public: + /** Clear and fills the back insertion sequence with the real roots of the polynomial + * i.e. the real part of the complex roots that have an imaginary part which + * absolute value is smaller than absImaginaryThreshold. + * absImaginaryThreshold takes the dummy_precision associated + * with the _Scalar template parameter of the PolynomialSolver class as the default value. + * + * \param[out] bi_seq : the back insertion sequence (stl concept) + * \param[in] absImaginaryThreshold : the maximum bound of the imaginary part of a complex + * number that is considered as real. + * */ + template<typename Stl_back_insertion_sequence> + inline void realRoots( Stl_back_insertion_sequence& bi_seq, + const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const + { + bi_seq.clear(); + for(Index i=0; i<m_roots.size(); ++i ) + { + if( internal::abs( m_roots[i].imag() ) < absImaginaryThreshold ){ + bi_seq.push_back( m_roots[i].real() ); } + } + } + + protected: + template<typename squaredNormBinaryPredicate> + inline const RootType& selectComplexRoot_withRespectToNorm( squaredNormBinaryPredicate& pred ) const + { + Index res=0; + RealScalar norm2 = internal::abs2( m_roots[0] ); + for( Index i=1; i<m_roots.size(); ++i ) + { + const RealScalar currNorm2 = internal::abs2( m_roots[i] ); + if( pred( currNorm2, norm2 ) ){ + res=i; norm2=currNorm2; } + } + return m_roots[res]; + } + + public: + /** + * \returns the complex root with greatest norm. + */ + inline const RootType& greatestRoot() const + { + std::greater<Scalar> greater; + return selectComplexRoot_withRespectToNorm( greater ); + } + + /** + * \returns the complex root with smallest norm. + */ + inline const RootType& smallestRoot() const + { + std::less<Scalar> less; + return selectComplexRoot_withRespectToNorm( less ); + } + + protected: + template<typename squaredRealPartBinaryPredicate> + inline const RealScalar& selectRealRoot_withRespectToAbsRealPart( + squaredRealPartBinaryPredicate& pred, + bool& hasArealRoot, + const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const + { + hasArealRoot = false; + Index res=0; + RealScalar abs2(0); + + for( Index i=0; i<m_roots.size(); ++i ) + { + if( internal::abs( m_roots[i].imag() ) < absImaginaryThreshold ) + { + if( !hasArealRoot ) + { + hasArealRoot = true; + res = i; + abs2 = m_roots[i].real() * m_roots[i].real(); + } + else + { + const RealScalar currAbs2 = m_roots[i].real() * m_roots[i].real(); + if( pred( currAbs2, abs2 ) ) + { + abs2 = currAbs2; + res = i; + } + } + } + else + { + if( internal::abs( m_roots[i].imag() ) < internal::abs( m_roots[res].imag() ) ){ + res = i; } + } + } + return internal::real_ref(m_roots[res]); + } + + + template<typename RealPartBinaryPredicate> + inline const RealScalar& selectRealRoot_withRespectToRealPart( + RealPartBinaryPredicate& pred, + bool& hasArealRoot, + const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const + { + hasArealRoot = false; + Index res=0; + RealScalar val(0); + + for( Index i=0; i<m_roots.size(); ++i ) + { + if( internal::abs( m_roots[i].imag() ) < absImaginaryThreshold ) + { + if( !hasArealRoot ) + { + hasArealRoot = true; + res = i; + val = m_roots[i].real(); + } + else + { + const RealScalar curr = m_roots[i].real(); + if( pred( curr, val ) ) + { + val = curr; + res = i; + } + } + } + else + { + if( internal::abs( m_roots[i].imag() ) < internal::abs( m_roots[res].imag() ) ){ + res = i; } + } + } + return internal::real_ref(m_roots[res]); + } + + public: + /** + * \returns a real root with greatest absolute magnitude. + * A real root is defined as the real part of a complex root with absolute imaginary + * part smallest than absImaginaryThreshold. + * absImaginaryThreshold takes the dummy_precision associated + * with the _Scalar template parameter of the PolynomialSolver class as the default value. + * If no real root is found the boolean hasArealRoot is set to false and the real part of + * the root with smallest absolute imaginary part is returned instead. + * + * \param[out] hasArealRoot : boolean true if a real root is found according to the + * absImaginaryThreshold criterion, false otherwise. + * \param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide + * whether or not a root is real. + */ + inline const RealScalar& absGreatestRealRoot( + bool& hasArealRoot, + const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const + { + std::greater<Scalar> greater; + return selectRealRoot_withRespectToAbsRealPart( greater, hasArealRoot, absImaginaryThreshold ); + } + + + /** + * \returns a real root with smallest absolute magnitude. + * A real root is defined as the real part of a complex root with absolute imaginary + * part smallest than absImaginaryThreshold. + * absImaginaryThreshold takes the dummy_precision associated + * with the _Scalar template parameter of the PolynomialSolver class as the default value. + * If no real root is found the boolean hasArealRoot is set to false and the real part of + * the root with smallest absolute imaginary part is returned instead. + * + * \param[out] hasArealRoot : boolean true if a real root is found according to the + * absImaginaryThreshold criterion, false otherwise. + * \param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide + * whether or not a root is real. + */ + inline const RealScalar& absSmallestRealRoot( + bool& hasArealRoot, + const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const + { + std::less<Scalar> less; + return selectRealRoot_withRespectToAbsRealPart( less, hasArealRoot, absImaginaryThreshold ); + } + + + /** + * \returns the real root with greatest value. + * A real root is defined as the real part of a complex root with absolute imaginary + * part smallest than absImaginaryThreshold. + * absImaginaryThreshold takes the dummy_precision associated + * with the _Scalar template parameter of the PolynomialSolver class as the default value. + * If no real root is found the boolean hasArealRoot is set to false and the real part of + * the root with smallest absolute imaginary part is returned instead. + * + * \param[out] hasArealRoot : boolean true if a real root is found according to the + * absImaginaryThreshold criterion, false otherwise. + * \param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide + * whether or not a root is real. + */ + inline const RealScalar& greatestRealRoot( + bool& hasArealRoot, + const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const + { + std::greater<Scalar> greater; + return selectRealRoot_withRespectToRealPart( greater, hasArealRoot, absImaginaryThreshold ); + } + + + /** + * \returns the real root with smallest value. + * A real root is defined as the real part of a complex root with absolute imaginary + * part smallest than absImaginaryThreshold. + * absImaginaryThreshold takes the dummy_precision associated + * with the _Scalar template parameter of the PolynomialSolver class as the default value. + * If no real root is found the boolean hasArealRoot is set to false and the real part of + * the root with smallest absolute imaginary part is returned instead. + * + * \param[out] hasArealRoot : boolean true if a real root is found according to the + * absImaginaryThreshold criterion, false otherwise. + * \param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide + * whether or not a root is real. + */ + inline const RealScalar& smallestRealRoot( + bool& hasArealRoot, + const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const + { + std::less<Scalar> less; + return selectRealRoot_withRespectToRealPart( less, hasArealRoot, absImaginaryThreshold ); + } + + protected: + RootsType m_roots; +}; + +#define EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( BASE ) \ + typedef typename BASE::Scalar Scalar; \ + typedef typename BASE::RealScalar RealScalar; \ + typedef typename BASE::RootType RootType; \ + typedef typename BASE::RootsType RootsType; + + + +/** \ingroup Polynomials_Module + * + * \class PolynomialSolver + * + * \brief A polynomial solver + * + * Computes the complex roots of a real polynomial. + * + * \param _Scalar the scalar type, i.e., the type of the polynomial coefficients + * \param _Deg the degree of the polynomial, can be a compile time value or Dynamic. + * Notice that the number of polynomial coefficients is _Deg+1. + * + * This class implements a polynomial solver and provides convenient methods such as + * - real roots, + * - greatest, smallest complex roots, + * - real roots with greatest, smallest absolute real value. + * - greatest, smallest real roots. + * + * WARNING: this polynomial solver is experimental, part of the unsuported Eigen modules. + * + * + * Currently a QR algorithm is used to compute the eigenvalues of the companion matrix of + * the polynomial to compute its roots. + * This supposes that the complex moduli of the roots are all distinct: e.g. there should + * be no multiple roots or conjugate roots for instance. + * With 32bit (float) floating types this problem shows up frequently. + * However, almost always, correct accuracy is reached even in these cases for 64bit + * (double) floating types and small polynomial degree (<20). + */ +template< typename _Scalar, int _Deg > +class PolynomialSolver : public PolynomialSolverBase<_Scalar,_Deg> +{ + public: + EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Deg==Dynamic ? Dynamic : _Deg) + + typedef PolynomialSolverBase<_Scalar,_Deg> PS_Base; + EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( PS_Base ) + + typedef Matrix<Scalar,_Deg,_Deg> CompanionMatrixType; + typedef EigenSolver<CompanionMatrixType> EigenSolverType; + + public: + /** Computes the complex roots of a new polynomial. */ + template< typename OtherPolynomial > + void compute( const OtherPolynomial& poly ) + { + assert( Scalar(0) != poly[poly.size()-1] ); + internal::companion<Scalar,_Deg> companion( poly ); + companion.balance(); + m_eigenSolver.compute( companion.denseMatrix() ); + m_roots = m_eigenSolver.eigenvalues(); + } + + public: + template< typename OtherPolynomial > + inline PolynomialSolver( const OtherPolynomial& poly ){ + compute( poly ); } + + inline PolynomialSolver(){} + + protected: + using PS_Base::m_roots; + EigenSolverType m_eigenSolver; +}; + + +template< typename _Scalar > +class PolynomialSolver<_Scalar,1> : public PolynomialSolverBase<_Scalar,1> +{ + public: + typedef PolynomialSolverBase<_Scalar,1> PS_Base; + EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( PS_Base ) + + public: + /** Computes the complex roots of a new polynomial. */ + template< typename OtherPolynomial > + void compute( const OtherPolynomial& poly ) + { + assert( Scalar(0) != poly[poly.size()-1] ); + m_roots[0] = -poly[0]/poly[poly.size()-1]; + } + + protected: + using PS_Base::m_roots; +}; + +} // end namespace Eigen + +#endif // EIGEN_POLYNOMIAL_SOLVER_H diff --git a/unsupported/Eigen/src/Polynomials/PolynomialUtils.h b/unsupported/Eigen/src/Polynomials/PolynomialUtils.h new file mode 100644 index 000000000..c23204c65 --- /dev/null +++ b/unsupported/Eigen/src/Polynomials/PolynomialUtils.h @@ -0,0 +1,141 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_POLYNOMIAL_UTILS_H +#define EIGEN_POLYNOMIAL_UTILS_H + +namespace Eigen { + +/** \ingroup Polynomials_Module + * \returns the evaluation of the polynomial at x using Horner algorithm. + * + * \param[in] poly : the vector of coefficients of the polynomial ordered + * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial + * e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$. + * \param[in] x : the value to evaluate the polynomial at. + * + * <i><b>Note for stability:</b></i> + * <dd> \f$ |x| \le 1 \f$ </dd> + */ +template <typename Polynomials, typename T> +inline +T poly_eval_horner( const Polynomials& poly, const T& x ) +{ + T val=poly[poly.size()-1]; + for(DenseIndex i=poly.size()-2; i>=0; --i ){ + val = val*x + poly[i]; } + return val; +} + +/** \ingroup Polynomials_Module + * \returns the evaluation of the polynomial at x using stabilized Horner algorithm. + * + * \param[in] poly : the vector of coefficients of the polynomial ordered + * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial + * e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$. + * \param[in] x : the value to evaluate the polynomial at. + */ +template <typename Polynomials, typename T> +inline +T poly_eval( const Polynomials& poly, const T& x ) +{ + typedef typename NumTraits<T>::Real Real; + + if( internal::abs2( x ) <= Real(1) ){ + return poly_eval_horner( poly, x ); } + else + { + T val=poly[0]; + T inv_x = T(1)/x; + for( DenseIndex i=1; i<poly.size(); ++i ){ + val = val*inv_x + poly[i]; } + + return std::pow(x,(T)(poly.size()-1)) * val; + } +} + +/** \ingroup Polynomials_Module + * \returns a maximum bound for the absolute value of any root of the polynomial. + * + * \param[in] poly : the vector of coefficients of the polynomial ordered + * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial + * e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$. + * + * <i><b>Precondition:</b></i> + * <dd> the leading coefficient of the input polynomial poly must be non zero </dd> + */ +template <typename Polynomial> +inline +typename NumTraits<typename Polynomial::Scalar>::Real cauchy_max_bound( const Polynomial& poly ) +{ + typedef typename Polynomial::Scalar Scalar; + typedef typename NumTraits<Scalar>::Real Real; + + assert( Scalar(0) != poly[poly.size()-1] ); + const Scalar inv_leading_coeff = Scalar(1)/poly[poly.size()-1]; + Real cb(0); + + for( DenseIndex i=0; i<poly.size()-1; ++i ){ + cb += internal::abs(poly[i]*inv_leading_coeff); } + return cb + Real(1); +} + +/** \ingroup Polynomials_Module + * \returns a minimum bound for the absolute value of any non zero root of the polynomial. + * \param[in] poly : the vector of coefficients of the polynomial ordered + * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial + * e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$. + */ +template <typename Polynomial> +inline +typename NumTraits<typename Polynomial::Scalar>::Real cauchy_min_bound( const Polynomial& poly ) +{ + typedef typename Polynomial::Scalar Scalar; + typedef typename NumTraits<Scalar>::Real Real; + + DenseIndex i=0; + while( i<poly.size()-1 && Scalar(0) == poly(i) ){ ++i; } + if( poly.size()-1 == i ){ + return Real(1); } + + const Scalar inv_min_coeff = Scalar(1)/poly[i]; + Real cb(1); + for( DenseIndex j=i+1; j<poly.size(); ++j ){ + cb += internal::abs(poly[j]*inv_min_coeff); } + return Real(1)/cb; +} + +/** \ingroup Polynomials_Module + * Given the roots of a polynomial compute the coefficients in the + * monomial basis of the monic polynomial with same roots and minimal degree. + * If RootVector is a vector of complexes, Polynomial should also be a vector + * of complexes. + * \param[in] rv : a vector containing the roots of a polynomial. + * \param[out] poly : the vector of coefficients of the polynomial ordered + * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial + * e.g. \f$ 3 + x^2 \f$ is stored as a vector \f$ [ 3, 0, 1 ] \f$. + */ +template <typename RootVector, typename Polynomial> +void roots_to_monicPolynomial( const RootVector& rv, Polynomial& poly ) +{ + + typedef typename Polynomial::Scalar Scalar; + + poly.setZero( rv.size()+1 ); + poly[0] = -rv[0]; poly[1] = Scalar(1); + for( DenseIndex i=1; i< rv.size(); ++i ) + { + for( DenseIndex j=i+1; j>0; --j ){ poly[j] = poly[j-1] - rv[i]*poly[j]; } + poly[0] = -rv[i]*poly[0]; + } +} + +} // end namespace Eigen + +#endif // EIGEN_POLYNOMIAL_UTILS_H diff --git a/unsupported/Eigen/src/Skyline/CMakeLists.txt b/unsupported/Eigen/src/Skyline/CMakeLists.txt new file mode 100644 index 000000000..3bf1b0dd4 --- /dev/null +++ b/unsupported/Eigen/src/Skyline/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_Skyline_SRCS "*.h") + +INSTALL(FILES + ${Eigen_Skyline_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/Skyline COMPONENT Devel + ) diff --git a/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h b/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h new file mode 100644 index 000000000..a1f54ed35 --- /dev/null +++ b/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h @@ -0,0 +1,352 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Guillaume Saupin <guillaume.saupin@cea.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SKYLINEINPLACELU_H +#define EIGEN_SKYLINEINPLACELU_H + +namespace Eigen { + +/** \ingroup Skyline_Module + * + * \class SkylineInplaceLU + * + * \brief Inplace LU decomposition of a skyline matrix and associated features + * + * \param MatrixType the type of the matrix of which we are computing the LU factorization + * + */ +template<typename MatrixType> +class SkylineInplaceLU { +protected: + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::Index Index; + + typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; + +public: + + /** Creates a LU object and compute the respective factorization of \a matrix using + * flags \a flags. */ + SkylineInplaceLU(MatrixType& matrix, int flags = 0) + : /*m_matrix(matrix.rows(), matrix.cols()),*/ m_flags(flags), m_status(0), m_lu(matrix) { + m_precision = RealScalar(0.1) * Eigen::dummy_precision<RealScalar > (); + m_lu.IsRowMajor ? computeRowMajor() : compute(); + } + + /** Sets the relative threshold value used to prune zero coefficients during the decomposition. + * + * Setting a value greater than zero speeds up computation, and yields to an imcomplete + * factorization with fewer non zero coefficients. Such approximate factors are especially + * useful to initialize an iterative solver. + * + * Note that the exact meaning of this parameter might depends on the actual + * backend. Moreover, not all backends support this feature. + * + * \sa precision() */ + void setPrecision(RealScalar v) { + m_precision = v; + } + + /** \returns the current precision. + * + * \sa setPrecision() */ + RealScalar precision() const { + return m_precision; + } + + /** Sets the flags. Possible values are: + * - CompleteFactorization + * - IncompleteFactorization + * - MemoryEfficient + * - one of the ordering methods + * - etc... + * + * \sa flags() */ + void setFlags(int f) { + m_flags = f; + } + + /** \returns the current flags */ + int flags() const { + return m_flags; + } + + void setOrderingMethod(int m) { + m_flags = m; + } + + int orderingMethod() const { + return m_flags; + } + + /** Computes/re-computes the LU factorization */ + void compute(); + void computeRowMajor(); + + /** \returns the lower triangular matrix L */ + //inline const MatrixType& matrixL() const { return m_matrixL; } + + /** \returns the upper triangular matrix U */ + //inline const MatrixType& matrixU() const { return m_matrixU; } + + template<typename BDerived, typename XDerived> + bool solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>* x, + const int transposed = 0) const; + + /** \returns true if the factorization succeeded */ + inline bool succeeded(void) const { + return m_succeeded; + } + +protected: + RealScalar m_precision; + int m_flags; + mutable int m_status; + bool m_succeeded; + MatrixType& m_lu; +}; + +/** Computes / recomputes the in place LU decomposition of the SkylineInplaceLU. + * using the default algorithm. + */ +template<typename MatrixType> +//template<typename _Scalar> +void SkylineInplaceLU<MatrixType>::compute() { + const size_t rows = m_lu.rows(); + const size_t cols = m_lu.cols(); + + eigen_assert(rows == cols && "We do not (yet) support rectangular LU."); + eigen_assert(!m_lu.IsRowMajor && "LU decomposition does not work with rowMajor Storage"); + + for (Index row = 0; row < rows; row++) { + const double pivot = m_lu.coeffDiag(row); + + //Lower matrix Columns update + const Index& col = row; + for (typename MatrixType::InnerLowerIterator lIt(m_lu, col); lIt; ++lIt) { + lIt.valueRef() /= pivot; + } + + //Upper matrix update -> contiguous memory access + typename MatrixType::InnerLowerIterator lIt(m_lu, col); + for (Index rrow = row + 1; rrow < m_lu.rows(); rrow++) { + typename MatrixType::InnerUpperIterator uItPivot(m_lu, row); + typename MatrixType::InnerUpperIterator uIt(m_lu, rrow); + const double coef = lIt.value(); + + uItPivot += (rrow - row - 1); + + //update upper part -> contiguous memory access + for (++uItPivot; uIt && uItPivot;) { + uIt.valueRef() -= uItPivot.value() * coef; + + ++uIt; + ++uItPivot; + } + ++lIt; + } + + //Upper matrix update -> non contiguous memory access + typename MatrixType::InnerLowerIterator lIt3(m_lu, col); + for (Index rrow = row + 1; rrow < m_lu.rows(); rrow++) { + typename MatrixType::InnerUpperIterator uItPivot(m_lu, row); + const double coef = lIt3.value(); + + //update lower part -> non contiguous memory access + for (Index i = 0; i < rrow - row - 1; i++) { + m_lu.coeffRefLower(rrow, row + i + 1) -= uItPivot.value() * coef; + ++uItPivot; + } + ++lIt3; + } + //update diag -> contiguous + typename MatrixType::InnerLowerIterator lIt2(m_lu, col); + for (Index rrow = row + 1; rrow < m_lu.rows(); rrow++) { + + typename MatrixType::InnerUpperIterator uItPivot(m_lu, row); + typename MatrixType::InnerUpperIterator uIt(m_lu, rrow); + const double coef = lIt2.value(); + + uItPivot += (rrow - row - 1); + m_lu.coeffRefDiag(rrow) -= uItPivot.value() * coef; + ++lIt2; + } + } +} + +template<typename MatrixType> +void SkylineInplaceLU<MatrixType>::computeRowMajor() { + const size_t rows = m_lu.rows(); + const size_t cols = m_lu.cols(); + + eigen_assert(rows == cols && "We do not (yet) support rectangular LU."); + eigen_assert(m_lu.IsRowMajor && "You're trying to apply rowMajor decomposition on a ColMajor matrix !"); + + for (Index row = 0; row < rows; row++) { + typename MatrixType::InnerLowerIterator llIt(m_lu, row); + + + for (Index col = llIt.col(); col < row; col++) { + if (m_lu.coeffExistLower(row, col)) { + const double diag = m_lu.coeffDiag(col); + + typename MatrixType::InnerLowerIterator lIt(m_lu, row); + typename MatrixType::InnerUpperIterator uIt(m_lu, col); + + + const Index offset = lIt.col() - uIt.row(); + + + Index stop = offset > 0 ? col - lIt.col() : col - uIt.row(); + + //#define VECTORIZE +#ifdef VECTORIZE + Map<VectorXd > rowVal(lIt.valuePtr() + (offset > 0 ? 0 : -offset), stop); + Map<VectorXd > colVal(uIt.valuePtr() + (offset > 0 ? offset : 0), stop); + + + Scalar newCoeff = m_lu.coeffLower(row, col) - rowVal.dot(colVal); +#else + if (offset > 0) //Skip zero value of lIt + uIt += offset; + else //Skip zero values of uIt + lIt += -offset; + Scalar newCoeff = m_lu.coeffLower(row, col); + + for (Index k = 0; k < stop; ++k) { + const Scalar tmp = newCoeff; + newCoeff = tmp - lIt.value() * uIt.value(); + ++lIt; + ++uIt; + } +#endif + + m_lu.coeffRefLower(row, col) = newCoeff / diag; + } + } + + //Upper matrix update + const Index col = row; + typename MatrixType::InnerUpperIterator uuIt(m_lu, col); + for (Index rrow = uuIt.row(); rrow < col; rrow++) { + + typename MatrixType::InnerLowerIterator lIt(m_lu, rrow); + typename MatrixType::InnerUpperIterator uIt(m_lu, col); + const Index offset = lIt.col() - uIt.row(); + + Index stop = offset > 0 ? rrow - lIt.col() : rrow - uIt.row(); + +#ifdef VECTORIZE + Map<VectorXd > rowVal(lIt.valuePtr() + (offset > 0 ? 0 : -offset), stop); + Map<VectorXd > colVal(uIt.valuePtr() + (offset > 0 ? offset : 0), stop); + + Scalar newCoeff = m_lu.coeffUpper(rrow, col) - rowVal.dot(colVal); +#else + if (offset > 0) //Skip zero value of lIt + uIt += offset; + else //Skip zero values of uIt + lIt += -offset; + Scalar newCoeff = m_lu.coeffUpper(rrow, col); + for (Index k = 0; k < stop; ++k) { + const Scalar tmp = newCoeff; + newCoeff = tmp - lIt.value() * uIt.value(); + + ++lIt; + ++uIt; + } +#endif + m_lu.coeffRefUpper(rrow, col) = newCoeff; + } + + + //Diag matrix update + typename MatrixType::InnerLowerIterator lIt(m_lu, row); + typename MatrixType::InnerUpperIterator uIt(m_lu, row); + + const Index offset = lIt.col() - uIt.row(); + + + Index stop = offset > 0 ? lIt.size() : uIt.size(); +#ifdef VECTORIZE + Map<VectorXd > rowVal(lIt.valuePtr() + (offset > 0 ? 0 : -offset), stop); + Map<VectorXd > colVal(uIt.valuePtr() + (offset > 0 ? offset : 0), stop); + Scalar newCoeff = m_lu.coeffDiag(row) - rowVal.dot(colVal); +#else + if (offset > 0) //Skip zero value of lIt + uIt += offset; + else //Skip zero values of uIt + lIt += -offset; + Scalar newCoeff = m_lu.coeffDiag(row); + for (Index k = 0; k < stop; ++k) { + const Scalar tmp = newCoeff; + newCoeff = tmp - lIt.value() * uIt.value(); + ++lIt; + ++uIt; + } +#endif + m_lu.coeffRefDiag(row) = newCoeff; + } +} + +/** Computes *x = U^-1 L^-1 b + * + * If \a transpose is set to SvTranspose or SvAdjoint, the solution + * of the transposed/adjoint system is computed instead. + * + * Not all backends implement the solution of the transposed or + * adjoint system. + */ +template<typename MatrixType> +template<typename BDerived, typename XDerived> +bool SkylineInplaceLU<MatrixType>::solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>* x, const int transposed) const { + const size_t rows = m_lu.rows(); + const size_t cols = m_lu.cols(); + + + for (Index row = 0; row < rows; row++) { + x->coeffRef(row) = b.coeff(row); + Scalar newVal = x->coeff(row); + typename MatrixType::InnerLowerIterator lIt(m_lu, row); + + Index col = lIt.col(); + while (lIt.col() < row) { + + newVal -= x->coeff(col++) * lIt.value(); + ++lIt; + } + + x->coeffRef(row) = newVal; + } + + + for (Index col = rows - 1; col > 0; col--) { + x->coeffRef(col) = x->coeff(col) / m_lu.coeffDiag(col); + + const Scalar x_col = x->coeff(col); + + typename MatrixType::InnerUpperIterator uIt(m_lu, col); + uIt += uIt.size()-1; + + + while (uIt) { + x->coeffRef(uIt.row()) -= x_col * uIt.value(); + //TODO : introduce --operator + uIt += -1; + } + + + } + x->coeffRef(0) = x->coeff(0) / m_lu.coeffDiag(0); + + return true; +} + +} // end namespace Eigen + +#endif // EIGEN_SKYLINELU_H diff --git a/unsupported/Eigen/src/Skyline/SkylineMatrix.h b/unsupported/Eigen/src/Skyline/SkylineMatrix.h new file mode 100644 index 000000000..a2a8933ca --- /dev/null +++ b/unsupported/Eigen/src/Skyline/SkylineMatrix.h @@ -0,0 +1,862 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SKYLINEMATRIX_H +#define EIGEN_SKYLINEMATRIX_H + +#include "SkylineStorage.h" +#include "SkylineMatrixBase.h" + +namespace Eigen { + +/** \ingroup Skyline_Module + * + * \class SkylineMatrix + * + * \brief The main skyline matrix class + * + * This class implements a skyline matrix using the very uncommon storage + * scheme. + * + * \param _Scalar the scalar type, i.e. the type of the coefficients + * \param _Options Union of bit flags controlling the storage scheme. Currently the only possibility + * is RowMajor. The default is 0 which means column-major. + * + * + */ +namespace internal { +template<typename _Scalar, int _Options> +struct traits<SkylineMatrix<_Scalar, _Options> > { + typedef _Scalar Scalar; + typedef Sparse StorageKind; + + enum { + RowsAtCompileTime = Dynamic, + ColsAtCompileTime = Dynamic, + MaxRowsAtCompileTime = Dynamic, + MaxColsAtCompileTime = Dynamic, + Flags = SkylineBit | _Options, + CoeffReadCost = NumTraits<Scalar>::ReadCost, + }; +}; +} + +template<typename _Scalar, int _Options> +class SkylineMatrix +: public SkylineMatrixBase<SkylineMatrix<_Scalar, _Options> > { +public: + EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(SkylineMatrix) + EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(SkylineMatrix, +=) + EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(SkylineMatrix, -=) + + using Base::IsRowMajor; + +protected: + + typedef SkylineMatrix<Scalar, (Flags&~RowMajorBit) | (IsRowMajor ? RowMajorBit : 0) > TransposedSkylineMatrix; + + Index m_outerSize; + Index m_innerSize; + +public: + Index* m_colStartIndex; + Index* m_rowStartIndex; + SkylineStorage<Scalar> m_data; + +public: + + inline Index rows() const { + return IsRowMajor ? m_outerSize : m_innerSize; + } + + inline Index cols() const { + return IsRowMajor ? m_innerSize : m_outerSize; + } + + inline Index innerSize() const { + return m_innerSize; + } + + inline Index outerSize() const { + return m_outerSize; + } + + inline Index upperNonZeros() const { + return m_data.upperSize(); + } + + inline Index lowerNonZeros() const { + return m_data.lowerSize(); + } + + inline Index upperNonZeros(Index j) const { + return m_colStartIndex[j + 1] - m_colStartIndex[j]; + } + + inline Index lowerNonZeros(Index j) const { + return m_rowStartIndex[j + 1] - m_rowStartIndex[j]; + } + + inline const Scalar* _diagPtr() const { + return &m_data.diag(0); + } + + inline Scalar* _diagPtr() { + return &m_data.diag(0); + } + + inline const Scalar* _upperPtr() const { + return &m_data.upper(0); + } + + inline Scalar* _upperPtr() { + return &m_data.upper(0); + } + + inline const Scalar* _lowerPtr() const { + return &m_data.lower(0); + } + + inline Scalar* _lowerPtr() { + return &m_data.lower(0); + } + + inline const Index* _upperProfilePtr() const { + return &m_data.upperProfile(0); + } + + inline Index* _upperProfilePtr() { + return &m_data.upperProfile(0); + } + + inline const Index* _lowerProfilePtr() const { + return &m_data.lowerProfile(0); + } + + inline Index* _lowerProfilePtr() { + return &m_data.lowerProfile(0); + } + + inline Scalar coeff(Index row, Index col) const { + const Index outer = IsRowMajor ? row : col; + const Index inner = IsRowMajor ? col : row; + + eigen_assert(outer < outerSize()); + eigen_assert(inner < innerSize()); + + if (outer == inner) + return this->m_data.diag(outer); + + if (IsRowMajor) { + if (inner > outer) //upper matrix + { + const Index minOuterIndex = inner - m_data.upperProfile(inner); + if (outer >= minOuterIndex) + return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner))); + else + return Scalar(0); + } + if (inner < outer) //lower matrix + { + const Index minInnerIndex = outer - m_data.lowerProfile(outer); + if (inner >= minInnerIndex) + return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer))); + else + return Scalar(0); + } + return m_data.upper(m_colStartIndex[inner] + outer - inner); + } else { + if (outer > inner) //upper matrix + { + const Index maxOuterIndex = inner + m_data.upperProfile(inner); + if (outer <= maxOuterIndex) + return this->m_data.upper(m_colStartIndex[inner] + (outer - inner)); + else + return Scalar(0); + } + if (outer < inner) //lower matrix + { + const Index maxInnerIndex = outer + m_data.lowerProfile(outer); + + if (inner <= maxInnerIndex) + return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer)); + else + return Scalar(0); + } + } + } + + inline Scalar& coeffRef(Index row, Index col) { + const Index outer = IsRowMajor ? row : col; + const Index inner = IsRowMajor ? col : row; + + eigen_assert(outer < outerSize()); + eigen_assert(inner < innerSize()); + + if (outer == inner) + return this->m_data.diag(outer); + + if (IsRowMajor) { + if (col > row) //upper matrix + { + const Index minOuterIndex = inner - m_data.upperProfile(inner); + eigen_assert(outer >= minOuterIndex && "you try to acces a coeff that do not exist in the storage"); + return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner))); + } + if (col < row) //lower matrix + { + const Index minInnerIndex = outer - m_data.lowerProfile(outer); + eigen_assert(inner >= minInnerIndex && "you try to acces a coeff that do not exist in the storage"); + return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer))); + } + } else { + if (outer > inner) //upper matrix + { + const Index maxOuterIndex = inner + m_data.upperProfile(inner); + eigen_assert(outer <= maxOuterIndex && "you try to acces a coeff that do not exist in the storage"); + return this->m_data.upper(m_colStartIndex[inner] + (outer - inner)); + } + if (outer < inner) //lower matrix + { + const Index maxInnerIndex = outer + m_data.lowerProfile(outer); + eigen_assert(inner <= maxInnerIndex && "you try to acces a coeff that do not exist in the storage"); + return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer)); + } + } + } + + inline Scalar coeffDiag(Index idx) const { + eigen_assert(idx < outerSize()); + eigen_assert(idx < innerSize()); + return this->m_data.diag(idx); + } + + inline Scalar coeffLower(Index row, Index col) const { + const Index outer = IsRowMajor ? row : col; + const Index inner = IsRowMajor ? col : row; + + eigen_assert(outer < outerSize()); + eigen_assert(inner < innerSize()); + eigen_assert(inner != outer); + + if (IsRowMajor) { + const Index minInnerIndex = outer - m_data.lowerProfile(outer); + if (inner >= minInnerIndex) + return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer))); + else + return Scalar(0); + + } else { + const Index maxInnerIndex = outer + m_data.lowerProfile(outer); + if (inner <= maxInnerIndex) + return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer)); + else + return Scalar(0); + } + } + + inline Scalar coeffUpper(Index row, Index col) const { + const Index outer = IsRowMajor ? row : col; + const Index inner = IsRowMajor ? col : row; + + eigen_assert(outer < outerSize()); + eigen_assert(inner < innerSize()); + eigen_assert(inner != outer); + + if (IsRowMajor) { + const Index minOuterIndex = inner - m_data.upperProfile(inner); + if (outer >= minOuterIndex) + return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner))); + else + return Scalar(0); + } else { + const Index maxOuterIndex = inner + m_data.upperProfile(inner); + if (outer <= maxOuterIndex) + return this->m_data.upper(m_colStartIndex[inner] + (outer - inner)); + else + return Scalar(0); + } + } + + inline Scalar& coeffRefDiag(Index idx) { + eigen_assert(idx < outerSize()); + eigen_assert(idx < innerSize()); + return this->m_data.diag(idx); + } + + inline Scalar& coeffRefLower(Index row, Index col) { + const Index outer = IsRowMajor ? row : col; + const Index inner = IsRowMajor ? col : row; + + eigen_assert(outer < outerSize()); + eigen_assert(inner < innerSize()); + eigen_assert(inner != outer); + + if (IsRowMajor) { + const Index minInnerIndex = outer - m_data.lowerProfile(outer); + eigen_assert(inner >= minInnerIndex && "you try to acces a coeff that do not exist in the storage"); + return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer))); + } else { + const Index maxInnerIndex = outer + m_data.lowerProfile(outer); + eigen_assert(inner <= maxInnerIndex && "you try to acces a coeff that do not exist in the storage"); + return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer)); + } + } + + inline bool coeffExistLower(Index row, Index col) { + const Index outer = IsRowMajor ? row : col; + const Index inner = IsRowMajor ? col : row; + + eigen_assert(outer < outerSize()); + eigen_assert(inner < innerSize()); + eigen_assert(inner != outer); + + if (IsRowMajor) { + const Index minInnerIndex = outer - m_data.lowerProfile(outer); + return inner >= minInnerIndex; + } else { + const Index maxInnerIndex = outer + m_data.lowerProfile(outer); + return inner <= maxInnerIndex; + } + } + + inline Scalar& coeffRefUpper(Index row, Index col) { + const Index outer = IsRowMajor ? row : col; + const Index inner = IsRowMajor ? col : row; + + eigen_assert(outer < outerSize()); + eigen_assert(inner < innerSize()); + eigen_assert(inner != outer); + + if (IsRowMajor) { + const Index minOuterIndex = inner - m_data.upperProfile(inner); + eigen_assert(outer >= minOuterIndex && "you try to acces a coeff that do not exist in the storage"); + return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner))); + } else { + const Index maxOuterIndex = inner + m_data.upperProfile(inner); + eigen_assert(outer <= maxOuterIndex && "you try to acces a coeff that do not exist in the storage"); + return this->m_data.upper(m_colStartIndex[inner] + (outer - inner)); + } + } + + inline bool coeffExistUpper(Index row, Index col) { + const Index outer = IsRowMajor ? row : col; + const Index inner = IsRowMajor ? col : row; + + eigen_assert(outer < outerSize()); + eigen_assert(inner < innerSize()); + eigen_assert(inner != outer); + + if (IsRowMajor) { + const Index minOuterIndex = inner - m_data.upperProfile(inner); + return outer >= minOuterIndex; + } else { + const Index maxOuterIndex = inner + m_data.upperProfile(inner); + return outer <= maxOuterIndex; + } + } + + +protected: + +public: + class InnerUpperIterator; + class InnerLowerIterator; + + class OuterUpperIterator; + class OuterLowerIterator; + + /** Removes all non zeros */ + inline void setZero() { + m_data.clear(); + memset(m_colStartIndex, 0, (m_outerSize + 1) * sizeof (Index)); + memset(m_rowStartIndex, 0, (m_outerSize + 1) * sizeof (Index)); + } + + /** \returns the number of non zero coefficients */ + inline Index nonZeros() const { + return m_data.diagSize() + m_data.upperSize() + m_data.lowerSize(); + } + + /** Preallocates \a reserveSize non zeros */ + inline void reserve(Index reserveSize, Index reserveUpperSize, Index reserveLowerSize) { + m_data.reserve(reserveSize, reserveUpperSize, reserveLowerSize); + } + + /** \returns a reference to a novel non zero coefficient with coordinates \a row x \a col. + + * + * \warning This function can be extremely slow if the non zero coefficients + * are not inserted in a coherent order. + * + * After an insertion session, you should call the finalize() function. + */ + EIGEN_DONT_INLINE Scalar & insert(Index row, Index col) { + const Index outer = IsRowMajor ? row : col; + const Index inner = IsRowMajor ? col : row; + + eigen_assert(outer < outerSize()); + eigen_assert(inner < innerSize()); + + if (outer == inner) + return m_data.diag(col); + + if (IsRowMajor) { + if (outer < inner) //upper matrix + { + Index minOuterIndex = 0; + minOuterIndex = inner - m_data.upperProfile(inner); + + if (outer < minOuterIndex) //The value does not yet exist + { + const Index previousProfile = m_data.upperProfile(inner); + + m_data.upperProfile(inner) = inner - outer; + + + const Index bandIncrement = m_data.upperProfile(inner) - previousProfile; + //shift data stored after this new one + const Index stop = m_colStartIndex[cols()]; + const Index start = m_colStartIndex[inner]; + + + for (Index innerIdx = stop; innerIdx >= start; innerIdx--) { + m_data.upper(innerIdx + bandIncrement) = m_data.upper(innerIdx); + } + + for (Index innerIdx = cols(); innerIdx > inner; innerIdx--) { + m_colStartIndex[innerIdx] += bandIncrement; + } + + //zeros new data + memset(this->_upperPtr() + start, 0, (bandIncrement - 1) * sizeof (Scalar)); + + return m_data.upper(m_colStartIndex[inner]); + } else { + return m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner))); + } + } + + if (outer > inner) //lower matrix + { + const Index minInnerIndex = outer - m_data.lowerProfile(outer); + if (inner < minInnerIndex) //The value does not yet exist + { + const Index previousProfile = m_data.lowerProfile(outer); + m_data.lowerProfile(outer) = outer - inner; + + const Index bandIncrement = m_data.lowerProfile(outer) - previousProfile; + //shift data stored after this new one + const Index stop = m_rowStartIndex[rows()]; + const Index start = m_rowStartIndex[outer]; + + + for (Index innerIdx = stop; innerIdx >= start; innerIdx--) { + m_data.lower(innerIdx + bandIncrement) = m_data.lower(innerIdx); + } + + for (Index innerIdx = rows(); innerIdx > outer; innerIdx--) { + m_rowStartIndex[innerIdx] += bandIncrement; + } + + //zeros new data + memset(this->_lowerPtr() + start, 0, (bandIncrement - 1) * sizeof (Scalar)); + return m_data.lower(m_rowStartIndex[outer]); + } else { + return m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer))); + } + } + } else { + if (outer > inner) //upper matrix + { + const Index maxOuterIndex = inner + m_data.upperProfile(inner); + if (outer > maxOuterIndex) //The value does not yet exist + { + const Index previousProfile = m_data.upperProfile(inner); + m_data.upperProfile(inner) = outer - inner; + + const Index bandIncrement = m_data.upperProfile(inner) - previousProfile; + //shift data stored after this new one + const Index stop = m_rowStartIndex[rows()]; + const Index start = m_rowStartIndex[inner + 1]; + + for (Index innerIdx = stop; innerIdx >= start; innerIdx--) { + m_data.upper(innerIdx + bandIncrement) = m_data.upper(innerIdx); + } + + for (Index innerIdx = inner + 1; innerIdx < outerSize() + 1; innerIdx++) { + m_rowStartIndex[innerIdx] += bandIncrement; + } + memset(this->_upperPtr() + m_rowStartIndex[inner] + previousProfile + 1, 0, (bandIncrement - 1) * sizeof (Scalar)); + return m_data.upper(m_rowStartIndex[inner] + m_data.upperProfile(inner)); + } else { + return m_data.upper(m_rowStartIndex[inner] + (outer - inner)); + } + } + + if (outer < inner) //lower matrix + { + const Index maxInnerIndex = outer + m_data.lowerProfile(outer); + if (inner > maxInnerIndex) //The value does not yet exist + { + const Index previousProfile = m_data.lowerProfile(outer); + m_data.lowerProfile(outer) = inner - outer; + + const Index bandIncrement = m_data.lowerProfile(outer) - previousProfile; + //shift data stored after this new one + const Index stop = m_colStartIndex[cols()]; + const Index start = m_colStartIndex[outer + 1]; + + for (Index innerIdx = stop; innerIdx >= start; innerIdx--) { + m_data.lower(innerIdx + bandIncrement) = m_data.lower(innerIdx); + } + + for (Index innerIdx = outer + 1; innerIdx < outerSize() + 1; innerIdx++) { + m_colStartIndex[innerIdx] += bandIncrement; + } + memset(this->_lowerPtr() + m_colStartIndex[outer] + previousProfile + 1, 0, (bandIncrement - 1) * sizeof (Scalar)); + return m_data.lower(m_colStartIndex[outer] + m_data.lowerProfile(outer)); + } else { + return m_data.lower(m_colStartIndex[outer] + (inner - outer)); + } + } + } + } + + /** Must be called after inserting a set of non zero entries. + */ + inline void finalize() { + if (IsRowMajor) { + if (rows() > cols()) + m_data.resize(cols(), cols(), rows(), m_colStartIndex[cols()] + 1, m_rowStartIndex[rows()] + 1); + else + m_data.resize(rows(), cols(), rows(), m_colStartIndex[cols()] + 1, m_rowStartIndex[rows()] + 1); + + // eigen_assert(rows() == cols() && "memory reorganisatrion only works with suare matrix"); + // + // Scalar* newArray = new Scalar[m_colStartIndex[cols()] + 1 + m_rowStartIndex[rows()] + 1]; + // Index dataIdx = 0; + // for (Index row = 0; row < rows(); row++) { + // + // const Index nbLowerElts = m_rowStartIndex[row + 1] - m_rowStartIndex[row]; + // // std::cout << "nbLowerElts" << nbLowerElts << std::endl; + // memcpy(newArray + dataIdx, m_data.m_lower + m_rowStartIndex[row], nbLowerElts * sizeof (Scalar)); + // m_rowStartIndex[row] = dataIdx; + // dataIdx += nbLowerElts; + // + // const Index nbUpperElts = m_colStartIndex[row + 1] - m_colStartIndex[row]; + // memcpy(newArray + dataIdx, m_data.m_upper + m_colStartIndex[row], nbUpperElts * sizeof (Scalar)); + // m_colStartIndex[row] = dataIdx; + // dataIdx += nbUpperElts; + // + // + // } + // //todo : don't access m_data profile directly : add an accessor from SkylineMatrix + // m_rowStartIndex[rows()] = m_rowStartIndex[rows()-1] + m_data.lowerProfile(rows()-1); + // m_colStartIndex[cols()] = m_colStartIndex[cols()-1] + m_data.upperProfile(cols()-1); + // + // delete[] m_data.m_lower; + // delete[] m_data.m_upper; + // + // m_data.m_lower = newArray; + // m_data.m_upper = newArray; + } else { + if (rows() > cols()) + m_data.resize(cols(), rows(), cols(), m_rowStartIndex[cols()] + 1, m_colStartIndex[cols()] + 1); + else + m_data.resize(rows(), rows(), cols(), m_rowStartIndex[rows()] + 1, m_colStartIndex[rows()] + 1); + } + } + + inline void squeeze() { + finalize(); + m_data.squeeze(); + } + + void prune(Scalar reference, RealScalar epsilon = dummy_precision<RealScalar > ()) { + //TODO + } + + /** Resizes the matrix to a \a rows x \a cols matrix and initializes it to zero + * \sa resizeNonZeros(Index), reserve(), setZero() + */ + void resize(size_t rows, size_t cols) { + const Index diagSize = rows > cols ? cols : rows; + m_innerSize = IsRowMajor ? cols : rows; + + eigen_assert(rows == cols && "Skyline matrix must be square matrix"); + + if (diagSize % 2) { // diagSize is odd + const Index k = (diagSize - 1) / 2; + + m_data.resize(diagSize, IsRowMajor ? cols : rows, IsRowMajor ? rows : cols, + 2 * k * k + k + 1, + 2 * k * k + k + 1); + + } else // diagSize is even + { + const Index k = diagSize / 2; + m_data.resize(diagSize, IsRowMajor ? cols : rows, IsRowMajor ? rows : cols, + 2 * k * k - k + 1, + 2 * k * k - k + 1); + } + + if (m_colStartIndex && m_rowStartIndex) { + delete[] m_colStartIndex; + delete[] m_rowStartIndex; + } + m_colStartIndex = new Index [cols + 1]; + m_rowStartIndex = new Index [rows + 1]; + m_outerSize = diagSize; + + m_data.reset(); + m_data.clear(); + + m_outerSize = diagSize; + memset(m_colStartIndex, 0, (cols + 1) * sizeof (Index)); + memset(m_rowStartIndex, 0, (rows + 1) * sizeof (Index)); + } + + void resizeNonZeros(Index size) { + m_data.resize(size); + } + + inline SkylineMatrix() + : m_outerSize(-1), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) { + resize(0, 0); + } + + inline SkylineMatrix(size_t rows, size_t cols) + : m_outerSize(0), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) { + resize(rows, cols); + } + + template<typename OtherDerived> + inline SkylineMatrix(const SkylineMatrixBase<OtherDerived>& other) + : m_outerSize(0), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) { + *this = other.derived(); + } + + inline SkylineMatrix(const SkylineMatrix & other) + : Base(), m_outerSize(0), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) { + *this = other.derived(); + } + + inline void swap(SkylineMatrix & other) { + //EIGEN_DBG_SKYLINE(std::cout << "SkylineMatrix:: swap\n"); + std::swap(m_colStartIndex, other.m_colStartIndex); + std::swap(m_rowStartIndex, other.m_rowStartIndex); + std::swap(m_innerSize, other.m_innerSize); + std::swap(m_outerSize, other.m_outerSize); + m_data.swap(other.m_data); + } + + inline SkylineMatrix & operator=(const SkylineMatrix & other) { + std::cout << "SkylineMatrix& operator=(const SkylineMatrix& other)\n"; + if (other.isRValue()) { + swap(other.const_cast_derived()); + } else { + resize(other.rows(), other.cols()); + memcpy(m_colStartIndex, other.m_colStartIndex, (m_outerSize + 1) * sizeof (Index)); + memcpy(m_rowStartIndex, other.m_rowStartIndex, (m_outerSize + 1) * sizeof (Index)); + m_data = other.m_data; + } + return *this; + } + + template<typename OtherDerived> + inline SkylineMatrix & operator=(const SkylineMatrixBase<OtherDerived>& other) { + const bool needToTranspose = (Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit); + if (needToTranspose) { + // TODO + // return *this; + } else { + // there is no special optimization + return SkylineMatrixBase<SkylineMatrix>::operator=(other.derived()); + } + } + + friend std::ostream & operator <<(std::ostream & s, const SkylineMatrix & m) { + + EIGEN_DBG_SKYLINE( + std::cout << "upper elements : " << std::endl; + for (Index i = 0; i < m.m_data.upperSize(); i++) + std::cout << m.m_data.upper(i) << "\t"; + std::cout << std::endl; + std::cout << "upper profile : " << std::endl; + for (Index i = 0; i < m.m_data.upperProfileSize(); i++) + std::cout << m.m_data.upperProfile(i) << "\t"; + std::cout << std::endl; + std::cout << "lower startIdx : " << std::endl; + for (Index i = 0; i < m.m_data.upperProfileSize(); i++) + std::cout << (IsRowMajor ? m.m_colStartIndex[i] : m.m_rowStartIndex[i]) << "\t"; + std::cout << std::endl; + + + std::cout << "lower elements : " << std::endl; + for (Index i = 0; i < m.m_data.lowerSize(); i++) + std::cout << m.m_data.lower(i) << "\t"; + std::cout << std::endl; + std::cout << "lower profile : " << std::endl; + for (Index i = 0; i < m.m_data.lowerProfileSize(); i++) + std::cout << m.m_data.lowerProfile(i) << "\t"; + std::cout << std::endl; + std::cout << "lower startIdx : " << std::endl; + for (Index i = 0; i < m.m_data.lowerProfileSize(); i++) + std::cout << (IsRowMajor ? m.m_rowStartIndex[i] : m.m_colStartIndex[i]) << "\t"; + std::cout << std::endl; + ); + for (Index rowIdx = 0; rowIdx < m.rows(); rowIdx++) { + for (Index colIdx = 0; colIdx < m.cols(); colIdx++) { + s << m.coeff(rowIdx, colIdx) << "\t"; + } + s << std::endl; + } + return s; + } + + /** Destructor */ + inline ~SkylineMatrix() { + delete[] m_colStartIndex; + delete[] m_rowStartIndex; + } + + /** Overloaded for performance */ + Scalar sum() const; +}; + +template<typename Scalar, int _Options> +class SkylineMatrix<Scalar, _Options>::InnerUpperIterator { +public: + + InnerUpperIterator(const SkylineMatrix& mat, Index outer) + : m_matrix(mat), m_outer(outer), + m_id(_Options == RowMajor ? mat.m_colStartIndex[outer] : mat.m_rowStartIndex[outer] + 1), + m_start(m_id), + m_end(_Options == RowMajor ? mat.m_colStartIndex[outer + 1] : mat.m_rowStartIndex[outer + 1] + 1) { + } + + inline InnerUpperIterator & operator++() { + m_id++; + return *this; + } + + inline InnerUpperIterator & operator+=(Index shift) { + m_id += shift; + return *this; + } + + inline Scalar value() const { + return m_matrix.m_data.upper(m_id); + } + + inline Scalar* valuePtr() { + return const_cast<Scalar*> (&(m_matrix.m_data.upper(m_id))); + } + + inline Scalar& valueRef() { + return const_cast<Scalar&> (m_matrix.m_data.upper(m_id)); + } + + inline Index index() const { + return IsRowMajor ? m_outer - m_matrix.m_data.upperProfile(m_outer) + (m_id - m_start) : + m_outer + (m_id - m_start) + 1; + } + + inline Index row() const { + return IsRowMajor ? index() : m_outer; + } + + inline Index col() const { + return IsRowMajor ? m_outer : index(); + } + + inline size_t size() const { + return m_matrix.m_data.upperProfile(m_outer); + } + + inline operator bool() const { + return (m_id < m_end) && (m_id >= m_start); + } + +protected: + const SkylineMatrix& m_matrix; + const Index m_outer; + Index m_id; + const Index m_start; + const Index m_end; +}; + +template<typename Scalar, int _Options> +class SkylineMatrix<Scalar, _Options>::InnerLowerIterator { +public: + + InnerLowerIterator(const SkylineMatrix& mat, Index outer) + : m_matrix(mat), + m_outer(outer), + m_id(_Options == RowMajor ? mat.m_rowStartIndex[outer] : mat.m_colStartIndex[outer] + 1), + m_start(m_id), + m_end(_Options == RowMajor ? mat.m_rowStartIndex[outer + 1] : mat.m_colStartIndex[outer + 1] + 1) { + } + + inline InnerLowerIterator & operator++() { + m_id++; + return *this; + } + + inline InnerLowerIterator & operator+=(Index shift) { + m_id += shift; + return *this; + } + + inline Scalar value() const { + return m_matrix.m_data.lower(m_id); + } + + inline Scalar* valuePtr() { + return const_cast<Scalar*> (&(m_matrix.m_data.lower(m_id))); + } + + inline Scalar& valueRef() { + return const_cast<Scalar&> (m_matrix.m_data.lower(m_id)); + } + + inline Index index() const { + return IsRowMajor ? m_outer - m_matrix.m_data.lowerProfile(m_outer) + (m_id - m_start) : + m_outer + (m_id - m_start) + 1; + ; + } + + inline Index row() const { + return IsRowMajor ? m_outer : index(); + } + + inline Index col() const { + return IsRowMajor ? index() : m_outer; + } + + inline size_t size() const { + return m_matrix.m_data.lowerProfile(m_outer); + } + + inline operator bool() const { + return (m_id < m_end) && (m_id >= m_start); + } + +protected: + const SkylineMatrix& m_matrix; + const Index m_outer; + Index m_id; + const Index m_start; + const Index m_end; +}; + +} // end namespace Eigen + +#endif // EIGEN_SkylineMatrix_H diff --git a/unsupported/Eigen/src/Skyline/SkylineMatrixBase.h b/unsupported/Eigen/src/Skyline/SkylineMatrixBase.h new file mode 100644 index 000000000..b3a237230 --- /dev/null +++ b/unsupported/Eigen/src/Skyline/SkylineMatrixBase.h @@ -0,0 +1,212 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SKYLINEMATRIXBASE_H +#define EIGEN_SKYLINEMATRIXBASE_H + +#include "SkylineUtil.h" + +namespace Eigen { + +/** \ingroup Skyline_Module + * + * \class SkylineMatrixBase + * + * \brief Base class of any skyline matrices or skyline expressions + * + * \param Derived + * + */ +template<typename Derived> class SkylineMatrixBase : public EigenBase<Derived> { +public: + + typedef typename internal::traits<Derived>::Scalar Scalar; + typedef typename internal::traits<Derived>::StorageKind StorageKind; + typedef typename internal::index<StorageKind>::type Index; + + enum { + RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime, + /**< The number of rows at compile-time. This is just a copy of the value provided + * by the \a Derived type. If a value is not known at compile-time, + * it is set to the \a Dynamic constant. + * \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */ + + ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime, + /**< The number of columns at compile-time. This is just a copy of the value provided + * by the \a Derived type. If a value is not known at compile-time, + * it is set to the \a Dynamic constant. + * \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */ + + + SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime, + internal::traits<Derived>::ColsAtCompileTime>::ret), + /**< This is equal to the number of coefficients, i.e. the number of + * rows times the number of columns, or to \a Dynamic if this is not + * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */ + + MaxRowsAtCompileTime = RowsAtCompileTime, + MaxColsAtCompileTime = ColsAtCompileTime, + + MaxSizeAtCompileTime = (internal::size_at_compile_time<MaxRowsAtCompileTime, + MaxColsAtCompileTime>::ret), + + IsVectorAtCompileTime = RowsAtCompileTime == 1 || ColsAtCompileTime == 1, + /**< This is set to true if either the number of rows or the number of + * columns is known at compile-time to be equal to 1. Indeed, in that case, + * we are dealing with a column-vector (if there is only one column) or with + * a row-vector (if there is only one row). */ + + Flags = internal::traits<Derived>::Flags, + /**< This stores expression \ref flags flags which may or may not be inherited by new expressions + * constructed from this one. See the \ref flags "list of flags". + */ + + CoeffReadCost = internal::traits<Derived>::CoeffReadCost, + /**< This is a rough measure of how expensive it is to read one coefficient from + * this expression. + */ + + IsRowMajor = Flags & RowMajorBit ? 1 : 0 + }; + +#ifndef EIGEN_PARSED_BY_DOXYGEN + /** This is the "real scalar" type; if the \a Scalar type is already real numbers + * (e.g. int, float or double) then \a RealScalar is just the same as \a Scalar. If + * \a Scalar is \a std::complex<T> then RealScalar is \a T. + * + * \sa class NumTraits + */ + typedef typename NumTraits<Scalar>::Real RealScalar; + + /** type of the equivalent square matrix */ + typedef Matrix<Scalar, EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime), + EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime) > SquareMatrixType; + + inline const Derived& derived() const { + return *static_cast<const Derived*> (this); + } + + inline Derived& derived() { + return *static_cast<Derived*> (this); + } + + inline Derived& const_cast_derived() const { + return *static_cast<Derived*> (const_cast<SkylineMatrixBase*> (this)); + } +#endif // not EIGEN_PARSED_BY_DOXYGEN + + /** \returns the number of rows. \sa cols(), RowsAtCompileTime */ + inline Index rows() const { + return derived().rows(); + } + + /** \returns the number of columns. \sa rows(), ColsAtCompileTime*/ + inline Index cols() const { + return derived().cols(); + } + + /** \returns the number of coefficients, which is \a rows()*cols(). + * \sa rows(), cols(), SizeAtCompileTime. */ + inline Index size() const { + return rows() * cols(); + } + + /** \returns the number of nonzero coefficients which is in practice the number + * of stored coefficients. */ + inline Index nonZeros() const { + return derived().nonZeros(); + } + + /** \returns the size of the storage major dimension, + * i.e., the number of columns for a columns major matrix, and the number of rows otherwise */ + Index outerSize() const { + return (int(Flags) & RowMajorBit) ? this->rows() : this->cols(); + } + + /** \returns the size of the inner dimension according to the storage order, + * i.e., the number of rows for a columns major matrix, and the number of cols otherwise */ + Index innerSize() const { + return (int(Flags) & RowMajorBit) ? this->cols() : this->rows(); + } + + bool isRValue() const { + return m_isRValue; + } + + Derived& markAsRValue() { + m_isRValue = true; + return derived(); + } + + SkylineMatrixBase() : m_isRValue(false) { + /* TODO check flags */ + } + + inline Derived & operator=(const Derived& other) { + this->operator=<Derived > (other); + return derived(); + } + + template<typename OtherDerived> + inline void assignGeneric(const OtherDerived& other) { + derived().resize(other.rows(), other.cols()); + for (Index row = 0; row < rows(); row++) + for (Index col = 0; col < cols(); col++) { + if (other.coeff(row, col) != Scalar(0)) + derived().insert(row, col) = other.coeff(row, col); + } + derived().finalize(); + } + + template<typename OtherDerived> + inline Derived & operator=(const SkylineMatrixBase<OtherDerived>& other) { + //TODO + } + + template<typename Lhs, typename Rhs> + inline Derived & operator=(const SkylineProduct<Lhs, Rhs, SkylineTimeSkylineProduct>& product); + + friend std::ostream & operator <<(std::ostream & s, const SkylineMatrixBase& m) { + s << m.derived(); + return s; + } + + template<typename OtherDerived> + const typename SkylineProductReturnType<Derived, OtherDerived>::Type + operator*(const MatrixBase<OtherDerived> &other) const; + + /** \internal use operator= */ + template<typename DenseDerived> + void evalTo(MatrixBase<DenseDerived>& dst) const { + dst.setZero(); + for (Index i = 0; i < rows(); i++) + for (Index j = 0; j < rows(); j++) + dst(i, j) = derived().coeff(i, j); + } + + Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime> toDense() const { + return derived(); + } + + /** \returns the matrix or vector obtained by evaluating this expression. + * + * Notice that in the case of a plain matrix or vector (not an expression) this function just returns + * a const reference, in order to avoid a useless copy. + */ + EIGEN_STRONG_INLINE const typename internal::eval<Derived, IsSkyline>::type eval() const { + return typename internal::eval<Derived>::type(derived()); + } + +protected: + bool m_isRValue; +}; + +} // end namespace Eigen + +#endif // EIGEN_SkylineMatrixBase_H diff --git a/unsupported/Eigen/src/Skyline/SkylineProduct.h b/unsupported/Eigen/src/Skyline/SkylineProduct.h new file mode 100644 index 000000000..1ddf455e2 --- /dev/null +++ b/unsupported/Eigen/src/Skyline/SkylineProduct.h @@ -0,0 +1,295 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SKYLINEPRODUCT_H +#define EIGEN_SKYLINEPRODUCT_H + +namespace Eigen { + +template<typename Lhs, typename Rhs, int ProductMode> +struct SkylineProductReturnType { + typedef const typename internal::nested<Lhs, Rhs::RowsAtCompileTime>::type LhsNested; + typedef const typename internal::nested<Rhs, Lhs::RowsAtCompileTime>::type RhsNested; + + typedef SkylineProduct<LhsNested, RhsNested, ProductMode> Type; +}; + +template<typename LhsNested, typename RhsNested, int ProductMode> +struct internal::traits<SkylineProduct<LhsNested, RhsNested, ProductMode> > { + // clean the nested types: + typedef typename internal::remove_all<LhsNested>::type _LhsNested; + typedef typename internal::remove_all<RhsNested>::type _RhsNested; + typedef typename _LhsNested::Scalar Scalar; + + enum { + LhsCoeffReadCost = _LhsNested::CoeffReadCost, + RhsCoeffReadCost = _RhsNested::CoeffReadCost, + LhsFlags = _LhsNested::Flags, + RhsFlags = _RhsNested::Flags, + + RowsAtCompileTime = _LhsNested::RowsAtCompileTime, + ColsAtCompileTime = _RhsNested::ColsAtCompileTime, + InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(_LhsNested::ColsAtCompileTime, _RhsNested::RowsAtCompileTime), + + MaxRowsAtCompileTime = _LhsNested::MaxRowsAtCompileTime, + MaxColsAtCompileTime = _RhsNested::MaxColsAtCompileTime, + + EvalToRowMajor = (RhsFlags & LhsFlags & RowMajorBit), + ResultIsSkyline = ProductMode == SkylineTimeSkylineProduct, + + RemovedBits = ~((EvalToRowMajor ? 0 : RowMajorBit) | (ResultIsSkyline ? 0 : SkylineBit)), + + Flags = (int(LhsFlags | RhsFlags) & HereditaryBits & RemovedBits) + | EvalBeforeAssigningBit + | EvalBeforeNestingBit, + + CoeffReadCost = Dynamic + }; + + typedef typename internal::conditional<ResultIsSkyline, + SkylineMatrixBase<SkylineProduct<LhsNested, RhsNested, ProductMode> >, + MatrixBase<SkylineProduct<LhsNested, RhsNested, ProductMode> > >::type Base; +}; + +namespace internal { +template<typename LhsNested, typename RhsNested, int ProductMode> +class SkylineProduct : no_assignment_operator, +public traits<SkylineProduct<LhsNested, RhsNested, ProductMode> >::Base { +public: + + EIGEN_GENERIC_PUBLIC_INTERFACE(SkylineProduct) + +private: + + typedef typename traits<SkylineProduct>::_LhsNested _LhsNested; + typedef typename traits<SkylineProduct>::_RhsNested _RhsNested; + +public: + + template<typename Lhs, typename Rhs> + EIGEN_STRONG_INLINE SkylineProduct(const Lhs& lhs, const Rhs& rhs) + : m_lhs(lhs), m_rhs(rhs) { + eigen_assert(lhs.cols() == rhs.rows()); + + enum { + ProductIsValid = _LhsNested::ColsAtCompileTime == Dynamic + || _RhsNested::RowsAtCompileTime == Dynamic + || int(_LhsNested::ColsAtCompileTime) == int(_RhsNested::RowsAtCompileTime), + AreVectors = _LhsNested::IsVectorAtCompileTime && _RhsNested::IsVectorAtCompileTime, + SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(_LhsNested, _RhsNested) + }; + // note to the lost user: + // * for a dot product use: v1.dot(v2) + // * for a coeff-wise product use: v1.cwise()*v2 + EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes), + INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS) + EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors), + INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION) + EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT) + } + + EIGEN_STRONG_INLINE Index rows() const { + return m_lhs.rows(); + } + + EIGEN_STRONG_INLINE Index cols() const { + return m_rhs.cols(); + } + + EIGEN_STRONG_INLINE const _LhsNested& lhs() const { + return m_lhs; + } + + EIGEN_STRONG_INLINE const _RhsNested& rhs() const { + return m_rhs; + } + +protected: + LhsNested m_lhs; + RhsNested m_rhs; +}; + +// dense = skyline * dense +// Note that here we force no inlining and separate the setZero() because GCC messes up otherwise + +template<typename Lhs, typename Rhs, typename Dest> +EIGEN_DONT_INLINE void skyline_row_major_time_dense_product(const Lhs& lhs, const Rhs& rhs, Dest& dst) { + typedef typename remove_all<Lhs>::type _Lhs; + typedef typename remove_all<Rhs>::type _Rhs; + typedef typename traits<Lhs>::Scalar Scalar; + + enum { + LhsIsRowMajor = (_Lhs::Flags & RowMajorBit) == RowMajorBit, + LhsIsSelfAdjoint = (_Lhs::Flags & SelfAdjointBit) == SelfAdjointBit, + ProcessFirstHalf = LhsIsSelfAdjoint + && (((_Lhs::Flags & (UpperTriangularBit | LowerTriangularBit)) == 0) + || ((_Lhs::Flags & UpperTriangularBit) && !LhsIsRowMajor) + || ((_Lhs::Flags & LowerTriangularBit) && LhsIsRowMajor)), + ProcessSecondHalf = LhsIsSelfAdjoint && (!ProcessFirstHalf) + }; + + //Use matrix diagonal part <- Improvement : use inner iterator on dense matrix. + for (Index col = 0; col < rhs.cols(); col++) { + for (Index row = 0; row < lhs.rows(); row++) { + dst(row, col) = lhs.coeffDiag(row) * rhs(row, col); + } + } + //Use matrix lower triangular part + for (Index row = 0; row < lhs.rows(); row++) { + typename _Lhs::InnerLowerIterator lIt(lhs, row); + const Index stop = lIt.col() + lIt.size(); + for (Index col = 0; col < rhs.cols(); col++) { + + Index k = lIt.col(); + Scalar tmp = 0; + while (k < stop) { + tmp += + lIt.value() * + rhs(k++, col); + ++lIt; + } + dst(row, col) += tmp; + lIt += -lIt.size(); + } + + } + + //Use matrix upper triangular part + for (Index lhscol = 0; lhscol < lhs.cols(); lhscol++) { + typename _Lhs::InnerUpperIterator uIt(lhs, lhscol); + const Index stop = uIt.size() + uIt.row(); + for (Index rhscol = 0; rhscol < rhs.cols(); rhscol++) { + + + const Scalar rhsCoeff = rhs.coeff(lhscol, rhscol); + Index k = uIt.row(); + while (k < stop) { + dst(k++, rhscol) += + uIt.value() * + rhsCoeff; + ++uIt; + } + uIt += -uIt.size(); + } + } + +} + +template<typename Lhs, typename Rhs, typename Dest> +EIGEN_DONT_INLINE void skyline_col_major_time_dense_product(const Lhs& lhs, const Rhs& rhs, Dest& dst) { + typedef typename remove_all<Lhs>::type _Lhs; + typedef typename remove_all<Rhs>::type _Rhs; + typedef typename traits<Lhs>::Scalar Scalar; + + enum { + LhsIsRowMajor = (_Lhs::Flags & RowMajorBit) == RowMajorBit, + LhsIsSelfAdjoint = (_Lhs::Flags & SelfAdjointBit) == SelfAdjointBit, + ProcessFirstHalf = LhsIsSelfAdjoint + && (((_Lhs::Flags & (UpperTriangularBit | LowerTriangularBit)) == 0) + || ((_Lhs::Flags & UpperTriangularBit) && !LhsIsRowMajor) + || ((_Lhs::Flags & LowerTriangularBit) && LhsIsRowMajor)), + ProcessSecondHalf = LhsIsSelfAdjoint && (!ProcessFirstHalf) + }; + + //Use matrix diagonal part <- Improvement : use inner iterator on dense matrix. + for (Index col = 0; col < rhs.cols(); col++) { + for (Index row = 0; row < lhs.rows(); row++) { + dst(row, col) = lhs.coeffDiag(row) * rhs(row, col); + } + } + + //Use matrix upper triangular part + for (Index row = 0; row < lhs.rows(); row++) { + typename _Lhs::InnerUpperIterator uIt(lhs, row); + const Index stop = uIt.col() + uIt.size(); + for (Index col = 0; col < rhs.cols(); col++) { + + Index k = uIt.col(); + Scalar tmp = 0; + while (k < stop) { + tmp += + uIt.value() * + rhs(k++, col); + ++uIt; + } + + + dst(row, col) += tmp; + uIt += -uIt.size(); + } + } + + //Use matrix lower triangular part + for (Index lhscol = 0; lhscol < lhs.cols(); lhscol++) { + typename _Lhs::InnerLowerIterator lIt(lhs, lhscol); + const Index stop = lIt.size() + lIt.row(); + for (Index rhscol = 0; rhscol < rhs.cols(); rhscol++) { + + const Scalar rhsCoeff = rhs.coeff(lhscol, rhscol); + Index k = lIt.row(); + while (k < stop) { + dst(k++, rhscol) += + lIt.value() * + rhsCoeff; + ++lIt; + } + lIt += -lIt.size(); + } + } + +} + +template<typename Lhs, typename Rhs, typename ResultType, + int LhsStorageOrder = traits<Lhs>::Flags&RowMajorBit> + struct skyline_product_selector; + +template<typename Lhs, typename Rhs, typename ResultType> +struct skyline_product_selector<Lhs, Rhs, ResultType, RowMajor> { + typedef typename traits<typename remove_all<Lhs>::type>::Scalar Scalar; + + static void run(const Lhs& lhs, const Rhs& rhs, ResultType & res) { + skyline_row_major_time_dense_product<Lhs, Rhs, ResultType > (lhs, rhs, res); + } +}; + +template<typename Lhs, typename Rhs, typename ResultType> +struct skyline_product_selector<Lhs, Rhs, ResultType, ColMajor> { + typedef typename traits<typename remove_all<Lhs>::type>::Scalar Scalar; + + static void run(const Lhs& lhs, const Rhs& rhs, ResultType & res) { + skyline_col_major_time_dense_product<Lhs, Rhs, ResultType > (lhs, rhs, res); + } +}; + +} // end namespace internal + +// template<typename Derived> +// template<typename Lhs, typename Rhs > +// Derived & MatrixBase<Derived>::lazyAssign(const SkylineProduct<Lhs, Rhs, SkylineTimeDenseProduct>& product) { +// typedef typename internal::remove_all<Lhs>::type _Lhs; +// internal::skyline_product_selector<typename internal::remove_all<Lhs>::type, +// typename internal::remove_all<Rhs>::type, +// Derived>::run(product.lhs(), product.rhs(), derived()); +// +// return derived(); +// } + +// skyline * dense + +template<typename Derived> +template<typename OtherDerived > +EIGEN_STRONG_INLINE const typename SkylineProductReturnType<Derived, OtherDerived>::Type +SkylineMatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const { + + return typename SkylineProductReturnType<Derived, OtherDerived>::Type(derived(), other.derived()); +} + +} // end namespace Eigen + +#endif // EIGEN_SKYLINEPRODUCT_H diff --git a/unsupported/Eigen/src/Skyline/SkylineStorage.h b/unsupported/Eigen/src/Skyline/SkylineStorage.h new file mode 100644 index 000000000..378a8deb4 --- /dev/null +++ b/unsupported/Eigen/src/Skyline/SkylineStorage.h @@ -0,0 +1,259 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SKYLINE_STORAGE_H +#define EIGEN_SKYLINE_STORAGE_H + +namespace Eigen { + +/** Stores a skyline set of values in three structures : + * The diagonal elements + * The upper elements + * The lower elements + * + */ +template<typename Scalar> +class SkylineStorage { + typedef typename NumTraits<Scalar>::Real RealScalar; + typedef SparseIndex Index; +public: + + SkylineStorage() + : m_diag(0), + m_lower(0), + m_upper(0), + m_lowerProfile(0), + m_upperProfile(0), + m_diagSize(0), + m_upperSize(0), + m_lowerSize(0), + m_upperProfileSize(0), + m_lowerProfileSize(0), + m_allocatedSize(0) { + } + + SkylineStorage(const SkylineStorage& other) + : m_diag(0), + m_lower(0), + m_upper(0), + m_lowerProfile(0), + m_upperProfile(0), + m_diagSize(0), + m_upperSize(0), + m_lowerSize(0), + m_upperProfileSize(0), + m_lowerProfileSize(0), + m_allocatedSize(0) { + *this = other; + } + + SkylineStorage & operator=(const SkylineStorage& other) { + resize(other.diagSize(), other.m_upperProfileSize, other.m_lowerProfileSize, other.upperSize(), other.lowerSize()); + memcpy(m_diag, other.m_diag, m_diagSize * sizeof (Scalar)); + memcpy(m_upper, other.m_upper, other.upperSize() * sizeof (Scalar)); + memcpy(m_lower, other.m_lower, other.lowerSize() * sizeof (Scalar)); + memcpy(m_upperProfile, other.m_upperProfile, m_upperProfileSize * sizeof (Index)); + memcpy(m_lowerProfile, other.m_lowerProfile, m_lowerProfileSize * sizeof (Index)); + return *this; + } + + void swap(SkylineStorage& other) { + std::swap(m_diag, other.m_diag); + std::swap(m_upper, other.m_upper); + std::swap(m_lower, other.m_lower); + std::swap(m_upperProfile, other.m_upperProfile); + std::swap(m_lowerProfile, other.m_lowerProfile); + std::swap(m_diagSize, other.m_diagSize); + std::swap(m_upperSize, other.m_upperSize); + std::swap(m_lowerSize, other.m_lowerSize); + std::swap(m_allocatedSize, other.m_allocatedSize); + } + + ~SkylineStorage() { + delete[] m_diag; + delete[] m_upper; + if (m_upper != m_lower) + delete[] m_lower; + delete[] m_upperProfile; + delete[] m_lowerProfile; + } + + void reserve(Index size, Index upperProfileSize, Index lowerProfileSize, Index upperSize, Index lowerSize) { + Index newAllocatedSize = size + upperSize + lowerSize; + if (newAllocatedSize > m_allocatedSize) + reallocate(size, upperProfileSize, lowerProfileSize, upperSize, lowerSize); + } + + void squeeze() { + if (m_allocatedSize > m_diagSize + m_upperSize + m_lowerSize) + reallocate(m_diagSize, m_upperProfileSize, m_lowerProfileSize, m_upperSize, m_lowerSize); + } + + void resize(Index diagSize, Index upperProfileSize, Index lowerProfileSize, Index upperSize, Index lowerSize, float reserveSizeFactor = 0) { + if (m_allocatedSize < diagSize + upperSize + lowerSize) + reallocate(diagSize, upperProfileSize, lowerProfileSize, upperSize + Index(reserveSizeFactor * upperSize), lowerSize + Index(reserveSizeFactor * lowerSize)); + m_diagSize = diagSize; + m_upperSize = upperSize; + m_lowerSize = lowerSize; + m_upperProfileSize = upperProfileSize; + m_lowerProfileSize = lowerProfileSize; + } + + inline Index diagSize() const { + return m_diagSize; + } + + inline Index upperSize() const { + return m_upperSize; + } + + inline Index lowerSize() const { + return m_lowerSize; + } + + inline Index upperProfileSize() const { + return m_upperProfileSize; + } + + inline Index lowerProfileSize() const { + return m_lowerProfileSize; + } + + inline Index allocatedSize() const { + return m_allocatedSize; + } + + inline void clear() { + m_diagSize = 0; + } + + inline Scalar& diag(Index i) { + return m_diag[i]; + } + + inline const Scalar& diag(Index i) const { + return m_diag[i]; + } + + inline Scalar& upper(Index i) { + return m_upper[i]; + } + + inline const Scalar& upper(Index i) const { + return m_upper[i]; + } + + inline Scalar& lower(Index i) { + return m_lower[i]; + } + + inline const Scalar& lower(Index i) const { + return m_lower[i]; + } + + inline Index& upperProfile(Index i) { + return m_upperProfile[i]; + } + + inline const Index& upperProfile(Index i) const { + return m_upperProfile[i]; + } + + inline Index& lowerProfile(Index i) { + return m_lowerProfile[i]; + } + + inline const Index& lowerProfile(Index i) const { + return m_lowerProfile[i]; + } + + static SkylineStorage Map(Index* upperProfile, Index* lowerProfile, Scalar* diag, Scalar* upper, Scalar* lower, Index size, Index upperSize, Index lowerSize) { + SkylineStorage res; + res.m_upperProfile = upperProfile; + res.m_lowerProfile = lowerProfile; + res.m_diag = diag; + res.m_upper = upper; + res.m_lower = lower; + res.m_allocatedSize = res.m_diagSize = size; + res.m_upperSize = upperSize; + res.m_lowerSize = lowerSize; + return res; + } + + inline void reset() { + memset(m_diag, 0, m_diagSize * sizeof (Scalar)); + memset(m_upper, 0, m_upperSize * sizeof (Scalar)); + memset(m_lower, 0, m_lowerSize * sizeof (Scalar)); + memset(m_upperProfile, 0, m_diagSize * sizeof (Index)); + memset(m_lowerProfile, 0, m_diagSize * sizeof (Index)); + } + + void prune(Scalar reference, RealScalar epsilon = dummy_precision<RealScalar>()) { + //TODO + } + +protected: + + inline void reallocate(Index diagSize, Index upperProfileSize, Index lowerProfileSize, Index upperSize, Index lowerSize) { + + Scalar* diag = new Scalar[diagSize]; + Scalar* upper = new Scalar[upperSize]; + Scalar* lower = new Scalar[lowerSize]; + Index* upperProfile = new Index[upperProfileSize]; + Index* lowerProfile = new Index[lowerProfileSize]; + + Index copyDiagSize = (std::min)(diagSize, m_diagSize); + Index copyUpperSize = (std::min)(upperSize, m_upperSize); + Index copyLowerSize = (std::min)(lowerSize, m_lowerSize); + Index copyUpperProfileSize = (std::min)(upperProfileSize, m_upperProfileSize); + Index copyLowerProfileSize = (std::min)(lowerProfileSize, m_lowerProfileSize); + + // copy + memcpy(diag, m_diag, copyDiagSize * sizeof (Scalar)); + memcpy(upper, m_upper, copyUpperSize * sizeof (Scalar)); + memcpy(lower, m_lower, copyLowerSize * sizeof (Scalar)); + memcpy(upperProfile, m_upperProfile, copyUpperProfileSize * sizeof (Index)); + memcpy(lowerProfile, m_lowerProfile, copyLowerProfileSize * sizeof (Index)); + + + + // delete old stuff + delete[] m_diag; + delete[] m_upper; + delete[] m_lower; + delete[] m_upperProfile; + delete[] m_lowerProfile; + m_diag = diag; + m_upper = upper; + m_lower = lower; + m_upperProfile = upperProfile; + m_lowerProfile = lowerProfile; + m_allocatedSize = diagSize + upperSize + lowerSize; + m_upperSize = upperSize; + m_lowerSize = lowerSize; + } + +public: + Scalar* m_diag; + Scalar* m_upper; + Scalar* m_lower; + Index* m_upperProfile; + Index* m_lowerProfile; + Index m_diagSize; + Index m_upperSize; + Index m_lowerSize; + Index m_upperProfileSize; + Index m_lowerProfileSize; + Index m_allocatedSize; + +}; + +} // end namespace Eigen + +#endif // EIGEN_COMPRESSED_STORAGE_H diff --git a/unsupported/Eigen/src/Skyline/SkylineUtil.h b/unsupported/Eigen/src/Skyline/SkylineUtil.h new file mode 100644 index 000000000..75eb612f4 --- /dev/null +++ b/unsupported/Eigen/src/Skyline/SkylineUtil.h @@ -0,0 +1,89 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Guillaume Saupin <guillaume.saupin@cea.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SKYLINEUTIL_H +#define EIGEN_SKYLINEUTIL_H + +namespace Eigen { + +#ifdef NDEBUG +#define EIGEN_DBG_SKYLINE(X) +#else +#define EIGEN_DBG_SKYLINE(X) X +#endif + +const unsigned int SkylineBit = 0x1200; +template<typename Lhs, typename Rhs, int ProductMode> class SkylineProduct; +enum AdditionalProductEvaluationMode {SkylineTimeDenseProduct, SkylineTimeSkylineProduct, DenseTimeSkylineProduct}; +enum {IsSkyline = SkylineBit}; + + +#define EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, Op) \ +template<typename OtherDerived> \ +EIGEN_STRONG_INLINE Derived& operator Op(const Eigen::SkylineMatrixBase<OtherDerived>& other) \ +{ \ + return Base::operator Op(other.derived()); \ +} \ +EIGEN_STRONG_INLINE Derived& operator Op(const Derived& other) \ +{ \ + return Base::operator Op(other); \ +} + +#define EIGEN_SKYLINE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, Op) \ +template<typename Other> \ +EIGEN_STRONG_INLINE Derived& operator Op(const Other& scalar) \ +{ \ + return Base::operator Op(scalar); \ +} + +#define EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATORS(Derived) \ + EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, =) \ + EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, +=) \ + EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, -=) \ + EIGEN_SKYLINE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, *=) \ + EIGEN_SKYLINE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, /=) + +#define _EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(Derived, BaseClass) \ + typedef BaseClass Base; \ + typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; \ + typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; \ + typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \ + typedef typename Eigen::internal::index<StorageKind>::type Index; \ + enum { Flags = Eigen::internal::traits<Derived>::Flags, }; + +#define EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(Derived) \ + _EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(Derived, Eigen::SkylineMatrixBase<Derived>) + +template<typename Derived> class SkylineMatrixBase; +template<typename _Scalar, int _Flags = 0> class SkylineMatrix; +template<typename _Scalar, int _Flags = 0> class DynamicSkylineMatrix; +template<typename _Scalar, int _Flags = 0> class SkylineVector; +template<typename _Scalar, int _Flags = 0> class MappedSkylineMatrix; + +namespace internal { + +template<typename Lhs, typename Rhs> struct skyline_product_mode; +template<typename Lhs, typename Rhs, int ProductMode = skyline_product_mode<Lhs,Rhs>::value> struct SkylineProductReturnType; + +template<typename T> class eval<T,IsSkyline> +{ + typedef typename traits<T>::Scalar _Scalar; + enum { + _Flags = traits<T>::Flags + }; + + public: + typedef SkylineMatrix<_Scalar, _Flags> type; +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_SKYLINEUTIL_H diff --git a/unsupported/Eigen/src/SparseExtra/BlockOfDynamicSparseMatrix.h b/unsupported/Eigen/src/SparseExtra/BlockOfDynamicSparseMatrix.h new file mode 100644 index 000000000..fd24a732d --- /dev/null +++ b/unsupported/Eigen/src/SparseExtra/BlockOfDynamicSparseMatrix.h @@ -0,0 +1,114 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPARSE_BLOCKFORDYNAMICMATRIX_H +#define EIGEN_SPARSE_BLOCKFORDYNAMICMATRIX_H + +namespace Eigen { + +/*************************************************************************** +* specialisation for DynamicSparseMatrix +***************************************************************************/ + +template<typename _Scalar, int _Options, typename _Index, int Size> +class SparseInnerVectorSet<DynamicSparseMatrix<_Scalar, _Options, _Index>, Size> + : public SparseMatrixBase<SparseInnerVectorSet<DynamicSparseMatrix<_Scalar, _Options, _Index>, Size> > +{ + typedef DynamicSparseMatrix<_Scalar, _Options, _Index> MatrixType; + public: + + enum { IsRowMajor = internal::traits<SparseInnerVectorSet>::IsRowMajor }; + + EIGEN_SPARSE_PUBLIC_INTERFACE(SparseInnerVectorSet) + class InnerIterator: public MatrixType::InnerIterator + { + public: + inline InnerIterator(const SparseInnerVectorSet& xpr, Index outer) + : MatrixType::InnerIterator(xpr.m_matrix, xpr.m_outerStart + outer), m_outer(outer) + {} + inline Index row() const { return IsRowMajor ? m_outer : this->index(); } + inline Index col() const { return IsRowMajor ? this->index() : m_outer; } + protected: + Index m_outer; + }; + + inline SparseInnerVectorSet(const MatrixType& matrix, Index outerStart, Index outerSize) + : m_matrix(matrix), m_outerStart(outerStart), m_outerSize(outerSize) + { + eigen_assert( (outerStart>=0) && ((outerStart+outerSize)<=matrix.outerSize()) ); + } + + inline SparseInnerVectorSet(const MatrixType& matrix, Index outer) + : m_matrix(matrix), m_outerStart(outer), m_outerSize(Size) + { + eigen_assert(Size!=Dynamic); + eigen_assert( (outer>=0) && (outer<matrix.outerSize()) ); + } + + template<typename OtherDerived> + inline SparseInnerVectorSet& operator=(const SparseMatrixBase<OtherDerived>& other) + { + if (IsRowMajor != ((OtherDerived::Flags&RowMajorBit)==RowMajorBit)) + { + // need to transpose => perform a block evaluation followed by a big swap + DynamicSparseMatrix<Scalar,IsRowMajor?RowMajorBit:0> aux(other); + *this = aux.markAsRValue(); + } + else + { + // evaluate/copy vector per vector + for (Index j=0; j<m_outerSize.value(); ++j) + { + SparseVector<Scalar,IsRowMajor ? RowMajorBit : 0> aux(other.innerVector(j)); + m_matrix.const_cast_derived()._data()[m_outerStart+j].swap(aux._data()); + } + } + return *this; + } + + inline SparseInnerVectorSet& operator=(const SparseInnerVectorSet& other) + { + return operator=<SparseInnerVectorSet>(other); + } + + Index nonZeros() const + { + Index count = 0; + for (Index j=0; j<m_outerSize.value(); ++j) + count += m_matrix._data()[m_outerStart+j].size(); + return count; + } + + const Scalar& lastCoeff() const + { + EIGEN_STATIC_ASSERT_VECTOR_ONLY(SparseInnerVectorSet); + eigen_assert(m_matrix.data()[m_outerStart].size()>0); + return m_matrix.data()[m_outerStart].vale(m_matrix.data()[m_outerStart].size()-1); + } + +// template<typename Sparse> +// inline SparseInnerVectorSet& operator=(const SparseMatrixBase<OtherDerived>& other) +// { +// return *this; +// } + + EIGEN_STRONG_INLINE Index rows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); } + EIGEN_STRONG_INLINE Index cols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); } + + protected: + + const typename MatrixType::Nested m_matrix; + Index m_outerStart; + const internal::variable_if_dynamic<Index, Size> m_outerSize; + +}; + +} // end namespace Eigen + +#endif // EIGEN_SPARSE_BLOCKFORDYNAMICMATRIX_H diff --git a/unsupported/Eigen/src/SparseExtra/CMakeLists.txt b/unsupported/Eigen/src/SparseExtra/CMakeLists.txt new file mode 100644 index 000000000..7ea32ca5e --- /dev/null +++ b/unsupported/Eigen/src/SparseExtra/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_SparseExtra_SRCS "*.h") + +INSTALL(FILES + ${Eigen_SparseExtra_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/SparseExtra COMPONENT Devel + ) diff --git a/unsupported/Eigen/src/SparseExtra/DynamicSparseMatrix.h b/unsupported/Eigen/src/SparseExtra/DynamicSparseMatrix.h new file mode 100644 index 000000000..dec16df28 --- /dev/null +++ b/unsupported/Eigen/src/SparseExtra/DynamicSparseMatrix.h @@ -0,0 +1,357 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_DYNAMIC_SPARSEMATRIX_H +#define EIGEN_DYNAMIC_SPARSEMATRIX_H + +namespace Eigen { + +/** \deprecated use a SparseMatrix in an uncompressed mode + * + * \class DynamicSparseMatrix + * + * \brief A sparse matrix class designed for matrix assembly purpose + * + * \param _Scalar the scalar type, i.e. the type of the coefficients + * + * Unlike SparseMatrix, this class provides a much higher degree of flexibility. In particular, it allows + * random read/write accesses in log(rho*outer_size) where \c rho is the probability that a coefficient is + * nonzero and outer_size is the number of columns if the matrix is column-major and the number of rows + * otherwise. + * + * Internally, the data are stored as a std::vector of compressed vector. The performances of random writes might + * decrease as the number of nonzeros per inner-vector increase. In practice, we observed very good performance + * till about 100 nonzeros/vector, and the performance remains relatively good till 500 nonzeros/vectors. + * + * \see SparseMatrix + */ + +namespace internal { +template<typename _Scalar, int _Options, typename _Index> +struct traits<DynamicSparseMatrix<_Scalar, _Options, _Index> > +{ + typedef _Scalar Scalar; + typedef _Index Index; + typedef Sparse StorageKind; + typedef MatrixXpr XprKind; + enum { + RowsAtCompileTime = Dynamic, + ColsAtCompileTime = Dynamic, + MaxRowsAtCompileTime = Dynamic, + MaxColsAtCompileTime = Dynamic, + Flags = _Options | NestByRefBit | LvalueBit, + CoeffReadCost = NumTraits<Scalar>::ReadCost, + SupportedAccessPatterns = OuterRandomAccessPattern + }; +}; +} + +template<typename _Scalar, int _Options, typename _Index> + class DynamicSparseMatrix + : public SparseMatrixBase<DynamicSparseMatrix<_Scalar, _Options, _Index> > +{ + public: + EIGEN_SPARSE_PUBLIC_INTERFACE(DynamicSparseMatrix) + // FIXME: why are these operator already alvailable ??? + // EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(DynamicSparseMatrix, +=) + // EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(DynamicSparseMatrix, -=) + typedef MappedSparseMatrix<Scalar,Flags> Map; + using Base::IsRowMajor; + using Base::operator=; + enum { + Options = _Options + }; + + protected: + + typedef DynamicSparseMatrix<Scalar,(Flags&~RowMajorBit)|(IsRowMajor?RowMajorBit:0)> TransposedSparseMatrix; + + Index m_innerSize; + std::vector<internal::CompressedStorage<Scalar,Index> > m_data; + + public: + + inline Index rows() const { return IsRowMajor ? outerSize() : m_innerSize; } + inline Index cols() const { return IsRowMajor ? m_innerSize : outerSize(); } + inline Index innerSize() const { return m_innerSize; } + inline Index outerSize() const { return static_cast<Index>(m_data.size()); } + inline Index innerNonZeros(Index j) const { return m_data[j].size(); } + + std::vector<internal::CompressedStorage<Scalar,Index> >& _data() { return m_data; } + const std::vector<internal::CompressedStorage<Scalar,Index> >& _data() const { return m_data; } + + /** \returns the coefficient value at given position \a row, \a col + * This operation involes a log(rho*outer_size) binary search. + */ + inline Scalar coeff(Index row, Index col) const + { + const Index outer = IsRowMajor ? row : col; + const Index inner = IsRowMajor ? col : row; + return m_data[outer].at(inner); + } + + /** \returns a reference to the coefficient value at given position \a row, \a col + * This operation involes a log(rho*outer_size) binary search. If the coefficient does not + * exist yet, then a sorted insertion into a sequential buffer is performed. + */ + inline Scalar& coeffRef(Index row, Index col) + { + const Index outer = IsRowMajor ? row : col; + const Index inner = IsRowMajor ? col : row; + return m_data[outer].atWithInsertion(inner); + } + + class InnerIterator; + class ReverseInnerIterator; + + void setZero() + { + for (Index j=0; j<outerSize(); ++j) + m_data[j].clear(); + } + + /** \returns the number of non zero coefficients */ + Index nonZeros() const + { + Index res = 0; + for (Index j=0; j<outerSize(); ++j) + res += static_cast<Index>(m_data[j].size()); + return res; + } + + + + void reserve(Index reserveSize = 1000) + { + if (outerSize()>0) + { + Index reserveSizePerVector = (std::max)(reserveSize/outerSize(),Index(4)); + for (Index j=0; j<outerSize(); ++j) + { + m_data[j].reserve(reserveSizePerVector); + } + } + } + + /** Does nothing: provided for compatibility with SparseMatrix */ + inline void startVec(Index /*outer*/) {} + + /** \returns a reference to the non zero coefficient at position \a row, \a col assuming that: + * - the nonzero does not already exist + * - the new coefficient is the last one of the given inner vector. + * + * \sa insert, insertBackByOuterInner */ + inline Scalar& insertBack(Index row, Index col) + { + return insertBackByOuterInner(IsRowMajor?row:col, IsRowMajor?col:row); + } + + /** \sa insertBack */ + inline Scalar& insertBackByOuterInner(Index outer, Index inner) + { + eigen_assert(outer<Index(m_data.size()) && inner<m_innerSize && "out of range"); + eigen_assert(((m_data[outer].size()==0) || (m_data[outer].index(m_data[outer].size()-1)<inner)) + && "wrong sorted insertion"); + m_data[outer].append(0, inner); + return m_data[outer].value(m_data[outer].size()-1); + } + + inline Scalar& insert(Index row, Index col) + { + const Index outer = IsRowMajor ? row : col; + const Index inner = IsRowMajor ? col : row; + + Index startId = 0; + Index id = static_cast<Index>(m_data[outer].size()) - 1; + m_data[outer].resize(id+2,1); + + while ( (id >= startId) && (m_data[outer].index(id) > inner) ) + { + m_data[outer].index(id+1) = m_data[outer].index(id); + m_data[outer].value(id+1) = m_data[outer].value(id); + --id; + } + m_data[outer].index(id+1) = inner; + m_data[outer].value(id+1) = 0; + return m_data[outer].value(id+1); + } + + /** Does nothing: provided for compatibility with SparseMatrix */ + inline void finalize() {} + + /** Suppress all nonzeros which are smaller than \a reference under the tolerence \a epsilon */ + void prune(Scalar reference, RealScalar epsilon = NumTraits<RealScalar>::dummy_precision()) + { + for (Index j=0; j<outerSize(); ++j) + m_data[j].prune(reference,epsilon); + } + + /** Resize the matrix without preserving the data (the matrix is set to zero) + */ + void resize(Index rows, Index cols) + { + const Index outerSize = IsRowMajor ? rows : cols; + m_innerSize = IsRowMajor ? cols : rows; + setZero(); + if (Index(m_data.size()) != outerSize) + { + m_data.resize(outerSize); + } + } + + void resizeAndKeepData(Index rows, Index cols) + { + const Index outerSize = IsRowMajor ? rows : cols; + const Index innerSize = IsRowMajor ? cols : rows; + if (m_innerSize>innerSize) + { + // remove all coefficients with innerCoord>=innerSize + // TODO + //std::cerr << "not implemented yet\n"; + exit(2); + } + if (m_data.size() != outerSize) + { + m_data.resize(outerSize); + } + } + + /** The class DynamicSparseMatrix is deprectaed */ + EIGEN_DEPRECATED inline DynamicSparseMatrix() + : m_innerSize(0), m_data(0) + { + eigen_assert(innerSize()==0 && outerSize()==0); + } + + /** The class DynamicSparseMatrix is deprectaed */ + EIGEN_DEPRECATED inline DynamicSparseMatrix(Index rows, Index cols) + : m_innerSize(0) + { + resize(rows, cols); + } + + /** The class DynamicSparseMatrix is deprectaed */ + template<typename OtherDerived> + EIGEN_DEPRECATED explicit inline DynamicSparseMatrix(const SparseMatrixBase<OtherDerived>& other) + : m_innerSize(0) + { + Base::operator=(other.derived()); + } + + inline DynamicSparseMatrix(const DynamicSparseMatrix& other) + : Base(), m_innerSize(0) + { + *this = other.derived(); + } + + inline void swap(DynamicSparseMatrix& other) + { + //EIGEN_DBG_SPARSE(std::cout << "SparseMatrix:: swap\n"); + std::swap(m_innerSize, other.m_innerSize); + //std::swap(m_outerSize, other.m_outerSize); + m_data.swap(other.m_data); + } + + inline DynamicSparseMatrix& operator=(const DynamicSparseMatrix& other) + { + if (other.isRValue()) + { + swap(other.const_cast_derived()); + } + else + { + resize(other.rows(), other.cols()); + m_data = other.m_data; + } + return *this; + } + + /** Destructor */ + inline ~DynamicSparseMatrix() {} + + public: + + /** \deprecated + * Set the matrix to zero and reserve the memory for \a reserveSize nonzero coefficients. */ + EIGEN_DEPRECATED void startFill(Index reserveSize = 1000) + { + setZero(); + reserve(reserveSize); + } + + /** \deprecated use insert() + * inserts a nonzero coefficient at given coordinates \a row, \a col and returns its reference assuming that: + * 1 - the coefficient does not exist yet + * 2 - this the coefficient with greater inner coordinate for the given outer coordinate. + * In other words, assuming \c *this is column-major, then there must not exists any nonzero coefficient of coordinates + * \c i \c x \a col such that \c i >= \a row. Otherwise the matrix is invalid. + * + * \see fillrand(), coeffRef() + */ + EIGEN_DEPRECATED Scalar& fill(Index row, Index col) + { + const Index outer = IsRowMajor ? row : col; + const Index inner = IsRowMajor ? col : row; + return insertBack(outer,inner); + } + + /** \deprecated use insert() + * Like fill() but with random inner coordinates. + * Compared to the generic coeffRef(), the unique limitation is that we assume + * the coefficient does not exist yet. + */ + EIGEN_DEPRECATED Scalar& fillrand(Index row, Index col) + { + return insert(row,col); + } + + /** \deprecated use finalize() + * Does nothing. Provided for compatibility with SparseMatrix. */ + EIGEN_DEPRECATED void endFill() {} + +# ifdef EIGEN_DYNAMICSPARSEMATRIX_PLUGIN +# include EIGEN_DYNAMICSPARSEMATRIX_PLUGIN +# endif + }; + +template<typename Scalar, int _Options, typename _Index> +class DynamicSparseMatrix<Scalar,_Options,_Index>::InnerIterator : public SparseVector<Scalar,_Options,_Index>::InnerIterator +{ + typedef typename SparseVector<Scalar,_Options,_Index>::InnerIterator Base; + public: + InnerIterator(const DynamicSparseMatrix& mat, Index outer) + : Base(mat.m_data[outer]), m_outer(outer) + {} + + inline Index row() const { return IsRowMajor ? m_outer : Base::index(); } + inline Index col() const { return IsRowMajor ? Base::index() : m_outer; } + + protected: + const Index m_outer; +}; + +template<typename Scalar, int _Options, typename _Index> +class DynamicSparseMatrix<Scalar,_Options,_Index>::ReverseInnerIterator : public SparseVector<Scalar,_Options,_Index>::ReverseInnerIterator +{ + typedef typename SparseVector<Scalar,_Options,_Index>::ReverseInnerIterator Base; + public: + ReverseInnerIterator(const DynamicSparseMatrix& mat, Index outer) + : Base(mat.m_data[outer]), m_outer(outer) + {} + + inline Index row() const { return IsRowMajor ? m_outer : Base::index(); } + inline Index col() const { return IsRowMajor ? Base::index() : m_outer; } + + protected: + const Index m_outer; +}; + +} // end namespace Eigen + +#endif // EIGEN_DYNAMIC_SPARSEMATRIX_H diff --git a/unsupported/Eigen/src/SparseExtra/MarketIO.h b/unsupported/Eigen/src/SparseExtra/MarketIO.h new file mode 100644 index 000000000..de958de9f --- /dev/null +++ b/unsupported/Eigen/src/SparseExtra/MarketIO.h @@ -0,0 +1,273 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr> +// Copyright (C) 2012 Desire NUENTSA WAKAM <desire.nuentsa_wakam@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPARSE_MARKET_IO_H +#define EIGEN_SPARSE_MARKET_IO_H + +#include <iostream> + +namespace Eigen { + +namespace internal +{ + template <typename Scalar> + inline bool GetMarketLine (std::stringstream& line, int& M, int& N, int& i, int& j, Scalar& value) + { + line >> i >> j >> value; + i--; + j--; + if(i>=0 && j>=0 && i<M && j<N) + { + return true; + } + else + return false; + } + template <typename Scalar> + inline bool GetMarketLine (std::stringstream& line, int& M, int& N, int& i, int& j, std::complex<Scalar>& value) + { + Scalar valR, valI; + line >> i >> j >> valR >> valI; + i--; + j--; + if(i>=0 && j>=0 && i<M && j<N) + { + value = std::complex<Scalar>(valR, valI); + return true; + } + else + return false; + } + + template <typename RealScalar> + inline void GetVectorElt (const std::string& line, RealScalar& val) + { + std::istringstream newline(line); + newline >> val; + } + + template <typename RealScalar> + inline void GetVectorElt (const std::string& line, std::complex<RealScalar>& val) + { + RealScalar valR, valI; + std::istringstream newline(line); + newline >> valR >> valI; + val = std::complex<RealScalar>(valR, valI); + } + + template<typename Scalar> + inline void putMarketHeader(std::string& header,int sym) + { + header= "%%MatrixMarket matrix coordinate "; + if(internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value) + { + header += " complex"; + if(sym == Symmetric) header += " symmetric"; + else if (sym == SelfAdjoint) header += " Hermitian"; + else header += " general"; + } + else + { + header += " real"; + if(sym == Symmetric) header += " symmetric"; + else header += " general"; + } + } + + template<typename Scalar> + inline void PutMatrixElt(Scalar value, int row, int col, std::ofstream& out) + { + out << row << " "<< col << " " << value << "\n"; + } + template<typename Scalar> + inline void PutMatrixElt(std::complex<Scalar> value, int row, int col, std::ofstream& out) + { + out << row << " " << col << " " << value.real() << " " << value.imag() << "\n"; + } + + + template<typename Scalar> + inline void putVectorElt(Scalar value, std::ofstream& out) + { + out << value << "\n"; + } + template<typename Scalar> + inline void putVectorElt(std::complex<Scalar> value, std::ofstream& out) + { + out << value.real << " " << value.imag()<< "\n"; + } + +} // end namepsace internal + +inline bool getMarketHeader(const std::string& filename, int& sym, bool& iscomplex, bool& isvector) +{ + sym = 0; + isvector = false; + std::ifstream in(filename.c_str(),std::ios::in); + if(!in) + return false; + + std::string line; + // The matrix header is always the first line in the file + std::getline(in, line); assert(in.good()); + + std::stringstream fmtline(line); + std::string substr[5]; + fmtline>> substr[0] >> substr[1] >> substr[2] >> substr[3] >> substr[4]; + if(substr[2].compare("array") == 0) isvector = true; + if(substr[3].compare("complex") == 0) iscomplex = true; + if(substr[4].compare("symmetric") == 0) sym = Symmetric; + else if (substr[4].compare("Hermitian") == 0) sym = SelfAdjoint; + + return true; +} + +template<typename SparseMatrixType> +bool loadMarket(SparseMatrixType& mat, const std::string& filename) +{ + typedef typename SparseMatrixType::Scalar Scalar; + std::ifstream input(filename.c_str(),std::ios::in); + if(!input) + return false; + + const int maxBuffersize = 2048; + char buffer[maxBuffersize]; + + bool readsizes = false; + + typedef Triplet<Scalar,int> T; + std::vector<T> elements; + + int M(-1), N(-1), NNZ(-1); + int count = 0; + while(input.getline(buffer, maxBuffersize)) + { + // skip comments + //NOTE An appropriate test should be done on the header to get the symmetry + if(buffer[0]=='%') + continue; + + std::stringstream line(buffer); + + if(!readsizes) + { + line >> M >> N >> NNZ; + if(M > 0 && N > 0 && NNZ > 0) + { + readsizes = true; + std::cout << "sizes: " << M << "," << N << "," << NNZ << "\n"; + mat.resize(M,N); + mat.reserve(NNZ); + } + } + else + { + int i(-1), j(-1); + Scalar value; + if( internal::GetMarketLine(line, M, N, i, j, value) ) + { + ++ count; + elements.push_back(T(i,j,value)); + } + else + std::cerr << "Invalid read: " << i << "," << j << "\n"; + } + } + mat.setFromTriplets(elements.begin(), elements.end()); + if(count!=NNZ) + std::cerr << count << "!=" << NNZ << "\n"; + + input.close(); + return true; +} + +template<typename VectorType> +bool loadMarketVector(VectorType& vec, const std::string& filename) +{ + typedef typename VectorType::Scalar Scalar; + std::ifstream in(filename.c_str(), std::ios::in); + if(!in) + return false; + + std::string line; + int n(0), col(0); + do + { // Skip comments + std::getline(in, line); assert(in.good()); + } while (line[0] == '%'); + std::istringstream newline(line); + newline >> n >> col; + assert(n>0 && col>0); + vec.resize(n); + int i = 0; + Scalar value; + while ( std::getline(in, line) && (i < n) ){ + internal::GetVectorElt(line, value); + vec(i++) = value; + } + in.close(); + if (i!=n){ + std::cerr<< "Unable to read all elements from file " << filename << "\n"; + return false; + } + return true; +} + +template<typename SparseMatrixType> +bool saveMarket(const SparseMatrixType& mat, const std::string& filename, int sym = 0) +{ + typedef typename SparseMatrixType::Scalar Scalar; + std::ofstream out(filename.c_str(),std::ios::out); + if(!out) + return false; + + out.flags(std::ios_base::scientific); + out.precision(64); + std::string header; + internal::putMarketHeader<Scalar>(header, sym); + out << header << std::endl; + out << mat.rows() << " " << mat.cols() << " " << mat.nonZeros() << "\n"; + int count = 0; + for(int j=0; j<mat.outerSize(); ++j) + for(typename SparseMatrixType::InnerIterator it(mat,j); it; ++it) + { + ++ count; + internal::PutMatrixElt(it.value(), it.row()+1, it.col()+1, out); + // out << it.row()+1 << " " << it.col()+1 << " " << it.value() << "\n"; + } + out.close(); + return true; +} + +template<typename VectorType> +bool saveMarketVector (const VectorType& vec, const std::string& filename) +{ + typedef typename VectorType::Scalar Scalar; + std::ofstream out(filename.c_str(),std::ios::out); + if(!out) + return false; + + out.flags(std::ios_base::scientific); + out.precision(64); + if(internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value) + out << "%%MatrixMarket matrix array complex general\n"; + else + out << "%%MatrixMarket matrix array real general\n"; + out << vec.size() << " "<< 1 << "\n"; + for (int i=0; i < vec.size(); i++){ + internal::putVectorElt(vec(i), out); + } + out.close(); + return true; +} + +} // end namespace Eigen + +#endif // EIGEN_SPARSE_MARKET_IO_H diff --git a/unsupported/Eigen/src/SparseExtra/MatrixMarketIterator.h b/unsupported/Eigen/src/SparseExtra/MatrixMarketIterator.h new file mode 100644 index 000000000..4716b68e7 --- /dev/null +++ b/unsupported/Eigen/src/SparseExtra/MatrixMarketIterator.h @@ -0,0 +1,221 @@ + +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Desire NUENTSA WAKAM <desire.nuentsa_wakam@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_BROWSE_MATRICES_H +#define EIGEN_BROWSE_MATRICES_H + +namespace Eigen { + +enum { + SPD = 0x100, + NonSymmetric = 0x0 +}; + +/** + * @brief Iterator to browse matrices from a specified folder + * + * This is used to load all the matrices from a folder. + * The matrices should be in Matrix Market format + * It is assumed that the matrices are named as matname.mtx + * and matname_SPD.mtx if the matrix is Symmetric and positive definite (or Hermitian) + * The right hand side vectors are loaded as well, if they exist. + * They should be named as matname_b.mtx. + * Note that the right hand side for a SPD matrix is named as matname_SPD_b.mtx + * + * Sometimes a reference solution is available. In this case, it should be named as matname_x.mtx + * + * Sample code + * \code + * + * \endcode + * + * \tparam Scalar The scalar type + */ +template <typename Scalar> +class MatrixMarketIterator +{ + public: + typedef Matrix<Scalar,Dynamic,1> VectorType; + typedef SparseMatrix<Scalar,ColMajor> MatrixType; + + public: + MatrixMarketIterator(const std::string folder):m_sym(0),m_isvalid(false),m_matIsLoaded(false),m_hasRhs(false),m_hasrefX(false),m_folder(folder) + { + m_folder_id = opendir(folder.c_str()); + if (!m_folder_id){ + m_isvalid = false; + std::cerr << "The provided Matrix folder could not be opened \n\n"; + abort(); + } + Getnextvalidmatrix(); + } + + ~MatrixMarketIterator() + { + if (m_folder_id) closedir(m_folder_id); + } + + inline MatrixMarketIterator& operator++() + { + m_matIsLoaded = false; + m_hasrefX = false; + m_hasRhs = false; + Getnextvalidmatrix(); + return *this; + } + inline operator bool() const { return m_isvalid;} + + /** Return the sparse matrix corresponding to the current file */ + inline MatrixType& matrix() + { + // Read the matrix + if (m_matIsLoaded) return m_mat; + + std::string matrix_file = m_folder + "/" + m_matname + ".mtx"; + if ( !loadMarket(m_mat, matrix_file)) + { + m_matIsLoaded = false; + return m_mat; + } + m_matIsLoaded = true; + + if (m_sym != NonSymmetric) + { // Store the upper part of the matrix. It is needed by the solvers dealing with nonsymmetric matrices ?? + MatrixType B; + B = m_mat; + m_mat = B.template selfadjointView<Lower>(); + } + return m_mat; + } + + /** Return the right hand side corresponding to the current matrix. + * If the rhs file is not provided, a random rhs is generated + */ + inline VectorType& rhs() + { + // Get the right hand side + if (m_hasRhs) return m_rhs; + + std::string rhs_file; + rhs_file = m_folder + "/" + m_matname + "_b.mtx"; // The pattern is matname_b.mtx + m_hasRhs = Fileexists(rhs_file); + if (m_hasRhs) + { + m_rhs.resize(m_mat.cols()); + m_hasRhs = loadMarketVector(m_rhs, rhs_file); + } + if (!m_hasRhs) + { + // Generate a random right hand side + if (!m_matIsLoaded) this->matrix(); + m_refX.resize(m_mat.cols()); + m_refX.setRandom(); + m_rhs = m_mat * m_refX; + m_hasrefX = true; + m_hasRhs = true; + } + return m_rhs; + } + + /** Return a reference solution + * If it is not provided and if the right hand side is not available + * then refX is randomly generated such that A*refX = b + * where A and b are the matrix and the rhs. + * Note that when a rhs is provided, refX is not available + */ + inline VectorType& refX() + { + // Check if a reference solution is provided + if (m_hasrefX) return m_refX; + + std::string lhs_file; + lhs_file = m_folder + "/" + m_matname + "_x.mtx"; + m_hasrefX = Fileexists(lhs_file); + if (m_hasrefX) + { + m_refX.resize(m_mat.cols()); + m_hasrefX = loadMarketVector(m_refX, lhs_file); + } + return m_refX; + } + + inline std::string& matname() { return m_matname; } + + inline int sym() { return m_sym; } + + inline bool hasRhs() {return m_hasRhs; } + inline bool hasrefX() {return m_hasrefX; } + + protected: + + inline bool Fileexists(std::string file) + { + std::ifstream file_id(file.c_str()); + if (!file_id.good() ) + { + return false; + } + else + { + file_id.close(); + return true; + } + } + + void Getnextvalidmatrix( ) + { + m_isvalid = false; + // Here, we return with the next valid matrix in the folder + while ( (m_curs_id = readdir(m_folder_id)) != NULL) { + m_isvalid = false; + std::string curfile; + curfile = m_folder + "/" + m_curs_id->d_name; + // Discard if it is a folder + if (m_curs_id->d_type == DT_DIR) continue; //FIXME This may not be available on non BSD systems +// struct stat st_buf; +// stat (curfile.c_str(), &st_buf); +// if (S_ISDIR(st_buf.st_mode)) continue; + + // Determine from the header if it is a matrix or a right hand side + bool isvector,iscomplex; + if(!getMarketHeader(curfile,m_sym,iscomplex,isvector)) continue; + if(isvector) continue; + + // Get the matrix name + std::string filename = m_curs_id->d_name; + m_matname = filename.substr(0, filename.length()-4); + + // Find if the matrix is SPD + size_t found = m_matname.find("SPD"); + if( (found!=std::string::npos) && (m_sym != NonSymmetric) ) + m_sym = SPD; + + m_isvalid = true; + break; + } + } + int m_sym; // Symmetry of the matrix + MatrixType m_mat; // Current matrix + VectorType m_rhs; // Current vector + VectorType m_refX; // The reference solution, if exists + std::string m_matname; // Matrix Name + bool m_isvalid; + bool m_matIsLoaded; // Determine if the matrix has already been loaded from the file + bool m_hasRhs; // The right hand side exists + bool m_hasrefX; // A reference solution is provided + std::string m_folder; + DIR * m_folder_id; + struct dirent *m_curs_id; + +}; + +} // end namespace Eigen + +#endif diff --git a/unsupported/Eigen/src/SparseExtra/RandomSetter.h b/unsupported/Eigen/src/SparseExtra/RandomSetter.h new file mode 100644 index 000000000..dee1708e7 --- /dev/null +++ b/unsupported/Eigen/src/SparseExtra/RandomSetter.h @@ -0,0 +1,327 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_RANDOMSETTER_H +#define EIGEN_RANDOMSETTER_H + +namespace Eigen { + +/** Represents a std::map + * + * \see RandomSetter + */ +template<typename Scalar> struct StdMapTraits +{ + typedef int KeyType; + typedef std::map<KeyType,Scalar> Type; + enum { + IsSorted = 1 + }; + + static void setInvalidKey(Type&, const KeyType&) {} +}; + +#ifdef EIGEN_UNORDERED_MAP_SUPPORT +/** Represents a std::unordered_map + * + * To use it you need to both define EIGEN_UNORDERED_MAP_SUPPORT and include the unordered_map header file + * yourself making sure that unordered_map is defined in the std namespace. + * + * For instance, with current version of gcc you can either enable C++0x standard (-std=c++0x) or do: + * \code + * #include <tr1/unordered_map> + * #define EIGEN_UNORDERED_MAP_SUPPORT + * namespace std { + * using std::tr1::unordered_map; + * } + * \endcode + * + * \see RandomSetter + */ +template<typename Scalar> struct StdUnorderedMapTraits +{ + typedef int KeyType; + typedef std::unordered_map<KeyType,Scalar> Type; + enum { + IsSorted = 0 + }; + + static void setInvalidKey(Type&, const KeyType&) {} +}; +#endif // EIGEN_UNORDERED_MAP_SUPPORT + +#ifdef _DENSE_HASH_MAP_H_ +/** Represents a google::dense_hash_map + * + * \see RandomSetter + */ +template<typename Scalar> struct GoogleDenseHashMapTraits +{ + typedef int KeyType; + typedef google::dense_hash_map<KeyType,Scalar> Type; + enum { + IsSorted = 0 + }; + + static void setInvalidKey(Type& map, const KeyType& k) + { map.set_empty_key(k); } +}; +#endif + +#ifdef _SPARSE_HASH_MAP_H_ +/** Represents a google::sparse_hash_map + * + * \see RandomSetter + */ +template<typename Scalar> struct GoogleSparseHashMapTraits +{ + typedef int KeyType; + typedef google::sparse_hash_map<KeyType,Scalar> Type; + enum { + IsSorted = 0 + }; + + static void setInvalidKey(Type&, const KeyType&) {} +}; +#endif + +/** \class RandomSetter + * + * \brief The RandomSetter is a wrapper object allowing to set/update a sparse matrix with random access + * + * \param SparseMatrixType the type of the sparse matrix we are updating + * \param MapTraits a traits class representing the map implementation used for the temporary sparse storage. + * Its default value depends on the system. + * \param OuterPacketBits defines the number of rows (or columns) manage by a single map object + * as a power of two exponent. + * + * This class temporarily represents a sparse matrix object using a generic map implementation allowing for + * efficient random access. The conversion from the compressed representation to a hash_map object is performed + * in the RandomSetter constructor, while the sparse matrix is updated back at destruction time. This strategy + * suggest the use of nested blocks as in this example: + * + * \code + * SparseMatrix<double> m(rows,cols); + * { + * RandomSetter<SparseMatrix<double> > w(m); + * // don't use m but w instead with read/write random access to the coefficients: + * for(;;) + * w(rand(),rand()) = rand; + * } + * // when w is deleted, the data are copied back to m + * // and m is ready to use. + * \endcode + * + * Since hash_map objects are not fully sorted, representing a full matrix as a single hash_map would + * involve a big and costly sort to update the compressed matrix back. To overcome this issue, a RandomSetter + * use multiple hash_map, each representing 2^OuterPacketBits columns or rows according to the storage order. + * To reach optimal performance, this value should be adjusted according to the average number of nonzeros + * per rows/columns. + * + * The possible values for the template parameter MapTraits are: + * - \b StdMapTraits: corresponds to std::map. (does not perform very well) + * - \b GnuHashMapTraits: corresponds to __gnu_cxx::hash_map (available only with GCC) + * - \b GoogleDenseHashMapTraits: corresponds to google::dense_hash_map (best efficiency, reasonable memory consumption) + * - \b GoogleSparseHashMapTraits: corresponds to google::sparse_hash_map (best memory consumption, relatively good performance) + * + * The default map implementation depends on the availability, and the preferred order is: + * GoogleSparseHashMapTraits, GnuHashMapTraits, and finally StdMapTraits. + * + * For performance and memory consumption reasons it is highly recommended to use one of + * the Google's hash_map implementation. To enable the support for them, you have two options: + * - \#include <google/dense_hash_map> yourself \b before Eigen/Sparse header + * - define EIGEN_GOOGLEHASH_SUPPORT + * In the later case the inclusion of <google/dense_hash_map> is made for you. + * + * \see http://code.google.com/p/google-sparsehash/ + */ +template<typename SparseMatrixType, + template <typename T> class MapTraits = +#if defined _DENSE_HASH_MAP_H_ + GoogleDenseHashMapTraits +#elif defined _HASH_MAP + GnuHashMapTraits +#else + StdMapTraits +#endif + ,int OuterPacketBits = 6> +class RandomSetter +{ + typedef typename SparseMatrixType::Scalar Scalar; + typedef typename SparseMatrixType::Index Index; + + struct ScalarWrapper + { + ScalarWrapper() : value(0) {} + Scalar value; + }; + typedef typename MapTraits<ScalarWrapper>::KeyType KeyType; + typedef typename MapTraits<ScalarWrapper>::Type HashMapType; + static const int OuterPacketMask = (1 << OuterPacketBits) - 1; + enum { + SwapStorage = 1 - MapTraits<ScalarWrapper>::IsSorted, + TargetRowMajor = (SparseMatrixType::Flags & RowMajorBit) ? 1 : 0, + SetterRowMajor = SwapStorage ? 1-TargetRowMajor : TargetRowMajor + }; + + public: + + /** Constructs a random setter object from the sparse matrix \a target + * + * Note that the initial value of \a target are imported. If you want to re-set + * a sparse matrix from scratch, then you must set it to zero first using the + * setZero() function. + */ + inline RandomSetter(SparseMatrixType& target) + : mp_target(&target) + { + const Index outerSize = SwapStorage ? target.innerSize() : target.outerSize(); + const Index innerSize = SwapStorage ? target.outerSize() : target.innerSize(); + m_outerPackets = outerSize >> OuterPacketBits; + if (outerSize&OuterPacketMask) + m_outerPackets += 1; + m_hashmaps = new HashMapType[m_outerPackets]; + // compute number of bits needed to store inner indices + Index aux = innerSize - 1; + m_keyBitsOffset = 0; + while (aux) + { + ++m_keyBitsOffset; + aux = aux >> 1; + } + KeyType ik = (1<<(OuterPacketBits+m_keyBitsOffset)); + for (Index k=0; k<m_outerPackets; ++k) + MapTraits<ScalarWrapper>::setInvalidKey(m_hashmaps[k],ik); + + // insert current coeffs + for (Index j=0; j<mp_target->outerSize(); ++j) + for (typename SparseMatrixType::InnerIterator it(*mp_target,j); it; ++it) + (*this)(TargetRowMajor?j:it.index(), TargetRowMajor?it.index():j) = it.value(); + } + + /** Destructor updating back the sparse matrix target */ + ~RandomSetter() + { + KeyType keyBitsMask = (1<<m_keyBitsOffset)-1; + if (!SwapStorage) // also means the map is sorted + { + mp_target->setZero(); + mp_target->makeCompressed(); + mp_target->reserve(nonZeros()); + Index prevOuter = -1; + for (Index k=0; k<m_outerPackets; ++k) + { + const Index outerOffset = (1<<OuterPacketBits) * k; + typename HashMapType::iterator end = m_hashmaps[k].end(); + for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it) + { + const Index outer = (it->first >> m_keyBitsOffset) + outerOffset; + const Index inner = it->first & keyBitsMask; + if (prevOuter!=outer) + { + for (Index j=prevOuter+1;j<=outer;++j) + mp_target->startVec(j); + prevOuter = outer; + } + mp_target->insertBackByOuterInner(outer, inner) = it->second.value; + } + } + mp_target->finalize(); + } + else + { + VectorXi positions(mp_target->outerSize()); + positions.setZero(); + // pass 1 + for (Index k=0; k<m_outerPackets; ++k) + { + typename HashMapType::iterator end = m_hashmaps[k].end(); + for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it) + { + const Index outer = it->first & keyBitsMask; + ++positions[outer]; + } + } + // prefix sum + Index count = 0; + for (Index j=0; j<mp_target->outerSize(); ++j) + { + Index tmp = positions[j]; + mp_target->outerIndexPtr()[j] = count; + positions[j] = count; + count += tmp; + } + mp_target->makeCompressed(); + mp_target->outerIndexPtr()[mp_target->outerSize()] = count; + mp_target->resizeNonZeros(count); + // pass 2 + for (Index k=0; k<m_outerPackets; ++k) + { + const Index outerOffset = (1<<OuterPacketBits) * k; + typename HashMapType::iterator end = m_hashmaps[k].end(); + for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it) + { + const Index inner = (it->first >> m_keyBitsOffset) + outerOffset; + const Index outer = it->first & keyBitsMask; + // sorted insertion + // Note that we have to deal with at most 2^OuterPacketBits unsorted coefficients, + // moreover those 2^OuterPacketBits coeffs are likely to be sparse, an so only a + // small fraction of them have to be sorted, whence the following simple procedure: + Index posStart = mp_target->outerIndexPtr()[outer]; + Index i = (positions[outer]++) - 1; + while ( (i >= posStart) && (mp_target->innerIndexPtr()[i] > inner) ) + { + mp_target->valuePtr()[i+1] = mp_target->valuePtr()[i]; + mp_target->innerIndexPtr()[i+1] = mp_target->innerIndexPtr()[i]; + --i; + } + mp_target->innerIndexPtr()[i+1] = inner; + mp_target->valuePtr()[i+1] = it->second.value; + } + } + } + delete[] m_hashmaps; + } + + /** \returns a reference to the coefficient at given coordinates \a row, \a col */ + Scalar& operator() (Index row, Index col) + { + const Index outer = SetterRowMajor ? row : col; + const Index inner = SetterRowMajor ? col : row; + const Index outerMajor = outer >> OuterPacketBits; // index of the packet/map + const Index outerMinor = outer & OuterPacketMask; // index of the inner vector in the packet + const KeyType key = (KeyType(outerMinor)<<m_keyBitsOffset) | inner; + return m_hashmaps[outerMajor][key].value; + } + + /** \returns the number of non zero coefficients + * + * \note According to the underlying map/hash_map implementation, + * this function might be quite expensive. + */ + Index nonZeros() const + { + Index nz = 0; + for (Index k=0; k<m_outerPackets; ++k) + nz += static_cast<Index>(m_hashmaps[k].size()); + return nz; + } + + + protected: + + HashMapType* m_hashmaps; + SparseMatrixType* mp_target; + Index m_outerPackets; + unsigned char m_keyBitsOffset; +}; + +} // end namespace Eigen + +#endif // EIGEN_RANDOMSETTER_H diff --git a/unsupported/Eigen/src/Splines/CMakeLists.txt b/unsupported/Eigen/src/Splines/CMakeLists.txt new file mode 100644 index 000000000..55c6271e9 --- /dev/null +++ b/unsupported/Eigen/src/Splines/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_Splines_SRCS "*.h") + +INSTALL(FILES + ${Eigen_Splines_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/Splines COMPONENT Devel + ) diff --git a/unsupported/Eigen/src/Splines/Spline.h b/unsupported/Eigen/src/Splines/Spline.h new file mode 100644 index 000000000..3680f013a --- /dev/null +++ b/unsupported/Eigen/src/Splines/Spline.h @@ -0,0 +1,464 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPLINE_H +#define EIGEN_SPLINE_H + +#include "SplineFwd.h" + +namespace Eigen +{ + /** + * \ingroup Splines_Module + * \class Spline class + * \brief A class representing multi-dimensional spline curves. + * + * The class represents B-splines with non-uniform knot vectors. Each control + * point of the B-spline is associated with a basis function + * \f{align*} + * C(u) & = \sum_{i=0}^{n}N_{i,p}(u)P_i + * \f} + * + * \tparam _Scalar The underlying data type (typically float or double) + * \tparam _Dim The curve dimension (e.g. 2 or 3) + * \tparam _Degree Per default set to Dynamic; could be set to the actual desired + * degree for optimization purposes (would result in stack allocation + * of several temporary variables). + **/ + template <typename _Scalar, int _Dim, int _Degree> + class Spline + { + public: + typedef _Scalar Scalar; /*!< The spline curve's scalar type. */ + enum { Dimension = _Dim /*!< The spline curve's dimension. */ }; + enum { Degree = _Degree /*!< The spline curve's degree. */ }; + + /** \brief The point type the spline is representing. */ + typedef typename SplineTraits<Spline>::PointType PointType; + + /** \brief The data type used to store knot vectors. */ + typedef typename SplineTraits<Spline>::KnotVectorType KnotVectorType; + + /** \brief The data type used to store non-zero basis functions. */ + typedef typename SplineTraits<Spline>::BasisVectorType BasisVectorType; + + /** \brief The data type representing the spline's control points. */ + typedef typename SplineTraits<Spline>::ControlPointVectorType ControlPointVectorType; + + /** + * \brief Creates a spline from a knot vector and control points. + * \param knots The spline's knot vector. + * \param ctrls The spline's control point vector. + **/ + template <typename OtherVectorType, typename OtherArrayType> + Spline(const OtherVectorType& knots, const OtherArrayType& ctrls) : m_knots(knots), m_ctrls(ctrls) {} + + /** + * \brief Copy constructor for splines. + * \param spline The input spline. + **/ + template <int OtherDegree> + Spline(const Spline<Scalar, Dimension, OtherDegree>& spline) : + m_knots(spline.knots()), m_ctrls(spline.ctrls()) {} + + /** + * \brief Returns the knots of the underlying spline. + **/ + const KnotVectorType& knots() const { return m_knots; } + + /** + * \brief Returns the knots of the underlying spline. + **/ + const ControlPointVectorType& ctrls() const { return m_ctrls; } + + /** + * \brief Returns the spline value at a given site \f$u\f$. + * + * The function returns + * \f{align*} + * C(u) & = \sum_{i=0}^{n}N_{i,p}P_i + * \f} + * + * \param u Parameter \f$u \in [0;1]\f$ at which the spline is evaluated. + * \return The spline value at the given location \f$u\f$. + **/ + PointType operator()(Scalar u) const; + + /** + * \brief Evaluation of spline derivatives of up-to given order. + * + * The function returns + * \f{align*} + * \frac{d^i}{du^i}C(u) & = \sum_{i=0}^{n} \frac{d^i}{du^i} N_{i,p}(u)P_i + * \f} + * for i ranging between 0 and order. + * + * \param u Parameter \f$u \in [0;1]\f$ at which the spline derivative is evaluated. + * \param order The order up to which the derivatives are computed. + **/ + typename SplineTraits<Spline>::DerivativeType + derivatives(Scalar u, DenseIndex order) const; + + /** + * \copydoc Spline::derivatives + * Using the template version of this function is more efficieent since + * temporary objects are allocated on the stack whenever this is possible. + **/ + template <int DerivativeOrder> + typename SplineTraits<Spline,DerivativeOrder>::DerivativeType + derivatives(Scalar u, DenseIndex order = DerivativeOrder) const; + + /** + * \brief Computes the non-zero basis functions at the given site. + * + * Splines have local support and a point from their image is defined + * by exactly \f$p+1\f$ control points \f$P_i\f$ where \f$p\f$ is the + * spline degree. + * + * This function computes the \f$p+1\f$ non-zero basis function values + * for a given parameter value \f$u\f$. It returns + * \f{align*}{ + * N_{i,p}(u), \hdots, N_{i+p+1,p}(u) + * \f} + * + * \param u Parameter \f$u \in [0;1]\f$ at which the non-zero basis functions + * are computed. + **/ + typename SplineTraits<Spline>::BasisVectorType + basisFunctions(Scalar u) const; + + /** + * \brief Computes the non-zero spline basis function derivatives up to given order. + * + * The function computes + * \f{align*}{ + * \frac{d^i}{du^i} N_{i,p}(u), \hdots, \frac{d^i}{du^i} N_{i+p+1,p}(u) + * \f} + * with i ranging from 0 up to the specified order. + * + * \param u Parameter \f$u \in [0;1]\f$ at which the non-zero basis function + * derivatives are computed. + * \param order The order up to which the basis function derivatives are computes. + **/ + typename SplineTraits<Spline>::BasisDerivativeType + basisFunctionDerivatives(Scalar u, DenseIndex order) const; + + /** + * \copydoc Spline::basisFunctionDerivatives + * Using the template version of this function is more efficieent since + * temporary objects are allocated on the stack whenever this is possible. + **/ + template <int DerivativeOrder> + typename SplineTraits<Spline,DerivativeOrder>::BasisDerivativeType + basisFunctionDerivatives(Scalar u, DenseIndex order = DerivativeOrder) const; + + /** + * \brief Returns the spline degree. + **/ + DenseIndex degree() const; + + /** + * \brief Returns the span within the knot vector in which u is falling. + * \param u The site for which the span is determined. + **/ + DenseIndex span(Scalar u) const; + + /** + * \brief Computes the spang within the provided knot vector in which u is falling. + **/ + static DenseIndex Span(typename SplineTraits<Spline>::Scalar u, DenseIndex degree, const typename SplineTraits<Spline>::KnotVectorType& knots); + + /** + * \brief Returns the spline's non-zero basis functions. + * + * The function computes and returns + * \f{align*}{ + * N_{i,p}(u), \hdots, N_{i+p+1,p}(u) + * \f} + * + * \param u The site at which the basis functions are computed. + * \param degree The degree of the underlying spline. + * \param knots The underlying spline's knot vector. + **/ + static BasisVectorType BasisFunctions(Scalar u, DenseIndex degree, const KnotVectorType& knots); + + + private: + KnotVectorType m_knots; /*!< Knot vector. */ + ControlPointVectorType m_ctrls; /*!< Control points. */ + }; + + template <typename _Scalar, int _Dim, int _Degree> + DenseIndex Spline<_Scalar, _Dim, _Degree>::Span( + typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::Scalar u, + DenseIndex degree, + const typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::KnotVectorType& knots) + { + // Piegl & Tiller, "The NURBS Book", A2.1 (p. 68) + if (u <= knots(0)) return degree; + const Scalar* pos = std::upper_bound(knots.data()+degree-1, knots.data()+knots.size()-degree-1, u); + return static_cast<DenseIndex>( std::distance(knots.data(), pos) - 1 ); + } + + template <typename _Scalar, int _Dim, int _Degree> + typename Spline<_Scalar, _Dim, _Degree>::BasisVectorType + Spline<_Scalar, _Dim, _Degree>::BasisFunctions( + typename Spline<_Scalar, _Dim, _Degree>::Scalar u, + DenseIndex degree, + const typename Spline<_Scalar, _Dim, _Degree>::KnotVectorType& knots) + { + typedef typename Spline<_Scalar, _Dim, _Degree>::BasisVectorType BasisVectorType; + + const DenseIndex p = degree; + const DenseIndex i = Spline::Span(u, degree, knots); + + const KnotVectorType& U = knots; + + BasisVectorType left(p+1); left(0) = Scalar(0); + BasisVectorType right(p+1); right(0) = Scalar(0); + + VectorBlock<BasisVectorType,Degree>(left,1,p) = u - VectorBlock<const KnotVectorType,Degree>(U,i+1-p,p).reverse(); + VectorBlock<BasisVectorType,Degree>(right,1,p) = VectorBlock<const KnotVectorType,Degree>(U,i+1,p) - u; + + BasisVectorType N(1,p+1); + N(0) = Scalar(1); + for (DenseIndex j=1; j<=p; ++j) + { + Scalar saved = Scalar(0); + for (DenseIndex r=0; r<j; r++) + { + const Scalar tmp = N(r)/(right(r+1)+left(j-r)); + N[r] = saved + right(r+1)*tmp; + saved = left(j-r)*tmp; + } + N(j) = saved; + } + return N; + } + + template <typename _Scalar, int _Dim, int _Degree> + DenseIndex Spline<_Scalar, _Dim, _Degree>::degree() const + { + if (_Degree == Dynamic) + return m_knots.size() - m_ctrls.cols() - 1; + else + return _Degree; + } + + template <typename _Scalar, int _Dim, int _Degree> + DenseIndex Spline<_Scalar, _Dim, _Degree>::span(Scalar u) const + { + return Spline::Span(u, degree(), knots()); + } + + template <typename _Scalar, int _Dim, int _Degree> + typename Spline<_Scalar, _Dim, _Degree>::PointType Spline<_Scalar, _Dim, _Degree>::operator()(Scalar u) const + { + enum { Order = SplineTraits<Spline>::OrderAtCompileTime }; + + const DenseIndex span = this->span(u); + const DenseIndex p = degree(); + const BasisVectorType basis_funcs = basisFunctions(u); + + const Replicate<BasisVectorType,Dimension,1> ctrl_weights(basis_funcs); + const Block<const ControlPointVectorType,Dimension,Order> ctrl_pts(ctrls(),0,span-p,Dimension,p+1); + return (ctrl_weights * ctrl_pts).rowwise().sum(); + } + + /* --------------------------------------------------------------------------------------------- */ + + template <typename SplineType, typename DerivativeType> + void derivativesImpl(const SplineType& spline, typename SplineType::Scalar u, DenseIndex order, DerivativeType& der) + { + enum { Dimension = SplineTraits<SplineType>::Dimension }; + enum { Order = SplineTraits<SplineType>::OrderAtCompileTime }; + enum { DerivativeOrder = DerivativeType::ColsAtCompileTime }; + + typedef typename SplineTraits<SplineType>::Scalar Scalar; + + typedef typename SplineTraits<SplineType>::BasisVectorType BasisVectorType; + typedef typename SplineTraits<SplineType>::ControlPointVectorType ControlPointVectorType; + + typedef typename SplineTraits<SplineType,DerivativeOrder>::BasisDerivativeType BasisDerivativeType; + typedef typename BasisDerivativeType::ConstRowXpr BasisDerivativeRowXpr; + + const DenseIndex p = spline.degree(); + const DenseIndex span = spline.span(u); + + const DenseIndex n = (std::min)(p, order); + + der.resize(Dimension,n+1); + + // Retrieve the basis function derivatives up to the desired order... + const BasisDerivativeType basis_func_ders = spline.template basisFunctionDerivatives<DerivativeOrder>(u, n+1); + + // ... and perform the linear combinations of the control points. + for (DenseIndex der_order=0; der_order<n+1; ++der_order) + { + const Replicate<BasisDerivativeRowXpr,Dimension,1> ctrl_weights( basis_func_ders.row(der_order) ); + const Block<const ControlPointVectorType,Dimension,Order> ctrl_pts(spline.ctrls(),0,span-p,Dimension,p+1); + der.col(der_order) = (ctrl_weights * ctrl_pts).rowwise().sum(); + } + } + + template <typename _Scalar, int _Dim, int _Degree> + typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::DerivativeType + Spline<_Scalar, _Dim, _Degree>::derivatives(Scalar u, DenseIndex order) const + { + typename SplineTraits< Spline >::DerivativeType res; + derivativesImpl(*this, u, order, res); + return res; + } + + template <typename _Scalar, int _Dim, int _Degree> + template <int DerivativeOrder> + typename SplineTraits< Spline<_Scalar, _Dim, _Degree>, DerivativeOrder >::DerivativeType + Spline<_Scalar, _Dim, _Degree>::derivatives(Scalar u, DenseIndex order) const + { + typename SplineTraits< Spline, DerivativeOrder >::DerivativeType res; + derivativesImpl(*this, u, order, res); + return res; + } + + template <typename _Scalar, int _Dim, int _Degree> + typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::BasisVectorType + Spline<_Scalar, _Dim, _Degree>::basisFunctions(Scalar u) const + { + return Spline::BasisFunctions(u, degree(), knots()); + } + + /* --------------------------------------------------------------------------------------------- */ + + template <typename SplineType, typename DerivativeType> + void basisFunctionDerivativesImpl(const SplineType& spline, typename SplineType::Scalar u, DenseIndex order, DerivativeType& N_) + { + enum { Order = SplineTraits<SplineType>::OrderAtCompileTime }; + + typedef typename SplineTraits<SplineType>::Scalar Scalar; + typedef typename SplineTraits<SplineType>::BasisVectorType BasisVectorType; + typedef typename SplineTraits<SplineType>::KnotVectorType KnotVectorType; + typedef typename SplineTraits<SplineType>::ControlPointVectorType ControlPointVectorType; + + const KnotVectorType& U = spline.knots(); + + const DenseIndex p = spline.degree(); + const DenseIndex span = spline.span(u); + + const DenseIndex n = (std::min)(p, order); + + N_.resize(n+1, p+1); + + BasisVectorType left = BasisVectorType::Zero(p+1); + BasisVectorType right = BasisVectorType::Zero(p+1); + + Matrix<Scalar,Order,Order> ndu(p+1,p+1); + + double saved, temp; + + ndu(0,0) = 1.0; + + DenseIndex j; + for (j=1; j<=p; ++j) + { + left[j] = u-U[span+1-j]; + right[j] = U[span+j]-u; + saved = 0.0; + + for (DenseIndex r=0; r<j; ++r) + { + /* Lower triangle */ + ndu(j,r) = right[r+1]+left[j-r]; + temp = ndu(r,j-1)/ndu(j,r); + /* Upper triangle */ + ndu(r,j) = static_cast<Scalar>(saved+right[r+1] * temp); + saved = left[j-r] * temp; + } + + ndu(j,j) = static_cast<Scalar>(saved); + } + + for (j = p; j>=0; --j) + N_(0,j) = ndu(j,p); + + // Compute the derivatives + DerivativeType a(n+1,p+1); + DenseIndex r=0; + for (; r<=p; ++r) + { + DenseIndex s1,s2; + s1 = 0; s2 = 1; // alternate rows in array a + a(0,0) = 1.0; + + // Compute the k-th derivative + for (DenseIndex k=1; k<=static_cast<DenseIndex>(n); ++k) + { + double d = 0.0; + DenseIndex rk,pk,j1,j2; + rk = r-k; pk = p-k; + + if (r>=k) + { + a(s2,0) = a(s1,0)/ndu(pk+1,rk); + d = a(s2,0)*ndu(rk,pk); + } + + if (rk>=-1) j1 = 1; + else j1 = -rk; + + if (r-1 <= pk) j2 = k-1; + else j2 = p-r; + + for (j=j1; j<=j2; ++j) + { + a(s2,j) = (a(s1,j)-a(s1,j-1))/ndu(pk+1,rk+j); + d += a(s2,j)*ndu(rk+j,pk); + } + + if (r<=pk) + { + a(s2,k) = -a(s1,k-1)/ndu(pk+1,r); + d += a(s2,k)*ndu(r,pk); + } + + N_(k,r) = static_cast<Scalar>(d); + j = s1; s1 = s2; s2 = j; // Switch rows + } + } + + /* Multiply through by the correct factors */ + /* (Eq. [2.9]) */ + r = p; + for (DenseIndex k=1; k<=static_cast<DenseIndex>(n); ++k) + { + for (DenseIndex j=p; j>=0; --j) N_(k,j) *= r; + r *= p-k; + } + } + + template <typename _Scalar, int _Dim, int _Degree> + typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::BasisDerivativeType + Spline<_Scalar, _Dim, _Degree>::basisFunctionDerivatives(Scalar u, DenseIndex order) const + { + typename SplineTraits< Spline >::BasisDerivativeType der; + basisFunctionDerivativesImpl(*this, u, order, der); + return der; + } + + template <typename _Scalar, int _Dim, int _Degree> + template <int DerivativeOrder> + typename SplineTraits< Spline<_Scalar, _Dim, _Degree>, DerivativeOrder >::BasisDerivativeType + Spline<_Scalar, _Dim, _Degree>::basisFunctionDerivatives(Scalar u, DenseIndex order) const + { + typename SplineTraits< Spline, DerivativeOrder >::BasisDerivativeType der; + basisFunctionDerivativesImpl(*this, u, order, der); + return der; + } +} + +#endif // EIGEN_SPLINE_H diff --git a/unsupported/Eigen/src/Splines/SplineFitting.h b/unsupported/Eigen/src/Splines/SplineFitting.h new file mode 100644 index 000000000..1b566332f --- /dev/null +++ b/unsupported/Eigen/src/Splines/SplineFitting.h @@ -0,0 +1,159 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPLINE_FITTING_H +#define EIGEN_SPLINE_FITTING_H + +#include <numeric> + +#include "SplineFwd.h" + +#include <Eigen/QR> + +namespace Eigen +{ + /** + * \brief Computes knot averages. + * \ingroup Splines_Module + * + * The knots are computed as + * \f{align*} + * u_0 & = \hdots = u_p = 0 \\ + * u_{m-p} & = \hdots = u_{m} = 1 \\ + * u_{j+p} & = \frac{1}{p}\sum_{i=j}^{j+p-1}\bar{u}_i \quad\quad j=1,\hdots,n-p + * \f} + * where \f$p\f$ is the degree and \f$m+1\f$ the number knots + * of the desired interpolating spline. + * + * \param[in] parameters The input parameters. During interpolation one for each data point. + * \param[in] degree The spline degree which is used during the interpolation. + * \param[out] knots The output knot vector. + * + * \sa Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data + **/ + template <typename KnotVectorType> + void KnotAveraging(const KnotVectorType& parameters, DenseIndex degree, KnotVectorType& knots) + { + typedef typename KnotVectorType::Scalar Scalar; + + knots.resize(parameters.size()+degree+1); + + for (DenseIndex j=1; j<parameters.size()-degree; ++j) + knots(j+degree) = parameters.segment(j,degree).mean(); + + knots.segment(0,degree+1) = KnotVectorType::Zero(degree+1); + knots.segment(knots.size()-degree-1,degree+1) = KnotVectorType::Ones(degree+1); + } + + /** + * \brief Computes chord length parameters which are required for spline interpolation. + * \ingroup Splines_Module + * + * \param[in] pts The data points to which a spline should be fit. + * \param[out] chord_lengths The resulting chord lenggth vector. + * + * \sa Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data + **/ + template <typename PointArrayType, typename KnotVectorType> + void ChordLengths(const PointArrayType& pts, KnotVectorType& chord_lengths) + { + typedef typename KnotVectorType::Scalar Scalar; + + const DenseIndex n = pts.cols(); + + // 1. compute the column-wise norms + chord_lengths.resize(pts.cols()); + chord_lengths[0] = 0; + chord_lengths.rightCols(n-1) = (pts.array().leftCols(n-1) - pts.array().rightCols(n-1)).matrix().colwise().norm(); + + // 2. compute the partial sums + std::partial_sum(chord_lengths.data(), chord_lengths.data()+n, chord_lengths.data()); + + // 3. normalize the data + chord_lengths /= chord_lengths(n-1); + chord_lengths(n-1) = Scalar(1); + } + + /** + * \brief Spline fitting methods. + * \ingroup Splines_Module + **/ + template <typename SplineType> + struct SplineFitting + { + typedef typename SplineType::KnotVectorType KnotVectorType; + + /** + * \brief Fits an interpolating Spline to the given data points. + * + * \param pts The points for which an interpolating spline will be computed. + * \param degree The degree of the interpolating spline. + * + * \returns A spline interpolating the initially provided points. + **/ + template <typename PointArrayType> + static SplineType Interpolate(const PointArrayType& pts, DenseIndex degree); + + /** + * \brief Fits an interpolating Spline to the given data points. + * + * \param pts The points for which an interpolating spline will be computed. + * \param degree The degree of the interpolating spline. + * \param knot_parameters The knot parameters for the interpolation. + * + * \returns A spline interpolating the initially provided points. + **/ + template <typename PointArrayType> + static SplineType Interpolate(const PointArrayType& pts, DenseIndex degree, const KnotVectorType& knot_parameters); + }; + + template <typename SplineType> + template <typename PointArrayType> + SplineType SplineFitting<SplineType>::Interpolate(const PointArrayType& pts, DenseIndex degree, const KnotVectorType& knot_parameters) + { + typedef typename SplineType::KnotVectorType::Scalar Scalar; + typedef typename SplineType::BasisVectorType BasisVectorType; + typedef typename SplineType::ControlPointVectorType ControlPointVectorType; + + typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType; + + KnotVectorType knots; + KnotAveraging(knot_parameters, degree, knots); + + DenseIndex n = pts.cols(); + MatrixType A = MatrixType::Zero(n,n); + for (DenseIndex i=1; i<n-1; ++i) + { + const DenseIndex span = SplineType::Span(knot_parameters[i], degree, knots); + + // The segment call should somehow be told the spline order at compile time. + A.row(i).segment(span-degree, degree+1) = SplineType::BasisFunctions(knot_parameters[i], degree, knots); + } + A(0,0) = 1.0; + A(n-1,n-1) = 1.0; + + HouseholderQR<MatrixType> qr(A); + + // Here, we are creating a temporary due to an Eigen issue. + ControlPointVectorType ctrls = qr.solve(MatrixType(pts.transpose())).transpose(); + + return SplineType(knots, ctrls); + } + + template <typename SplineType> + template <typename PointArrayType> + SplineType SplineFitting<SplineType>::Interpolate(const PointArrayType& pts, DenseIndex degree) + { + KnotVectorType chord_lengths; // knot parameters + ChordLengths(pts, chord_lengths); + return Interpolate(pts, degree, chord_lengths); + } +} + +#endif // EIGEN_SPLINE_FITTING_H diff --git a/unsupported/Eigen/src/Splines/SplineFwd.h b/unsupported/Eigen/src/Splines/SplineFwd.h new file mode 100644 index 000000000..49db8d35d --- /dev/null +++ b/unsupported/Eigen/src/Splines/SplineFwd.h @@ -0,0 +1,86 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPLINES_FWD_H +#define EIGEN_SPLINES_FWD_H + +#include <Eigen/Core> + +namespace Eigen +{ + template <typename Scalar, int Dim, int Degree = Dynamic> class Spline; + + template < typename SplineType, int DerivativeOrder = Dynamic > struct SplineTraits {}; + + /** + * \ingroup Splines_Module + * \brief Compile-time attributes of the Spline class for Dynamic degree. + **/ + template <typename _Scalar, int _Dim, int _Degree> + struct SplineTraits< Spline<_Scalar, _Dim, _Degree>, Dynamic > + { + typedef _Scalar Scalar; /*!< The spline curve's scalar type. */ + enum { Dimension = _Dim /*!< The spline curve's dimension. */ }; + enum { Degree = _Degree /*!< The spline curve's degree. */ }; + + enum { OrderAtCompileTime = _Degree==Dynamic ? Dynamic : _Degree+1 /*!< The spline curve's order at compile-time. */ }; + enum { NumOfDerivativesAtCompileTime = OrderAtCompileTime /*!< The number of derivatives defined for the current spline. */ }; + + /** \brief The data type used to store non-zero basis functions. */ + typedef Array<Scalar,1,OrderAtCompileTime> BasisVectorType; + + /** \brief The data type used to store the values of the basis function derivatives. */ + typedef Array<Scalar,Dynamic,Dynamic,RowMajor,NumOfDerivativesAtCompileTime,OrderAtCompileTime> BasisDerivativeType; + + /** \brief The data type used to store the spline's derivative values. */ + typedef Array<Scalar,Dimension,Dynamic,ColMajor,Dimension,NumOfDerivativesAtCompileTime> DerivativeType; + + /** \brief The point type the spline is representing. */ + typedef Array<Scalar,Dimension,1> PointType; + + /** \brief The data type used to store knot vectors. */ + typedef Array<Scalar,1,Dynamic> KnotVectorType; + + /** \brief The data type representing the spline's control points. */ + typedef Array<Scalar,Dimension,Dynamic> ControlPointVectorType; + }; + + /** + * \ingroup Splines_Module + * \brief Compile-time attributes of the Spline class for fixed degree. + * + * The traits class inherits all attributes from the SplineTraits of Dynamic degree. + **/ + template < typename _Scalar, int _Dim, int _Degree, int _DerivativeOrder > + struct SplineTraits< Spline<_Scalar, _Dim, _Degree>, _DerivativeOrder > : public SplineTraits< Spline<_Scalar, _Dim, _Degree> > + { + enum { OrderAtCompileTime = _Degree==Dynamic ? Dynamic : _Degree+1 /*!< The spline curve's order at compile-time. */ }; + enum { NumOfDerivativesAtCompileTime = _DerivativeOrder==Dynamic ? Dynamic : _DerivativeOrder+1 /*!< The number of derivatives defined for the current spline. */ }; + + /** \brief The data type used to store the values of the basis function derivatives. */ + typedef Array<_Scalar,Dynamic,Dynamic,RowMajor,NumOfDerivativesAtCompileTime,OrderAtCompileTime> BasisDerivativeType; + + /** \brief The data type used to store the spline's derivative values. */ + typedef Array<_Scalar,_Dim,Dynamic,ColMajor,_Dim,NumOfDerivativesAtCompileTime> DerivativeType; + }; + + /** \brief 2D float B-spline with dynamic degree. */ + typedef Spline<float,2> Spline2f; + + /** \brief 3D float B-spline with dynamic degree. */ + typedef Spline<float,3> Spline3f; + + /** \brief 2D double B-spline with dynamic degree. */ + typedef Spline<double,2> Spline2d; + + /** \brief 3D double B-spline with dynamic degree. */ + typedef Spline<double,3> Spline3d; +} + +#endif // EIGEN_SPLINES_FWD_H diff --git a/unsupported/README.txt b/unsupported/README.txt new file mode 100644 index 000000000..83479ff0b --- /dev/null +++ b/unsupported/README.txt @@ -0,0 +1,50 @@ +This directory contains contributions from various users. +They are provided "as is", without any support. Nevertheless, +most of them are subject to be included in Eigen in the future. + +In order to use an unsupported module you have to do either: + + - add the path_to_eigen/unsupported directory to your include path and do: + #include <Eigen/ModuleHeader> + + - or directly do: + #include <unsupported/Eigen/ModuleHeader> + + +If you are interested in contributing to one of them, or have other stuff +you would like to share, feel free to contact us: +http://eigen.tuxfamily.org/index.php?title=Main_Page#Mailing_list + +Any kind of contributions are much appreciated, even very preliminary ones. +However, it: + - must rely on Eigen, + - must be highly related to math, + - should have some general purpose in the sense that it could + potentially become an offical Eigen module (or be merged into another one). + +In doubt feel free to contact us. For instance, if your addons is very too specific +but it shows an interesting way of using Eigen, then it could be a nice demo. + + +This directory is organized as follow: + +unsupported/Eigen/ModuleHeader1 +unsupported/Eigen/ModuleHeader2 +unsupported/Eigen/... +unsupported/Eigen/src/Module1/SourceFile1.h +unsupported/Eigen/src/Module1/SourceFile2.h +unsupported/Eigen/src/Module1/... +unsupported/Eigen/src/Module2/SourceFile1.h +unsupported/Eigen/src/Module2/SourceFile2.h +unsupported/Eigen/src/Module2/... +unsupported/Eigen/src/... +unsupported/doc/snippets/.cpp <- code snippets for the doc +unsupported/doc/examples/.cpp <- examples for the doc +unsupported/doc/TutorialModule1.dox +unsupported/doc/TutorialModule2.dox +unsupported/doc/... +unsupported/test/.cpp <- unit test files + +The documentation is generated at the same time than the main Eigen documentation. +The .html files are generated in: build_dir/doc/html/unsupported/ + diff --git a/unsupported/doc/CMakeLists.txt b/unsupported/doc/CMakeLists.txt new file mode 100644 index 000000000..9e9ab9800 --- /dev/null +++ b/unsupported/doc/CMakeLists.txt @@ -0,0 +1,4 @@ +set_directory_properties(PROPERTIES EXCLUDE_FROM_ALL TRUE) + +add_subdirectory(examples) +add_subdirectory(snippets) diff --git a/unsupported/doc/Doxyfile.in b/unsupported/doc/Doxyfile.in new file mode 100644 index 000000000..1facf2985 --- /dev/null +++ b/unsupported/doc/Doxyfile.in @@ -0,0 +1,1460 @@ +# This file describes the settings to be used by the documentation system +# doxygen (www.doxygen.org) for a project +# +# All text after a hash (#) is considered a comment and will be ignored +# The format is: +# TAG = value [value, ...] +# For lists items can also be appended using: +# TAG += value [value, ...] +# Values that contain spaces should be placed between quotes (" ") + +#--------------------------------------------------------------------------- +# Project related configuration options +#--------------------------------------------------------------------------- + +# This tag specifies the encoding used for all characters in the config file +# that follow. The default is UTF-8 which is also the encoding used for all +# text before the first occurrence of this tag. Doxygen uses libiconv (or the +# iconv built into libc) for the transcoding. See +# http://www.gnu.org/software/libiconv for the list of possible encodings. + +DOXYFILE_ENCODING = UTF-8 + +# The PROJECT_NAME tag is a single word (or a sequence of words surrounded +# by quotes) that should identify the project. + +PROJECT_NAME = Eigen - unsupported modules + +# The PROJECT_NUMBER tag can be used to enter a project or revision number. +# This could be handy for archiving the generated documentation or +# if some version control system is used. + +#EIGEN_VERSION is set in the root CMakeLists.txt +PROJECT_NUMBER = "${EIGEN_VERSION}" + +# The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) +# base path where the generated documentation will be put. +# If a relative path is entered, it will be relative to the location +# where doxygen was started. If left blank the current directory will be used. + +OUTPUT_DIRECTORY = "${Eigen_BINARY_DIR}/doc/unsupported" + +# If the CREATE_SUBDIRS tag is set to YES, then doxygen will create +# 4096 sub-directories (in 2 levels) under the output directory of each output +# format and will distribute the generated files over these directories. +# Enabling this option can be useful when feeding doxygen a huge amount of +# source files, where putting all generated files in the same directory would +# otherwise cause performance problems for the file system. + +CREATE_SUBDIRS = NO + +# The OUTPUT_LANGUAGE tag is used to specify the language in which all +# documentation generated by doxygen is written. Doxygen will use this +# information to generate all constant output in the proper language. +# The default language is English, other supported languages are: +# Afrikaans, Arabic, Brazilian, Catalan, Chinese, Chinese-Traditional, +# Croatian, Czech, Danish, Dutch, Farsi, Finnish, French, German, Greek, +# Hungarian, Italian, Japanese, Japanese-en (Japanese with English messages), +# Korean, Korean-en, Lithuanian, Norwegian, Macedonian, Persian, Polish, +# Portuguese, Romanian, Russian, Serbian, Slovak, Slovene, Spanish, Swedish, +# and Ukrainian. + +OUTPUT_LANGUAGE = English + +# If the BRIEF_MEMBER_DESC tag is set to YES (the default) Doxygen will +# include brief member descriptions after the members that are listed in +# the file and class documentation (similar to JavaDoc). +# Set to NO to disable this. + +BRIEF_MEMBER_DESC = YES + +# If the REPEAT_BRIEF tag is set to YES (the default) Doxygen will prepend +# the brief description of a member or function before the detailed description. +# Note: if both HIDE_UNDOC_MEMBERS and BRIEF_MEMBER_DESC are set to NO, the +# brief descriptions will be completely suppressed. + +REPEAT_BRIEF = YES + +# This tag implements a quasi-intelligent brief description abbreviator +# that is used to form the text in various listings. Each string +# in this list, if found as the leading text of the brief description, will be +# stripped from the text and the result after processing the whole list, is +# used as the annotated text. Otherwise, the brief description is used as-is. +# If left blank, the following values are used ("$name" is automatically +# replaced with the name of the entity): "The $name class" "The $name widget" +# "The $name file" "is" "provides" "specifies" "contains" +# "represents" "a" "an" "the" + +ABBREVIATE_BRIEF = "The $name class" \ + "The $name widget" \ + "The $name file" \ + is \ + provides \ + specifies \ + contains \ + represents \ + a \ + an \ + the + +# If the ALWAYS_DETAILED_SEC and REPEAT_BRIEF tags are both set to YES then +# Doxygen will generate a detailed section even if there is only a brief +# description. + +ALWAYS_DETAILED_SEC = NO + +# If the INLINE_INHERITED_MEMB tag is set to YES, doxygen will show all +# inherited members of a class in the documentation of that class as if those +# members were ordinary class members. Constructors, destructors and assignment +# operators of the base classes will not be shown. + +INLINE_INHERITED_MEMB = NO + +# If the FULL_PATH_NAMES tag is set to YES then Doxygen will prepend the full +# path before files name in the file list and in the header files. If set +# to NO the shortest path that makes the file name unique will be used. + +FULL_PATH_NAMES = NO + +# If the FULL_PATH_NAMES tag is set to YES then the STRIP_FROM_PATH tag +# can be used to strip a user-defined part of the path. Stripping is +# only done if one of the specified strings matches the left-hand part of +# the path. The tag can be used to show relative paths in the file list. +# If left blank the directory from which doxygen is run is used as the +# path to strip. + +STRIP_FROM_PATH = + +# The STRIP_FROM_INC_PATH tag can be used to strip a user-defined part of +# the path mentioned in the documentation of a class, which tells +# the reader which header file to include in order to use a class. +# If left blank only the name of the header file containing the class +# definition is used. Otherwise one should specify the include paths that +# are normally passed to the compiler using the -I flag. + +STRIP_FROM_INC_PATH = + +# If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter +# (but less readable) file names. This can be useful is your file systems +# doesn't support long names like on DOS, Mac, or CD-ROM. + +SHORT_NAMES = NO + +# If the JAVADOC_AUTOBRIEF tag is set to YES then Doxygen +# will interpret the first line (until the first dot) of a JavaDoc-style +# comment as the brief description. If set to NO, the JavaDoc +# comments will behave just like regular Qt-style comments +# (thus requiring an explicit @brief command for a brief description.) + +JAVADOC_AUTOBRIEF = NO + +# If the QT_AUTOBRIEF tag is set to YES then Doxygen will +# interpret the first line (until the first dot) of a Qt-style +# comment as the brief description. If set to NO, the comments +# will behave just like regular Qt-style comments (thus requiring +# an explicit \brief command for a brief description.) + +QT_AUTOBRIEF = NO + +# The MULTILINE_CPP_IS_BRIEF tag can be set to YES to make Doxygen +# treat a multi-line C++ special comment block (i.e. a block of //! or /// +# comments) as a brief description. This used to be the default behaviour. +# The new default is to treat a multi-line C++ comment block as a detailed +# description. Set this tag to YES if you prefer the old behaviour instead. + +MULTILINE_CPP_IS_BRIEF = NO + +# If the DETAILS_AT_TOP tag is set to YES then Doxygen +# will output the detailed description near the top, like JavaDoc. +# If set to NO, the detailed description appears after the member +# documentation. + +DETAILS_AT_TOP = YES + +# If the INHERIT_DOCS tag is set to YES (the default) then an undocumented +# member inherits the documentation from any documented member that it +# re-implements. + +INHERIT_DOCS = YES + +# If the SEPARATE_MEMBER_PAGES tag is set to YES, then doxygen will produce +# a new page for each member. If set to NO, the documentation of a member will +# be part of the file/class/namespace that contains it. + +SEPARATE_MEMBER_PAGES = NO + +# The TAB_SIZE tag can be used to set the number of spaces in a tab. +# Doxygen uses this value to replace tabs by spaces in code fragments. + +TAB_SIZE = 8 + +# This tag can be used to specify a number of aliases that acts +# as commands in the documentation. An alias has the form "name=value". +# For example adding "sideeffect=\par Side Effects:\n" will allow you to +# put the command \sideeffect (or @sideeffect) in the documentation, which +# will result in a user-defined paragraph with heading "Side Effects:". +# You can put \n's in the value part of an alias to insert newlines. + +ALIASES = "only_for_vectors=This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column." \ + "array_module=This is defined in the %Array module. \code #include <Eigen/Array> \endcode" \ + "lu_module=This is defined in the %LU module. \code #include <Eigen/LU> \endcode" \ + "cholesky_module=This is defined in the %Cholesky module. \code #include <Eigen/Cholesky> \endcode" \ + "qr_module=This is defined in the %QR module. \code #include <Eigen/QR> \endcode" \ + "svd_module=This is defined in the %SVD module. \code #include <Eigen/SVD> \endcode" \ + "geometry_module=This is defined in the %Geometry module. \code #include <Eigen/Geometry> \endcode" \ + "label=\bug" \ + "nonstableyet=\warning This is not considered to be part of the stable public API yet. Changes may happen in future releases. See \ref Experimental \"Experimental parts of Eigen\"" + +# Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C +# sources only. Doxygen will then generate output that is more tailored for C. +# For instance, some of the names that are used will be different. The list +# of all members will be omitted, etc. + +OPTIMIZE_OUTPUT_FOR_C = NO + +# Set the OPTIMIZE_OUTPUT_JAVA tag to YES if your project consists of Java +# sources only. Doxygen will then generate output that is more tailored for +# Java. For instance, namespaces will be presented as packages, qualified +# scopes will look different, etc. + +OPTIMIZE_OUTPUT_JAVA = NO + +# Set the OPTIMIZE_FOR_FORTRAN tag to YES if your project consists of Fortran +# sources only. Doxygen will then generate output that is more tailored for +# Fortran. + +OPTIMIZE_FOR_FORTRAN = NO + +# Set the OPTIMIZE_OUTPUT_VHDL tag to YES if your project consists of VHDL +# sources. Doxygen will then generate output that is tailored for +# VHDL. + +OPTIMIZE_OUTPUT_VHDL = NO + +# If you use STL classes (i.e. std::string, std::vector, etc.) but do not want +# to include (a tag file for) the STL sources as input, then you should +# set this tag to YES in order to let doxygen match functions declarations and +# definitions whose arguments contain STL classes (e.g. func(std::string); v.s. +# func(std::string) {}). This also make the inheritance and collaboration +# diagrams that involve STL classes more complete and accurate. + +BUILTIN_STL_SUPPORT = NO + +# If you use Microsoft's C++/CLI language, you should set this option to YES to +# enable parsing support. + +CPP_CLI_SUPPORT = NO + +# Set the SIP_SUPPORT tag to YES if your project consists of sip sources only. +# Doxygen will parse them like normal C++ but will assume all classes use public +# instead of private inheritance when no explicit protection keyword is present. + +SIP_SUPPORT = NO + +# For Microsoft's IDL there are propget and propput attributes to indicate getter +# and setter methods for a property. Setting this option to YES (the default) +# will make doxygen to replace the get and set methods by a property in the +# documentation. This will only work if the methods are indeed getting or +# setting a simple type. If this is not the case, or you want to show the +# methods anyway, you should set this option to NO. + +IDL_PROPERTY_SUPPORT = YES + +# If member grouping is used in the documentation and the DISTRIBUTE_GROUP_DOC +# tag is set to YES, then doxygen will reuse the documentation of the first +# member in the group (if any) for the other members of the group. By default +# all members of a group must be documented explicitly. + +DISTRIBUTE_GROUP_DOC = NO + +# Set the SUBGROUPING tag to YES (the default) to allow class member groups of +# the same type (for instance a group of public functions) to be put as a +# subgroup of that type (e.g. under the Public Functions section). Set it to +# NO to prevent subgrouping. Alternatively, this can be done per class using +# the \nosubgrouping command. + +SUBGROUPING = YES + +# When TYPEDEF_HIDES_STRUCT is enabled, a typedef of a struct, union, or enum +# is documented as struct, union, or enum with the name of the typedef. So +# typedef struct TypeS {} TypeT, will appear in the documentation as a struct +# with name TypeT. When disabled the typedef will appear as a member of a file, +# namespace, or class. And the struct will be named TypeS. This can typically +# be useful for C code in case the coding convention dictates that all compound +# types are typedef'ed and only the typedef is referenced, never the tag name. + +TYPEDEF_HIDES_STRUCT = NO + +#--------------------------------------------------------------------------- +# Build related configuration options +#--------------------------------------------------------------------------- + +# If the EXTRACT_ALL tag is set to YES doxygen will assume all entities in +# documentation are documented, even if no documentation was available. +# Private class members and static file members will be hidden unless +# the EXTRACT_PRIVATE and EXTRACT_STATIC tags are set to YES + +EXTRACT_ALL = NO + +# If the EXTRACT_PRIVATE tag is set to YES all private members of a class +# will be included in the documentation. + +EXTRACT_PRIVATE = NO + +# If the EXTRACT_STATIC tag is set to YES all static members of a file +# will be included in the documentation. + +EXTRACT_STATIC = NO + +# If the EXTRACT_LOCAL_CLASSES tag is set to YES classes (and structs) +# defined locally in source files will be included in the documentation. +# If set to NO only classes defined in header files are included. + +EXTRACT_LOCAL_CLASSES = NO + +# This flag is only useful for Objective-C code. When set to YES local +# methods, which are defined in the implementation section but not in +# the interface are included in the documentation. +# If set to NO (the default) only methods in the interface are included. + +EXTRACT_LOCAL_METHODS = NO + +# If this flag is set to YES, the members of anonymous namespaces will be +# extracted and appear in the documentation as a namespace called +# 'anonymous_namespace{file}', where file will be replaced with the base +# name of the file that contains the anonymous namespace. By default +# anonymous namespace are hidden. + +EXTRACT_ANON_NSPACES = NO + +# If the HIDE_UNDOC_MEMBERS tag is set to YES, Doxygen will hide all +# undocumented members of documented classes, files or namespaces. +# If set to NO (the default) these members will be included in the +# various overviews, but no documentation section is generated. +# This option has no effect if EXTRACT_ALL is enabled. + +HIDE_UNDOC_MEMBERS = NO + +# If the HIDE_UNDOC_CLASSES tag is set to YES, Doxygen will hide all +# undocumented classes that are normally visible in the class hierarchy. +# If set to NO (the default) these classes will be included in the various +# overviews. This option has no effect if EXTRACT_ALL is enabled. + +HIDE_UNDOC_CLASSES = YES + +# If the HIDE_FRIEND_COMPOUNDS tag is set to YES, Doxygen will hide all +# friend (class|struct|union) declarations. +# If set to NO (the default) these declarations will be included in the +# documentation. + +HIDE_FRIEND_COMPOUNDS = YES + +# If the HIDE_IN_BODY_DOCS tag is set to YES, Doxygen will hide any +# documentation blocks found inside the body of a function. +# If set to NO (the default) these blocks will be appended to the +# function's detailed documentation block. + +HIDE_IN_BODY_DOCS = NO + +# The INTERNAL_DOCS tag determines if documentation +# that is typed after a \internal command is included. If the tag is set +# to NO (the default) then the documentation will be excluded. +# Set it to YES to include the internal documentation. + +INTERNAL_DOCS = NO + +# If the CASE_SENSE_NAMES tag is set to NO then Doxygen will only generate +# file names in lower-case letters. If set to YES upper-case letters are also +# allowed. This is useful if you have classes or files whose names only differ +# in case and if your file system supports case sensitive file names. Windows +# and Mac users are advised to set this option to NO. + +CASE_SENSE_NAMES = YES + +# If the HIDE_SCOPE_NAMES tag is set to NO (the default) then Doxygen +# will show members with their full class and namespace scopes in the +# documentation. If set to YES the scope will be hidden. + +HIDE_SCOPE_NAMES = YES + +# If the SHOW_INCLUDE_FILES tag is set to YES (the default) then Doxygen +# will put a list of the files that are included by a file in the documentation +# of that file. + +SHOW_INCLUDE_FILES = YES + +# If the INLINE_INFO tag is set to YES (the default) then a tag [inline] +# is inserted in the documentation for inline members. + +INLINE_INFO = YES + +# If the SORT_MEMBER_DOCS tag is set to YES (the default) then doxygen +# will sort the (detailed) documentation of file and class members +# alphabetically by member name. If set to NO the members will appear in +# declaration order. + +SORT_MEMBER_DOCS = YES + +# If the SORT_BRIEF_DOCS tag is set to YES then doxygen will sort the +# brief documentation of file, namespace and class members alphabetically +# by member name. If set to NO (the default) the members will appear in +# declaration order. + +SORT_BRIEF_DOCS = YES + +# If the SORT_GROUP_NAMES tag is set to YES then doxygen will sort the +# hierarchy of group names into alphabetical order. If set to NO (the default) +# the group names will appear in their defined order. + +SORT_GROUP_NAMES = NO + +# If the SORT_BY_SCOPE_NAME tag is set to YES, the class list will be +# sorted by fully-qualified names, including namespaces. If set to +# NO (the default), the class list will be sorted only by class name, +# not including the namespace part. +# Note: This option is not very useful if HIDE_SCOPE_NAMES is set to YES. +# Note: This option applies only to the class list, not to the +# alphabetical list. + +SORT_BY_SCOPE_NAME = NO + +# The GENERATE_TODOLIST tag can be used to enable (YES) or +# disable (NO) the todo list. This list is created by putting \todo +# commands in the documentation. + +GENERATE_TODOLIST = NO + +# The GENERATE_TESTLIST tag can be used to enable (YES) or +# disable (NO) the test list. This list is created by putting \test +# commands in the documentation. + +GENERATE_TESTLIST = NO + +# The GENERATE_BUGLIST tag can be used to enable (YES) or +# disable (NO) the bug list. This list is created by putting \bug +# commands in the documentation. + +GENERATE_BUGLIST = NO + +# The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or +# disable (NO) the deprecated list. This list is created by putting +# \deprecated commands in the documentation. + +GENERATE_DEPRECATEDLIST= NO + +# The ENABLED_SECTIONS tag can be used to enable conditional +# documentation sections, marked by \if sectionname ... \endif. + +ENABLED_SECTIONS = + +# The MAX_INITIALIZER_LINES tag determines the maximum number of lines +# the initial value of a variable or define consists of for it to appear in +# the documentation. If the initializer consists of more lines than specified +# here it will be hidden. Use a value of 0 to hide initializers completely. +# The appearance of the initializer of individual variables and defines in the +# documentation can be controlled using \showinitializer or \hideinitializer +# command in the documentation regardless of this setting. + +MAX_INITIALIZER_LINES = 0 + +# Set the SHOW_USED_FILES tag to NO to disable the list of files generated +# at the bottom of the documentation of classes and structs. If set to YES the +# list will mention the files that were used to generate the documentation. + +SHOW_USED_FILES = YES + +# If the sources in your project are distributed over multiple directories +# then setting the SHOW_DIRECTORIES tag to YES will show the directory hierarchy +# in the documentation. The default is NO. + +SHOW_DIRECTORIES = NO + +# Set the SHOW_FILES tag to NO to disable the generation of the Files page. +# This will remove the Files entry from the Quick Index and from the +# Folder Tree View (if specified). The default is YES. + +SHOW_FILES = YES + +# Set the SHOW_NAMESPACES tag to NO to disable the generation of the +# Namespaces page. This will remove the Namespaces entry from the Quick Index +# and from the Folder Tree View (if specified). The default is YES. + +SHOW_NAMESPACES = NO + +# The FILE_VERSION_FILTER tag can be used to specify a program or script that +# doxygen should invoke to get the current version for each file (typically from +# the version control system). Doxygen will invoke the program by executing (via +# popen()) the command <command> <input-file>, where <command> is the value of +# the FILE_VERSION_FILTER tag, and <input-file> is the name of an input file +# provided by doxygen. Whatever the program writes to standard output +# is used as the file version. See the manual for examples. + +FILE_VERSION_FILTER = + +#--------------------------------------------------------------------------- +# configuration options related to warning and progress messages +#--------------------------------------------------------------------------- + +# The QUIET tag can be used to turn on/off the messages that are generated +# by doxygen. Possible values are YES and NO. If left blank NO is used. + +QUIET = NO + +# The WARNINGS tag can be used to turn on/off the warning messages that are +# generated by doxygen. Possible values are YES and NO. If left blank +# NO is used. + +WARNINGS = YES + +# If WARN_IF_UNDOCUMENTED is set to YES, then doxygen will generate warnings +# for undocumented members. If EXTRACT_ALL is set to YES then this flag will +# automatically be disabled. + +WARN_IF_UNDOCUMENTED = NO + +# If WARN_IF_DOC_ERROR is set to YES, doxygen will generate warnings for +# potential errors in the documentation, such as not documenting some +# parameters in a documented function, or documenting parameters that +# don't exist or using markup commands wrongly. + +WARN_IF_DOC_ERROR = YES + +# This WARN_NO_PARAMDOC option can be abled to get warnings for +# functions that are documented, but have no documentation for their parameters +# or return value. If set to NO (the default) doxygen will only warn about +# wrong or incomplete parameter documentation, but not about the absence of +# documentation. + +WARN_NO_PARAMDOC = NO + +# The WARN_FORMAT tag determines the format of the warning messages that +# doxygen can produce. The string should contain the $file, $line, and $text +# tags, which will be replaced by the file and line number from which the +# warning originated and the warning text. Optionally the format may contain +# $version, which will be replaced by the version of the file (if it could +# be obtained via FILE_VERSION_FILTER) + +WARN_FORMAT = "$file:$line: $text" + +# The WARN_LOGFILE tag can be used to specify a file to which warning +# and error messages should be written. If left blank the output is written +# to stderr. + +WARN_LOGFILE = + +#--------------------------------------------------------------------------- +# configuration options related to the input files +#--------------------------------------------------------------------------- + +# The INPUT tag can be used to specify the files and/or directories that contain +# documented source files. You may enter file names like "myfile.cpp" or +# directories like "/usr/src/myproject". Separate the files or directories +# with spaces. + +INPUT = "${Eigen_SOURCE_DIR}/unsupported/Eigen" \ + "${Eigen_SOURCE_DIR}/unsupported/doc" + +# This tag can be used to specify the character encoding of the source files +# that doxygen parses. Internally doxygen uses the UTF-8 encoding, which is +# also the default input encoding. Doxygen uses libiconv (or the iconv built +# into libc) for the transcoding. See http://www.gnu.org/software/libiconv for +# the list of possible encodings. + +INPUT_ENCODING = UTF-8 + +# If the value of the INPUT tag contains directories, you can use the +# FILE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp +# and *.h) to filter out the source-files in the directories. If left +# blank the following patterns are tested: +# *.c *.cc *.cxx *.cpp *.c++ *.java *.ii *.ixx *.ipp *.i++ *.inl *.h *.hh *.hxx +# *.hpp *.h++ *.idl *.odl *.cs *.php *.php3 *.inc *.m *.mm *.py *.f90 + +FILE_PATTERNS = * + +# The RECURSIVE tag can be used to turn specify whether or not subdirectories +# should be searched for input files as well. Possible values are YES and NO. +# If left blank NO is used. + +RECURSIVE = YES + +# The EXCLUDE tag can be used to specify files and/or directories that should +# excluded from the INPUT source files. This way you can easily exclude a +# subdirectory from a directory tree whose root is specified with the INPUT tag. + +EXCLUDE = "${Eigen_SOURCE_DIR}/unsupported/doc/examples" \ + "${Eigen_SOURCE_DIR}/unsupported/doc/snippets" + +# The EXCLUDE_SYMLINKS tag can be used select whether or not files or +# directories that are symbolic links (a Unix filesystem feature) are excluded +# from the input. + +EXCLUDE_SYMLINKS = NO + +# If the value of the INPUT tag contains directories, you can use the +# EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude +# certain files from those directories. Note that the wildcards are matched +# against the file with absolute path, so to exclude all test directories +# for example use the pattern */test/* + +EXCLUDE_PATTERNS = CMake* \ + *.txt \ + *.sh \ + *.diff \ + *.orig \ + diff \ + *~ + +# The EXCLUDE_SYMBOLS tag can be used to specify one or more symbol names +# (namespaces, classes, functions, etc.) that should be excluded from the +# output. The symbol name can be a fully qualified name, a word, or if the +# wildcard * is used, a substring. Examples: ANamespace, AClass, +# AClass::ANamespace, ANamespace::*Test + +EXCLUDE_SYMBOLS = MatrixBase<* MapBase<* RotationBase<* Matrix<* + +# The EXAMPLE_PATH tag can be used to specify one or more files or +# directories that contain example code fragments that are included (see +# the \include command). + +EXAMPLE_PATH = "${Eigen_SOURCE_DIR}/doc/snippets" \ + "${Eigen_BINARY_DIR}/doc/snippets" \ + "${Eigen_SOURCE_DIR}/doc/examples" \ + "${Eigen_BINARY_DIR}/doc/examples" \ + "${Eigen_SOURCE_DIR}/unsupported/doc/snippets" \ + "${Eigen_BINARY_DIR}/unsupported/doc/snippets" \ + "${Eigen_SOURCE_DIR}/unsupported/doc/examples" \ + "${Eigen_BINARY_DIR}/unsupported/doc/examples" + +# If the value of the EXAMPLE_PATH tag contains directories, you can use the +# EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp +# and *.h) to filter out the source-files in the directories. If left +# blank all files are included. + +EXAMPLE_PATTERNS = * + +# If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be +# searched for input files to be used with the \include or \dontinclude +# commands irrespective of the value of the RECURSIVE tag. +# Possible values are YES and NO. If left blank NO is used. + +EXAMPLE_RECURSIVE = NO + +# The IMAGE_PATH tag can be used to specify one or more files or +# directories that contain image that are included in the documentation (see +# the \image command). + +IMAGE_PATH = + +# The INPUT_FILTER tag can be used to specify a program that doxygen should +# invoke to filter for each input file. Doxygen will invoke the filter program +# by executing (via popen()) the command <filter> <input-file>, where <filter> +# is the value of the INPUT_FILTER tag, and <input-file> is the name of an +# input file. Doxygen will then use the output that the filter program writes +# to standard output. If FILTER_PATTERNS is specified, this tag will be +# ignored. + +INPUT_FILTER = + +# The FILTER_PATTERNS tag can be used to specify filters on a per file pattern +# basis. Doxygen will compare the file name with each pattern and apply the +# filter if there is a match. The filters are a list of the form: +# pattern=filter (like *.cpp=my_cpp_filter). See INPUT_FILTER for further +# info on how filters are used. If FILTER_PATTERNS is empty, INPUT_FILTER +# is applied to all files. + +FILTER_PATTERNS = + +# If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using +# INPUT_FILTER) will be used to filter the input files when producing source +# files to browse (i.e. when SOURCE_BROWSER is set to YES). + +FILTER_SOURCE_FILES = NO + +#--------------------------------------------------------------------------- +# configuration options related to source browsing +#--------------------------------------------------------------------------- + +# If the SOURCE_BROWSER tag is set to YES then a list of source files will +# be generated. Documented entities will be cross-referenced with these sources. +# Note: To get rid of all source code in the generated output, make sure also +# VERBATIM_HEADERS is set to NO. + +SOURCE_BROWSER = NO + +# Setting the INLINE_SOURCES tag to YES will include the body +# of functions and classes directly in the documentation. + +INLINE_SOURCES = NO + +# Setting the STRIP_CODE_COMMENTS tag to YES (the default) will instruct +# doxygen to hide any special comment blocks from generated source code +# fragments. Normal C and C++ comments will always remain visible. + +STRIP_CODE_COMMENTS = YES + +# If the REFERENCED_BY_RELATION tag is set to YES +# then for each documented function all documented +# functions referencing it will be listed. + +REFERENCED_BY_RELATION = YES + +# If the REFERENCES_RELATION tag is set to YES +# then for each documented function all documented entities +# called/used by that function will be listed. + +REFERENCES_RELATION = YES + +# If the REFERENCES_LINK_SOURCE tag is set to YES (the default) +# and SOURCE_BROWSER tag is set to YES, then the hyperlinks from +# functions in REFERENCES_RELATION and REFERENCED_BY_RELATION lists will +# link to the source code. Otherwise they will link to the documentstion. + +REFERENCES_LINK_SOURCE = YES + +# If the USE_HTAGS tag is set to YES then the references to source code +# will point to the HTML generated by the htags(1) tool instead of doxygen +# built-in source browser. The htags tool is part of GNU's global source +# tagging system (see http://www.gnu.org/software/global/global.html). You +# will need version 4.8.6 or higher. + +USE_HTAGS = NO + +# If the VERBATIM_HEADERS tag is set to YES (the default) then Doxygen +# will generate a verbatim copy of the header file for each class for +# which an include is specified. Set to NO to disable this. + +VERBATIM_HEADERS = YES + +#--------------------------------------------------------------------------- +# configuration options related to the alphabetical class index +#--------------------------------------------------------------------------- + +# If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index +# of all compounds will be generated. Enable this if the project +# contains a lot of classes, structs, unions or interfaces. + +ALPHABETICAL_INDEX = NO + +# If the alphabetical index is enabled (see ALPHABETICAL_INDEX) then +# the COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns +# in which this list will be split (can be a number in the range [1..20]) + +COLS_IN_ALPHA_INDEX = 5 + +# In case all classes in a project start with a common prefix, all +# classes will be put under the same header in the alphabetical index. +# The IGNORE_PREFIX tag can be used to specify one or more prefixes that +# should be ignored while generating the index headers. + +IGNORE_PREFIX = + +#--------------------------------------------------------------------------- +# configuration options related to the HTML output +#--------------------------------------------------------------------------- + +# If the GENERATE_HTML tag is set to YES (the default) Doxygen will +# generate HTML output. + +GENERATE_HTML = YES + +# The HTML_OUTPUT tag is used to specify where the HTML docs will be put. +# If a relative path is entered the value of OUTPUT_DIRECTORY will be +# put in front of it. If left blank `html' will be used as the default path. + +HTML_OUTPUT = "${Eigen_BINARY_DIR}/doc/html/unsupported" + +# The HTML_FILE_EXTENSION tag can be used to specify the file extension for +# each generated HTML page (for example: .htm,.php,.asp). If it is left blank +# doxygen will generate files with .html extension. + +HTML_FILE_EXTENSION = .html + +# The HTML_HEADER tag can be used to specify a personal HTML header for +# each generated HTML page. If it is left blank doxygen will generate a +# standard header. + +HTML_HEADER = "${Eigen_BINARY_DIR}/doc/eigendoxy_header.html" + +# The HTML_FOOTER tag can be used to specify a personal HTML footer for +# each generated HTML page. If it is left blank doxygen will generate a +# standard footer. + +# the footer has not been customized yet, so let's use the default one +# ${Eigen_BINARY_DIR}/doc/eigendoxy_footer.html +HTML_FOOTER = + +# The HTML_STYLESHEET tag can be used to specify a user-defined cascading +# style sheet that is used by each HTML page. It can be used to +# fine-tune the look of the HTML output. If the tag is left blank doxygen +# will generate a default style sheet. Note that doxygen will try to copy +# the style sheet file to the HTML output directory, so don't put your own +# stylesheet in the HTML output directory as well, or it will be erased! + +HTML_STYLESHEET = "${Eigen_SOURCE_DIR}/doc/eigendoxy.css" + +# If the HTML_ALIGN_MEMBERS tag is set to YES, the members of classes, +# files or namespaces will be aligned in HTML using tables. If set to +# NO a bullet list will be used. + +HTML_ALIGN_MEMBERS = YES + +# If the GENERATE_HTMLHELP tag is set to YES, additional index files +# will be generated that can be used as input for tools like the +# Microsoft HTML help workshop to generate a compiled HTML help file (.chm) +# of the generated HTML documentation. + +GENERATE_HTMLHELP = NO + +# If the GENERATE_DOCSET tag is set to YES, additional index files +# will be generated that can be used as input for Apple's Xcode 3 +# integrated development environment, introduced with OSX 10.5 (Leopard). +# To create a documentation set, doxygen will generate a Makefile in the +# HTML output directory. Running make will produce the docset in that +# directory and running "make install" will install the docset in +# ~/Library/Developer/Shared/Documentation/DocSets so that Xcode will find +# it at startup. + +GENERATE_DOCSET = NO + +# When GENERATE_DOCSET tag is set to YES, this tag determines the name of the +# feed. A documentation feed provides an umbrella under which multiple +# documentation sets from a single provider (such as a company or product suite) +# can be grouped. + +DOCSET_FEEDNAME = "Doxygen generated docs" + +# When GENERATE_DOCSET tag is set to YES, this tag specifies a string that +# should uniquely identify the documentation set bundle. This should be a +# reverse domain-name style string, e.g. com.mycompany.MyDocSet. Doxygen +# will append .docset to the name. + +DOCSET_BUNDLE_ID = org.doxygen.Project + +# If the HTML_DYNAMIC_SECTIONS tag is set to YES then the generated HTML +# documentation will contain sections that can be hidden and shown after the +# page has loaded. For this to work a browser that supports +# JavaScript and DHTML is required (for instance Mozilla 1.0+, Firefox +# Netscape 6.0+, Internet explorer 5.0+, Konqueror, or Safari). + +HTML_DYNAMIC_SECTIONS = NO + +# If the GENERATE_HTMLHELP tag is set to YES, the CHM_FILE tag can +# be used to specify the file name of the resulting .chm file. You +# can add a path in front of the file if the result should not be +# written to the html output directory. + +CHM_FILE = + +# If the GENERATE_HTMLHELP tag is set to YES, the HHC_LOCATION tag can +# be used to specify the location (absolute path including file name) of +# the HTML help compiler (hhc.exe). If non-empty doxygen will try to run +# the HTML help compiler on the generated index.hhp. + +HHC_LOCATION = + +# If the GENERATE_HTMLHELP tag is set to YES, the GENERATE_CHI flag +# controls if a separate .chi index file is generated (YES) or that +# it should be included in the master .chm file (NO). + +GENERATE_CHI = NO + +# If the GENERATE_HTMLHELP tag is set to YES, the CHM_INDEX_ENCODING +# is used to encode HtmlHelp index (hhk), content (hhc) and project file +# content. + +CHM_INDEX_ENCODING = + +# If the GENERATE_HTMLHELP tag is set to YES, the BINARY_TOC flag +# controls whether a binary table of contents is generated (YES) or a +# normal table of contents (NO) in the .chm file. + +BINARY_TOC = NO + +# The TOC_EXPAND flag can be set to YES to add extra items for group members +# to the contents of the HTML help documentation and to the tree view. + +TOC_EXPAND = NO + +# The DISABLE_INDEX tag can be used to turn on/off the condensed index at +# top of each HTML page. The value NO (the default) enables the index and +# the value YES disables it. + +DISABLE_INDEX = NO + +# This tag can be used to set the number of enum values (range [1..20]) +# that doxygen will group on one line in the generated HTML documentation. + +ENUM_VALUES_PER_LINE = 1 + +# The GENERATE_TREEVIEW tag is used to specify whether a tree-like index +# structure should be generated to display hierarchical information. +# If the tag value is set to FRAME, a side panel will be generated +# containing a tree-like index structure (just like the one that +# is generated for HTML Help). For this to work a browser that supports +# JavaScript, DHTML, CSS and frames is required (for instance Mozilla 1.0+, +# Netscape 6.0+, Internet explorer 5.0+, or Konqueror). Windows users are +# probably better off using the HTML help feature. Other possible values +# for this tag are: HIERARCHIES, which will generate the Groups, Directories, +# and Class Hiererachy pages using a tree view instead of an ordered list; +# ALL, which combines the behavior of FRAME and HIERARCHIES; and NONE, which +# disables this behavior completely. For backwards compatibility with previous +# releases of Doxygen, the values YES and NO are equivalent to FRAME and NONE +# respectively. + +GENERATE_TREEVIEW = NO + +# If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be +# used to set the initial width (in pixels) of the frame in which the tree +# is shown. + +TREEVIEW_WIDTH = 250 + +# Use this tag to change the font size of Latex formulas included +# as images in the HTML documentation. The default is 10. Note that +# when you change the font size after a successful doxygen run you need +# to manually remove any form_*.png images from the HTML output directory +# to force them to be regenerated. + +FORMULA_FONTSIZE = 12 + +#--------------------------------------------------------------------------- +# configuration options related to the LaTeX output +#--------------------------------------------------------------------------- + +# If the GENERATE_LATEX tag is set to YES (the default) Doxygen will +# generate Latex output. + +GENERATE_LATEX = NO + +# The LATEX_OUTPUT tag is used to specify where the LaTeX docs will be put. +# If a relative path is entered the value of OUTPUT_DIRECTORY will be +# put in front of it. If left blank `latex' will be used as the default path. + +LATEX_OUTPUT = latex + +# The LATEX_CMD_NAME tag can be used to specify the LaTeX command name to be +# invoked. If left blank `latex' will be used as the default command name. + +LATEX_CMD_NAME = latex + +# The MAKEINDEX_CMD_NAME tag can be used to specify the command name to +# generate index for LaTeX. If left blank `makeindex' will be used as the +# default command name. + +MAKEINDEX_CMD_NAME = makeindex + +# If the COMPACT_LATEX tag is set to YES Doxygen generates more compact +# LaTeX documents. This may be useful for small projects and may help to +# save some trees in general. + +COMPACT_LATEX = NO + +# The PAPER_TYPE tag can be used to set the paper type that is used +# by the printer. Possible values are: a4, a4wide, letter, legal and +# executive. If left blank a4wide will be used. + +PAPER_TYPE = a4wide + +# The EXTRA_PACKAGES tag can be to specify one or more names of LaTeX +# packages that should be included in the LaTeX output. + +EXTRA_PACKAGES = amssymb \ + amsmath + +# The LATEX_HEADER tag can be used to specify a personal LaTeX header for +# the generated latex document. The header should contain everything until +# the first chapter. If it is left blank doxygen will generate a +# standard header. Notice: only use this tag if you know what you are doing! + +LATEX_HEADER = + +# If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated +# is prepared for conversion to pdf (using ps2pdf). The pdf file will +# contain links (just like the HTML output) instead of page references +# This makes the output suitable for online browsing using a pdf viewer. + +PDF_HYPERLINKS = NO + +# If the USE_PDFLATEX tag is set to YES, pdflatex will be used instead of +# plain latex in the generated Makefile. Set this option to YES to get a +# higher quality PDF documentation. + +USE_PDFLATEX = NO + +# If the LATEX_BATCHMODE tag is set to YES, doxygen will add the \\batchmode. +# command to the generated LaTeX files. This will instruct LaTeX to keep +# running if errors occur, instead of asking the user for help. +# This option is also used when generating formulas in HTML. + +LATEX_BATCHMODE = NO + +# If LATEX_HIDE_INDICES is set to YES then doxygen will not +# include the index chapters (such as File Index, Compound Index, etc.) +# in the output. + +LATEX_HIDE_INDICES = NO + +#--------------------------------------------------------------------------- +# configuration options related to the RTF output +#--------------------------------------------------------------------------- + +# If the GENERATE_RTF tag is set to YES Doxygen will generate RTF output +# The RTF output is optimized for Word 97 and may not look very pretty with +# other RTF readers or editors. + +GENERATE_RTF = NO + +# The RTF_OUTPUT tag is used to specify where the RTF docs will be put. +# If a relative path is entered the value of OUTPUT_DIRECTORY will be +# put in front of it. If left blank `rtf' will be used as the default path. + +RTF_OUTPUT = rtf + +# If the COMPACT_RTF tag is set to YES Doxygen generates more compact +# RTF documents. This may be useful for small projects and may help to +# save some trees in general. + +COMPACT_RTF = NO + +# If the RTF_HYPERLINKS tag is set to YES, the RTF that is generated +# will contain hyperlink fields. The RTF file will +# contain links (just like the HTML output) instead of page references. +# This makes the output suitable for online browsing using WORD or other +# programs which support those fields. +# Note: wordpad (write) and others do not support links. + +RTF_HYPERLINKS = NO + +# Load stylesheet definitions from file. Syntax is similar to doxygen's +# config file, i.e. a series of assignments. You only have to provide +# replacements, missing definitions are set to their default value. + +RTF_STYLESHEET_FILE = + +# Set optional variables used in the generation of an rtf document. +# Syntax is similar to doxygen's config file. + +RTF_EXTENSIONS_FILE = + +#--------------------------------------------------------------------------- +# configuration options related to the man page output +#--------------------------------------------------------------------------- + +# If the GENERATE_MAN tag is set to YES (the default) Doxygen will +# generate man pages + +GENERATE_MAN = NO + +# The MAN_OUTPUT tag is used to specify where the man pages will be put. +# If a relative path is entered the value of OUTPUT_DIRECTORY will be +# put in front of it. If left blank `man' will be used as the default path. + +MAN_OUTPUT = man + +# The MAN_EXTENSION tag determines the extension that is added to +# the generated man pages (default is the subroutine's section .3) + +MAN_EXTENSION = .3 + +# If the MAN_LINKS tag is set to YES and Doxygen generates man output, +# then it will generate one additional man file for each entity +# documented in the real man page(s). These additional files +# only source the real man page, but without them the man command +# would be unable to find the correct page. The default is NO. + +MAN_LINKS = NO + +#--------------------------------------------------------------------------- +# configuration options related to the XML output +#--------------------------------------------------------------------------- + +# If the GENERATE_XML tag is set to YES Doxygen will +# generate an XML file that captures the structure of +# the code including all documentation. + +GENERATE_XML = NO + +# The XML_OUTPUT tag is used to specify where the XML pages will be put. +# If a relative path is entered the value of OUTPUT_DIRECTORY will be +# put in front of it. If left blank `xml' will be used as the default path. + +XML_OUTPUT = xml + +# The XML_SCHEMA tag can be used to specify an XML schema, +# which can be used by a validating XML parser to check the +# syntax of the XML files. + +XML_SCHEMA = + +# The XML_DTD tag can be used to specify an XML DTD, +# which can be used by a validating XML parser to check the +# syntax of the XML files. + +XML_DTD = + +# If the XML_PROGRAMLISTING tag is set to YES Doxygen will +# dump the program listings (including syntax highlighting +# and cross-referencing information) to the XML output. Note that +# enabling this will significantly increase the size of the XML output. + +XML_PROGRAMLISTING = YES + +#--------------------------------------------------------------------------- +# configuration options for the AutoGen Definitions output +#--------------------------------------------------------------------------- + +# If the GENERATE_AUTOGEN_DEF tag is set to YES Doxygen will +# generate an AutoGen Definitions (see autogen.sf.net) file +# that captures the structure of the code including all +# documentation. Note that this feature is still experimental +# and incomplete at the moment. + +GENERATE_AUTOGEN_DEF = NO + +#--------------------------------------------------------------------------- +# configuration options related to the Perl module output +#--------------------------------------------------------------------------- + +# If the GENERATE_PERLMOD tag is set to YES Doxygen will +# generate a Perl module file that captures the structure of +# the code including all documentation. Note that this +# feature is still experimental and incomplete at the +# moment. + +GENERATE_PERLMOD = NO + +# If the PERLMOD_LATEX tag is set to YES Doxygen will generate +# the necessary Makefile rules, Perl scripts and LaTeX code to be able +# to generate PDF and DVI output from the Perl module output. + +PERLMOD_LATEX = NO + +# If the PERLMOD_PRETTY tag is set to YES the Perl module output will be +# nicely formatted so it can be parsed by a human reader. This is useful +# if you want to understand what is going on. On the other hand, if this +# tag is set to NO the size of the Perl module output will be much smaller +# and Perl will parse it just the same. + +PERLMOD_PRETTY = YES + +# The names of the make variables in the generated doxyrules.make file +# are prefixed with the string contained in PERLMOD_MAKEVAR_PREFIX. +# This is useful so different doxyrules.make files included by the same +# Makefile don't overwrite each other's variables. + +PERLMOD_MAKEVAR_PREFIX = + +#--------------------------------------------------------------------------- +# Configuration options related to the preprocessor +#--------------------------------------------------------------------------- + +# If the ENABLE_PREPROCESSING tag is set to YES (the default) Doxygen will +# evaluate all C-preprocessor directives found in the sources and include +# files. + +ENABLE_PREPROCESSING = YES + +# If the MACRO_EXPANSION tag is set to YES Doxygen will expand all macro +# names in the source code. If set to NO (the default) only conditional +# compilation will be performed. Macro expansion can be done in a controlled +# way by setting EXPAND_ONLY_PREDEF to YES. + +MACRO_EXPANSION = YES + +# If the EXPAND_ONLY_PREDEF and MACRO_EXPANSION tags are both set to YES +# then the macro expansion is limited to the macros specified with the +# PREDEFINED and EXPAND_AS_DEFINED tags. + +EXPAND_ONLY_PREDEF = YES + +# If the SEARCH_INCLUDES tag is set to YES (the default) the includes files +# in the INCLUDE_PATH (see below) will be search if a #include is found. + +SEARCH_INCLUDES = YES + +# The INCLUDE_PATH tag can be used to specify one or more directories that +# contain include files that are not input files but should be processed by +# the preprocessor. + +INCLUDE_PATH = + +# You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard +# patterns (like *.h and *.hpp) to filter out the header-files in the +# directories. If left blank, the patterns specified with FILE_PATTERNS will +# be used. + +INCLUDE_FILE_PATTERNS = + +# The PREDEFINED tag can be used to specify one or more macro names that +# are defined before the preprocessor is started (similar to the -D option of +# gcc). The argument of the tag is a list of macros of the form: name +# or name=definition (no spaces). If the definition and the = are +# omitted =1 is assumed. To prevent a macro definition from being +# undefined via #undef or recursively expanded use the := operator +# instead of the = operator. + +PREDEFINED = EIGEN_EMPTY_STRUCT \ + EIGEN_PARSED_BY_DOXYGEN \ + EIGEN_VECTORIZE \ + EIGEN_QT_SUPPORT \ + EIGEN_STRONG_INLINE=inline + +# If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then +# this tag can be used to specify a list of macro names that should be expanded. +# The macro definition that is found in the sources will be used. +# Use the PREDEFINED tag if you want to use a different macro definition. + +EXPAND_AS_DEFINED = EIGEN_MAKE_SCALAR_OPS \ + EIGEN_MAKE_TYPEDEFS \ + EIGEN_MAKE_TYPEDEFS_ALL_SIZES \ + EIGEN_CWISE_UNOP_RETURN_TYPE \ + EIGEN_CWISE_BINOP_RETURN_TYPE + +# If the SKIP_FUNCTION_MACROS tag is set to YES (the default) then +# doxygen's preprocessor will remove all function-like macros that are alone +# on a line, have an all uppercase name, and do not end with a semicolon. Such +# function macros are typically used for boiler-plate code, and will confuse +# the parser if not removed. + +SKIP_FUNCTION_MACROS = YES + +#--------------------------------------------------------------------------- +# Configuration::additions related to external references +#--------------------------------------------------------------------------- + +# The TAGFILES option can be used to specify one or more tagfiles. +# Optionally an initial location of the external documentation +# can be added for each tagfile. The format of a tag file without +# this location is as follows: +# TAGFILES = file1 file2 ... +# Adding location for the tag files is done as follows: +# TAGFILES = file1=loc1 "file2 = loc2" ... +# where "loc1" and "loc2" can be relative or absolute paths or +# URLs. If a location is present for each tag, the installdox tool +# does not have to be run to correct the links. +# Note that each tag file must have a unique name +# (where the name does NOT include the path) +# If a tag file is not located in the directory in which doxygen +# is run, you must also specify the path to the tagfile here. + +TAGFILES = "${Eigen_BINARY_DIR}/doc/eigen.doxytags"=../ + +# When a file name is specified after GENERATE_TAGFILE, doxygen will create +# a tag file that is based on the input files it reads. + +GENERATE_TAGFILE = "${Eigen_BINARY_DIR}/doc/eigen-unsupported.doxytags" + +# If the ALLEXTERNALS tag is set to YES all external classes will be listed +# in the class index. If set to NO only the inherited external classes +# will be listed. + +ALLEXTERNALS = NO + +# If the EXTERNAL_GROUPS tag is set to YES all external groups will be listed +# in the modules index. If set to NO, only the current project's groups will +# be listed. + +EXTERNAL_GROUPS = YES + +# The PERL_PATH should be the absolute path and name of the perl script +# interpreter (i.e. the result of `which perl'). + +PERL_PATH = /usr/bin/perl + +#--------------------------------------------------------------------------- +# Configuration options related to the dot tool +#--------------------------------------------------------------------------- + +# If the CLASS_DIAGRAMS tag is set to YES (the default) Doxygen will +# generate a inheritance diagram (in HTML, RTF and LaTeX) for classes with base +# or super classes. Setting the tag to NO turns the diagrams off. Note that +# this option is superseded by the HAVE_DOT option below. This is only a +# fallback. It is recommended to install and use dot, since it yields more +# powerful graphs. + +CLASS_DIAGRAMS = NO + +# You can define message sequence charts within doxygen comments using the \msc +# command. Doxygen will then run the mscgen tool (see +# http://www.mcternan.me.uk/mscgen/) to produce the chart and insert it in the +# documentation. The MSCGEN_PATH tag allows you to specify the directory where +# the mscgen tool resides. If left empty the tool is assumed to be found in the +# default search path. + +MSCGEN_PATH = NO + +# If set to YES, the inheritance and collaboration graphs will hide +# inheritance and usage relations if the target is undocumented +# or is not a class. + +HIDE_UNDOC_RELATIONS = NO + +# If you set the HAVE_DOT tag to YES then doxygen will assume the dot tool is +# available from the path. This tool is part of Graphviz, a graph visualization +# toolkit from AT&T and Lucent Bell Labs. The other options in this section +# have no effect if this option is set to NO (the default) + +HAVE_DOT = NO + +# By default doxygen will write a font called FreeSans.ttf to the output +# directory and reference it in all dot files that doxygen generates. This +# font does not include all possible unicode characters however, so when you need +# these (or just want a differently looking font) you can specify the font name +# using DOT_FONTNAME. You need need to make sure dot is able to find the font, +# which can be done by putting it in a standard location or by setting the +# DOTFONTPATH environment variable or by setting DOT_FONTPATH to the directory +# containing the font. + +DOT_FONTNAME = FreeSans + +# By default doxygen will tell dot to use the output directory to look for the +# FreeSans.ttf font (which doxygen will put there itself). If you specify a +# different font using DOT_FONTNAME you can set the path where dot +# can find it using this tag. + +DOT_FONTPATH = + +# If the CLASS_GRAPH and HAVE_DOT tags are set to YES then doxygen +# will generate a graph for each documented class showing the direct and +# indirect inheritance relations. Setting this tag to YES will force the +# the CLASS_DIAGRAMS tag to NO. + +CLASS_GRAPH = NO + +# If the COLLABORATION_GRAPH and HAVE_DOT tags are set to YES then doxygen +# will generate a graph for each documented class showing the direct and +# indirect implementation dependencies (inheritance, containment, and +# class references variables) of the class with other documented classes. + +COLLABORATION_GRAPH = NO + +# If the GROUP_GRAPHS and HAVE_DOT tags are set to YES then doxygen +# will generate a graph for groups, showing the direct groups dependencies + +GROUP_GRAPHS = NO + +# If the UML_LOOK tag is set to YES doxygen will generate inheritance and +# collaboration diagrams in a style similar to the OMG's Unified Modeling +# Language. + +UML_LOOK = NO + +# If set to YES, the inheritance and collaboration graphs will show the +# relations between templates and their instances. + +TEMPLATE_RELATIONS = NO + +# If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDE_GRAPH, and HAVE_DOT +# tags are set to YES then doxygen will generate a graph for each documented +# file showing the direct and indirect include dependencies of the file with +# other documented files. + +INCLUDE_GRAPH = NO + +# If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDED_BY_GRAPH, and +# HAVE_DOT tags are set to YES then doxygen will generate a graph for each +# documented header file showing the documented files that directly or +# indirectly include this file. + +INCLUDED_BY_GRAPH = NO + +# If the CALL_GRAPH and HAVE_DOT options are set to YES then +# doxygen will generate a call dependency graph for every global function +# or class method. Note that enabling this option will significantly increase +# the time of a run. So in most cases it will be better to enable call graphs +# for selected functions only using the \callgraph command. + +CALL_GRAPH = NO + +# If the CALLER_GRAPH and HAVE_DOT tags are set to YES then +# doxygen will generate a caller dependency graph for every global function +# or class method. Note that enabling this option will significantly increase +# the time of a run. So in most cases it will be better to enable caller +# graphs for selected functions only using the \callergraph command. + +CALLER_GRAPH = NO + +# If the GRAPHICAL_HIERARCHY and HAVE_DOT tags are set to YES then doxygen +# will graphical hierarchy of all classes instead of a textual one. + +GRAPHICAL_HIERARCHY = NO + +# If the DIRECTORY_GRAPH, SHOW_DIRECTORIES and HAVE_DOT tags are set to YES +# then doxygen will show the dependencies a directory has on other directories +# in a graphical way. The dependency relations are determined by the #include +# relations between the files in the directories. + +DIRECTORY_GRAPH = NO + +# The DOT_IMAGE_FORMAT tag can be used to set the image format of the images +# generated by dot. Possible values are png, jpg, or gif +# If left blank png will be used. + +DOT_IMAGE_FORMAT = png + +# The tag DOT_PATH can be used to specify the path where the dot tool can be +# found. If left blank, it is assumed the dot tool can be found in the path. + +DOT_PATH = + +# The DOTFILE_DIRS tag can be used to specify one or more directories that +# contain dot files that are included in the documentation (see the +# \dotfile command). + +DOTFILE_DIRS = + +# The DOT_GRAPH_MAX_NODES tag can be used to set the maximum number of +# nodes that will be shown in the graph. If the number of nodes in a graph +# becomes larger than this value, doxygen will truncate the graph, which is +# visualized by representing a node as a red box. Note that doxygen if the +# number of direct children of the root node in a graph is already larger than +# DOT_GRAPH_MAX_NODES then the graph will not be shown at all. Also note +# that the size of a graph can be further restricted by MAX_DOT_GRAPH_DEPTH. + +DOT_GRAPH_MAX_NODES = 50 + +# The MAX_DOT_GRAPH_DEPTH tag can be used to set the maximum depth of the +# graphs generated by dot. A depth value of 3 means that only nodes reachable +# from the root by following a path via at most 3 edges will be shown. Nodes +# that lay further from the root node will be omitted. Note that setting this +# option to 1 or 2 may greatly reduce the computation time needed for large +# code bases. Also note that the size of a graph can be further restricted by +# DOT_GRAPH_MAX_NODES. Using a depth of 0 means no depth restriction. + +MAX_DOT_GRAPH_DEPTH = 1000 + +# Set the DOT_TRANSPARENT tag to YES to generate images with a transparent +# background. This is enabled by default, which results in a transparent +# background. Warning: Depending on the platform used, enabling this option +# may lead to badly anti-aliased labels on the edges of a graph (i.e. they +# become hard to read). + +DOT_TRANSPARENT = NO + +# Set the DOT_MULTI_TARGETS tag to YES allow dot to generate multiple output +# files in one run (i.e. multiple -o and -T options on the command line). This +# makes dot run faster, but since only newer versions of dot (>1.8.10) +# support this, this feature is disabled by default. + +DOT_MULTI_TARGETS = NO + +# If the GENERATE_LEGEND tag is set to YES (the default) Doxygen will +# generate a legend page explaining the meaning of the various boxes and +# arrows in the dot generated graphs. + +GENERATE_LEGEND = NO + +# If the DOT_CLEANUP tag is set to YES (the default) Doxygen will +# remove the intermediate dot files that are used to generate +# the various graphs. + +DOT_CLEANUP = NO + +#--------------------------------------------------------------------------- +# Configuration::additions related to the search engine +#--------------------------------------------------------------------------- + +# The SEARCHENGINE tag specifies whether or not a search engine should be +# used. If set to NO the values of all tags below this one will be ignored. + +SEARCHENGINE = NO diff --git a/unsupported/doc/Overview.dox b/unsupported/doc/Overview.dox new file mode 100644 index 000000000..458b507b5 --- /dev/null +++ b/unsupported/doc/Overview.dox @@ -0,0 +1,22 @@ +namespace Eigen { + +/** \mainpage Eigen's unsupported modules + +This is the API documentation for Eigen's unsupported modules. + +These modules are contributions from various users. They are provided "as is", without any support. + +Click on the \e Modules tab at the top of this page to get a list of all unsupported modules. + +Don't miss the <a href="..//index.html">official Eigen documentation</a>. + + +\defgroup Unsupported_modules Unsupported modules + +The unsupported modules are contributions from various users. They are +provided "as is", without any support. Nevertheless, some of them are +subject to be included in Eigen in the future. + +*/ + +} diff --git a/unsupported/doc/examples/BVH_Example.cpp b/unsupported/doc/examples/BVH_Example.cpp new file mode 100644 index 000000000..6b6fac075 --- /dev/null +++ b/unsupported/doc/examples/BVH_Example.cpp @@ -0,0 +1,52 @@ +#include <Eigen/StdVector> +#include <unsupported/Eigen/BVH> +#include <iostream> + +using namespace Eigen; +typedef AlignedBox<double, 2> Box2d; + +namespace Eigen { + namespace internal { + Box2d bounding_box(const Vector2d &v) { return Box2d(v, v); } //compute the bounding box of a single point + } +} + +struct PointPointMinimizer //how to compute squared distances between points and rectangles +{ + PointPointMinimizer() : calls(0) {} + typedef double Scalar; + + double minimumOnVolumeVolume(const Box2d &r1, const Box2d &r2) { ++calls; return r1.squaredExteriorDistance(r2); } + double minimumOnVolumeObject(const Box2d &r, const Vector2d &v) { ++calls; return r.squaredExteriorDistance(v); } + double minimumOnObjectVolume(const Vector2d &v, const Box2d &r) { ++calls; return r.squaredExteriorDistance(v); } + double minimumOnObjectObject(const Vector2d &v1, const Vector2d &v2) { ++calls; return (v1 - v2).squaredNorm(); } + + int calls; +}; + +int main() +{ + typedef std::vector<Vector2d, aligned_allocator<Vector2d> > StdVectorOfVector2d; + StdVectorOfVector2d redPoints, bluePoints; + for(int i = 0; i < 100; ++i) { //initialize random set of red points and blue points + redPoints.push_back(Vector2d::Random()); + bluePoints.push_back(Vector2d::Random()); + } + + PointPointMinimizer minimizer; + double minDistSq = std::numeric_limits<double>::max(); + + //brute force to find closest red-blue pair + for(int i = 0; i < (int)redPoints.size(); ++i) + for(int j = 0; j < (int)bluePoints.size(); ++j) + minDistSq = std::min(minDistSq, minimizer.minimumOnObjectObject(redPoints[i], bluePoints[j])); + std::cout << "Brute force distance = " << sqrt(minDistSq) << ", calls = " << minimizer.calls << std::endl; + + //using BVH to find closest red-blue pair + minimizer.calls = 0; + KdBVH<double, 2, Vector2d> redTree(redPoints.begin(), redPoints.end()), blueTree(bluePoints.begin(), bluePoints.end()); //construct the trees + minDistSq = BVMinimize(redTree, blueTree, minimizer); //actual BVH minimization call + std::cout << "BVH distance = " << sqrt(minDistSq) << ", calls = " << minimizer.calls << std::endl; + + return 0; +} diff --git a/unsupported/doc/examples/CMakeLists.txt b/unsupported/doc/examples/CMakeLists.txt new file mode 100644 index 000000000..978f9afd8 --- /dev/null +++ b/unsupported/doc/examples/CMakeLists.txt @@ -0,0 +1,22 @@ +FILE(GLOB examples_SRCS "*.cpp") + +ADD_CUSTOM_TARGET(unsupported_examples) + +INCLUDE_DIRECTORIES(../../../unsupported ../../../unsupported/test) + +FOREACH(example_src ${examples_SRCS}) + GET_FILENAME_COMPONENT(example ${example_src} NAME_WE) + ADD_EXECUTABLE(example_${example} ${example_src}) + if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO) + target_link_libraries(example_${example} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}) + endif() + GET_TARGET_PROPERTY(example_executable + example_${example} LOCATION) + ADD_CUSTOM_COMMAND( + TARGET example_${example} + POST_BUILD + COMMAND ${example_executable} + ARGS >${CMAKE_CURRENT_BINARY_DIR}/${example}.out + ) + ADD_DEPENDENCIES(unsupported_examples example_${example}) +ENDFOREACH(example_src) diff --git a/unsupported/doc/examples/FFT.cpp b/unsupported/doc/examples/FFT.cpp new file mode 100644 index 000000000..fcbf81276 --- /dev/null +++ b/unsupported/doc/examples/FFT.cpp @@ -0,0 +1,118 @@ +// To use the simple FFT implementation +// g++ -o demofft -I.. -Wall -O3 FFT.cpp + +// To use the FFTW implementation +// g++ -o demofft -I.. -DUSE_FFTW -Wall -O3 FFT.cpp -lfftw3 -lfftw3f -lfftw3l + +#ifdef USE_FFTW +#include <fftw3.h> +#endif + +#include <vector> +#include <complex> +#include <algorithm> +#include <iterator> +#include <iostream> +#include <Eigen/Core> +#include <unsupported/Eigen/FFT> + +using namespace std; +using namespace Eigen; + +template <typename T> +T mag2(T a) +{ + return a*a; +} +template <typename T> +T mag2(std::complex<T> a) +{ + return norm(a); +} + +template <typename T> +T mag2(const std::vector<T> & vec) +{ + T out=0; + for (size_t k=0;k<vec.size();++k) + out += mag2(vec[k]); + return out; +} + +template <typename T> +T mag2(const std::vector<std::complex<T> > & vec) +{ + T out=0; + for (size_t k=0;k<vec.size();++k) + out += mag2(vec[k]); + return out; +} + +template <typename T> +vector<T> operator-(const vector<T> & a,const vector<T> & b ) +{ + vector<T> c(a); + for (size_t k=0;k<b.size();++k) + c[k] -= b[k]; + return c; +} + +template <typename T> +void RandomFill(std::vector<T> & vec) +{ + for (size_t k=0;k<vec.size();++k) + vec[k] = T( rand() )/T(RAND_MAX) - .5; +} + +template <typename T> +void RandomFill(std::vector<std::complex<T> > & vec) +{ + for (size_t k=0;k<vec.size();++k) + vec[k] = std::complex<T> ( T( rand() )/T(RAND_MAX) - .5, T( rand() )/T(RAND_MAX) - .5); +} + +template <typename T_time,typename T_freq> +void fwd_inv(size_t nfft) +{ + typedef typename NumTraits<T_freq>::Real Scalar; + vector<T_time> timebuf(nfft); + RandomFill(timebuf); + + vector<T_freq> freqbuf; + static FFT<Scalar> fft; + fft.fwd(freqbuf,timebuf); + + vector<T_time> timebuf2; + fft.inv(timebuf2,freqbuf); + + long double rmse = mag2(timebuf - timebuf2) / mag2(timebuf); + cout << "roundtrip rmse: " << rmse << endl; +} + +template <typename T_scalar> +void two_demos(int nfft) +{ + cout << " scalar "; + fwd_inv<T_scalar,std::complex<T_scalar> >(nfft); + cout << " complex "; + fwd_inv<std::complex<T_scalar>,std::complex<T_scalar> >(nfft); +} + +void demo_all_types(int nfft) +{ + cout << "nfft=" << nfft << endl; + cout << " float" << endl; + two_demos<float>(nfft); + cout << " double" << endl; + two_demos<double>(nfft); + cout << " long double" << endl; + two_demos<long double>(nfft); +} + +int main() +{ + demo_all_types( 2*3*4*5*7 ); + demo_all_types( 2*9*16*25 ); + demo_all_types( 1024 ); + return 0; +} diff --git a/unsupported/doc/examples/MatrixExponential.cpp b/unsupported/doc/examples/MatrixExponential.cpp new file mode 100644 index 000000000..ebd3b9675 --- /dev/null +++ b/unsupported/doc/examples/MatrixExponential.cpp @@ -0,0 +1,16 @@ +#include <unsupported/Eigen/MatrixFunctions> +#include <iostream> + +using namespace Eigen; + +int main() +{ + const double pi = std::acos(-1.0); + + MatrixXd A(3,3); + A << 0, -pi/4, 0, + pi/4, 0, 0, + 0, 0, 0; + std::cout << "The matrix A is:\n" << A << "\n\n"; + std::cout << "The matrix exponential of A is:\n" << A.exp() << "\n\n"; +} diff --git a/unsupported/doc/examples/MatrixFunction.cpp b/unsupported/doc/examples/MatrixFunction.cpp new file mode 100644 index 000000000..a4172e4ae --- /dev/null +++ b/unsupported/doc/examples/MatrixFunction.cpp @@ -0,0 +1,23 @@ +#include <unsupported/Eigen/MatrixFunctions> +#include <iostream> + +using namespace Eigen; + +std::complex<double> expfn(std::complex<double> x, int) +{ + return std::exp(x); +} + +int main() +{ + const double pi = std::acos(-1.0); + + MatrixXd A(3,3); + A << 0, -pi/4, 0, + pi/4, 0, 0, + 0, 0, 0; + + std::cout << "The matrix A is:\n" << A << "\n\n"; + std::cout << "The matrix exponential of A is:\n" + << A.matrixFunction(expfn) << "\n\n"; +} diff --git a/unsupported/doc/examples/MatrixLogarithm.cpp b/unsupported/doc/examples/MatrixLogarithm.cpp new file mode 100644 index 000000000..8c5d97054 --- /dev/null +++ b/unsupported/doc/examples/MatrixLogarithm.cpp @@ -0,0 +1,15 @@ +#include <unsupported/Eigen/MatrixFunctions> +#include <iostream> + +using namespace Eigen; + +int main() +{ + using std::sqrt; + MatrixXd A(3,3); + A << 0.5*sqrt(2), -0.5*sqrt(2), 0, + 0.5*sqrt(2), 0.5*sqrt(2), 0, + 0, 0, 1; + std::cout << "The matrix A is:\n" << A << "\n\n"; + std::cout << "The matrix logarithm of A is:\n" << A.log() << "\n"; +} diff --git a/unsupported/doc/examples/MatrixSine.cpp b/unsupported/doc/examples/MatrixSine.cpp new file mode 100644 index 000000000..9eea9a081 --- /dev/null +++ b/unsupported/doc/examples/MatrixSine.cpp @@ -0,0 +1,20 @@ +#include <unsupported/Eigen/MatrixFunctions> +#include <iostream> + +using namespace Eigen; + +int main() +{ + MatrixXd A = MatrixXd::Random(3,3); + std::cout << "A = \n" << A << "\n\n"; + + MatrixXd sinA = A.sin(); + std::cout << "sin(A) = \n" << sinA << "\n\n"; + + MatrixXd cosA = A.cos(); + std::cout << "cos(A) = \n" << cosA << "\n\n"; + + // The matrix functions satisfy sin^2(A) + cos^2(A) = I, + // like the scalar functions. + std::cout << "sin^2(A) + cos^2(A) = \n" << sinA*sinA + cosA*cosA << "\n\n"; +} diff --git a/unsupported/doc/examples/MatrixSinh.cpp b/unsupported/doc/examples/MatrixSinh.cpp new file mode 100644 index 000000000..f77186724 --- /dev/null +++ b/unsupported/doc/examples/MatrixSinh.cpp @@ -0,0 +1,20 @@ +#include <unsupported/Eigen/MatrixFunctions> +#include <iostream> + +using namespace Eigen; + +int main() +{ + MatrixXf A = MatrixXf::Random(3,3); + std::cout << "A = \n" << A << "\n\n"; + + MatrixXf sinhA = A.sinh(); + std::cout << "sinh(A) = \n" << sinhA << "\n\n"; + + MatrixXf coshA = A.cosh(); + std::cout << "cosh(A) = \n" << coshA << "\n\n"; + + // The matrix functions satisfy cosh^2(A) - sinh^2(A) = I, + // like the scalar functions. + std::cout << "cosh^2(A) - sinh^2(A) = \n" << coshA*coshA - sinhA*sinhA << "\n\n"; +} diff --git a/unsupported/doc/examples/MatrixSquareRoot.cpp b/unsupported/doc/examples/MatrixSquareRoot.cpp new file mode 100644 index 000000000..88e7557d7 --- /dev/null +++ b/unsupported/doc/examples/MatrixSquareRoot.cpp @@ -0,0 +1,16 @@ +#include <unsupported/Eigen/MatrixFunctions> +#include <iostream> + +using namespace Eigen; + +int main() +{ + const double pi = std::acos(-1.0); + + MatrixXd A(2,2); + A << cos(pi/3), -sin(pi/3), + sin(pi/3), cos(pi/3); + std::cout << "The matrix A is:\n" << A << "\n\n"; + std::cout << "The matrix square root of A is:\n" << A.sqrt() << "\n\n"; + std::cout << "The square of the last matrix is:\n" << A.sqrt() * A.sqrt() << "\n"; +} diff --git a/unsupported/doc/examples/PolynomialSolver1.cpp b/unsupported/doc/examples/PolynomialSolver1.cpp new file mode 100644 index 000000000..71e6b825f --- /dev/null +++ b/unsupported/doc/examples/PolynomialSolver1.cpp @@ -0,0 +1,53 @@ +#include <unsupported/Eigen/Polynomials> +#include <vector> +#include <iostream> + +using namespace Eigen; +using namespace std; + +int main() +{ + typedef Matrix<double,5,1> Vector5d; + + Vector5d roots = Vector5d::Random(); + cout << "Roots: " << roots.transpose() << endl; + Eigen::Matrix<double,6,1> polynomial; + roots_to_monicPolynomial( roots, polynomial ); + + PolynomialSolver<double,5> psolve( polynomial ); + cout << "Complex roots: " << psolve.roots().transpose() << endl; + + std::vector<double> realRoots; + psolve.realRoots( realRoots ); + Map<Vector5d> mapRR( &realRoots[0] ); + cout << "Real roots: " << mapRR.transpose() << endl; + + cout << endl; + cout << "Illustration of the convergence problem with the QR algorithm: " << endl; + cout << "---------------------------------------------------------------" << endl; + Eigen::Matrix<float,7,1> hardCase_polynomial; + hardCase_polynomial << + -0.957, 0.9219, 0.3516, 0.9453, -0.4023, -0.5508, -0.03125; + cout << "Hard case polynomial defined by floats: " << hardCase_polynomial.transpose() << endl; + PolynomialSolver<float,6> psolvef( hardCase_polynomial ); + cout << "Complex roots: " << psolvef.roots().transpose() << endl; + Eigen::Matrix<float,6,1> evals; + for( int i=0; i<6; ++i ){ evals[i] = std::abs( poly_eval( hardCase_polynomial, psolvef.roots()[i] ) ); } + cout << "Norms of the evaluations of the polynomial at the roots: " << evals.transpose() << endl << endl; + + cout << "Using double's almost always solves the problem for small degrees: " << endl; + cout << "-------------------------------------------------------------------" << endl; + PolynomialSolver<double,6> psolve6d( hardCase_polynomial.cast<double>() ); + cout << "Complex roots: " << psolve6d.roots().transpose() << endl; + for( int i=0; i<6; ++i ) + { + std::complex<float> castedRoot( psolve6d.roots()[i].real(), psolve6d.roots()[i].imag() ); + evals[i] = std::abs( poly_eval( hardCase_polynomial, castedRoot ) ); + } + cout << "Norms of the evaluations of the polynomial at the roots: " << evals.transpose() << endl << endl; + + cout.precision(10); + cout << "The last root in float then in double: " << psolvef.roots()[5] << "\t" << psolve6d.roots()[5] << endl; + std::complex<float> castedRoot( psolve6d.roots()[5].real(), psolve6d.roots()[5].imag() ); + cout << "Norm of the difference: " << internal::abs( psolvef.roots()[5] - castedRoot ) << endl; +} diff --git a/unsupported/doc/examples/PolynomialUtils1.cpp b/unsupported/doc/examples/PolynomialUtils1.cpp new file mode 100644 index 000000000..dbfe520b5 --- /dev/null +++ b/unsupported/doc/examples/PolynomialUtils1.cpp @@ -0,0 +1,20 @@ +#include <unsupported/Eigen/Polynomials> +#include <iostream> + +using namespace Eigen; +using namespace std; + +int main() +{ + Vector4d roots = Vector4d::Random(); + cout << "Roots: " << roots.transpose() << endl; + Eigen::Matrix<double,5,1> polynomial; + roots_to_monicPolynomial( roots, polynomial ); + cout << "Polynomial: "; + for( int i=0; i<4; ++i ){ cout << polynomial[i] << ".x^" << i << "+ "; } + cout << polynomial[4] << ".x^4" << endl; + Vector4d evaluation; + for( int i=0; i<4; ++i ){ + evaluation[i] = poly_eval( polynomial, roots[i] ); } + cout << "Evaluation of the polynomial at the roots: " << evaluation.transpose(); +} diff --git a/unsupported/doc/snippets/CMakeLists.txt b/unsupported/doc/snippets/CMakeLists.txt new file mode 100644 index 000000000..4a4157933 --- /dev/null +++ b/unsupported/doc/snippets/CMakeLists.txt @@ -0,0 +1,28 @@ +FILE(GLOB snippets_SRCS "*.cpp") + +ADD_CUSTOM_TARGET(unsupported_snippets) + +FOREACH(snippet_src ${snippets_SRCS}) + GET_FILENAME_COMPONENT(snippet ${snippet_src} NAME_WE) + SET(compile_snippet_target compile_${snippet}) + SET(compile_snippet_src ${compile_snippet_target}.cpp) + FILE(READ ${snippet_src} snippet_source_code) + CONFIGURE_FILE(${PROJECT_SOURCE_DIR}/doc/snippets/compile_snippet.cpp.in + ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src}) + ADD_EXECUTABLE(${compile_snippet_target} + ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src}) + if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO) + target_link_libraries(${compile_snippet_target} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}) + endif() + GET_TARGET_PROPERTY(compile_snippet_executable + ${compile_snippet_target} LOCATION) + ADD_CUSTOM_COMMAND( + TARGET ${compile_snippet_target} + POST_BUILD + COMMAND ${compile_snippet_executable} + ARGS >${CMAKE_CURRENT_BINARY_DIR}/${snippet}.out + ) + ADD_DEPENDENCIES(unsupported_snippets ${compile_snippet_target}) + set_source_files_properties(${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src} + PROPERTIES OBJECT_DEPENDS ${snippet_src}) +ENDFOREACH(snippet_src) diff --git a/unsupported/test/BVH.cpp b/unsupported/test/BVH.cpp new file mode 100644 index 000000000..ff5b3299d --- /dev/null +++ b/unsupported/test/BVH.cpp @@ -0,0 +1,222 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Ilya Baran <ibaran@mit.edu> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include <Eigen/StdVector> +#include <Eigen/Geometry> +#include <unsupported/Eigen/BVH> + +namespace Eigen { + +template<typename Scalar, int Dim> AlignedBox<Scalar, Dim> bounding_box(const Matrix<Scalar, Dim, 1> &v) { return AlignedBox<Scalar, Dim>(v); } + +} + + +template<int Dim> +struct Ball +{ +EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(double, Dim) + + typedef Matrix<double, Dim, 1> VectorType; + + Ball() {} + Ball(const VectorType &c, double r) : center(c), radius(r) {} + + VectorType center; + double radius; +}; +template<int Dim> AlignedBox<double, Dim> bounding_box(const Ball<Dim> &b) +{ return AlignedBox<double, Dim>(b.center.array() - b.radius, b.center.array() + b.radius); } + +inline double SQR(double x) { return x * x; } + +template<int Dim> +struct BallPointStuff //this class provides functions to be both an intersector and a minimizer, both for a ball and a point and for two trees +{ + typedef double Scalar; + typedef Matrix<double, Dim, 1> VectorType; + typedef Ball<Dim> BallType; + typedef AlignedBox<double, Dim> BoxType; + + BallPointStuff() : calls(0), count(0) {} + BallPointStuff(const VectorType &inP) : p(inP), calls(0), count(0) {} + + + bool intersectVolume(const BoxType &r) { ++calls; return r.contains(p); } + bool intersectObject(const BallType &b) { + ++calls; + if((b.center - p).squaredNorm() < SQR(b.radius)) + ++count; + return false; //continue + } + + bool intersectVolumeVolume(const BoxType &r1, const BoxType &r2) { ++calls; return !(r1.intersection(r2)).isNull(); } + bool intersectVolumeObject(const BoxType &r, const BallType &b) { ++calls; return r.squaredExteriorDistance(b.center) < SQR(b.radius); } + bool intersectObjectVolume(const BallType &b, const BoxType &r) { ++calls; return r.squaredExteriorDistance(b.center) < SQR(b.radius); } + bool intersectObjectObject(const BallType &b1, const BallType &b2){ + ++calls; + if((b1.center - b2.center).norm() < b1.radius + b2.radius) + ++count; + return false; + } + bool intersectVolumeObject(const BoxType &r, const VectorType &v) { ++calls; return r.contains(v); } + bool intersectObjectObject(const BallType &b, const VectorType &v){ + ++calls; + if((b.center - v).squaredNorm() < SQR(b.radius)) + ++count; + return false; + } + + double minimumOnVolume(const BoxType &r) { ++calls; return r.squaredExteriorDistance(p); } + double minimumOnObject(const BallType &b) { ++calls; return (std::max)(0., (b.center - p).squaredNorm() - SQR(b.radius)); } + double minimumOnVolumeVolume(const BoxType &r1, const BoxType &r2) { ++calls; return r1.squaredExteriorDistance(r2); } + double minimumOnVolumeObject(const BoxType &r, const BallType &b) { ++calls; return SQR((std::max)(0., r.exteriorDistance(b.center) - b.radius)); } + double minimumOnObjectVolume(const BallType &b, const BoxType &r) { ++calls; return SQR((std::max)(0., r.exteriorDistance(b.center) - b.radius)); } + double minimumOnObjectObject(const BallType &b1, const BallType &b2){ ++calls; return SQR((std::max)(0., (b1.center - b2.center).norm() - b1.radius - b2.radius)); } + double minimumOnVolumeObject(const BoxType &r, const VectorType &v) { ++calls; return r.squaredExteriorDistance(v); } + double minimumOnObjectObject(const BallType &b, const VectorType &v){ ++calls; return SQR((std::max)(0., (b.center - v).norm() - b.radius)); } + + VectorType p; + int calls; + int count; +}; + + +template<int Dim> +struct TreeTest +{ + typedef Matrix<double, Dim, 1> VectorType; + typedef std::vector<VectorType, aligned_allocator<VectorType> > VectorTypeList; + typedef Ball<Dim> BallType; + typedef std::vector<BallType, aligned_allocator<BallType> > BallTypeList; + typedef AlignedBox<double, Dim> BoxType; + + void testIntersect1() + { + BallTypeList b; + for(int i = 0; i < 500; ++i) { + b.push_back(BallType(VectorType::Random(), 0.5 * internal::random(0., 1.))); + } + KdBVH<double, Dim, BallType> tree(b.begin(), b.end()); + + VectorType pt = VectorType::Random(); + BallPointStuff<Dim> i1(pt), i2(pt); + + for(int i = 0; i < (int)b.size(); ++i) + i1.intersectObject(b[i]); + + BVIntersect(tree, i2); + + VERIFY(i1.count == i2.count); + } + + void testMinimize1() + { + BallTypeList b; + for(int i = 0; i < 500; ++i) { + b.push_back(BallType(VectorType::Random(), 0.01 * internal::random(0., 1.))); + } + KdBVH<double, Dim, BallType> tree(b.begin(), b.end()); + + VectorType pt = VectorType::Random(); + BallPointStuff<Dim> i1(pt), i2(pt); + + double m1 = (std::numeric_limits<double>::max)(), m2 = m1; + + for(int i = 0; i < (int)b.size(); ++i) + m1 = (std::min)(m1, i1.minimumOnObject(b[i])); + + m2 = BVMinimize(tree, i2); + + VERIFY_IS_APPROX(m1, m2); + } + + void testIntersect2() + { + BallTypeList b; + VectorTypeList v; + + for(int i = 0; i < 50; ++i) { + b.push_back(BallType(VectorType::Random(), 0.5 * internal::random(0., 1.))); + for(int j = 0; j < 3; ++j) + v.push_back(VectorType::Random()); + } + + KdBVH<double, Dim, BallType> tree(b.begin(), b.end()); + KdBVH<double, Dim, VectorType> vTree(v.begin(), v.end()); + + BallPointStuff<Dim> i1, i2; + + for(int i = 0; i < (int)b.size(); ++i) + for(int j = 0; j < (int)v.size(); ++j) + i1.intersectObjectObject(b[i], v[j]); + + BVIntersect(tree, vTree, i2); + + VERIFY(i1.count == i2.count); + } + + void testMinimize2() + { + BallTypeList b; + VectorTypeList v; + + for(int i = 0; i < 50; ++i) { + b.push_back(BallType(VectorType::Random(), 1e-7 + 1e-6 * internal::random(0., 1.))); + for(int j = 0; j < 3; ++j) + v.push_back(VectorType::Random()); + } + + KdBVH<double, Dim, BallType> tree(b.begin(), b.end()); + KdBVH<double, Dim, VectorType> vTree(v.begin(), v.end()); + + BallPointStuff<Dim> i1, i2; + + double m1 = (std::numeric_limits<double>::max)(), m2 = m1; + + for(int i = 0; i < (int)b.size(); ++i) + for(int j = 0; j < (int)v.size(); ++j) + m1 = (std::min)(m1, i1.minimumOnObjectObject(b[i], v[j])); + + m2 = BVMinimize(tree, vTree, i2); + + VERIFY_IS_APPROX(m1, m2); + } +}; + + +void test_BVH() +{ + for(int i = 0; i < g_repeat; i++) { +#ifdef EIGEN_TEST_PART_1 + TreeTest<2> test2; + CALL_SUBTEST(test2.testIntersect1()); + CALL_SUBTEST(test2.testMinimize1()); + CALL_SUBTEST(test2.testIntersect2()); + CALL_SUBTEST(test2.testMinimize2()); +#endif + +#ifdef EIGEN_TEST_PART_2 + TreeTest<3> test3; + CALL_SUBTEST(test3.testIntersect1()); + CALL_SUBTEST(test3.testMinimize1()); + CALL_SUBTEST(test3.testIntersect2()); + CALL_SUBTEST(test3.testMinimize2()); +#endif + +#ifdef EIGEN_TEST_PART_3 + TreeTest<4> test4; + CALL_SUBTEST(test4.testIntersect1()); + CALL_SUBTEST(test4.testMinimize1()); + CALL_SUBTEST(test4.testIntersect2()); + CALL_SUBTEST(test4.testMinimize2()); +#endif + } +} diff --git a/unsupported/test/CMakeLists.txt b/unsupported/test/CMakeLists.txt new file mode 100644 index 000000000..b34b151b1 --- /dev/null +++ b/unsupported/test/CMakeLists.txt @@ -0,0 +1,87 @@ + +include_directories(../../test ../../unsupported ../../Eigen + ${CMAKE_CURRENT_BINARY_DIR}/../../test) + +find_package(GoogleHash) +if(GOOGLEHASH_FOUND) + add_definitions("-DEIGEN_GOOGLEHASH_SUPPORT") + include_directories(${GOOGLEHASH_INCLUDES}) + ei_add_property(EIGEN_TESTED_BACKENDS "GoogleHash, ") +else(GOOGLEHASH_FOUND) + ei_add_property(EIGEN_MISSING_BACKENDS "GoogleHash, ") +endif(GOOGLEHASH_FOUND) + +find_package(Adolc) +if(ADOLC_FOUND) + include_directories(${ADOLC_INCLUDES}) + ei_add_property(EIGEN_TESTED_BACKENDS "Adolc, ") + ei_add_test(forward_adolc "" ${ADOLC_LIBRARIES}) +else(ADOLC_FOUND) + ei_add_property(EIGEN_MISSING_BACKENDS "Adolc, ") +endif(ADOLC_FOUND) + +# this test seems to never have been successful on x87, so is considered to contain a FP-related bug. +# see thread: "non-linear optimization test summary" +#ei_add_test(NonLinearOptimization) + +ei_add_test(NumericalDiff) +ei_add_test(autodiff) + +if (NOT CMAKE_CXX_COMPILER MATCHES "clang\\+\\+$") +ei_add_test(BVH) +endif() + +ei_add_test(matrix_exponential) +ei_add_test(matrix_function) +ei_add_test(matrix_square_root) +ei_add_test(alignedvector3) +ei_add_test(FFT) + +find_package(MPFR 2.3.0) +find_package(GMP) +if(MPFR_FOUND) + include_directories(${MPFR_INCLUDES} ./mpreal) + ei_add_property(EIGEN_TESTED_BACKENDS "MPFR C++, ") + set(EIGEN_MPFR_TEST_LIBRARIES ${MPFR_LIBRARIES} ${GMP_LIBRARIES}) + ei_add_test(mpreal_support "" "${EIGEN_MPFR_TEST_LIBRARIES}" ) +else() + ei_add_property(EIGEN_MISSING_BACKENDS "MPFR C++, ") +endif() + +ei_add_test(sparse_extra "" "") + +find_package(FFTW) +if(FFTW_FOUND) + ei_add_property(EIGEN_TESTED_BACKENDS "fftw, ") + include_directories( ${FFTW_INCLUDES} ) + if(FFTWL_LIB) + ei_add_test(FFTW "-DEIGEN_FFTW_DEFAULT -DEIGEN_HAS_FFTWL" "${FFTW_LIBRARIES}" ) + else() + ei_add_test(FFTW "-DEIGEN_FFTW_DEFAULT" "${FFTW_LIBRARIES}" ) + endif() +else() + ei_add_property(EIGEN_MISSING_BACKENDS "fftw, ") +endif() + +option(EIGEN_TEST_NO_OPENGL "Disable OpenGL support in unit tests" OFF) +if(NOT EIGEN_TEST_NO_OPENGL) + find_package(OpenGL) + find_package(GLUT) + find_package(GLEW) + if(OPENGL_FOUND AND GLUT_FOUND AND GLEW_FOUND) + ei_add_property(EIGEN_TESTED_BACKENDS "OpenGL, ") + set(EIGEN_GL_LIB ${GLUT_LIBRARIES} ${GLEW_LIBRARIES}) + ei_add_test(openglsupport "" "${EIGEN_GL_LIB}" ) + else() + ei_add_property(EIGEN_MISSING_BACKENDS "OpenGL, ") + endif() +else() + ei_add_property(EIGEN_MISSING_BACKENDS "OpenGL, ") +endif() + +ei_add_test(polynomialsolver) +ei_add_test(polynomialutils) +ei_add_test(kronecker_product) +ei_add_test(splines) +ei_add_test(gmres) + diff --git a/unsupported/test/FFT.cpp b/unsupported/test/FFT.cpp new file mode 100644 index 000000000..45c87f5a7 --- /dev/null +++ b/unsupported/test/FFT.cpp @@ -0,0 +1,2 @@ +#define test_FFTW test_FFT +#include "FFTW.cpp" diff --git a/unsupported/test/FFTW.cpp b/unsupported/test/FFTW.cpp new file mode 100644 index 000000000..a07bf274b --- /dev/null +++ b/unsupported/test/FFTW.cpp @@ -0,0 +1,265 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Mark Borgerding mark a borgerding net +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include <unsupported/Eigen/FFT> + +template <typename T> +std::complex<T> RandomCpx() { return std::complex<T>( (T)(rand()/(T)RAND_MAX - .5), (T)(rand()/(T)RAND_MAX - .5) ); } + +using namespace std; +using namespace Eigen; + +float norm(float x) {return x*x;} +double norm(double x) {return x*x;} +long double norm(long double x) {return x*x;} + +template < typename T> +complex<long double> promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); } + +complex<long double> promote(float x) { return complex<long double>( x); } +complex<long double> promote(double x) { return complex<long double>( x); } +complex<long double> promote(long double x) { return complex<long double>( x); } + + + template <typename VT1,typename VT2> + long double fft_rmse( const VT1 & fftbuf,const VT2 & timebuf) + { + long double totalpower=0; + long double difpower=0; + long double pi = acos((long double)-1 ); + for (size_t k0=0;k0<(size_t)fftbuf.size();++k0) { + complex<long double> acc = 0; + long double phinc = -2.*k0* pi / timebuf.size(); + for (size_t k1=0;k1<(size_t)timebuf.size();++k1) { + acc += promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) ); + } + totalpower += norm(acc); + complex<long double> x = promote(fftbuf[k0]); + complex<long double> dif = acc - x; + difpower += norm(dif); + //cerr << k0 << "\t" << acc << "\t" << x << "\t" << sqrt(norm(dif)) << endl; + } + cerr << "rmse:" << sqrt(difpower/totalpower) << endl; + return sqrt(difpower/totalpower); + } + + template <typename VT1,typename VT2> + long double dif_rmse( const VT1 buf1,const VT2 buf2) + { + long double totalpower=0; + long double difpower=0; + size_t n = (min)( buf1.size(),buf2.size() ); + for (size_t k=0;k<n;++k) { + totalpower += (norm( buf1[k] ) + norm(buf2[k]) )/2.; + difpower += norm(buf1[k] - buf2[k]); + } + return sqrt(difpower/totalpower); + } + +enum { StdVectorContainer, EigenVectorContainer }; + +template<int Container, typename Scalar> struct VectorType; + +template<typename Scalar> struct VectorType<StdVectorContainer,Scalar> +{ + typedef vector<Scalar> type; +}; + +template<typename Scalar> struct VectorType<EigenVectorContainer,Scalar> +{ + typedef Matrix<Scalar,Dynamic,1> type; +}; + +template <int Container, typename T> +void test_scalar_generic(int nfft) +{ + typedef typename FFT<T>::Complex Complex; + typedef typename FFT<T>::Scalar Scalar; + typedef typename VectorType<Container,Scalar>::type ScalarVector; + typedef typename VectorType<Container,Complex>::type ComplexVector; + + FFT<T> fft; + ScalarVector tbuf(nfft); + ComplexVector freqBuf; + for (int k=0;k<nfft;++k) + tbuf[k]= (T)( rand()/(double)RAND_MAX - .5); + + // make sure it DOESN'T give the right full spectrum answer + // if we've asked for half-spectrum + fft.SetFlag(fft.HalfSpectrum ); + fft.fwd( freqBuf,tbuf); + VERIFY((size_t)freqBuf.size() == (size_t)( (nfft>>1)+1) ); + VERIFY( fft_rmse(freqBuf,tbuf) < test_precision<T>() );// gross check + + fft.ClearFlag(fft.HalfSpectrum ); + fft.fwd( freqBuf,tbuf); + VERIFY( (size_t)freqBuf.size() == (size_t)nfft); + VERIFY( fft_rmse(freqBuf,tbuf) < test_precision<T>() );// gross check + + if (nfft&1) + return; // odd FFTs get the wrong size inverse FFT + + ScalarVector tbuf2; + fft.inv( tbuf2 , freqBuf); + VERIFY( dif_rmse(tbuf,tbuf2) < test_precision<T>() );// gross check + + + // verify that the Unscaled flag takes effect + ScalarVector tbuf3; + fft.SetFlag(fft.Unscaled); + + fft.inv( tbuf3 , freqBuf); + + for (int k=0;k<nfft;++k) + tbuf3[k] *= T(1./nfft); + + + //for (size_t i=0;i<(size_t) tbuf.size();++i) + // cout << "freqBuf=" << freqBuf[i] << " in2=" << tbuf3[i] << " - in=" << tbuf[i] << " => " << (tbuf3[i] - tbuf[i] ) << endl; + + VERIFY( dif_rmse(tbuf,tbuf3) < test_precision<T>() );// gross check + + // verify that ClearFlag works + fft.ClearFlag(fft.Unscaled); + fft.inv( tbuf2 , freqBuf); + VERIFY( dif_rmse(tbuf,tbuf2) < test_precision<T>() );// gross check +} + +template <typename T> +void test_scalar(int nfft) +{ + test_scalar_generic<StdVectorContainer,T>(nfft); + //test_scalar_generic<EigenVectorContainer,T>(nfft); +} + + +template <int Container, typename T> +void test_complex_generic(int nfft) +{ + typedef typename FFT<T>::Complex Complex; + typedef typename VectorType<Container,Complex>::type ComplexVector; + + FFT<T> fft; + + ComplexVector inbuf(nfft); + ComplexVector outbuf; + ComplexVector buf3; + for (int k=0;k<nfft;++k) + inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) ); + fft.fwd( outbuf , inbuf); + + VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check + fft.inv( buf3 , outbuf); + + VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check + + // verify that the Unscaled flag takes effect + ComplexVector buf4; + fft.SetFlag(fft.Unscaled); + fft.inv( buf4 , outbuf); + for (int k=0;k<nfft;++k) + buf4[k] *= T(1./nfft); + VERIFY( dif_rmse(inbuf,buf4) < test_precision<T>() );// gross check + + // verify that ClearFlag works + fft.ClearFlag(fft.Unscaled); + fft.inv( buf3 , outbuf); + VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check +} + +template <typename T> +void test_complex(int nfft) +{ + test_complex_generic<StdVectorContainer,T>(nfft); + test_complex_generic<EigenVectorContainer,T>(nfft); +} +/* +template <typename T,int nrows,int ncols> +void test_complex2d() +{ + typedef typename Eigen::FFT<T>::Complex Complex; + FFT<T> fft; + Eigen::Matrix<Complex,nrows,ncols> src,src2,dst,dst2; + + src = Eigen::Matrix<Complex,nrows,ncols>::Random(); + //src = Eigen::Matrix<Complex,nrows,ncols>::Identity(); + + for (int k=0;k<ncols;k++) { + Eigen::Matrix<Complex,nrows,1> tmpOut; + fft.fwd( tmpOut,src.col(k) ); + dst2.col(k) = tmpOut; + } + + for (int k=0;k<nrows;k++) { + Eigen::Matrix<Complex,1,ncols> tmpOut; + fft.fwd( tmpOut, dst2.row(k) ); + dst2.row(k) = tmpOut; + } + + fft.fwd2(dst.data(),src.data(),ncols,nrows); + fft.inv2(src2.data(),dst.data(),ncols,nrows); + VERIFY( (src-src2).norm() < test_precision<T>() ); + VERIFY( (dst-dst2).norm() < test_precision<T>() ); +} +*/ + + +void test_return_by_value(int len) +{ + VectorXf in; + VectorXf in1; + in.setRandom( len ); + VectorXcf out1,out2; + FFT<float> fft; + + fft.SetFlag(fft.HalfSpectrum ); + + fft.fwd(out1,in); + out2 = fft.fwd(in); + VERIFY( (out1-out2).norm() < test_precision<float>() ); + in1 = fft.inv(out1); + VERIFY( (in1-in).norm() < test_precision<float>() ); +} + +void test_FFTW() +{ + CALL_SUBTEST( test_return_by_value(32) ); + //CALL_SUBTEST( ( test_complex2d<float,4,8> () ) ); CALL_SUBTEST( ( test_complex2d<double,4,8> () ) ); + //CALL_SUBTEST( ( test_complex2d<long double,4,8> () ) ); + CALL_SUBTEST( test_complex<float>(32) ); CALL_SUBTEST( test_complex<double>(32) ); + CALL_SUBTEST( test_complex<float>(256) ); CALL_SUBTEST( test_complex<double>(256) ); + CALL_SUBTEST( test_complex<float>(3*8) ); CALL_SUBTEST( test_complex<double>(3*8) ); + CALL_SUBTEST( test_complex<float>(5*32) ); CALL_SUBTEST( test_complex<double>(5*32) ); + CALL_SUBTEST( test_complex<float>(2*3*4) ); CALL_SUBTEST( test_complex<double>(2*3*4) ); + CALL_SUBTEST( test_complex<float>(2*3*4*5) ); CALL_SUBTEST( test_complex<double>(2*3*4*5) ); + CALL_SUBTEST( test_complex<float>(2*3*4*5*7) ); CALL_SUBTEST( test_complex<double>(2*3*4*5*7) ); + + CALL_SUBTEST( test_scalar<float>(32) ); CALL_SUBTEST( test_scalar<double>(32) ); + CALL_SUBTEST( test_scalar<float>(45) ); CALL_SUBTEST( test_scalar<double>(45) ); + CALL_SUBTEST( test_scalar<float>(50) ); CALL_SUBTEST( test_scalar<double>(50) ); + CALL_SUBTEST( test_scalar<float>(256) ); CALL_SUBTEST( test_scalar<double>(256) ); + CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) ); CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) ); + + #ifdef EIGEN_HAS_FFTWL + CALL_SUBTEST( test_complex<long double>(32) ); + CALL_SUBTEST( test_complex<long double>(256) ); + CALL_SUBTEST( test_complex<long double>(3*8) ); + CALL_SUBTEST( test_complex<long double>(5*32) ); + CALL_SUBTEST( test_complex<long double>(2*3*4) ); + CALL_SUBTEST( test_complex<long double>(2*3*4*5) ); + CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) ); + + CALL_SUBTEST( test_scalar<long double>(32) ); + CALL_SUBTEST( test_scalar<long double>(45) ); + CALL_SUBTEST( test_scalar<long double>(50) ); + CALL_SUBTEST( test_scalar<long double>(256) ); + CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) ); + #endif +} diff --git a/unsupported/test/NonLinearOptimization.cpp b/unsupported/test/NonLinearOptimization.cpp new file mode 100644 index 000000000..81b066897 --- /dev/null +++ b/unsupported/test/NonLinearOptimization.cpp @@ -0,0 +1,1861 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org> + +#include <stdio.h> + +#include "main.h" +#include <unsupported/Eigen/NonLinearOptimization> + +// This disables some useless Warnings on MSVC. +// It is intended to be done for this test only. +#include <Eigen/src/Core/util/DisableStupidWarnings.h> + +int fcn_chkder(const VectorXd &x, VectorXd &fvec, MatrixXd &fjac, int iflag) +{ + /* subroutine fcn for chkder example. */ + + int i; + assert(15 == fvec.size()); + assert(3 == x.size()); + double tmp1, tmp2, tmp3, tmp4; + static const double y[15]={1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1, + 3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39}; + + + if (iflag == 0) + return 0; + + if (iflag != 2) + for (i=0; i<15; i++) { + tmp1 = i+1; + tmp2 = 16-i-1; + tmp3 = tmp1; + if (i >= 8) tmp3 = tmp2; + fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3)); + } + else { + for (i = 0; i < 15; i++) { + tmp1 = i+1; + tmp2 = 16-i-1; + + /* error introduced into next statement for illustration. */ + /* corrected statement should read tmp3 = tmp1 . */ + + tmp3 = tmp2; + if (i >= 8) tmp3 = tmp2; + tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4=tmp4*tmp4; + fjac(i,0) = -1.; + fjac(i,1) = tmp1*tmp2/tmp4; + fjac(i,2) = tmp1*tmp3/tmp4; + } + } + return 0; +} + + +void testChkder() +{ + const int m=15, n=3; + VectorXd x(n), fvec(m), xp, fvecp(m), err; + MatrixXd fjac(m,n); + VectorXi ipvt; + + /* the following values should be suitable for */ + /* checking the jacobian matrix. */ + x << 9.2e-1, 1.3e-1, 5.4e-1; + + internal::chkder(x, fvec, fjac, xp, fvecp, 1, err); + fcn_chkder(x, fvec, fjac, 1); + fcn_chkder(x, fvec, fjac, 2); + fcn_chkder(xp, fvecp, fjac, 1); + internal::chkder(x, fvec, fjac, xp, fvecp, 2, err); + + fvecp -= fvec; + + // check those + VectorXd fvec_ref(m), fvecp_ref(m), err_ref(m); + fvec_ref << + -1.181606, -1.429655, -1.606344, + -1.745269, -1.840654, -1.921586, + -1.984141, -2.022537, -2.468977, + -2.827562, -3.473582, -4.437612, + -6.047662, -9.267761, -18.91806; + fvecp_ref << + -7.724666e-09, -3.432406e-09, -2.034843e-10, + 2.313685e-09, 4.331078e-09, 5.984096e-09, + 7.363281e-09, 8.53147e-09, 1.488591e-08, + 2.33585e-08, 3.522012e-08, 5.301255e-08, + 8.26666e-08, 1.419747e-07, 3.19899e-07; + err_ref << + 0.1141397, 0.09943516, 0.09674474, + 0.09980447, 0.1073116, 0.1220445, + 0.1526814, 1, 1, + 1, 1, 1, + 1, 1, 1; + + VERIFY_IS_APPROX(fvec, fvec_ref); + VERIFY_IS_APPROX(fvecp, fvecp_ref); + VERIFY_IS_APPROX(err, err_ref); +} + +// Generic functor +template<typename _Scalar, int NX=Dynamic, int NY=Dynamic> +struct Functor +{ + typedef _Scalar Scalar; + enum { + InputsAtCompileTime = NX, + ValuesAtCompileTime = NY + }; + typedef Matrix<Scalar,InputsAtCompileTime,1> InputType; + typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType; + typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType; + + const int m_inputs, m_values; + + Functor() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {} + Functor(int inputs, int values) : m_inputs(inputs), m_values(values) {} + + int inputs() const { return m_inputs; } + int values() const { return m_values; } + + // you should define that in the subclass : +// void operator() (const InputType& x, ValueType* v, JacobianType* _j=0) const; +}; + +struct lmder_functor : Functor<double> +{ + lmder_functor(void): Functor<double>(3,15) {} + int operator()(const VectorXd &x, VectorXd &fvec) const + { + double tmp1, tmp2, tmp3; + static const double y[15] = {1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1, + 3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39}; + + for (int i = 0; i < values(); i++) + { + tmp1 = i+1; + tmp2 = 16 - i - 1; + tmp3 = (i>=8)? tmp2 : tmp1; + fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3)); + } + return 0; + } + + int df(const VectorXd &x, MatrixXd &fjac) const + { + double tmp1, tmp2, tmp3, tmp4; + for (int i = 0; i < values(); i++) + { + tmp1 = i+1; + tmp2 = 16 - i - 1; + tmp3 = (i>=8)? tmp2 : tmp1; + tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4; + fjac(i,0) = -1; + fjac(i,1) = tmp1*tmp2/tmp4; + fjac(i,2) = tmp1*tmp3/tmp4; + } + return 0; + } +}; + +void testLmder1() +{ + int n=3, info; + + VectorXd x; + + /* the following starting values provide a rough fit. */ + x.setConstant(n, 1.); + + // do the computation + lmder_functor functor; + LevenbergMarquardt<lmder_functor> lm(functor); + info = lm.lmder1(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 6); + VERIFY_IS_EQUAL(lm.njev, 5); + + // check norm + VERIFY_IS_APPROX(lm.fvec.blueNorm(), 0.09063596); + + // check x + VectorXd x_ref(n); + x_ref << 0.08241058, 1.133037, 2.343695; + VERIFY_IS_APPROX(x, x_ref); +} + +void testLmder() +{ + const int m=15, n=3; + int info; + double fnorm, covfac; + VectorXd x; + + /* the following starting values provide a rough fit. */ + x.setConstant(n, 1.); + + // do the computation + lmder_functor functor; + LevenbergMarquardt<lmder_functor> lm(functor); + info = lm.minimize(x); + + // check return values + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 6); + VERIFY_IS_EQUAL(lm.njev, 5); + + // check norm + fnorm = lm.fvec.blueNorm(); + VERIFY_IS_APPROX(fnorm, 0.09063596); + + // check x + VectorXd x_ref(n); + x_ref << 0.08241058, 1.133037, 2.343695; + VERIFY_IS_APPROX(x, x_ref); + + // check covariance + covfac = fnorm*fnorm/(m-n); + internal::covar(lm.fjac, lm.permutation.indices()); // TODO : move this as a function of lm + + MatrixXd cov_ref(n,n); + cov_ref << + 0.0001531202, 0.002869941, -0.002656662, + 0.002869941, 0.09480935, -0.09098995, + -0.002656662, -0.09098995, 0.08778727; + +// std::cout << fjac*covfac << std::endl; + + MatrixXd cov; + cov = covfac*lm.fjac.topLeftCorner<n,n>(); + VERIFY_IS_APPROX( cov, cov_ref); + // TODO: why isn't this allowed ? : + // VERIFY_IS_APPROX( covfac*fjac.topLeftCorner<n,n>() , cov_ref); +} + +struct hybrj_functor : Functor<double> +{ + hybrj_functor(void) : Functor<double>(9,9) {} + + int operator()(const VectorXd &x, VectorXd &fvec) + { + double temp, temp1, temp2; + const int n = x.size(); + assert(fvec.size()==n); + for (int k = 0; k < n; k++) + { + temp = (3. - 2.*x[k])*x[k]; + temp1 = 0.; + if (k) temp1 = x[k-1]; + temp2 = 0.; + if (k != n-1) temp2 = x[k+1]; + fvec[k] = temp - temp1 - 2.*temp2 + 1.; + } + return 0; + } + int df(const VectorXd &x, MatrixXd &fjac) + { + const int n = x.size(); + assert(fjac.rows()==n); + assert(fjac.cols()==n); + for (int k = 0; k < n; k++) + { + for (int j = 0; j < n; j++) + fjac(k,j) = 0.; + fjac(k,k) = 3.- 4.*x[k]; + if (k) fjac(k,k-1) = -1.; + if (k != n-1) fjac(k,k+1) = -2.; + } + return 0; + } +}; + + +void testHybrj1() +{ + const int n=9; + int info; + VectorXd x(n); + + /* the following starting values provide a rough fit. */ + x.setConstant(n, -1.); + + // do the computation + hybrj_functor functor; + HybridNonLinearSolver<hybrj_functor> solver(functor); + info = solver.hybrj1(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(solver.nfev, 11); + VERIFY_IS_EQUAL(solver.njev, 1); + + // check norm + VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08); + + +// check x + VectorXd x_ref(n); + x_ref << + -0.5706545, -0.6816283, -0.7017325, + -0.7042129, -0.701369, -0.6918656, + -0.665792, -0.5960342, -0.4164121; + VERIFY_IS_APPROX(x, x_ref); +} + +void testHybrj() +{ + const int n=9; + int info; + VectorXd x(n); + + /* the following starting values provide a rough fit. */ + x.setConstant(n, -1.); + + + // do the computation + hybrj_functor functor; + HybridNonLinearSolver<hybrj_functor> solver(functor); + solver.diag.setConstant(n, 1.); + solver.useExternalScaling = true; + info = solver.solve(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(solver.nfev, 11); + VERIFY_IS_EQUAL(solver.njev, 1); + + // check norm + VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08); + + +// check x + VectorXd x_ref(n); + x_ref << + -0.5706545, -0.6816283, -0.7017325, + -0.7042129, -0.701369, -0.6918656, + -0.665792, -0.5960342, -0.4164121; + VERIFY_IS_APPROX(x, x_ref); + +} + +struct hybrd_functor : Functor<double> +{ + hybrd_functor(void) : Functor<double>(9,9) {} + int operator()(const VectorXd &x, VectorXd &fvec) const + { + double temp, temp1, temp2; + const int n = x.size(); + + assert(fvec.size()==n); + for (int k=0; k < n; k++) + { + temp = (3. - 2.*x[k])*x[k]; + temp1 = 0.; + if (k) temp1 = x[k-1]; + temp2 = 0.; + if (k != n-1) temp2 = x[k+1]; + fvec[k] = temp - temp1 - 2.*temp2 + 1.; + } + return 0; + } +}; + +void testHybrd1() +{ + int n=9, info; + VectorXd x(n); + + /* the following starting values provide a rough solution. */ + x.setConstant(n, -1.); + + // do the computation + hybrd_functor functor; + HybridNonLinearSolver<hybrd_functor> solver(functor); + info = solver.hybrd1(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(solver.nfev, 20); + + // check norm + VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08); + + // check x + VectorXd x_ref(n); + x_ref << -0.5706545, -0.6816283, -0.7017325, -0.7042129, -0.701369, -0.6918656, -0.665792, -0.5960342, -0.4164121; + VERIFY_IS_APPROX(x, x_ref); +} + +void testHybrd() +{ + const int n=9; + int info; + VectorXd x; + + /* the following starting values provide a rough fit. */ + x.setConstant(n, -1.); + + // do the computation + hybrd_functor functor; + HybridNonLinearSolver<hybrd_functor> solver(functor); + solver.parameters.nb_of_subdiagonals = 1; + solver.parameters.nb_of_superdiagonals = 1; + solver.diag.setConstant(n, 1.); + solver.useExternalScaling = true; + info = solver.solveNumericalDiff(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(solver.nfev, 14); + + // check norm + VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08); + + // check x + VectorXd x_ref(n); + x_ref << + -0.5706545, -0.6816283, -0.7017325, + -0.7042129, -0.701369, -0.6918656, + -0.665792, -0.5960342, -0.4164121; + VERIFY_IS_APPROX(x, x_ref); +} + +struct lmstr_functor : Functor<double> +{ + lmstr_functor(void) : Functor<double>(3,15) {} + int operator()(const VectorXd &x, VectorXd &fvec) + { + /* subroutine fcn for lmstr1 example. */ + double tmp1, tmp2, tmp3; + static const double y[15]={1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1, + 3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39}; + + assert(15==fvec.size()); + assert(3==x.size()); + + for (int i=0; i<15; i++) + { + tmp1 = i+1; + tmp2 = 16 - i - 1; + tmp3 = (i>=8)? tmp2 : tmp1; + fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3)); + } + return 0; + } + int df(const VectorXd &x, VectorXd &jac_row, VectorXd::Index rownb) + { + assert(x.size()==3); + assert(jac_row.size()==x.size()); + double tmp1, tmp2, tmp3, tmp4; + + int i = rownb-2; + tmp1 = i+1; + tmp2 = 16 - i - 1; + tmp3 = (i>=8)? tmp2 : tmp1; + tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4; + jac_row[0] = -1; + jac_row[1] = tmp1*tmp2/tmp4; + jac_row[2] = tmp1*tmp3/tmp4; + return 0; + } +}; + +void testLmstr1() +{ + const int n=3; + int info; + + VectorXd x(n); + + /* the following starting values provide a rough fit. */ + x.setConstant(n, 1.); + + // do the computation + lmstr_functor functor; + LevenbergMarquardt<lmstr_functor> lm(functor); + info = lm.lmstr1(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 6); + VERIFY_IS_EQUAL(lm.njev, 5); + + // check norm + VERIFY_IS_APPROX(lm.fvec.blueNorm(), 0.09063596); + + // check x + VectorXd x_ref(n); + x_ref << 0.08241058, 1.133037, 2.343695 ; + VERIFY_IS_APPROX(x, x_ref); +} + +void testLmstr() +{ + const int n=3; + int info; + double fnorm; + VectorXd x(n); + + /* the following starting values provide a rough fit. */ + x.setConstant(n, 1.); + + // do the computation + lmstr_functor functor; + LevenbergMarquardt<lmstr_functor> lm(functor); + info = lm.minimizeOptimumStorage(x); + + // check return values + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 6); + VERIFY_IS_EQUAL(lm.njev, 5); + + // check norm + fnorm = lm.fvec.blueNorm(); + VERIFY_IS_APPROX(fnorm, 0.09063596); + + // check x + VectorXd x_ref(n); + x_ref << 0.08241058, 1.133037, 2.343695; + VERIFY_IS_APPROX(x, x_ref); + +} + +struct lmdif_functor : Functor<double> +{ + lmdif_functor(void) : Functor<double>(3,15) {} + int operator()(const VectorXd &x, VectorXd &fvec) const + { + int i; + double tmp1,tmp2,tmp3; + static const double y[15]={1.4e-1,1.8e-1,2.2e-1,2.5e-1,2.9e-1,3.2e-1,3.5e-1,3.9e-1, + 3.7e-1,5.8e-1,7.3e-1,9.6e-1,1.34e0,2.1e0,4.39e0}; + + assert(x.size()==3); + assert(fvec.size()==15); + for (i=0; i<15; i++) + { + tmp1 = i+1; + tmp2 = 15 - i; + tmp3 = tmp1; + + if (i >= 8) tmp3 = tmp2; + fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3)); + } + return 0; + } +}; + +void testLmdif1() +{ + const int n=3; + int info; + + VectorXd x(n), fvec(15); + + /* the following starting values provide a rough fit. */ + x.setConstant(n, 1.); + + // do the computation + lmdif_functor functor; + DenseIndex nfev; + info = LevenbergMarquardt<lmdif_functor>::lmdif1(functor, x, &nfev); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(nfev, 26); + + // check norm + functor(x, fvec); + VERIFY_IS_APPROX(fvec.blueNorm(), 0.09063596); + + // check x + VectorXd x_ref(n); + x_ref << 0.0824106, 1.1330366, 2.3436947; + VERIFY_IS_APPROX(x, x_ref); + +} + +void testLmdif() +{ + const int m=15, n=3; + int info; + double fnorm, covfac; + VectorXd x(n); + + /* the following starting values provide a rough fit. */ + x.setConstant(n, 1.); + + // do the computation + lmdif_functor functor; + NumericalDiff<lmdif_functor> numDiff(functor); + LevenbergMarquardt<NumericalDiff<lmdif_functor> > lm(numDiff); + info = lm.minimize(x); + + // check return values + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 26); + + // check norm + fnorm = lm.fvec.blueNorm(); + VERIFY_IS_APPROX(fnorm, 0.09063596); + + // check x + VectorXd x_ref(n); + x_ref << 0.08241058, 1.133037, 2.343695; + VERIFY_IS_APPROX(x, x_ref); + + // check covariance + covfac = fnorm*fnorm/(m-n); + internal::covar(lm.fjac, lm.permutation.indices()); // TODO : move this as a function of lm + + MatrixXd cov_ref(n,n); + cov_ref << + 0.0001531202, 0.002869942, -0.002656662, + 0.002869942, 0.09480937, -0.09098997, + -0.002656662, -0.09098997, 0.08778729; + +// std::cout << fjac*covfac << std::endl; + + MatrixXd cov; + cov = covfac*lm.fjac.topLeftCorner<n,n>(); + VERIFY_IS_APPROX( cov, cov_ref); + // TODO: why isn't this allowed ? : + // VERIFY_IS_APPROX( covfac*fjac.topLeftCorner<n,n>() , cov_ref); +} + +struct chwirut2_functor : Functor<double> +{ + chwirut2_functor(void) : Functor<double>(3,54) {} + static const double m_x[54]; + static const double m_y[54]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + int i; + + assert(b.size()==3); + assert(fvec.size()==54); + for(i=0; i<54; i++) { + double x = m_x[i]; + fvec[i] = exp(-b[0]*x)/(b[1]+b[2]*x) - m_y[i]; + } + return 0; + } + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==3); + assert(fjac.rows()==54); + assert(fjac.cols()==3); + for(int i=0; i<54; i++) { + double x = m_x[i]; + double factor = 1./(b[1]+b[2]*x); + double e = exp(-b[0]*x); + fjac(i,0) = -x*e*factor; + fjac(i,1) = -e*factor*factor; + fjac(i,2) = -x*e*factor*factor; + } + return 0; + } +}; +const double chwirut2_functor::m_x[54] = { 0.500E0, 1.000E0, 1.750E0, 3.750E0, 5.750E0, 0.875E0, 2.250E0, 3.250E0, 5.250E0, 0.750E0, 1.750E0, 2.750E0, 4.750E0, 0.625E0, 1.250E0, 2.250E0, 4.250E0, .500E0, 3.000E0, .750E0, 3.000E0, 1.500E0, 6.000E0, 3.000E0, 6.000E0, 1.500E0, 3.000E0, .500E0, 2.000E0, 4.000E0, .750E0, 2.000E0, 5.000E0, .750E0, 2.250E0, 3.750E0, 5.750E0, 3.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .500E0, 6.000E0, 3.000E0, .500E0, 2.750E0, .500E0, 1.750E0}; +const double chwirut2_functor::m_y[54] = { 92.9000E0 ,57.1000E0 ,31.0500E0 ,11.5875E0 ,8.0250E0 ,63.6000E0 ,21.4000E0 ,14.2500E0 ,8.4750E0 ,63.8000E0 ,26.8000E0 ,16.4625E0 ,7.1250E0 ,67.3000E0 ,41.0000E0 ,21.1500E0 ,8.1750E0 ,81.5000E0 ,13.1200E0 ,59.9000E0 ,14.6200E0 ,32.9000E0 ,5.4400E0 ,12.5600E0 ,5.4400E0 ,32.0000E0 ,13.9500E0 ,75.8000E0 ,20.0000E0 ,10.4200E0 ,59.5000E0 ,21.6700E0 ,8.5500E0 ,62.0000E0 ,20.2000E0 ,7.7600E0 ,3.7500E0 ,11.8100E0 ,54.7000E0 ,23.7000E0 ,11.5500E0 ,61.3000E0 ,17.7000E0 ,8.7400E0 ,59.2000E0 ,16.3000E0 ,8.6200E0 ,81.0000E0 ,4.8700E0 ,14.6200E0 ,81.7000E0 ,17.1700E0 ,81.3000E0 ,28.9000E0 }; + +// http://www.itl.nist.gov/div898/strd/nls/data/chwirut2.shtml +void testNistChwirut2(void) +{ + const int n=3; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< 0.1, 0.01, 0.02; + // do the computation + chwirut2_functor functor; + LevenbergMarquardt<chwirut2_functor> lm(functor); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 10); + VERIFY_IS_EQUAL(lm.njev, 8); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.1304802941E+02); + // check x + VERIFY_IS_APPROX(x[0], 1.6657666537E-01); + VERIFY_IS_APPROX(x[1], 5.1653291286E-03); + VERIFY_IS_APPROX(x[2], 1.2150007096E-02); + + /* + * Second try + */ + x<< 0.15, 0.008, 0.010; + // do the computation + lm.resetParameters(); + lm.parameters.ftol = 1.E6*NumTraits<double>::epsilon(); + lm.parameters.xtol = 1.E6*NumTraits<double>::epsilon(); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 7); + VERIFY_IS_EQUAL(lm.njev, 6); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.1304802941E+02); + // check x + VERIFY_IS_APPROX(x[0], 1.6657666537E-01); + VERIFY_IS_APPROX(x[1], 5.1653291286E-03); + VERIFY_IS_APPROX(x[2], 1.2150007096E-02); +} + + +struct misra1a_functor : Functor<double> +{ + misra1a_functor(void) : Functor<double>(2,14) {} + static const double m_x[14]; + static const double m_y[14]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + assert(b.size()==2); + assert(fvec.size()==14); + for(int i=0; i<14; i++) { + fvec[i] = b[0]*(1.-exp(-b[1]*m_x[i])) - m_y[i] ; + } + return 0; + } + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==2); + assert(fjac.rows()==14); + assert(fjac.cols()==2); + for(int i=0; i<14; i++) { + fjac(i,0) = (1.-exp(-b[1]*m_x[i])); + fjac(i,1) = (b[0]*m_x[i]*exp(-b[1]*m_x[i])); + } + return 0; + } +}; +const double misra1a_functor::m_x[14] = { 77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0}; +const double misra1a_functor::m_y[14] = { 10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0}; + +// http://www.itl.nist.gov/div898/strd/nls/data/misra1a.shtml +void testNistMisra1a(void) +{ + const int n=2; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< 500., 0.0001; + // do the computation + misra1a_functor functor; + LevenbergMarquardt<misra1a_functor> lm(functor); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 19); + VERIFY_IS_EQUAL(lm.njev, 15); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.2455138894E-01); + // check x + VERIFY_IS_APPROX(x[0], 2.3894212918E+02); + VERIFY_IS_APPROX(x[1], 5.5015643181E-04); + + /* + * Second try + */ + x<< 250., 0.0005; + // do the computation + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 5); + VERIFY_IS_EQUAL(lm.njev, 4); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.2455138894E-01); + // check x + VERIFY_IS_APPROX(x[0], 2.3894212918E+02); + VERIFY_IS_APPROX(x[1], 5.5015643181E-04); +} + +struct hahn1_functor : Functor<double> +{ + hahn1_functor(void) : Functor<double>(7,236) {} + static const double m_x[236]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + static const double m_y[236] = { .591E0 , 1.547E0 , 2.902E0 , 2.894E0 , 4.703E0 , 6.307E0 , 7.03E0 , 7.898E0 , 9.470E0 , 9.484E0 , 10.072E0 , 10.163E0 , 11.615E0 , 12.005E0 , 12.478E0 , 12.982E0 , 12.970E0 , 13.926E0 , 14.452E0 , 14.404E0 , 15.190E0 , 15.550E0 , 15.528E0 , 15.499E0 , 16.131E0 , 16.438E0 , 16.387E0 , 16.549E0 , 16.872E0 , 16.830E0 , 16.926E0 , 16.907E0 , 16.966E0 , 17.060E0 , 17.122E0 , 17.311E0 , 17.355E0 , 17.668E0 , 17.767E0 , 17.803E0 , 17.765E0 , 17.768E0 , 17.736E0 , 17.858E0 , 17.877E0 , 17.912E0 , 18.046E0 , 18.085E0 , 18.291E0 , 18.357E0 , 18.426E0 , 18.584E0 , 18.610E0 , 18.870E0 , 18.795E0 , 19.111E0 , .367E0 , .796E0 , 0.892E0 , 1.903E0 , 2.150E0 , 3.697E0 , 5.870E0 , 6.421E0 , 7.422E0 , 9.944E0 , 11.023E0 , 11.87E0 , 12.786E0 , 14.067E0 , 13.974E0 , 14.462E0 , 14.464E0 , 15.381E0 , 15.483E0 , 15.59E0 , 16.075E0 , 16.347E0 , 16.181E0 , 16.915E0 , 17.003E0 , 16.978E0 , 17.756E0 , 17.808E0 , 17.868E0 , 18.481E0 , 18.486E0 , 19.090E0 , 16.062E0 , 16.337E0 , 16.345E0 , 16.388E0 , 17.159E0 , 17.116E0 , 17.164E0 , 17.123E0 , 17.979E0 , 17.974E0 , 18.007E0 , 17.993E0 , 18.523E0 , 18.669E0 , 18.617E0 , 19.371E0 , 19.330E0 , 0.080E0 , 0.248E0 , 1.089E0 , 1.418E0 , 2.278E0 , 3.624E0 , 4.574E0 , 5.556E0 , 7.267E0 , 7.695E0 , 9.136E0 , 9.959E0 , 9.957E0 , 11.600E0 , 13.138E0 , 13.564E0 , 13.871E0 , 13.994E0 , 14.947E0 , 15.473E0 , 15.379E0 , 15.455E0 , 15.908E0 , 16.114E0 , 17.071E0 , 17.135E0 , 17.282E0 , 17.368E0 , 17.483E0 , 17.764E0 , 18.185E0 , 18.271E0 , 18.236E0 , 18.237E0 , 18.523E0 , 18.627E0 , 18.665E0 , 19.086E0 , 0.214E0 , 0.943E0 , 1.429E0 , 2.241E0 , 2.951E0 , 3.782E0 , 4.757E0 , 5.602E0 , 7.169E0 , 8.920E0 , 10.055E0 , 12.035E0 , 12.861E0 , 13.436E0 , 14.167E0 , 14.755E0 , 15.168E0 , 15.651E0 , 15.746E0 , 16.216E0 , 16.445E0 , 16.965E0 , 17.121E0 , 17.206E0 , 17.250E0 , 17.339E0 , 17.793E0 , 18.123E0 , 18.49E0 , 18.566E0 , 18.645E0 , 18.706E0 , 18.924E0 , 19.1E0 , 0.375E0 , 0.471E0 , 1.504E0 , 2.204E0 , 2.813E0 , 4.765E0 , 9.835E0 , 10.040E0 , 11.946E0 , 12.596E0 , 13.303E0 , 13.922E0 , 14.440E0 , 14.951E0 , 15.627E0 , 15.639E0 , 15.814E0 , 16.315E0 , 16.334E0 , 16.430E0 , 16.423E0 , 17.024E0 , 17.009E0 , 17.165E0 , 17.134E0 , 17.349E0 , 17.576E0 , 17.848E0 , 18.090E0 , 18.276E0 , 18.404E0 , 18.519E0 , 19.133E0 , 19.074E0 , 19.239E0 , 19.280E0 , 19.101E0 , 19.398E0 , 19.252E0 , 19.89E0 , 20.007E0 , 19.929E0 , 19.268E0 , 19.324E0 , 20.049E0 , 20.107E0 , 20.062E0 , 20.065E0 , 19.286E0 , 19.972E0 , 20.088E0 , 20.743E0 , 20.83E0 , 20.935E0 , 21.035E0 , 20.93E0 , 21.074E0 , 21.085E0 , 20.935E0 }; + + // int called=0; printf("call hahn1_functor with iflag=%d, called=%d\n", iflag, called); if (iflag==1) called++; + + assert(b.size()==7); + assert(fvec.size()==236); + for(int i=0; i<236; i++) { + double x=m_x[i], xx=x*x, xxx=xx*x; + fvec[i] = (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) / (1.+b[4]*x+b[5]*xx+b[6]*xxx) - m_y[i]; + } + return 0; + } + + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==7); + assert(fjac.rows()==236); + assert(fjac.cols()==7); + for(int i=0; i<236; i++) { + double x=m_x[i], xx=x*x, xxx=xx*x; + double fact = 1./(1.+b[4]*x+b[5]*xx+b[6]*xxx); + fjac(i,0) = 1.*fact; + fjac(i,1) = x*fact; + fjac(i,2) = xx*fact; + fjac(i,3) = xxx*fact; + fact = - (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) * fact * fact; + fjac(i,4) = x*fact; + fjac(i,5) = xx*fact; + fjac(i,6) = xxx*fact; + } + return 0; + } +}; +const double hahn1_functor::m_x[236] = { 24.41E0 , 34.82E0 , 44.09E0 , 45.07E0 , 54.98E0 , 65.51E0 , 70.53E0 , 75.70E0 , 89.57E0 , 91.14E0 , 96.40E0 , 97.19E0 , 114.26E0 , 120.25E0 , 127.08E0 , 133.55E0 , 133.61E0 , 158.67E0 , 172.74E0 , 171.31E0 , 202.14E0 , 220.55E0 , 221.05E0 , 221.39E0 , 250.99E0 , 268.99E0 , 271.80E0 , 271.97E0 , 321.31E0 , 321.69E0 , 330.14E0 , 333.03E0 , 333.47E0 , 340.77E0 , 345.65E0 , 373.11E0 , 373.79E0 , 411.82E0 , 419.51E0 , 421.59E0 , 422.02E0 , 422.47E0 , 422.61E0 , 441.75E0 , 447.41E0 , 448.7E0 , 472.89E0 , 476.69E0 , 522.47E0 , 522.62E0 , 524.43E0 , 546.75E0 , 549.53E0 , 575.29E0 , 576.00E0 , 625.55E0 , 20.15E0 , 28.78E0 , 29.57E0 , 37.41E0 , 39.12E0 , 50.24E0 , 61.38E0 , 66.25E0 , 73.42E0 , 95.52E0 , 107.32E0 , 122.04E0 , 134.03E0 , 163.19E0 , 163.48E0 , 175.70E0 , 179.86E0 , 211.27E0 , 217.78E0 , 219.14E0 , 262.52E0 , 268.01E0 , 268.62E0 , 336.25E0 , 337.23E0 , 339.33E0 , 427.38E0 , 428.58E0 , 432.68E0 , 528.99E0 , 531.08E0 , 628.34E0 , 253.24E0 , 273.13E0 , 273.66E0 , 282.10E0 , 346.62E0 , 347.19E0 , 348.78E0 , 351.18E0 , 450.10E0 , 450.35E0 , 451.92E0 , 455.56E0 , 552.22E0 , 553.56E0 , 555.74E0 , 652.59E0 , 656.20E0 , 14.13E0 , 20.41E0 , 31.30E0 , 33.84E0 , 39.70E0 , 48.83E0 , 54.50E0 , 60.41E0 , 72.77E0 , 75.25E0 , 86.84E0 , 94.88E0 , 96.40E0 , 117.37E0 , 139.08E0 , 147.73E0 , 158.63E0 , 161.84E0 , 192.11E0 , 206.76E0 , 209.07E0 , 213.32E0 , 226.44E0 , 237.12E0 , 330.90E0 , 358.72E0 , 370.77E0 , 372.72E0 , 396.24E0 , 416.59E0 , 484.02E0 , 495.47E0 , 514.78E0 , 515.65E0 , 519.47E0 , 544.47E0 , 560.11E0 , 620.77E0 , 18.97E0 , 28.93E0 , 33.91E0 , 40.03E0 , 44.66E0 , 49.87E0 , 55.16E0 , 60.90E0 , 72.08E0 , 85.15E0 , 97.06E0 , 119.63E0 , 133.27E0 , 143.84E0 , 161.91E0 , 180.67E0 , 198.44E0 , 226.86E0 , 229.65E0 , 258.27E0 , 273.77E0 , 339.15E0 , 350.13E0 , 362.75E0 , 371.03E0 , 393.32E0 , 448.53E0 , 473.78E0 , 511.12E0 , 524.70E0 , 548.75E0 , 551.64E0 , 574.02E0 , 623.86E0 , 21.46E0 , 24.33E0 , 33.43E0 , 39.22E0 , 44.18E0 , 55.02E0 , 94.33E0 , 96.44E0 , 118.82E0 , 128.48E0 , 141.94E0 , 156.92E0 , 171.65E0 , 190.00E0 , 223.26E0 , 223.88E0 , 231.50E0 , 265.05E0 , 269.44E0 , 271.78E0 , 273.46E0 , 334.61E0 , 339.79E0 , 349.52E0 , 358.18E0 , 377.98E0 , 394.77E0 , 429.66E0 , 468.22E0 , 487.27E0 , 519.54E0 , 523.03E0 , 612.99E0 , 638.59E0 , 641.36E0 , 622.05E0 , 631.50E0 , 663.97E0 , 646.9E0 , 748.29E0 , 749.21E0 , 750.14E0 , 647.04E0 , 646.89E0 , 746.9E0 , 748.43E0 , 747.35E0 , 749.27E0 , 647.61E0 , 747.78E0 , 750.51E0 , 851.37E0 , 845.97E0 , 847.54E0 , 849.93E0 , 851.61E0 , 849.75E0 , 850.98E0 , 848.23E0}; + +// http://www.itl.nist.gov/div898/strd/nls/data/hahn1.shtml +void testNistHahn1(void) +{ + const int n=7; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< 10., -1., .05, -.00001, -.05, .001, -.000001; + // do the computation + hahn1_functor functor; + LevenbergMarquardt<hahn1_functor> lm(functor); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 11); + VERIFY_IS_EQUAL(lm.njev, 10); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.5324382854E+00); + // check x + VERIFY_IS_APPROX(x[0], 1.0776351733E+00); + VERIFY_IS_APPROX(x[1],-1.2269296921E-01); + VERIFY_IS_APPROX(x[2], 4.0863750610E-03); + VERIFY_IS_APPROX(x[3],-1.426264e-06); // shoulde be : -1.4262662514E-06 + VERIFY_IS_APPROX(x[4],-5.7609940901E-03); + VERIFY_IS_APPROX(x[5], 2.4053735503E-04); + VERIFY_IS_APPROX(x[6],-1.2314450199E-07); + + /* + * Second try + */ + x<< .1, -.1, .005, -.000001, -.005, .0001, -.0000001; + // do the computation + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 11); + VERIFY_IS_EQUAL(lm.njev, 10); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.5324382854E+00); + // check x + VERIFY_IS_APPROX(x[0], 1.077640); // should be : 1.0776351733E+00 + VERIFY_IS_APPROX(x[1], -0.1226933); // should be : -1.2269296921E-01 + VERIFY_IS_APPROX(x[2], 0.004086383); // should be : 4.0863750610E-03 + VERIFY_IS_APPROX(x[3], -1.426277e-06); // shoulde be : -1.4262662514E-06 + VERIFY_IS_APPROX(x[4],-5.7609940901E-03); + VERIFY_IS_APPROX(x[5], 0.00024053772); // should be : 2.4053735503E-04 + VERIFY_IS_APPROX(x[6], -1.231450e-07); // should be : -1.2314450199E-07 + +} + +struct misra1d_functor : Functor<double> +{ + misra1d_functor(void) : Functor<double>(2,14) {} + static const double x[14]; + static const double y[14]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + assert(b.size()==2); + assert(fvec.size()==14); + for(int i=0; i<14; i++) { + fvec[i] = b[0]*b[1]*x[i]/(1.+b[1]*x[i]) - y[i]; + } + return 0; + } + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==2); + assert(fjac.rows()==14); + assert(fjac.cols()==2); + for(int i=0; i<14; i++) { + double den = 1.+b[1]*x[i]; + fjac(i,0) = b[1]*x[i] / den; + fjac(i,1) = b[0]*x[i]*(den-b[1]*x[i])/den/den; + } + return 0; + } +}; +const double misra1d_functor::x[14] = { 77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0}; +const double misra1d_functor::y[14] = { 10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0}; + +// http://www.itl.nist.gov/div898/strd/nls/data/misra1d.shtml +void testNistMisra1d(void) +{ + const int n=2; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< 500., 0.0001; + // do the computation + misra1d_functor functor; + LevenbergMarquardt<misra1d_functor> lm(functor); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 3); + VERIFY_IS_EQUAL(lm.nfev, 9); + VERIFY_IS_EQUAL(lm.njev, 7); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6419295283E-02); + // check x + VERIFY_IS_APPROX(x[0], 4.3736970754E+02); + VERIFY_IS_APPROX(x[1], 3.0227324449E-04); + + /* + * Second try + */ + x<< 450., 0.0003; + // do the computation + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 4); + VERIFY_IS_EQUAL(lm.njev, 3); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6419295283E-02); + // check x + VERIFY_IS_APPROX(x[0], 4.3736970754E+02); + VERIFY_IS_APPROX(x[1], 3.0227324449E-04); +} + + +struct lanczos1_functor : Functor<double> +{ + lanczos1_functor(void) : Functor<double>(6,24) {} + static const double x[24]; + static const double y[24]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + assert(b.size()==6); + assert(fvec.size()==24); + for(int i=0; i<24; i++) + fvec[i] = b[0]*exp(-b[1]*x[i]) + b[2]*exp(-b[3]*x[i]) + b[4]*exp(-b[5]*x[i]) - y[i]; + return 0; + } + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==6); + assert(fjac.rows()==24); + assert(fjac.cols()==6); + for(int i=0; i<24; i++) { + fjac(i,0) = exp(-b[1]*x[i]); + fjac(i,1) = -b[0]*x[i]*exp(-b[1]*x[i]); + fjac(i,2) = exp(-b[3]*x[i]); + fjac(i,3) = -b[2]*x[i]*exp(-b[3]*x[i]); + fjac(i,4) = exp(-b[5]*x[i]); + fjac(i,5) = -b[4]*x[i]*exp(-b[5]*x[i]); + } + return 0; + } +}; +const double lanczos1_functor::x[24] = { 0.000000000000E+00, 5.000000000000E-02, 1.000000000000E-01, 1.500000000000E-01, 2.000000000000E-01, 2.500000000000E-01, 3.000000000000E-01, 3.500000000000E-01, 4.000000000000E-01, 4.500000000000E-01, 5.000000000000E-01, 5.500000000000E-01, 6.000000000000E-01, 6.500000000000E-01, 7.000000000000E-01, 7.500000000000E-01, 8.000000000000E-01, 8.500000000000E-01, 9.000000000000E-01, 9.500000000000E-01, 1.000000000000E+00, 1.050000000000E+00, 1.100000000000E+00, 1.150000000000E+00 }; +const double lanczos1_functor::y[24] = { 2.513400000000E+00 ,2.044333373291E+00 ,1.668404436564E+00 ,1.366418021208E+00 ,1.123232487372E+00 ,9.268897180037E-01 ,7.679338563728E-01 ,6.388775523106E-01 ,5.337835317402E-01 ,4.479363617347E-01 ,3.775847884350E-01 ,3.197393199326E-01 ,2.720130773746E-01 ,2.324965529032E-01 ,1.996589546065E-01 ,1.722704126914E-01 ,1.493405660168E-01 ,1.300700206922E-01 ,1.138119324644E-01 ,1.000415587559E-01 ,8.833209084540E-02 ,7.833544019350E-02 ,6.976693743449E-02 ,6.239312536719E-02 }; + +// http://www.itl.nist.gov/div898/strd/nls/data/lanczos1.shtml +void testNistLanczos1(void) +{ + const int n=6; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< 1.2, 0.3, 5.6, 5.5, 6.5, 7.6; + // do the computation + lanczos1_functor functor; + LevenbergMarquardt<lanczos1_functor> lm(functor); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 2); + VERIFY_IS_EQUAL(lm.nfev, 79); + VERIFY_IS_EQUAL(lm.njev, 72); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.430899764097e-25); // should be 1.4307867721E-25, but nist results are on 128-bit floats + // check x + VERIFY_IS_APPROX(x[0], 9.5100000027E-02); + VERIFY_IS_APPROX(x[1], 1.0000000001E+00); + VERIFY_IS_APPROX(x[2], 8.6070000013E-01); + VERIFY_IS_APPROX(x[3], 3.0000000002E+00); + VERIFY_IS_APPROX(x[4], 1.5575999998E+00); + VERIFY_IS_APPROX(x[5], 5.0000000001E+00); + + /* + * Second try + */ + x<< 0.5, 0.7, 3.6, 4.2, 4., 6.3; + // do the computation + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 2); + VERIFY_IS_EQUAL(lm.nfev, 9); + VERIFY_IS_EQUAL(lm.njev, 8); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.428595533845e-25); // should be 1.4307867721E-25, but nist results are on 128-bit floats + // check x + VERIFY_IS_APPROX(x[0], 9.5100000027E-02); + VERIFY_IS_APPROX(x[1], 1.0000000001E+00); + VERIFY_IS_APPROX(x[2], 8.6070000013E-01); + VERIFY_IS_APPROX(x[3], 3.0000000002E+00); + VERIFY_IS_APPROX(x[4], 1.5575999998E+00); + VERIFY_IS_APPROX(x[5], 5.0000000001E+00); + +} + +struct rat42_functor : Functor<double> +{ + rat42_functor(void) : Functor<double>(3,9) {} + static const double x[9]; + static const double y[9]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + assert(b.size()==3); + assert(fvec.size()==9); + for(int i=0; i<9; i++) { + fvec[i] = b[0] / (1.+exp(b[1]-b[2]*x[i])) - y[i]; + } + return 0; + } + + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==3); + assert(fjac.rows()==9); + assert(fjac.cols()==3); + for(int i=0; i<9; i++) { + double e = exp(b[1]-b[2]*x[i]); + fjac(i,0) = 1./(1.+e); + fjac(i,1) = -b[0]*e/(1.+e)/(1.+e); + fjac(i,2) = +b[0]*e*x[i]/(1.+e)/(1.+e); + } + return 0; + } +}; +const double rat42_functor::x[9] = { 9.000E0, 14.000E0, 21.000E0, 28.000E0, 42.000E0, 57.000E0, 63.000E0, 70.000E0, 79.000E0 }; +const double rat42_functor::y[9] = { 8.930E0 ,10.800E0 ,18.590E0 ,22.330E0 ,39.350E0 ,56.110E0 ,61.730E0 ,64.620E0 ,67.080E0 }; + +// http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky2.shtml +void testNistRat42(void) +{ + const int n=3; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< 100., 1., 0.1; + // do the computation + rat42_functor functor; + LevenbergMarquardt<rat42_functor> lm(functor); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 10); + VERIFY_IS_EQUAL(lm.njev, 8); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.0565229338E+00); + // check x + VERIFY_IS_APPROX(x[0], 7.2462237576E+01); + VERIFY_IS_APPROX(x[1], 2.6180768402E+00); + VERIFY_IS_APPROX(x[2], 6.7359200066E-02); + + /* + * Second try + */ + x<< 75., 2.5, 0.07; + // do the computation + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 6); + VERIFY_IS_EQUAL(lm.njev, 5); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.0565229338E+00); + // check x + VERIFY_IS_APPROX(x[0], 7.2462237576E+01); + VERIFY_IS_APPROX(x[1], 2.6180768402E+00); + VERIFY_IS_APPROX(x[2], 6.7359200066E-02); +} + +struct MGH10_functor : Functor<double> +{ + MGH10_functor(void) : Functor<double>(3,16) {} + static const double x[16]; + static const double y[16]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + assert(b.size()==3); + assert(fvec.size()==16); + for(int i=0; i<16; i++) + fvec[i] = b[0] * exp(b[1]/(x[i]+b[2])) - y[i]; + return 0; + } + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==3); + assert(fjac.rows()==16); + assert(fjac.cols()==3); + for(int i=0; i<16; i++) { + double factor = 1./(x[i]+b[2]); + double e = exp(b[1]*factor); + fjac(i,0) = e; + fjac(i,1) = b[0]*factor*e; + fjac(i,2) = -b[1]*b[0]*factor*factor*e; + } + return 0; + } +}; +const double MGH10_functor::x[16] = { 5.000000E+01, 5.500000E+01, 6.000000E+01, 6.500000E+01, 7.000000E+01, 7.500000E+01, 8.000000E+01, 8.500000E+01, 9.000000E+01, 9.500000E+01, 1.000000E+02, 1.050000E+02, 1.100000E+02, 1.150000E+02, 1.200000E+02, 1.250000E+02 }; +const double MGH10_functor::y[16] = { 3.478000E+04, 2.861000E+04, 2.365000E+04, 1.963000E+04, 1.637000E+04, 1.372000E+04, 1.154000E+04, 9.744000E+03, 8.261000E+03, 7.030000E+03, 6.005000E+03, 5.147000E+03, 4.427000E+03, 3.820000E+03, 3.307000E+03, 2.872000E+03 }; + +// http://www.itl.nist.gov/div898/strd/nls/data/mgh10.shtml +void testNistMGH10(void) +{ + const int n=3; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< 2., 400000., 25000.; + // do the computation + MGH10_functor functor; + LevenbergMarquardt<MGH10_functor> lm(functor); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 2); + VERIFY_IS_EQUAL(lm.nfev, 284 ); + VERIFY_IS_EQUAL(lm.njev, 249 ); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7945855171E+01); + // check x + VERIFY_IS_APPROX(x[0], 5.6096364710E-03); + VERIFY_IS_APPROX(x[1], 6.1813463463E+03); + VERIFY_IS_APPROX(x[2], 3.4522363462E+02); + + /* + * Second try + */ + x<< 0.02, 4000., 250.; + // do the computation + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 3); + VERIFY_IS_EQUAL(lm.nfev, 126); + VERIFY_IS_EQUAL(lm.njev, 116); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7945855171E+01); + // check x + VERIFY_IS_APPROX(x[0], 5.6096364710E-03); + VERIFY_IS_APPROX(x[1], 6.1813463463E+03); + VERIFY_IS_APPROX(x[2], 3.4522363462E+02); +} + + +struct BoxBOD_functor : Functor<double> +{ + BoxBOD_functor(void) : Functor<double>(2,6) {} + static const double x[6]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + static const double y[6] = { 109., 149., 149., 191., 213., 224. }; + assert(b.size()==2); + assert(fvec.size()==6); + for(int i=0; i<6; i++) + fvec[i] = b[0]*(1.-exp(-b[1]*x[i])) - y[i]; + return 0; + } + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==2); + assert(fjac.rows()==6); + assert(fjac.cols()==2); + for(int i=0; i<6; i++) { + double e = exp(-b[1]*x[i]); + fjac(i,0) = 1.-e; + fjac(i,1) = b[0]*x[i]*e; + } + return 0; + } +}; +const double BoxBOD_functor::x[6] = { 1., 2., 3., 5., 7., 10. }; + +// http://www.itl.nist.gov/div898/strd/nls/data/boxbod.shtml +void testNistBoxBOD(void) +{ + const int n=2; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< 1., 1.; + // do the computation + BoxBOD_functor functor; + LevenbergMarquardt<BoxBOD_functor> lm(functor); + lm.parameters.ftol = 1.E6*NumTraits<double>::epsilon(); + lm.parameters.xtol = 1.E6*NumTraits<double>::epsilon(); + lm.parameters.factor = 10.; + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 31); + VERIFY_IS_EQUAL(lm.njev, 25); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.1680088766E+03); + // check x + VERIFY_IS_APPROX(x[0], 2.1380940889E+02); + VERIFY_IS_APPROX(x[1], 5.4723748542E-01); + + /* + * Second try + */ + x<< 100., 0.75; + // do the computation + lm.resetParameters(); + lm.parameters.ftol = NumTraits<double>::epsilon(); + lm.parameters.xtol = NumTraits<double>::epsilon(); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 15 ); + VERIFY_IS_EQUAL(lm.njev, 14 ); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.1680088766E+03); + // check x + VERIFY_IS_APPROX(x[0], 2.1380940889E+02); + VERIFY_IS_APPROX(x[1], 5.4723748542E-01); +} + +struct MGH17_functor : Functor<double> +{ + MGH17_functor(void) : Functor<double>(5,33) {} + static const double x[33]; + static const double y[33]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + assert(b.size()==5); + assert(fvec.size()==33); + for(int i=0; i<33; i++) + fvec[i] = b[0] + b[1]*exp(-b[3]*x[i]) + b[2]*exp(-b[4]*x[i]) - y[i]; + return 0; + } + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==5); + assert(fjac.rows()==33); + assert(fjac.cols()==5); + for(int i=0; i<33; i++) { + fjac(i,0) = 1.; + fjac(i,1) = exp(-b[3]*x[i]); + fjac(i,2) = exp(-b[4]*x[i]); + fjac(i,3) = -x[i]*b[1]*exp(-b[3]*x[i]); + fjac(i,4) = -x[i]*b[2]*exp(-b[4]*x[i]); + } + return 0; + } +}; +const double MGH17_functor::x[33] = { 0.000000E+00, 1.000000E+01, 2.000000E+01, 3.000000E+01, 4.000000E+01, 5.000000E+01, 6.000000E+01, 7.000000E+01, 8.000000E+01, 9.000000E+01, 1.000000E+02, 1.100000E+02, 1.200000E+02, 1.300000E+02, 1.400000E+02, 1.500000E+02, 1.600000E+02, 1.700000E+02, 1.800000E+02, 1.900000E+02, 2.000000E+02, 2.100000E+02, 2.200000E+02, 2.300000E+02, 2.400000E+02, 2.500000E+02, 2.600000E+02, 2.700000E+02, 2.800000E+02, 2.900000E+02, 3.000000E+02, 3.100000E+02, 3.200000E+02 }; +const double MGH17_functor::y[33] = { 8.440000E-01, 9.080000E-01, 9.320000E-01, 9.360000E-01, 9.250000E-01, 9.080000E-01, 8.810000E-01, 8.500000E-01, 8.180000E-01, 7.840000E-01, 7.510000E-01, 7.180000E-01, 6.850000E-01, 6.580000E-01, 6.280000E-01, 6.030000E-01, 5.800000E-01, 5.580000E-01, 5.380000E-01, 5.220000E-01, 5.060000E-01, 4.900000E-01, 4.780000E-01, 4.670000E-01, 4.570000E-01, 4.480000E-01, 4.380000E-01, 4.310000E-01, 4.240000E-01, 4.200000E-01, 4.140000E-01, 4.110000E-01, 4.060000E-01 }; + +// http://www.itl.nist.gov/div898/strd/nls/data/mgh17.shtml +void testNistMGH17(void) +{ + const int n=5; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< 50., 150., -100., 1., 2.; + // do the computation + MGH17_functor functor; + LevenbergMarquardt<MGH17_functor> lm(functor); + lm.parameters.ftol = NumTraits<double>::epsilon(); + lm.parameters.xtol = NumTraits<double>::epsilon(); + lm.parameters.maxfev = 1000; + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 2); + VERIFY_IS_EQUAL(lm.nfev, 602 ); + VERIFY_IS_EQUAL(lm.njev, 545 ); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.4648946975E-05); + // check x + VERIFY_IS_APPROX(x[0], 3.7541005211E-01); + VERIFY_IS_APPROX(x[1], 1.9358469127E+00); + VERIFY_IS_APPROX(x[2], -1.4646871366E+00); + VERIFY_IS_APPROX(x[3], 1.2867534640E-02); + VERIFY_IS_APPROX(x[4], 2.2122699662E-02); + + /* + * Second try + */ + x<< 0.5 ,1.5 ,-1 ,0.01 ,0.02; + // do the computation + lm.resetParameters(); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 18); + VERIFY_IS_EQUAL(lm.njev, 15); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.4648946975E-05); + // check x + VERIFY_IS_APPROX(x[0], 3.7541005211E-01); + VERIFY_IS_APPROX(x[1], 1.9358469127E+00); + VERIFY_IS_APPROX(x[2], -1.4646871366E+00); + VERIFY_IS_APPROX(x[3], 1.2867534640E-02); + VERIFY_IS_APPROX(x[4], 2.2122699662E-02); +} + +struct MGH09_functor : Functor<double> +{ + MGH09_functor(void) : Functor<double>(4,11) {} + static const double _x[11]; + static const double y[11]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + assert(b.size()==4); + assert(fvec.size()==11); + for(int i=0; i<11; i++) { + double x = _x[i], xx=x*x; + fvec[i] = b[0]*(xx+x*b[1])/(xx+x*b[2]+b[3]) - y[i]; + } + return 0; + } + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==4); + assert(fjac.rows()==11); + assert(fjac.cols()==4); + for(int i=0; i<11; i++) { + double x = _x[i], xx=x*x; + double factor = 1./(xx+x*b[2]+b[3]); + fjac(i,0) = (xx+x*b[1]) * factor; + fjac(i,1) = b[0]*x* factor; + fjac(i,2) = - b[0]*(xx+x*b[1]) * x * factor * factor; + fjac(i,3) = - b[0]*(xx+x*b[1]) * factor * factor; + } + return 0; + } +}; +const double MGH09_functor::_x[11] = { 4., 2., 1., 5.E-1 , 2.5E-01, 1.670000E-01, 1.250000E-01, 1.E-01, 8.330000E-02, 7.140000E-02, 6.250000E-02 }; +const double MGH09_functor::y[11] = { 1.957000E-01, 1.947000E-01, 1.735000E-01, 1.600000E-01, 8.440000E-02, 6.270000E-02, 4.560000E-02, 3.420000E-02, 3.230000E-02, 2.350000E-02, 2.460000E-02 }; + +// http://www.itl.nist.gov/div898/strd/nls/data/mgh09.shtml +void testNistMGH09(void) +{ + const int n=4; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< 25., 39, 41.5, 39.; + // do the computation + MGH09_functor functor; + LevenbergMarquardt<MGH09_functor> lm(functor); + lm.parameters.maxfev = 1000; + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 490 ); + VERIFY_IS_EQUAL(lm.njev, 376 ); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 3.0750560385E-04); + // check x + VERIFY_IS_APPROX(x[0], 0.1928077089); // should be 1.9280693458E-01 + VERIFY_IS_APPROX(x[1], 0.19126423573); // should be 1.9128232873E-01 + VERIFY_IS_APPROX(x[2], 0.12305309914); // should be 1.2305650693E-01 + VERIFY_IS_APPROX(x[3], 0.13605395375); // should be 1.3606233068E-01 + + /* + * Second try + */ + x<< 0.25, 0.39, 0.415, 0.39; + // do the computation + lm.resetParameters(); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 18); + VERIFY_IS_EQUAL(lm.njev, 16); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 3.0750560385E-04); + // check x + VERIFY_IS_APPROX(x[0], 0.19280781); // should be 1.9280693458E-01 + VERIFY_IS_APPROX(x[1], 0.19126265); // should be 1.9128232873E-01 + VERIFY_IS_APPROX(x[2], 0.12305280); // should be 1.2305650693E-01 + VERIFY_IS_APPROX(x[3], 0.13605322); // should be 1.3606233068E-01 +} + + + +struct Bennett5_functor : Functor<double> +{ + Bennett5_functor(void) : Functor<double>(3,154) {} + static const double x[154]; + static const double y[154]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + assert(b.size()==3); + assert(fvec.size()==154); + for(int i=0; i<154; i++) + fvec[i] = b[0]* pow(b[1]+x[i],-1./b[2]) - y[i]; + return 0; + } + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==3); + assert(fjac.rows()==154); + assert(fjac.cols()==3); + for(int i=0; i<154; i++) { + double e = pow(b[1]+x[i],-1./b[2]); + fjac(i,0) = e; + fjac(i,1) = - b[0]*e/b[2]/(b[1]+x[i]); + fjac(i,2) = b[0]*e*log(b[1]+x[i])/b[2]/b[2]; + } + return 0; + } +}; +const double Bennett5_functor::x[154] = { 7.447168E0, 8.102586E0, 8.452547E0, 8.711278E0, 8.916774E0, 9.087155E0, 9.232590E0, 9.359535E0, 9.472166E0, 9.573384E0, 9.665293E0, 9.749461E0, 9.827092E0, 9.899128E0, 9.966321E0, 10.029280E0, 10.088510E0, 10.144430E0, 10.197380E0, 10.247670E0, 10.295560E0, 10.341250E0, 10.384950E0, 10.426820E0, 10.467000E0, 10.505640E0, 10.542830E0, 10.578690E0, 10.613310E0, 10.646780E0, 10.679150E0, 10.710520E0, 10.740920E0, 10.770440E0, 10.799100E0, 10.826970E0, 10.854080E0, 10.880470E0, 10.906190E0, 10.931260E0, 10.955720E0, 10.979590E0, 11.002910E0, 11.025700E0, 11.047980E0, 11.069770E0, 11.091100E0, 11.111980E0, 11.132440E0, 11.152480E0, 11.172130E0, 11.191410E0, 11.210310E0, 11.228870E0, 11.247090E0, 11.264980E0, 11.282560E0, 11.299840E0, 11.316820E0, 11.333520E0, 11.349940E0, 11.366100E0, 11.382000E0, 11.397660E0, 11.413070E0, 11.428240E0, 11.443200E0, 11.457930E0, 11.472440E0, 11.486750E0, 11.500860E0, 11.514770E0, 11.528490E0, 11.542020E0, 11.555380E0, 11.568550E0, 11.581560E0, 11.594420E0, 11.607121E0, 11.619640E0, 11.632000E0, 11.644210E0, 11.656280E0, 11.668200E0, 11.679980E0, 11.691620E0, 11.703130E0, 11.714510E0, 11.725760E0, 11.736880E0, 11.747890E0, 11.758780E0, 11.769550E0, 11.780200E0, 11.790730E0, 11.801160E0, 11.811480E0, 11.821700E0, 11.831810E0, 11.841820E0, 11.851730E0, 11.861550E0, 11.871270E0, 11.880890E0, 11.890420E0, 11.899870E0, 11.909220E0, 11.918490E0, 11.927680E0, 11.936780E0, 11.945790E0, 11.954730E0, 11.963590E0, 11.972370E0, 11.981070E0, 11.989700E0, 11.998260E0, 12.006740E0, 12.015150E0, 12.023490E0, 12.031760E0, 12.039970E0, 12.048100E0, 12.056170E0, 12.064180E0, 12.072120E0, 12.080010E0, 12.087820E0, 12.095580E0, 12.103280E0, 12.110920E0, 12.118500E0, 12.126030E0, 12.133500E0, 12.140910E0, 12.148270E0, 12.155570E0, 12.162830E0, 12.170030E0, 12.177170E0, 12.184270E0, 12.191320E0, 12.198320E0, 12.205270E0, 12.212170E0, 12.219030E0, 12.225840E0, 12.232600E0, 12.239320E0, 12.245990E0, 12.252620E0, 12.259200E0, 12.265750E0, 12.272240E0 }; +const double Bennett5_functor::y[154] = { -34.834702E0 ,-34.393200E0 ,-34.152901E0 ,-33.979099E0 ,-33.845901E0 ,-33.732899E0 ,-33.640301E0 ,-33.559200E0 ,-33.486801E0 ,-33.423100E0 ,-33.365101E0 ,-33.313000E0 ,-33.260899E0 ,-33.217400E0 ,-33.176899E0 ,-33.139198E0 ,-33.101601E0 ,-33.066799E0 ,-33.035000E0 ,-33.003101E0 ,-32.971298E0 ,-32.942299E0 ,-32.916302E0 ,-32.890202E0 ,-32.864101E0 ,-32.841000E0 ,-32.817799E0 ,-32.797501E0 ,-32.774300E0 ,-32.757000E0 ,-32.733799E0 ,-32.716400E0 ,-32.699100E0 ,-32.678799E0 ,-32.661400E0 ,-32.644001E0 ,-32.626701E0 ,-32.612202E0 ,-32.597698E0 ,-32.583199E0 ,-32.568699E0 ,-32.554298E0 ,-32.539799E0 ,-32.525299E0 ,-32.510799E0 ,-32.499199E0 ,-32.487598E0 ,-32.473202E0 ,-32.461601E0 ,-32.435501E0 ,-32.435501E0 ,-32.426800E0 ,-32.412300E0 ,-32.400799E0 ,-32.392101E0 ,-32.380501E0 ,-32.366001E0 ,-32.357300E0 ,-32.348598E0 ,-32.339901E0 ,-32.328400E0 ,-32.319698E0 ,-32.311001E0 ,-32.299400E0 ,-32.290699E0 ,-32.282001E0 ,-32.273300E0 ,-32.264599E0 ,-32.256001E0 ,-32.247299E0 ,-32.238602E0 ,-32.229900E0 ,-32.224098E0 ,-32.215401E0 ,-32.203800E0 ,-32.198002E0 ,-32.189400E0 ,-32.183601E0 ,-32.174900E0 ,-32.169102E0 ,-32.163300E0 ,-32.154598E0 ,-32.145901E0 ,-32.140099E0 ,-32.131401E0 ,-32.125599E0 ,-32.119801E0 ,-32.111198E0 ,-32.105400E0 ,-32.096699E0 ,-32.090900E0 ,-32.088001E0 ,-32.079300E0 ,-32.073502E0 ,-32.067699E0 ,-32.061901E0 ,-32.056099E0 ,-32.050301E0 ,-32.044498E0 ,-32.038799E0 ,-32.033001E0 ,-32.027199E0 ,-32.024300E0 ,-32.018501E0 ,-32.012699E0 ,-32.004002E0 ,-32.001099E0 ,-31.995300E0 ,-31.989500E0 ,-31.983700E0 ,-31.977900E0 ,-31.972099E0 ,-31.969299E0 ,-31.963501E0 ,-31.957701E0 ,-31.951900E0 ,-31.946100E0 ,-31.940300E0 ,-31.937401E0 ,-31.931601E0 ,-31.925800E0 ,-31.922899E0 ,-31.917101E0 ,-31.911301E0 ,-31.908400E0 ,-31.902599E0 ,-31.896900E0 ,-31.893999E0 ,-31.888201E0 ,-31.885300E0 ,-31.882401E0 ,-31.876600E0 ,-31.873699E0 ,-31.867901E0 ,-31.862101E0 ,-31.859200E0 ,-31.856300E0 ,-31.850500E0 ,-31.844700E0 ,-31.841801E0 ,-31.838900E0 ,-31.833099E0 ,-31.830200E0 ,-31.827299E0 ,-31.821600E0 ,-31.818701E0 ,-31.812901E0 ,-31.809999E0 ,-31.807100E0 ,-31.801300E0 ,-31.798401E0 ,-31.795500E0 ,-31.789700E0 ,-31.786800E0 }; + +// http://www.itl.nist.gov/div898/strd/nls/data/bennett5.shtml +void testNistBennett5(void) +{ + const int n=3; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< -2000., 50., 0.8; + // do the computation + Bennett5_functor functor; + LevenbergMarquardt<Bennett5_functor> lm(functor); + lm.parameters.maxfev = 1000; + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 758); + VERIFY_IS_EQUAL(lm.njev, 744); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.2404744073E-04); + // check x + VERIFY_IS_APPROX(x[0], -2.5235058043E+03); + VERIFY_IS_APPROX(x[1], 4.6736564644E+01); + VERIFY_IS_APPROX(x[2], 9.3218483193E-01); + /* + * Second try + */ + x<< -1500., 45., 0.85; + // do the computation + lm.resetParameters(); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 203); + VERIFY_IS_EQUAL(lm.njev, 192); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.2404744073E-04); + // check x + VERIFY_IS_APPROX(x[0], -2523.3007865); // should be -2.5235058043E+03 + VERIFY_IS_APPROX(x[1], 46.735705771); // should be 4.6736564644E+01); + VERIFY_IS_APPROX(x[2], 0.93219881891); // should be 9.3218483193E-01); +} + +struct thurber_functor : Functor<double> +{ + thurber_functor(void) : Functor<double>(7,37) {} + static const double _x[37]; + static const double _y[37]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + // int called=0; printf("call hahn1_functor with iflag=%d, called=%d\n", iflag, called); if (iflag==1) called++; + assert(b.size()==7); + assert(fvec.size()==37); + for(int i=0; i<37; i++) { + double x=_x[i], xx=x*x, xxx=xx*x; + fvec[i] = (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) / (1.+b[4]*x+b[5]*xx+b[6]*xxx) - _y[i]; + } + return 0; + } + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==7); + assert(fjac.rows()==37); + assert(fjac.cols()==7); + for(int i=0; i<37; i++) { + double x=_x[i], xx=x*x, xxx=xx*x; + double fact = 1./(1.+b[4]*x+b[5]*xx+b[6]*xxx); + fjac(i,0) = 1.*fact; + fjac(i,1) = x*fact; + fjac(i,2) = xx*fact; + fjac(i,3) = xxx*fact; + fact = - (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) * fact * fact; + fjac(i,4) = x*fact; + fjac(i,5) = xx*fact; + fjac(i,6) = xxx*fact; + } + return 0; + } +}; +const double thurber_functor::_x[37] = { -3.067E0, -2.981E0, -2.921E0, -2.912E0, -2.840E0, -2.797E0, -2.702E0, -2.699E0, -2.633E0, -2.481E0, -2.363E0, -2.322E0, -1.501E0, -1.460E0, -1.274E0, -1.212E0, -1.100E0, -1.046E0, -0.915E0, -0.714E0, -0.566E0, -0.545E0, -0.400E0, -0.309E0, -0.109E0, -0.103E0, 0.010E0, 0.119E0, 0.377E0, 0.790E0, 0.963E0, 1.006E0, 1.115E0, 1.572E0, 1.841E0, 2.047E0, 2.200E0 }; +const double thurber_functor::_y[37] = { 80.574E0, 84.248E0, 87.264E0, 87.195E0, 89.076E0, 89.608E0, 89.868E0, 90.101E0, 92.405E0, 95.854E0, 100.696E0, 101.060E0, 401.672E0, 390.724E0, 567.534E0, 635.316E0, 733.054E0, 759.087E0, 894.206E0, 990.785E0, 1090.109E0, 1080.914E0, 1122.643E0, 1178.351E0, 1260.531E0, 1273.514E0, 1288.339E0, 1327.543E0, 1353.863E0, 1414.509E0, 1425.208E0, 1421.384E0, 1442.962E0, 1464.350E0, 1468.705E0, 1447.894E0, 1457.628E0}; + +// http://www.itl.nist.gov/div898/strd/nls/data/thurber.shtml +void testNistThurber(void) +{ + const int n=7; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< 1000 ,1000 ,400 ,40 ,0.7,0.3,0.0 ; + // do the computation + thurber_functor functor; + LevenbergMarquardt<thurber_functor> lm(functor); + lm.parameters.ftol = 1.E4*NumTraits<double>::epsilon(); + lm.parameters.xtol = 1.E4*NumTraits<double>::epsilon(); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 39); + VERIFY_IS_EQUAL(lm.njev, 36); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6427082397E+03); + // check x + VERIFY_IS_APPROX(x[0], 1.2881396800E+03); + VERIFY_IS_APPROX(x[1], 1.4910792535E+03); + VERIFY_IS_APPROX(x[2], 5.8323836877E+02); + VERIFY_IS_APPROX(x[3], 7.5416644291E+01); + VERIFY_IS_APPROX(x[4], 9.6629502864E-01); + VERIFY_IS_APPROX(x[5], 3.9797285797E-01); + VERIFY_IS_APPROX(x[6], 4.9727297349E-02); + + /* + * Second try + */ + x<< 1300 ,1500 ,500 ,75 ,1 ,0.4 ,0.05 ; + // do the computation + lm.resetParameters(); + lm.parameters.ftol = 1.E4*NumTraits<double>::epsilon(); + lm.parameters.xtol = 1.E4*NumTraits<double>::epsilon(); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 29); + VERIFY_IS_EQUAL(lm.njev, 28); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6427082397E+03); + // check x + VERIFY_IS_APPROX(x[0], 1.2881396800E+03); + VERIFY_IS_APPROX(x[1], 1.4910792535E+03); + VERIFY_IS_APPROX(x[2], 5.8323836877E+02); + VERIFY_IS_APPROX(x[3], 7.5416644291E+01); + VERIFY_IS_APPROX(x[4], 9.6629502864E-01); + VERIFY_IS_APPROX(x[5], 3.9797285797E-01); + VERIFY_IS_APPROX(x[6], 4.9727297349E-02); +} + +struct rat43_functor : Functor<double> +{ + rat43_functor(void) : Functor<double>(4,15) {} + static const double x[15]; + static const double y[15]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + assert(b.size()==4); + assert(fvec.size()==15); + for(int i=0; i<15; i++) + fvec[i] = b[0] * pow(1.+exp(b[1]-b[2]*x[i]),-1./b[3]) - y[i]; + return 0; + } + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==4); + assert(fjac.rows()==15); + assert(fjac.cols()==4); + for(int i=0; i<15; i++) { + double e = exp(b[1]-b[2]*x[i]); + double power = -1./b[3]; + fjac(i,0) = pow(1.+e, power); + fjac(i,1) = power*b[0]*e*pow(1.+e, power-1.); + fjac(i,2) = -power*b[0]*e*x[i]*pow(1.+e, power-1.); + fjac(i,3) = b[0]*power*power*log(1.+e)*pow(1.+e, power); + } + return 0; + } +}; +const double rat43_functor::x[15] = { 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15. }; +const double rat43_functor::y[15] = { 16.08, 33.83, 65.80, 97.20, 191.55, 326.20, 386.87, 520.53, 590.03, 651.92, 724.93, 699.56, 689.96, 637.56, 717.41 }; + +// http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky3.shtml +void testNistRat43(void) +{ + const int n=4; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< 100., 10., 1., 1.; + // do the computation + rat43_functor functor; + LevenbergMarquardt<rat43_functor> lm(functor); + lm.parameters.ftol = 1.E6*NumTraits<double>::epsilon(); + lm.parameters.xtol = 1.E6*NumTraits<double>::epsilon(); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 27); + VERIFY_IS_EQUAL(lm.njev, 20); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7864049080E+03); + // check x + VERIFY_IS_APPROX(x[0], 6.9964151270E+02); + VERIFY_IS_APPROX(x[1], 5.2771253025E+00); + VERIFY_IS_APPROX(x[2], 7.5962938329E-01); + VERIFY_IS_APPROX(x[3], 1.2792483859E+00); + + /* + * Second try + */ + x<< 700., 5., 0.75, 1.3; + // do the computation + lm.resetParameters(); + lm.parameters.ftol = 1.E5*NumTraits<double>::epsilon(); + lm.parameters.xtol = 1.E5*NumTraits<double>::epsilon(); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 9); + VERIFY_IS_EQUAL(lm.njev, 8); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7864049080E+03); + // check x + VERIFY_IS_APPROX(x[0], 6.9964151270E+02); + VERIFY_IS_APPROX(x[1], 5.2771253025E+00); + VERIFY_IS_APPROX(x[2], 7.5962938329E-01); + VERIFY_IS_APPROX(x[3], 1.2792483859E+00); +} + + + +struct eckerle4_functor : Functor<double> +{ + eckerle4_functor(void) : Functor<double>(3,35) {} + static const double x[35]; + static const double y[35]; + int operator()(const VectorXd &b, VectorXd &fvec) + { + assert(b.size()==3); + assert(fvec.size()==35); + for(int i=0; i<35; i++) + fvec[i] = b[0]/b[1] * exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/(b[1]*b[1])) - y[i]; + return 0; + } + int df(const VectorXd &b, MatrixXd &fjac) + { + assert(b.size()==3); + assert(fjac.rows()==35); + assert(fjac.cols()==3); + for(int i=0; i<35; i++) { + double b12 = b[1]*b[1]; + double e = exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/b12); + fjac(i,0) = e / b[1]; + fjac(i,1) = ((x[i]-b[2])*(x[i]-b[2])/b12-1.) * b[0]*e/b12; + fjac(i,2) = (x[i]-b[2])*e*b[0]/b[1]/b12; + } + return 0; + } +}; +const double eckerle4_functor::x[35] = { 400.0, 405.0, 410.0, 415.0, 420.0, 425.0, 430.0, 435.0, 436.5, 438.0, 439.5, 441.0, 442.5, 444.0, 445.5, 447.0, 448.5, 450.0, 451.5, 453.0, 454.5, 456.0, 457.5, 459.0, 460.5, 462.0, 463.5, 465.0, 470.0, 475.0, 480.0, 485.0, 490.0, 495.0, 500.0}; +const double eckerle4_functor::y[35] = { 0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917, 0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302, 0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458, 0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534, 0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200, 0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800, 0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710 }; + +// http://www.itl.nist.gov/div898/strd/nls/data/eckerle4.shtml +void testNistEckerle4(void) +{ + const int n=3; + int info; + + VectorXd x(n); + + /* + * First try + */ + x<< 1., 10., 500.; + // do the computation + eckerle4_functor functor; + LevenbergMarquardt<eckerle4_functor> lm(functor); + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 18); + VERIFY_IS_EQUAL(lm.njev, 15); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.4635887487E-03); + // check x + VERIFY_IS_APPROX(x[0], 1.5543827178); + VERIFY_IS_APPROX(x[1], 4.0888321754); + VERIFY_IS_APPROX(x[2], 4.5154121844E+02); + + /* + * Second try + */ + x<< 1.5, 5., 450.; + // do the computation + info = lm.minimize(x); + + // check return value + VERIFY_IS_EQUAL(info, 1); + VERIFY_IS_EQUAL(lm.nfev, 7); + VERIFY_IS_EQUAL(lm.njev, 6); + // check norm^2 + VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.4635887487E-03); + // check x + VERIFY_IS_APPROX(x[0], 1.5543827178); + VERIFY_IS_APPROX(x[1], 4.0888321754); + VERIFY_IS_APPROX(x[2], 4.5154121844E+02); +} + +void test_NonLinearOptimization() +{ + // Tests using the examples provided by (c)minpack + CALL_SUBTEST/*_1*/(testChkder()); + CALL_SUBTEST/*_1*/(testLmder1()); + CALL_SUBTEST/*_1*/(testLmder()); + CALL_SUBTEST/*_2*/(testHybrj1()); + CALL_SUBTEST/*_2*/(testHybrj()); + CALL_SUBTEST/*_2*/(testHybrd1()); + CALL_SUBTEST/*_2*/(testHybrd()); + CALL_SUBTEST/*_3*/(testLmstr1()); + CALL_SUBTEST/*_3*/(testLmstr()); + CALL_SUBTEST/*_3*/(testLmdif1()); + CALL_SUBTEST/*_3*/(testLmdif()); + + // NIST tests, level of difficulty = "Lower" + CALL_SUBTEST/*_4*/(testNistMisra1a()); + CALL_SUBTEST/*_4*/(testNistChwirut2()); + + // NIST tests, level of difficulty = "Average" + CALL_SUBTEST/*_5*/(testNistHahn1()); + CALL_SUBTEST/*_6*/(testNistMisra1d()); + CALL_SUBTEST/*_7*/(testNistMGH17()); + CALL_SUBTEST/*_8*/(testNistLanczos1()); + + // NIST tests, level of difficulty = "Higher" + CALL_SUBTEST/*_9*/(testNistRat42()); + CALL_SUBTEST/*_10*/(testNistMGH10()); + CALL_SUBTEST/*_11*/(testNistBoxBOD()); + CALL_SUBTEST/*_12*/(testNistMGH09()); + CALL_SUBTEST/*_13*/(testNistBennett5()); + CALL_SUBTEST/*_14*/(testNistThurber()); + CALL_SUBTEST/*_15*/(testNistRat43()); + CALL_SUBTEST/*_16*/(testNistEckerle4()); +} + +/* + * Can be useful for debugging... + printf("info, nfev : %d, %d\n", info, lm.nfev); + printf("info, nfev, njev : %d, %d, %d\n", info, solver.nfev, solver.njev); + printf("info, nfev : %d, %d\n", info, solver.nfev); + printf("x[0] : %.32g\n", x[0]); + printf("x[1] : %.32g\n", x[1]); + printf("x[2] : %.32g\n", x[2]); + printf("x[3] : %.32g\n", x[3]); + printf("fvec.blueNorm() : %.32g\n", solver.fvec.blueNorm()); + printf("fvec.blueNorm() : %.32g\n", lm.fvec.blueNorm()); + + printf("info, nfev, njev : %d, %d, %d\n", info, lm.nfev, lm.njev); + printf("fvec.squaredNorm() : %.13g\n", lm.fvec.squaredNorm()); + std::cout << x << std::endl; + std::cout.precision(9); + std::cout << x[0] << std::endl; + std::cout << x[1] << std::endl; + std::cout << x[2] << std::endl; + std::cout << x[3] << std::endl; +*/ + diff --git a/unsupported/test/NumericalDiff.cpp b/unsupported/test/NumericalDiff.cpp new file mode 100644 index 000000000..27d888056 --- /dev/null +++ b/unsupported/test/NumericalDiff.cpp @@ -0,0 +1,114 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org> + +#include <stdio.h> + +#include "main.h" +#include <unsupported/Eigen/NumericalDiff> + +// Generic functor +template<typename _Scalar, int NX=Dynamic, int NY=Dynamic> +struct Functor +{ + typedef _Scalar Scalar; + enum { + InputsAtCompileTime = NX, + ValuesAtCompileTime = NY + }; + typedef Matrix<Scalar,InputsAtCompileTime,1> InputType; + typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType; + typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType; + + int m_inputs, m_values; + + Functor() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {} + Functor(int inputs, int values) : m_inputs(inputs), m_values(values) {} + + int inputs() const { return m_inputs; } + int values() const { return m_values; } + +}; + +struct my_functor : Functor<double> +{ + my_functor(void): Functor<double>(3,15) {} + int operator()(const VectorXd &x, VectorXd &fvec) const + { + double tmp1, tmp2, tmp3; + double y[15] = {1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1, + 3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39}; + + for (int i = 0; i < values(); i++) + { + tmp1 = i+1; + tmp2 = 16 - i - 1; + tmp3 = (i>=8)? tmp2 : tmp1; + fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3)); + } + return 0; + } + + int actual_df(const VectorXd &x, MatrixXd &fjac) const + { + double tmp1, tmp2, tmp3, tmp4; + for (int i = 0; i < values(); i++) + { + tmp1 = i+1; + tmp2 = 16 - i - 1; + tmp3 = (i>=8)? tmp2 : tmp1; + tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4; + fjac(i,0) = -1; + fjac(i,1) = tmp1*tmp2/tmp4; + fjac(i,2) = tmp1*tmp3/tmp4; + } + return 0; + } +}; + +void test_forward() +{ + VectorXd x(3); + MatrixXd jac(15,3); + MatrixXd actual_jac(15,3); + my_functor functor; + + x << 0.082, 1.13, 2.35; + + // real one + functor.actual_df(x, actual_jac); +// std::cout << actual_jac << std::endl << std::endl; + + // using NumericalDiff + NumericalDiff<my_functor> numDiff(functor); + numDiff.df(x, jac); +// std::cout << jac << std::endl; + + VERIFY_IS_APPROX(jac, actual_jac); +} + +void test_central() +{ + VectorXd x(3); + MatrixXd jac(15,3); + MatrixXd actual_jac(15,3); + my_functor functor; + + x << 0.082, 1.13, 2.35; + + // real one + functor.actual_df(x, actual_jac); + + // using NumericalDiff + NumericalDiff<my_functor,Central> numDiff(functor); + numDiff.df(x, jac); + + VERIFY_IS_APPROX(jac, actual_jac); +} + +void test_NumericalDiff() +{ + CALL_SUBTEST(test_forward()); + CALL_SUBTEST(test_central()); +} diff --git a/unsupported/test/alignedvector3.cpp b/unsupported/test/alignedvector3.cpp new file mode 100644 index 000000000..fc2bc2135 --- /dev/null +++ b/unsupported/test/alignedvector3.cpp @@ -0,0 +1,59 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include <unsupported/Eigen/AlignedVector3> + +template<typename Scalar> +void alignedvector3() +{ + Scalar s1 = internal::random<Scalar>(); + Scalar s2 = internal::random<Scalar>(); + typedef Matrix<Scalar,3,1> RefType; + typedef Matrix<Scalar,3,3> Mat33; + typedef AlignedVector3<Scalar> FastType; + RefType r1(RefType::Random()), r2(RefType::Random()), r3(RefType::Random()), + r4(RefType::Random()), r5(RefType::Random()), r6(RefType::Random()); + FastType f1(r1), f2(r2), f3(r3), f4(r4), f5(r5), f6(r6); + Mat33 m1(Mat33::Random()); + + VERIFY_IS_APPROX(f1,r1); + VERIFY_IS_APPROX(f4,r4); + + VERIFY_IS_APPROX(f4+f1,r4+r1); + VERIFY_IS_APPROX(f4-f1,r4-r1); + VERIFY_IS_APPROX(f4+f1-f2,r4+r1-r2); + VERIFY_IS_APPROX(f4+=f3,r4+=r3); + VERIFY_IS_APPROX(f4-=f5,r4-=r5); + VERIFY_IS_APPROX(f4-=f5+f1,r4-=r5+r1); + VERIFY_IS_APPROX(f5+f1-s1*f2,r5+r1-s1*r2); + VERIFY_IS_APPROX(f5+f1/s2-s1*f2,r5+r1/s2-s1*r2); + + VERIFY_IS_APPROX(m1*f4,m1*r4); + VERIFY_IS_APPROX(f4.transpose()*m1,r4.transpose()*m1); + + VERIFY_IS_APPROX(f2.dot(f3),r2.dot(r3)); + VERIFY_IS_APPROX(f2.cross(f3),r2.cross(r3)); + VERIFY_IS_APPROX(f2.norm(),r2.norm()); + + VERIFY_IS_APPROX(f2.normalized(),r2.normalized()); + + VERIFY_IS_APPROX((f2+f1).normalized(),(r2+r1).normalized()); + + f2.normalize(); + r2.normalize(); + VERIFY_IS_APPROX(f2,r2); +} + +void test_alignedvector3() +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST( alignedvector3<float>() ); + } +} diff --git a/unsupported/test/autodiff.cpp b/unsupported/test/autodiff.cpp new file mode 100644 index 000000000..6eb417e8d --- /dev/null +++ b/unsupported/test/autodiff.cpp @@ -0,0 +1,172 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include <unsupported/Eigen/AutoDiff> + +template<typename Scalar> +EIGEN_DONT_INLINE Scalar foo(const Scalar& x, const Scalar& y) +{ + using namespace std; +// return x+std::sin(y); + EIGEN_ASM_COMMENT("mybegin"); + return static_cast<Scalar>(x*2 - pow(x,2) + 2*sqrt(y*y) - 4 * sin(x) + 2 * cos(y) - exp(-0.5*x*x)); + //return x+2*y*x;//x*2 -std::pow(x,2);//(2*y/x);// - y*2; + EIGEN_ASM_COMMENT("myend"); +} + +template<typename Vector> +EIGEN_DONT_INLINE typename Vector::Scalar foo(const Vector& p) +{ + typedef typename Vector::Scalar Scalar; + return (p-Vector(Scalar(-1),Scalar(1.))).norm() + (p.array() * p.array()).sum() + p.dot(p); +} + +template<typename _Scalar, int NX=Dynamic, int NY=Dynamic> +struct TestFunc1 +{ + typedef _Scalar Scalar; + enum { + InputsAtCompileTime = NX, + ValuesAtCompileTime = NY + }; + typedef Matrix<Scalar,InputsAtCompileTime,1> InputType; + typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType; + typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType; + + int m_inputs, m_values; + + TestFunc1() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {} + TestFunc1(int inputs, int values) : m_inputs(inputs), m_values(values) {} + + int inputs() const { return m_inputs; } + int values() const { return m_values; } + + template<typename T> + void operator() (const Matrix<T,InputsAtCompileTime,1>& x, Matrix<T,ValuesAtCompileTime,1>* _v) const + { + Matrix<T,ValuesAtCompileTime,1>& v = *_v; + + v[0] = 2 * x[0] * x[0] + x[0] * x[1]; + v[1] = 3 * x[1] * x[0] + 0.5 * x[1] * x[1]; + if(inputs()>2) + { + v[0] += 0.5 * x[2]; + v[1] += x[2]; + } + if(values()>2) + { + v[2] = 3 * x[1] * x[0] * x[0]; + } + if (inputs()>2 && values()>2) + v[2] *= x[2]; + } + + void operator() (const InputType& x, ValueType* v, JacobianType* _j) const + { + (*this)(x, v); + + if(_j) + { + JacobianType& j = *_j; + + j(0,0) = 4 * x[0] + x[1]; + j(1,0) = 3 * x[1]; + + j(0,1) = x[0]; + j(1,1) = 3 * x[0] + 2 * 0.5 * x[1]; + + if (inputs()>2) + { + j(0,2) = 0.5; + j(1,2) = 1; + } + if(values()>2) + { + j(2,0) = 3 * x[1] * 2 * x[0]; + j(2,1) = 3 * x[0] * x[0]; + } + if (inputs()>2 && values()>2) + { + j(2,0) *= x[2]; + j(2,1) *= x[2]; + + j(2,2) = 3 * x[1] * x[0] * x[0]; + j(2,2) = 3 * x[1] * x[0] * x[0]; + } + } + } +}; + +template<typename Func> void forward_jacobian(const Func& f) +{ + typename Func::InputType x = Func::InputType::Random(f.inputs()); + typename Func::ValueType y(f.values()), yref(f.values()); + typename Func::JacobianType j(f.values(),f.inputs()), jref(f.values(),f.inputs()); + + jref.setZero(); + yref.setZero(); + f(x,&yref,&jref); +// std::cerr << y.transpose() << "\n\n";; +// std::cerr << j << "\n\n";; + + j.setZero(); + y.setZero(); + AutoDiffJacobian<Func> autoj(f); + autoj(x, &y, &j); +// std::cerr << y.transpose() << "\n\n";; +// std::cerr << j << "\n\n";; + + VERIFY_IS_APPROX(y, yref); + VERIFY_IS_APPROX(j, jref); +} + +void test_autodiff_scalar() +{ + std::cerr << foo<float>(1,2) << "\n"; + typedef AutoDiffScalar<Vector2f> AD; + AD ax(1,Vector2f::UnitX()); + AD ay(2,Vector2f::UnitY()); + AD res = foo<AD>(ax,ay); + std::cerr << res.value() << " <> " + << res.derivatives().transpose() << "\n\n"; +} + +void test_autodiff_vector() +{ + std::cerr << foo<Vector2f>(Vector2f(1,2)) << "\n"; + typedef AutoDiffScalar<Vector2f> AD; + typedef Matrix<AD,2,1> VectorAD; + VectorAD p(AD(1),AD(-1)); + p.x().derivatives() = Vector2f::UnitX(); + p.y().derivatives() = Vector2f::UnitY(); + + AD res = foo<VectorAD>(p); + std::cerr << res.value() << " <> " + << res.derivatives().transpose() << "\n\n"; +} + +void test_autodiff_jacobian() +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST(( forward_jacobian(TestFunc1<double,2,2>()) )); + CALL_SUBTEST(( forward_jacobian(TestFunc1<double,2,3>()) )); + CALL_SUBTEST(( forward_jacobian(TestFunc1<double,3,2>()) )); + CALL_SUBTEST(( forward_jacobian(TestFunc1<double,3,3>()) )); + CALL_SUBTEST(( forward_jacobian(TestFunc1<double>(3,3)) )); + } +} + +void test_autodiff() +{ + test_autodiff_scalar(); + test_autodiff_vector(); +// test_autodiff_jacobian(); +} + diff --git a/unsupported/test/forward_adolc.cpp b/unsupported/test/forward_adolc.cpp new file mode 100644 index 000000000..d4baafe62 --- /dev/null +++ b/unsupported/test/forward_adolc.cpp @@ -0,0 +1,143 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include <Eigen/Dense> + +#define NUMBER_DIRECTIONS 16 +#include <unsupported/Eigen/AdolcForward> + +int adtl::ADOLC_numDir; + +template<typename Vector> +EIGEN_DONT_INLINE typename Vector::Scalar foo(const Vector& p) +{ + typedef typename Vector::Scalar Scalar; + return (p-Vector(Scalar(-1),Scalar(1.))).norm() + (p.array().sqrt().abs() * p.array().sin()).sum() + p.dot(p); +} + +template<typename _Scalar, int NX=Dynamic, int NY=Dynamic> +struct TestFunc1 +{ + typedef _Scalar Scalar; + enum { + InputsAtCompileTime = NX, + ValuesAtCompileTime = NY + }; + typedef Matrix<Scalar,InputsAtCompileTime,1> InputType; + typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType; + typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType; + + int m_inputs, m_values; + + TestFunc1() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {} + TestFunc1(int inputs, int values) : m_inputs(inputs), m_values(values) {} + + int inputs() const { return m_inputs; } + int values() const { return m_values; } + + template<typename T> + void operator() (const Matrix<T,InputsAtCompileTime,1>& x, Matrix<T,ValuesAtCompileTime,1>* _v) const + { + Matrix<T,ValuesAtCompileTime,1>& v = *_v; + + v[0] = 2 * x[0] * x[0] + x[0] * x[1]; + v[1] = 3 * x[1] * x[0] + 0.5 * x[1] * x[1]; + if(inputs()>2) + { + v[0] += 0.5 * x[2]; + v[1] += x[2]; + } + if(values()>2) + { + v[2] = 3 * x[1] * x[0] * x[0]; + } + if (inputs()>2 && values()>2) + v[2] *= x[2]; + } + + void operator() (const InputType& x, ValueType* v, JacobianType* _j) const + { + (*this)(x, v); + + if(_j) + { + JacobianType& j = *_j; + + j(0,0) = 4 * x[0] + x[1]; + j(1,0) = 3 * x[1]; + + j(0,1) = x[0]; + j(1,1) = 3 * x[0] + 2 * 0.5 * x[1]; + + if (inputs()>2) + { + j(0,2) = 0.5; + j(1,2) = 1; + } + if(values()>2) + { + j(2,0) = 3 * x[1] * 2 * x[0]; + j(2,1) = 3 * x[0] * x[0]; + } + if (inputs()>2 && values()>2) + { + j(2,0) *= x[2]; + j(2,1) *= x[2]; + + j(2,2) = 3 * x[1] * x[0] * x[0]; + j(2,2) = 3 * x[1] * x[0] * x[0]; + } + } + } +}; + +template<typename Func> void adolc_forward_jacobian(const Func& f) +{ + typename Func::InputType x = Func::InputType::Random(f.inputs()); + typename Func::ValueType y(f.values()), yref(f.values()); + typename Func::JacobianType j(f.values(),f.inputs()), jref(f.values(),f.inputs()); + + jref.setZero(); + yref.setZero(); + f(x,&yref,&jref); +// std::cerr << y.transpose() << "\n\n";; +// std::cerr << j << "\n\n";; + + j.setZero(); + y.setZero(); + AdolcForwardJacobian<Func> autoj(f); + autoj(x, &y, &j); +// std::cerr << y.transpose() << "\n\n";; +// std::cerr << j << "\n\n";; + + VERIFY_IS_APPROX(y, yref); + VERIFY_IS_APPROX(j, jref); +} + +void test_forward_adolc() +{ + adtl::ADOLC_numDir = NUMBER_DIRECTIONS; + + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,2,2>()) )); + CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,2,3>()) )); + CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,3,2>()) )); + CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,3,3>()) )); + CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double>(3,3)) )); + } + + { + // simple instanciation tests + Matrix<adtl::adouble,2,1> x; + foo(x); + Matrix<adtl::adouble,Dynamic,Dynamic> A(4,4);; + A.selfadjointView<Lower>().eigenvalues(); + } +} diff --git a/unsupported/test/gmres.cpp b/unsupported/test/gmres.cpp new file mode 100644 index 000000000..647c16927 --- /dev/null +++ b/unsupported/test/gmres.cpp @@ -0,0 +1,33 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr> +// Copyright (C) 2012 Kolja Brix <brix@igpm.rwth-aaachen.de> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "../../test/sparse_solver.h" +#include <Eigen/IterativeSolvers> + +template<typename T> void test_gmres_T() +{ + GMRES<SparseMatrix<T>, DiagonalPreconditioner<T> > gmres_colmajor_diag; + GMRES<SparseMatrix<T>, IdentityPreconditioner > gmres_colmajor_I; + GMRES<SparseMatrix<T>, IncompleteLUT<T> > gmres_colmajor_ilut; + //GMRES<SparseMatrix<T>, SSORPreconditioner<T> > gmres_colmajor_ssor; + + CALL_SUBTEST( check_sparse_square_solving(gmres_colmajor_diag) ); +// CALL_SUBTEST( check_sparse_square_solving(gmres_colmajor_I) ); + CALL_SUBTEST( check_sparse_square_solving(gmres_colmajor_ilut) ); + //CALL_SUBTEST( check_sparse_square_solving(gmres_colmajor_ssor) ); +} + +void test_gmres() +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1(test_gmres_T<double>()); + CALL_SUBTEST_2(test_gmres_T<std::complex<double> >()); + } +} diff --git a/unsupported/test/kronecker_product.cpp b/unsupported/test/kronecker_product.cpp new file mode 100644 index 000000000..a60bd3022 --- /dev/null +++ b/unsupported/test/kronecker_product.cpp @@ -0,0 +1,179 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de> +// Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + + +#include "sparse.h" +#include <Eigen/SparseExtra> +#include <Eigen/KroneckerProduct> + + +template<typename MatrixType> +void check_dimension(const MatrixType& ab, const unsigned int rows, const unsigned int cols) +{ + VERIFY_IS_EQUAL(ab.rows(), rows); + VERIFY_IS_EQUAL(ab.cols(), cols); +} + + +template<typename MatrixType> +void check_kronecker_product(const MatrixType& ab) +{ + VERIFY_IS_EQUAL(ab.rows(), 6); + VERIFY_IS_EQUAL(ab.cols(), 6); + VERIFY_IS_EQUAL(ab.nonZeros(), 36); + VERIFY_IS_APPROX(ab.coeff(0,0), -0.4017367630386106); + VERIFY_IS_APPROX(ab.coeff(0,1), 0.1056863433932735); + VERIFY_IS_APPROX(ab.coeff(0,2), -0.7255206194554212); + VERIFY_IS_APPROX(ab.coeff(0,3), 0.1908653336744706); + VERIFY_IS_APPROX(ab.coeff(0,4), 0.350864567234111); + VERIFY_IS_APPROX(ab.coeff(0,5), -0.0923032108308013); + VERIFY_IS_APPROX(ab.coeff(1,0), 0.415417514804677); + VERIFY_IS_APPROX(ab.coeff(1,1), -0.2369227701722048); + VERIFY_IS_APPROX(ab.coeff(1,2), 0.7502275131458511); + VERIFY_IS_APPROX(ab.coeff(1,3), -0.4278731019742696); + VERIFY_IS_APPROX(ab.coeff(1,4), -0.3628129162264507); + VERIFY_IS_APPROX(ab.coeff(1,5), 0.2069210808481275); + VERIFY_IS_APPROX(ab.coeff(2,0), 0.05465890160863986); + VERIFY_IS_APPROX(ab.coeff(2,1), -0.2634092511419858); + VERIFY_IS_APPROX(ab.coeff(2,2), 0.09871180285793758); + VERIFY_IS_APPROX(ab.coeff(2,3), -0.4757066334017702); + VERIFY_IS_APPROX(ab.coeff(2,4), -0.04773740823058334); + VERIFY_IS_APPROX(ab.coeff(2,5), 0.2300535609645254); + VERIFY_IS_APPROX(ab.coeff(3,0), -0.8172945853260133); + VERIFY_IS_APPROX(ab.coeff(3,1), 0.2150086428359221); + VERIFY_IS_APPROX(ab.coeff(3,2), 0.5825113847292743); + VERIFY_IS_APPROX(ab.coeff(3,3), -0.1532433770097174); + VERIFY_IS_APPROX(ab.coeff(3,4), -0.329383387282399); + VERIFY_IS_APPROX(ab.coeff(3,5), 0.08665207912033064); + VERIFY_IS_APPROX(ab.coeff(4,0), 0.8451267514863225); + VERIFY_IS_APPROX(ab.coeff(4,1), -0.481996458918977); + VERIFY_IS_APPROX(ab.coeff(4,2), -0.6023482390791535); + VERIFY_IS_APPROX(ab.coeff(4,3), 0.3435339347164565); + VERIFY_IS_APPROX(ab.coeff(4,4), 0.3406002157428891); + VERIFY_IS_APPROX(ab.coeff(4,5), -0.1942526344200915); + VERIFY_IS_APPROX(ab.coeff(5,0), 0.1111982482925399); + VERIFY_IS_APPROX(ab.coeff(5,1), -0.5358806424754169); + VERIFY_IS_APPROX(ab.coeff(5,2), -0.07925446559335647); + VERIFY_IS_APPROX(ab.coeff(5,3), 0.3819388757769038); + VERIFY_IS_APPROX(ab.coeff(5,4), 0.04481475387219876); + VERIFY_IS_APPROX(ab.coeff(5,5), -0.2159688616158057); +} + + +template<typename MatrixType> +void check_sparse_kronecker_product(const MatrixType& ab) +{ + VERIFY_IS_EQUAL(ab.rows(), 12); + VERIFY_IS_EQUAL(ab.cols(), 10); + VERIFY_IS_EQUAL(ab.nonZeros(), 3*2); + VERIFY_IS_APPROX(ab.coeff(3,0), -0.04); + VERIFY_IS_APPROX(ab.coeff(5,1), 0.05); + VERIFY_IS_APPROX(ab.coeff(0,6), -0.08); + VERIFY_IS_APPROX(ab.coeff(2,7), 0.10); + VERIFY_IS_APPROX(ab.coeff(6,8), 0.12); + VERIFY_IS_APPROX(ab.coeff(8,9), -0.15); +} + + +void test_kronecker_product() +{ + // DM = dense matrix; SM = sparse matrix + Matrix<double, 2, 3> DM_a; + MatrixXd DM_b(3,2); + SparseMatrix<double> SM_a(2,3); + SparseMatrix<double> SM_b(3,2); + SM_a.insert(0,0) = DM_a(0,0) = -0.4461540300782201; + SM_a.insert(0,1) = DM_a(0,1) = -0.8057364375283049; + SM_a.insert(0,2) = DM_a(0,2) = 0.3896572459516341; + SM_a.insert(1,0) = DM_a(1,0) = -0.9076572187376921; + SM_a.insert(1,1) = DM_a(1,1) = 0.6469156566545853; + SM_a.insert(1,2) = DM_a(1,2) = -0.3658010398782789; + SM_b.insert(0,0) = DM_b(0,0) = 0.9004440976767099; + SM_b.insert(0,1) = DM_b(0,1) = -0.2368830858139832; + SM_b.insert(1,0) = DM_b(1,0) = -0.9311078389941825; + SM_b.insert(1,1) = DM_b(1,1) = 0.5310335762980047; + SM_b.insert(2,0) = DM_b(2,0) = -0.1225112806872035; + SM_b.insert(2,1) = DM_b(2,1) = 0.5903998022741264; + SparseMatrix<double,RowMajor> SM_row_a(SM_a), SM_row_b(SM_b); + + // test kroneckerProduct(DM_block,DM,DM_fixedSize) + Matrix<double, 6, 6> DM_fix_ab; + DM_fix_ab(0,0)=37.0; + kroneckerProduct(DM_a.block(0,0,2,3),DM_b,DM_fix_ab); + CALL_SUBTEST(check_kronecker_product(DM_fix_ab)); + + // test kroneckerProduct(DM,DM,DM_block) + MatrixXd DM_block_ab(10,15); + DM_block_ab(0,0)=37.0; + kroneckerProduct(DM_a,DM_b,DM_block_ab.block(2,5,6,6)); + CALL_SUBTEST(check_kronecker_product(DM_block_ab.block(2,5,6,6))); + + // test kroneckerProduct(DM,DM,DM) + MatrixXd DM_ab(1,5); + DM_ab(0,0)=37.0; + kroneckerProduct(DM_a,DM_b,DM_ab); + CALL_SUBTEST(check_kronecker_product(DM_ab)); + + // test kroneckerProduct(SM,DM,SM) + SparseMatrix<double> SM_ab(1,20); + SM_ab.insert(0,0)=37.0; + kroneckerProduct(SM_a,DM_b,SM_ab); + CALL_SUBTEST(check_kronecker_product(SM_ab)); + SparseMatrix<double,RowMajor> SM_ab2(10,3); + SM_ab2.insert(0,0)=37.0; + kroneckerProduct(SM_a,DM_b,SM_ab2); + CALL_SUBTEST(check_kronecker_product(SM_ab2)); + + // test kroneckerProduct(DM,SM,SM) + SM_ab.insert(0,0)=37.0; + kroneckerProduct(DM_a,SM_b,SM_ab); + CALL_SUBTEST(check_kronecker_product(SM_ab)); + SM_ab2.insert(0,0)=37.0; + kroneckerProduct(DM_a,SM_b,SM_ab2); + CALL_SUBTEST(check_kronecker_product(SM_ab2)); + + // test kroneckerProduct(SM,SM,SM) + SM_ab.resize(2,33); + SM_ab.insert(0,0)=37.0; + kroneckerProduct(SM_a,SM_b,SM_ab); + CALL_SUBTEST(check_kronecker_product(SM_ab)); + SM_ab2.resize(5,11); + SM_ab2.insert(0,0)=37.0; + kroneckerProduct(SM_a,SM_b,SM_ab2); + CALL_SUBTEST(check_kronecker_product(SM_ab2)); + + // test kroneckerProduct(SM,SM,SM) with sparse pattern + SM_a.resize(4,5); + SM_b.resize(3,2); + SM_a.resizeNonZeros(0); + SM_b.resizeNonZeros(0); + SM_a.insert(1,0) = -0.1; + SM_a.insert(0,3) = -0.2; + SM_a.insert(2,4) = 0.3; + SM_a.finalize(); + SM_b.insert(0,0) = 0.4; + SM_b.insert(2,1) = -0.5; + SM_b.finalize(); + SM_ab.resize(1,1); + SM_ab.insert(0,0)=37.0; + kroneckerProduct(SM_a,SM_b,SM_ab); + CALL_SUBTEST(check_sparse_kronecker_product(SM_ab)); + + // test dimension of result of kroneckerProduct(DM,DM,DM) + MatrixXd DM_a2(2,1); + MatrixXd DM_b2(5,4); + MatrixXd DM_ab2; + kroneckerProduct(DM_a2,DM_b2,DM_ab2); + CALL_SUBTEST(check_dimension(DM_ab2,2*5,1*4)); + DM_a2.resize(10,9); + DM_b2.resize(4,8); + kroneckerProduct(DM_a2,DM_b2,DM_ab2); + CALL_SUBTEST(check_dimension(DM_ab2,10*4,9*8)); +} diff --git a/unsupported/test/matrix_exponential.cpp b/unsupported/test/matrix_exponential.cpp new file mode 100644 index 000000000..695472f91 --- /dev/null +++ b/unsupported/test/matrix_exponential.cpp @@ -0,0 +1,149 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include <unsupported/Eigen/MatrixFunctions> + +double binom(int n, int k) +{ + double res = 1; + for (int i=0; i<k; i++) + res = res * (n-k+i+1) / (i+1); + return res; +} + +template <typename Derived, typename OtherDerived> +double relerr(const MatrixBase<Derived>& A, const MatrixBase<OtherDerived>& B) +{ + return std::sqrt((A - B).cwiseAbs2().sum() / (std::min)(A.cwiseAbs2().sum(), B.cwiseAbs2().sum())); +} + +template <typename T> +T expfn(T x, int) +{ + return std::exp(x); +} + +template <typename T> +void test2dRotation(double tol) +{ + Matrix<T,2,2> A, B, C; + T angle; + + A << 0, 1, -1, 0; + for (int i=0; i<=20; i++) + { + angle = static_cast<T>(pow(10, i / 5. - 2)); + B << std::cos(angle), std::sin(angle), -std::sin(angle), std::cos(angle); + + C = (angle*A).matrixFunction(expfn); + std::cout << "test2dRotation: i = " << i << " error funm = " << relerr(C, B); + VERIFY(C.isApprox(B, static_cast<T>(tol))); + + C = (angle*A).exp(); + std::cout << " error expm = " << relerr(C, B) << "\n"; + VERIFY(C.isApprox(B, static_cast<T>(tol))); + } +} + +template <typename T> +void test2dHyperbolicRotation(double tol) +{ + Matrix<std::complex<T>,2,2> A, B, C; + std::complex<T> imagUnit(0,1); + T angle, ch, sh; + + for (int i=0; i<=20; i++) + { + angle = static_cast<T>((i-10) / 2.0); + ch = std::cosh(angle); + sh = std::sinh(angle); + A << 0, angle*imagUnit, -angle*imagUnit, 0; + B << ch, sh*imagUnit, -sh*imagUnit, ch; + + C = A.matrixFunction(expfn); + std::cout << "test2dHyperbolicRotation: i = " << i << " error funm = " << relerr(C, B); + VERIFY(C.isApprox(B, static_cast<T>(tol))); + + C = A.exp(); + std::cout << " error expm = " << relerr(C, B) << "\n"; + VERIFY(C.isApprox(B, static_cast<T>(tol))); + } +} + +template <typename T> +void testPascal(double tol) +{ + for (int size=1; size<20; size++) + { + Matrix<T,Dynamic,Dynamic> A(size,size), B(size,size), C(size,size); + A.setZero(); + for (int i=0; i<size-1; i++) + A(i+1,i) = static_cast<T>(i+1); + B.setZero(); + for (int i=0; i<size; i++) + for (int j=0; j<=i; j++) + B(i,j) = static_cast<T>(binom(i,j)); + + C = A.matrixFunction(expfn); + std::cout << "testPascal: size = " << size << " error funm = " << relerr(C, B); + VERIFY(C.isApprox(B, static_cast<T>(tol))); + + C = A.exp(); + std::cout << " error expm = " << relerr(C, B) << "\n"; + VERIFY(C.isApprox(B, static_cast<T>(tol))); + } +} + +template<typename MatrixType> +void randomTest(const MatrixType& m, double tol) +{ + /* this test covers the following files: + Inverse.h + */ + typename MatrixType::Index rows = m.rows(); + typename MatrixType::Index cols = m.cols(); + MatrixType m1(rows, cols), m2(rows, cols), m3(rows, cols), + identity = MatrixType::Identity(rows, rows); + + typedef typename NumTraits<typename internal::traits<MatrixType>::Scalar>::Real RealScalar; + + for(int i = 0; i < g_repeat; i++) { + m1 = MatrixType::Random(rows, cols); + + m2 = m1.matrixFunction(expfn) * (-m1).matrixFunction(expfn); + std::cout << "randomTest: error funm = " << relerr(identity, m2); + VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol))); + + m2 = m1.exp() * (-m1).exp(); + std::cout << " error expm = " << relerr(identity, m2) << "\n"; + VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol))); + } +} + +void test_matrix_exponential() +{ + CALL_SUBTEST_2(test2dRotation<double>(1e-13)); + CALL_SUBTEST_1(test2dRotation<float>(2e-5)); // was 1e-5, relaxed for clang 2.8 / linux / x86-64 + CALL_SUBTEST_8(test2dRotation<long double>(1e-13)); + CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14)); + CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5)); + CALL_SUBTEST_8(test2dHyperbolicRotation<long double>(1e-14)); + CALL_SUBTEST_6(testPascal<float>(1e-6)); + CALL_SUBTEST_5(testPascal<double>(1e-15)); + CALL_SUBTEST_2(randomTest(Matrix2d(), 1e-13)); + CALL_SUBTEST_7(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13)); + CALL_SUBTEST_3(randomTest(Matrix4cd(), 1e-13)); + CALL_SUBTEST_4(randomTest(MatrixXd(8,8), 1e-13)); + CALL_SUBTEST_1(randomTest(Matrix2f(), 1e-4)); + CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4)); + CALL_SUBTEST_1(randomTest(Matrix4f(), 1e-4)); + CALL_SUBTEST_6(randomTest(MatrixXf(8,8), 1e-4)); + CALL_SUBTEST_9(randomTest(Matrix<long double,Dynamic,Dynamic>(7,7), 1e-13)); +} diff --git a/unsupported/test/matrix_function.cpp b/unsupported/test/matrix_function.cpp new file mode 100644 index 000000000..0439c5a7d --- /dev/null +++ b/unsupported/test/matrix_function.cpp @@ -0,0 +1,194 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include <unsupported/Eigen/MatrixFunctions> + +// Variant of VERIFY_IS_APPROX which uses absolute error instead of +// relative error. +#define VERIFY_IS_APPROX_ABS(a, b) VERIFY(test_isApprox_abs(a, b)) + +template<typename Type1, typename Type2> +inline bool test_isApprox_abs(const Type1& a, const Type2& b) +{ + return ((a-b).array().abs() < test_precision<typename Type1::RealScalar>()).all(); +} + + +// Returns a matrix with eigenvalues clustered around 0, 1 and 2. +template<typename MatrixType> +MatrixType randomMatrixWithRealEivals(const typename MatrixType::Index size) +{ + typedef typename MatrixType::Index Index; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + MatrixType diag = MatrixType::Zero(size, size); + for (Index i = 0; i < size; ++i) { + diag(i, i) = Scalar(RealScalar(internal::random<int>(0,2))) + + internal::random<Scalar>() * Scalar(RealScalar(0.01)); + } + MatrixType A = MatrixType::Random(size, size); + HouseholderQR<MatrixType> QRofA(A); + return QRofA.householderQ().inverse() * diag * QRofA.householderQ(); +} + +template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex> +struct randomMatrixWithImagEivals +{ + // Returns a matrix with eigenvalues clustered around 0 and +/- i. + static MatrixType run(const typename MatrixType::Index size); +}; + +// Partial specialization for real matrices +template<typename MatrixType> +struct randomMatrixWithImagEivals<MatrixType, 0> +{ + static MatrixType run(const typename MatrixType::Index size) + { + typedef typename MatrixType::Index Index; + typedef typename MatrixType::Scalar Scalar; + MatrixType diag = MatrixType::Zero(size, size); + Index i = 0; + while (i < size) { + Index randomInt = internal::random<Index>(-1, 1); + if (randomInt == 0 || i == size-1) { + diag(i, i) = internal::random<Scalar>() * Scalar(0.01); + ++i; + } else { + Scalar alpha = Scalar(randomInt) + internal::random<Scalar>() * Scalar(0.01); + diag(i, i+1) = alpha; + diag(i+1, i) = -alpha; + i += 2; + } + } + MatrixType A = MatrixType::Random(size, size); + HouseholderQR<MatrixType> QRofA(A); + return QRofA.householderQ().inverse() * diag * QRofA.householderQ(); + } +}; + +// Partial specialization for complex matrices +template<typename MatrixType> +struct randomMatrixWithImagEivals<MatrixType, 1> +{ + static MatrixType run(const typename MatrixType::Index size) + { + typedef typename MatrixType::Index Index; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + const Scalar imagUnit(0, 1); + MatrixType diag = MatrixType::Zero(size, size); + for (Index i = 0; i < size; ++i) { + diag(i, i) = Scalar(RealScalar(internal::random<Index>(-1, 1))) * imagUnit + + internal::random<Scalar>() * Scalar(RealScalar(0.01)); + } + MatrixType A = MatrixType::Random(size, size); + HouseholderQR<MatrixType> QRofA(A); + return QRofA.householderQ().inverse() * diag * QRofA.householderQ(); + } +}; + + +template<typename MatrixType> +void testMatrixExponential(const MatrixType& A) +{ + typedef typename internal::traits<MatrixType>::Scalar Scalar; + typedef typename NumTraits<Scalar>::Real RealScalar; + typedef std::complex<RealScalar> ComplexScalar; + + VERIFY_IS_APPROX(A.exp(), A.matrixFunction(StdStemFunctions<ComplexScalar>::exp)); +} + +template<typename MatrixType> +void testMatrixLogarithm(const MatrixType& A) +{ + typedef typename internal::traits<MatrixType>::Scalar Scalar; + typedef typename NumTraits<Scalar>::Real RealScalar; + typedef std::complex<RealScalar> ComplexScalar; + + MatrixType scaledA; + RealScalar maxImagPartOfSpectrum = A.eigenvalues().imag().cwiseAbs().maxCoeff(); + if (maxImagPartOfSpectrum >= 0.9 * M_PI) + scaledA = A * 0.9 * M_PI / maxImagPartOfSpectrum; + else + scaledA = A; + + // identity X.exp().log() = X only holds if Im(lambda) < pi for all eigenvalues of X + MatrixType expA = scaledA.exp(); + MatrixType logExpA = expA.log(); + VERIFY_IS_APPROX(logExpA, scaledA); +} + +template<typename MatrixType> +void testHyperbolicFunctions(const MatrixType& A) +{ + // Need to use absolute error because of possible cancellation when + // adding/subtracting expA and expmA. + VERIFY_IS_APPROX_ABS(A.sinh(), (A.exp() - (-A).exp()) / 2); + VERIFY_IS_APPROX_ABS(A.cosh(), (A.exp() + (-A).exp()) / 2); +} + +template<typename MatrixType> +void testGonioFunctions(const MatrixType& A) +{ + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits<Scalar>::Real RealScalar; + typedef std::complex<RealScalar> ComplexScalar; + typedef Matrix<ComplexScalar, MatrixType::RowsAtCompileTime, + MatrixType::ColsAtCompileTime, MatrixType::Options> ComplexMatrix; + + ComplexScalar imagUnit(0,1); + ComplexScalar two(2,0); + + ComplexMatrix Ac = A.template cast<ComplexScalar>(); + + ComplexMatrix exp_iA = (imagUnit * Ac).exp(); + ComplexMatrix exp_miA = (-imagUnit * Ac).exp(); + + ComplexMatrix sinAc = A.sin().template cast<ComplexScalar>(); + VERIFY_IS_APPROX_ABS(sinAc, (exp_iA - exp_miA) / (two*imagUnit)); + + ComplexMatrix cosAc = A.cos().template cast<ComplexScalar>(); + VERIFY_IS_APPROX_ABS(cosAc, (exp_iA + exp_miA) / 2); +} + +template<typename MatrixType> +void testMatrix(const MatrixType& A) +{ + testMatrixExponential(A); + testMatrixLogarithm(A); + testHyperbolicFunctions(A); + testGonioFunctions(A); +} + +template<typename MatrixType> +void testMatrixType(const MatrixType& m) +{ + // Matrices with clustered eigenvalue lead to different code paths + // in MatrixFunction.h and are thus useful for testing. + typedef typename MatrixType::Index Index; + + const Index size = m.rows(); + for (int i = 0; i < g_repeat; i++) { + testMatrix(MatrixType::Random(size, size).eval()); + testMatrix(randomMatrixWithRealEivals<MatrixType>(size)); + testMatrix(randomMatrixWithImagEivals<MatrixType>::run(size)); + } +} + +void test_matrix_function() +{ + CALL_SUBTEST_1(testMatrixType(Matrix<float,1,1>())); + CALL_SUBTEST_2(testMatrixType(Matrix3cf())); + CALL_SUBTEST_3(testMatrixType(MatrixXf(8,8))); + CALL_SUBTEST_4(testMatrixType(Matrix2d())); + CALL_SUBTEST_5(testMatrixType(Matrix<double,5,5,RowMajor>())); + CALL_SUBTEST_6(testMatrixType(Matrix4cd())); + CALL_SUBTEST_7(testMatrixType(MatrixXd(13,13))); +} diff --git a/unsupported/test/matrix_square_root.cpp b/unsupported/test/matrix_square_root.cpp new file mode 100644 index 000000000..508619a7a --- /dev/null +++ b/unsupported/test/matrix_square_root.cpp @@ -0,0 +1,62 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Jitse Niesen <jitse@maths.leeds.ac.uk> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include <unsupported/Eigen/MatrixFunctions> + +template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex> +struct generateTestMatrix; + +// for real matrices, make sure none of the eigenvalues are negative +template <typename MatrixType> +struct generateTestMatrix<MatrixType,0> +{ + static void run(MatrixType& result, typename MatrixType::Index size) + { + MatrixType mat = MatrixType::Random(size, size); + EigenSolver<MatrixType> es(mat); + typename EigenSolver<MatrixType>::EigenvalueType eivals = es.eigenvalues(); + for (typename MatrixType::Index i = 0; i < size; ++i) { + if (eivals(i).imag() == 0 && eivals(i).real() < 0) + eivals(i) = -eivals(i); + } + result = (es.eigenvectors() * eivals.asDiagonal() * es.eigenvectors().inverse()).real(); + } +}; + +// for complex matrices, any matrix is fine +template <typename MatrixType> +struct generateTestMatrix<MatrixType,1> +{ + static void run(MatrixType& result, typename MatrixType::Index size) + { + result = MatrixType::Random(size, size); + } +}; + +template<typename MatrixType> +void testMatrixSqrt(const MatrixType& m) +{ + MatrixType A; + generateTestMatrix<MatrixType>::run(A, m.rows()); + MatrixType sqrtA = A.sqrt(); + VERIFY_IS_APPROX(sqrtA * sqrtA, A); +} + +void test_matrix_square_root() +{ + for (int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1(testMatrixSqrt(Matrix3cf())); + CALL_SUBTEST_2(testMatrixSqrt(MatrixXcd(12,12))); + CALL_SUBTEST_3(testMatrixSqrt(Matrix4f())); + CALL_SUBTEST_4(testMatrixSqrt(Matrix<double,Dynamic,Dynamic,RowMajor>(9, 9))); + CALL_SUBTEST_5(testMatrixSqrt(Matrix<float,1,1>())); + CALL_SUBTEST_5(testMatrixSqrt(Matrix<std::complex<float>,1,1>())); + } +} diff --git a/unsupported/test/mpreal/dlmalloc.c b/unsupported/test/mpreal/dlmalloc.c new file mode 100755 index 000000000..7ce8feb07 --- /dev/null +++ b/unsupported/test/mpreal/dlmalloc.c @@ -0,0 +1,5703 @@ +/*
+ This is a version (aka dlmalloc) of malloc/free/realloc written by
+ Doug Lea and released to the public domain, as explained at
+ http://creativecommons.org/licenses/publicdomain. Send questions,
+ comments, complaints, performance data, etc to dl@cs.oswego.edu
+
+* Version 2.8.4 Wed May 27 09:56:23 2009 Doug Lea (dl at gee)
+
+ Note: There may be an updated version of this malloc obtainable at
+ ftp://gee.cs.oswego.edu/pub/misc/malloc.c
+ Check before installing!
+
+* Quickstart
+
+ This library is all in one file to simplify the most common usage:
+ ftp it, compile it (-O3), and link it into another program. All of
+ the compile-time options default to reasonable values for use on
+ most platforms. You might later want to step through various
+ compile-time and dynamic tuning options.
+
+ For convenience, an include file for code using this malloc is at:
+ ftp://gee.cs.oswego.edu/pub/misc/malloc-2.8.4.h
+ You don't really need this .h file unless you call functions not
+ defined in your system include files. The .h file contains only the
+ excerpts from this file needed for using this malloc on ANSI C/C++
+ systems, so long as you haven't changed compile-time options about
+ naming and tuning parameters. If you do, then you can create your
+ own malloc.h that does include all settings by cutting at the point
+ indicated below. Note that you may already by default be using a C
+ library containing a malloc that is based on some version of this
+ malloc (for example in linux). You might still want to use the one
+ in this file to customize settings or to avoid overheads associated
+ with library versions.
+
+* Vital statistics:
+
+ Supported pointer/size_t representation: 4 or 8 bytes
+ size_t MUST be an unsigned type of the same width as
+ pointers. (If you are using an ancient system that declares
+ size_t as a signed type, or need it to be a different width
+ than pointers, you can use a previous release of this malloc
+ (e.g. 2.7.2) supporting these.)
+
+ Alignment: 8 bytes (default)
+ This suffices for nearly all current machines and C compilers.
+ However, you can define MALLOC_ALIGNMENT to be wider than this
+ if necessary (up to 128bytes), at the expense of using more space.
+
+ Minimum overhead per allocated chunk: 4 or 8 bytes (if 4byte sizes)
+ 8 or 16 bytes (if 8byte sizes)
+ Each malloced chunk has a hidden word of overhead holding size
+ and status information, and additional cross-check word
+ if FOOTERS is defined.
+
+ Minimum allocated size: 4-byte ptrs: 16 bytes (including overhead)
+ 8-byte ptrs: 32 bytes (including overhead)
+
+ Even a request for zero bytes (i.e., malloc(0)) returns a
+ pointer to something of the minimum allocatable size.
+ The maximum overhead wastage (i.e., number of extra bytes
+ allocated than were requested in malloc) is less than or equal
+ to the minimum size, except for requests >= mmap_threshold that
+ are serviced via mmap(), where the worst case wastage is about
+ 32 bytes plus the remainder from a system page (the minimal
+ mmap unit); typically 4096 or 8192 bytes.
+
+ Security: static-safe; optionally more or less
+ The "security" of malloc refers to the ability of malicious
+ code to accentuate the effects of errors (for example, freeing
+ space that is not currently malloc'ed or overwriting past the
+ ends of chunks) in code that calls malloc. This malloc
+ guarantees not to modify any memory locations below the base of
+ heap, i.e., static variables, even in the presence of usage
+ errors. The routines additionally detect most improper frees
+ and reallocs. All this holds as long as the static bookkeeping
+ for malloc itself is not corrupted by some other means. This
+ is only one aspect of security -- these checks do not, and
+ cannot, detect all possible programming errors.
+
+ If FOOTERS is defined nonzero, then each allocated chunk
+ carries an additional check word to verify that it was malloced
+ from its space. These check words are the same within each
+ execution of a program using malloc, but differ across
+ executions, so externally crafted fake chunks cannot be
+ freed. This improves security by rejecting frees/reallocs that
+ could corrupt heap memory, in addition to the checks preventing
+ writes to statics that are always on. This may further improve
+ security at the expense of time and space overhead. (Note that
+ FOOTERS may also be worth using with MSPACES.)
+
+ By default detected errors cause the program to abort (calling
+ "abort()"). You can override this to instead proceed past
+ errors by defining PROCEED_ON_ERROR. In this case, a bad free
+ has no effect, and a malloc that encounters a bad address
+ caused by user overwrites will ignore the bad address by
+ dropping pointers and indices to all known memory. This may
+ be appropriate for programs that should continue if at all
+ possible in the face of programming errors, although they may
+ run out of memory because dropped memory is never reclaimed.
+
+ If you don't like either of these options, you can define
+ CORRUPTION_ERROR_ACTION and USAGE_ERROR_ACTION to do anything
+ else. And if if you are sure that your program using malloc has
+ no errors or vulnerabilities, you can define INSECURE to 1,
+ which might (or might not) provide a small performance improvement.
+
+ Thread-safety: NOT thread-safe unless USE_LOCKS defined
+ When USE_LOCKS is defined, each public call to malloc, free,
+ etc is surrounded with either a pthread mutex or a win32
+ spinlock (depending on WIN32). This is not especially fast, and
+ can be a major bottleneck. It is designed only to provide
+ minimal protection in concurrent environments, and to provide a
+ basis for extensions. If you are using malloc in a concurrent
+ program, consider instead using nedmalloc
+ (http://www.nedprod.com/programs/portable/nedmalloc/) or
+ ptmalloc (See http://www.malloc.de), which are derived
+ from versions of this malloc.
+
+ System requirements: Any combination of MORECORE and/or MMAP/MUNMAP
+ This malloc can use unix sbrk or any emulation (invoked using
+ the CALL_MORECORE macro) and/or mmap/munmap or any emulation
+ (invoked using CALL_MMAP/CALL_MUNMAP) to get and release system
+ memory. On most unix systems, it tends to work best if both
+ MORECORE and MMAP are enabled. On Win32, it uses emulations
+ based on VirtualAlloc. It also uses common C library functions
+ like memset.
+
+ Compliance: I believe it is compliant with the Single Unix Specification
+ (See http://www.unix.org). Also SVID/XPG, ANSI C, and probably
+ others as well.
+
+* Overview of algorithms
+
+ This is not the fastest, most space-conserving, most portable, or
+ most tunable malloc ever written. However it is among the fastest
+ while also being among the most space-conserving, portable and
+ tunable. Consistent balance across these factors results in a good
+ general-purpose allocator for malloc-intensive programs.
+
+ In most ways, this malloc is a best-fit allocator. Generally, it
+ chooses the best-fitting existing chunk for a request, with ties
+ broken in approximately least-recently-used order. (This strategy
+ normally maintains low fragmentation.) However, for requests less
+ than 256bytes, it deviates from best-fit when there is not an
+ exactly fitting available chunk by preferring to use space adjacent
+ to that used for the previous small request, as well as by breaking
+ ties in approximately most-recently-used order. (These enhance
+ locality of series of small allocations.) And for very large requests
+ (>= 256Kb by default), it relies on system memory mapping
+ facilities, if supported. (This helps avoid carrying around and
+ possibly fragmenting memory used only for large chunks.)
+
+ All operations (except malloc_stats and mallinfo) have execution
+ times that are bounded by a constant factor of the number of bits in
+ a size_t, not counting any clearing in calloc or copying in realloc,
+ or actions surrounding MORECORE and MMAP that have times
+ proportional to the number of non-contiguous regions returned by
+ system allocation routines, which is often just 1. In real-time
+ applications, you can optionally suppress segment traversals using
+ NO_SEGMENT_TRAVERSAL, which assures bounded execution even when
+ system allocators return non-contiguous spaces, at the typical
+ expense of carrying around more memory and increased fragmentation.
+
+ The implementation is not very modular and seriously overuses
+ macros. Perhaps someday all C compilers will do as good a job
+ inlining modular code as can now be done by brute-force expansion,
+ but now, enough of them seem not to.
+
+ Some compilers issue a lot of warnings about code that is
+ dead/unreachable only on some platforms, and also about intentional
+ uses of negation on unsigned types. All known cases of each can be
+ ignored.
+
+ For a longer but out of date high-level description, see
+ http://gee.cs.oswego.edu/dl/html/malloc.html
+
+* MSPACES
+ If MSPACES is defined, then in addition to malloc, free, etc.,
+ this file also defines mspace_malloc, mspace_free, etc. These
+ are versions of malloc routines that take an "mspace" argument
+ obtained using create_mspace, to control all internal bookkeeping.
+ If ONLY_MSPACES is defined, only these versions are compiled.
+ So if you would like to use this allocator for only some allocations,
+ and your system malloc for others, you can compile with
+ ONLY_MSPACES and then do something like...
+ static mspace mymspace = create_mspace(0,0); // for example
+ #define mymalloc(bytes) mspace_malloc(mymspace, bytes)
+
+ (Note: If you only need one instance of an mspace, you can instead
+ use "USE_DL_PREFIX" to relabel the global malloc.)
+
+ You can similarly create thread-local allocators by storing
+ mspaces as thread-locals. For example:
+ static __thread mspace tlms = 0;
+ void* tlmalloc(size_t bytes) {
+ if (tlms == 0) tlms = create_mspace(0, 0);
+ return mspace_malloc(tlms, bytes);
+ }
+ void tlfree(void* mem) { mspace_free(tlms, mem); }
+
+ Unless FOOTERS is defined, each mspace is completely independent.
+ You cannot allocate from one and free to another (although
+ conformance is only weakly checked, so usage errors are not always
+ caught). If FOOTERS is defined, then each chunk carries around a tag
+ indicating its originating mspace, and frees are directed to their
+ originating spaces.
+
+ ------------------------- Compile-time options ---------------------------
+
+Be careful in setting #define values for numerical constants of type
+size_t. On some systems, literal values are not automatically extended
+to size_t precision unless they are explicitly casted. You can also
+use the symbolic values MAX_SIZE_T, SIZE_T_ONE, etc below.
+
+WIN32 default: defined if _WIN32 defined
+ Defining WIN32 sets up defaults for MS environment and compilers.
+ Otherwise defaults are for unix. Beware that there seem to be some
+ cases where this malloc might not be a pure drop-in replacement for
+ Win32 malloc: Random-looking failures from Win32 GDI API's (eg;
+ SetDIBits()) may be due to bugs in some video driver implementations
+ when pixel buffers are malloc()ed, and the region spans more than
+ one VirtualAlloc()ed region. Because dlmalloc uses a small (64Kb)
+ default granularity, pixel buffers may straddle virtual allocation
+ regions more often than when using the Microsoft allocator. You can
+ avoid this by using VirtualAlloc() and VirtualFree() for all pixel
+ buffers rather than using malloc(). If this is not possible,
+ recompile this malloc with a larger DEFAULT_GRANULARITY.
+
+MALLOC_ALIGNMENT default: (size_t)8
+ Controls the minimum alignment for malloc'ed chunks. It must be a
+ power of two and at least 8, even on machines for which smaller
+ alignments would suffice. It may be defined as larger than this
+ though. Note however that code and data structures are optimized for
+ the case of 8-byte alignment.
+
+MSPACES default: 0 (false)
+ If true, compile in support for independent allocation spaces.
+ This is only supported if HAVE_MMAP is true.
+
+ONLY_MSPACES default: 0 (false)
+ If true, only compile in mspace versions, not regular versions.
+
+USE_LOCKS default: 0 (false)
+ Causes each call to each public routine to be surrounded with
+ pthread or WIN32 mutex lock/unlock. (If set true, this can be
+ overridden on a per-mspace basis for mspace versions.) If set to a
+ non-zero value other than 1, locks are used, but their
+ implementation is left out, so lock functions must be supplied manually,
+ as described below.
+
+USE_SPIN_LOCKS default: 1 iff USE_LOCKS and on x86 using gcc or MSC
+ If true, uses custom spin locks for locking. This is currently
+ supported only for x86 platforms using gcc or recent MS compilers.
+ Otherwise, posix locks or win32 critical sections are used.
+
+FOOTERS default: 0
+ If true, provide extra checking and dispatching by placing
+ information in the footers of allocated chunks. This adds
+ space and time overhead.
+
+INSECURE default: 0
+ If true, omit checks for usage errors and heap space overwrites.
+
+USE_DL_PREFIX default: NOT defined
+ Causes compiler to prefix all public routines with the string 'dl'.
+ This can be useful when you only want to use this malloc in one part
+ of a program, using your regular system malloc elsewhere.
+
+ABORT default: defined as abort()
+ Defines how to abort on failed checks. On most systems, a failed
+ check cannot die with an "assert" or even print an informative
+ message, because the underlying print routines in turn call malloc,
+ which will fail again. Generally, the best policy is to simply call
+ abort(). It's not very useful to do more than this because many
+ errors due to overwriting will show up as address faults (null, odd
+ addresses etc) rather than malloc-triggered checks, so will also
+ abort. Also, most compilers know that abort() does not return, so
+ can better optimize code conditionally calling it.
+
+PROCEED_ON_ERROR default: defined as 0 (false)
+ Controls whether detected bad addresses cause them to bypassed
+ rather than aborting. If set, detected bad arguments to free and
+ realloc are ignored. And all bookkeeping information is zeroed out
+ upon a detected overwrite of freed heap space, thus losing the
+ ability to ever return it from malloc again, but enabling the
+ application to proceed. If PROCEED_ON_ERROR is defined, the
+ static variable malloc_corruption_error_count is compiled in
+ and can be examined to see if errors have occurred. This option
+ generates slower code than the default abort policy.
+
+DEBUG default: NOT defined
+ The DEBUG setting is mainly intended for people trying to modify
+ this code or diagnose problems when porting to new platforms.
+ However, it may also be able to better isolate user errors than just
+ using runtime checks. The assertions in the check routines spell
+ out in more detail the assumptions and invariants underlying the
+ algorithms. The checking is fairly extensive, and will slow down
+ execution noticeably. Calling malloc_stats or mallinfo with DEBUG
+ set will attempt to check every non-mmapped allocated and free chunk
+ in the course of computing the summaries.
+
+ABORT_ON_ASSERT_FAILURE default: defined as 1 (true)
+ Debugging assertion failures can be nearly impossible if your
+ version of the assert macro causes malloc to be called, which will
+ lead to a cascade of further failures, blowing the runtime stack.
+ ABORT_ON_ASSERT_FAILURE cause assertions failures to call abort(),
+ which will usually make debugging easier.
+
+MALLOC_FAILURE_ACTION default: sets errno to ENOMEM, or no-op on win32
+ The action to take before "return 0" when malloc fails to be able to
+ return memory because there is none available.
+
+HAVE_MORECORE default: 1 (true) unless win32 or ONLY_MSPACES
+ True if this system supports sbrk or an emulation of it.
+
+MORECORE default: sbrk
+ The name of the sbrk-style system routine to call to obtain more
+ memory. See below for guidance on writing custom MORECORE
+ functions. The type of the argument to sbrk/MORECORE varies across
+ systems. It cannot be size_t, because it supports negative
+ arguments, so it is normally the signed type of the same width as
+ size_t (sometimes declared as "intptr_t"). It doesn't much matter
+ though. Internally, we only call it with arguments less than half
+ the max value of a size_t, which should work across all reasonable
+ possibilities, although sometimes generating compiler warnings.
+
+MORECORE_CONTIGUOUS default: 1 (true) if HAVE_MORECORE
+ If true, take advantage of fact that consecutive calls to MORECORE
+ with positive arguments always return contiguous increasing
+ addresses. This is true of unix sbrk. It does not hurt too much to
+ set it true anyway, since malloc copes with non-contiguities.
+ Setting it false when definitely non-contiguous saves time
+ and possibly wasted space it would take to discover this though.
+
+MORECORE_CANNOT_TRIM default: NOT defined
+ True if MORECORE cannot release space back to the system when given
+ negative arguments. This is generally necessary only if you are
+ using a hand-crafted MORECORE function that cannot handle negative
+ arguments.
+
+NO_SEGMENT_TRAVERSAL default: 0
+ If non-zero, suppresses traversals of memory segments
+ returned by either MORECORE or CALL_MMAP. This disables
+ merging of segments that are contiguous, and selectively
+ releasing them to the OS if unused, but bounds execution times.
+
+HAVE_MMAP default: 1 (true)
+ True if this system supports mmap or an emulation of it. If so, and
+ HAVE_MORECORE is not true, MMAP is used for all system
+ allocation. If set and HAVE_MORECORE is true as well, MMAP is
+ primarily used to directly allocate very large blocks. It is also
+ used as a backup strategy in cases where MORECORE fails to provide
+ space from system. Note: A single call to MUNMAP is assumed to be
+ able to unmap memory that may have be allocated using multiple calls
+ to MMAP, so long as they are adjacent.
+
+HAVE_MREMAP default: 1 on linux, else 0
+ If true realloc() uses mremap() to re-allocate large blocks and
+ extend or shrink allocation spaces.
+
+MMAP_CLEARS default: 1 except on WINCE.
+ True if mmap clears memory so calloc doesn't need to. This is true
+ for standard unix mmap using /dev/zero and on WIN32 except for WINCE.
+
+USE_BUILTIN_FFS default: 0 (i.e., not used)
+ Causes malloc to use the builtin ffs() function to compute indices.
+ Some compilers may recognize and intrinsify ffs to be faster than the
+ supplied C version. Also, the case of x86 using gcc is special-cased
+ to an asm instruction, so is already as fast as it can be, and so
+ this setting has no effect. Similarly for Win32 under recent MS compilers.
+ (On most x86s, the asm version is only slightly faster than the C version.)
+
+malloc_getpagesize default: derive from system includes, or 4096.
+ The system page size. To the extent possible, this malloc manages
+ memory from the system in page-size units. This may be (and
+ usually is) a function rather than a constant. This is ignored
+ if WIN32, where page size is determined using getSystemInfo during
+ initialization.
+
+USE_DEV_RANDOM default: 0 (i.e., not used)
+ Causes malloc to use /dev/random to initialize secure magic seed for
+ stamping footers. Otherwise, the current time is used.
+
+NO_MALLINFO default: 0
+ If defined, don't compile "mallinfo". This can be a simple way
+ of dealing with mismatches between system declarations and
+ those in this file.
+
+MALLINFO_FIELD_TYPE default: size_t
+ The type of the fields in the mallinfo struct. This was originally
+ defined as "int" in SVID etc, but is more usefully defined as
+ size_t. The value is used only if HAVE_USR_INCLUDE_MALLOC_H is not set
+
+REALLOC_ZERO_BYTES_FREES default: not defined
+ This should be set if a call to realloc with zero bytes should
+ be the same as a call to free. Some people think it should. Otherwise,
+ since this malloc returns a unique pointer for malloc(0), so does
+ realloc(p, 0).
+
+LACKS_UNISTD_H, LACKS_FCNTL_H, LACKS_SYS_PARAM_H, LACKS_SYS_MMAN_H
+LACKS_STRINGS_H, LACKS_STRING_H, LACKS_SYS_TYPES_H, LACKS_ERRNO_H
+LACKS_STDLIB_H default: NOT defined unless on WIN32
+ Define these if your system does not have these header files.
+ You might need to manually insert some of the declarations they provide.
+
+DEFAULT_GRANULARITY default: page size if MORECORE_CONTIGUOUS,
+ system_info.dwAllocationGranularity in WIN32,
+ otherwise 64K.
+ Also settable using mallopt(M_GRANULARITY, x)
+ The unit for allocating and deallocating memory from the system. On
+ most systems with contiguous MORECORE, there is no reason to
+ make this more than a page. However, systems with MMAP tend to
+ either require or encourage larger granularities. You can increase
+ this value to prevent system allocation functions to be called so
+ often, especially if they are slow. The value must be at least one
+ page and must be a power of two. Setting to 0 causes initialization
+ to either page size or win32 region size. (Note: In previous
+ versions of malloc, the equivalent of this option was called
+ "TOP_PAD")
+
+DEFAULT_TRIM_THRESHOLD default: 2MB
+ Also settable using mallopt(M_TRIM_THRESHOLD, x)
+ The maximum amount of unused top-most memory to keep before
+ releasing via malloc_trim in free(). Automatic trimming is mainly
+ useful in long-lived programs using contiguous MORECORE. Because
+ trimming via sbrk can be slow on some systems, and can sometimes be
+ wasteful (in cases where programs immediately afterward allocate
+ more large chunks) the value should be high enough so that your
+ overall system performance would improve by releasing this much
+ memory. As a rough guide, you might set to a value close to the
+ average size of a process (program) running on your system.
+ Releasing this much memory would allow such a process to run in
+ memory. Generally, it is worth tuning trim thresholds when a
+ program undergoes phases where several large chunks are allocated
+ and released in ways that can reuse each other's storage, perhaps
+ mixed with phases where there are no such chunks at all. The trim
+ value must be greater than page size to have any useful effect. To
+ disable trimming completely, you can set to MAX_SIZE_T. Note that the trick
+ some people use of mallocing a huge space and then freeing it at
+ program startup, in an attempt to reserve system memory, doesn't
+ have the intended effect under automatic trimming, since that memory
+ will immediately be returned to the system.
+
+DEFAULT_MMAP_THRESHOLD default: 256K
+ Also settable using mallopt(M_MMAP_THRESHOLD, x)
+ The request size threshold for using MMAP to directly service a
+ request. Requests of at least this size that cannot be allocated
+ using already-existing space will be serviced via mmap. (If enough
+ normal freed space already exists it is used instead.) Using mmap
+ segregates relatively large chunks of memory so that they can be
+ individually obtained and released from the host system. A request
+ serviced through mmap is never reused by any other request (at least
+ not directly; the system may just so happen to remap successive
+ requests to the same locations). Segregating space in this way has
+ the benefits that: Mmapped space can always be individually released
+ back to the system, which helps keep the system level memory demands
+ of a long-lived program low. Also, mapped memory doesn't become
+ `locked' between other chunks, as can happen with normally allocated
+ chunks, which means that even trimming via malloc_trim would not
+ release them. However, it has the disadvantage that the space
+ cannot be reclaimed, consolidated, and then used to service later
+ requests, as happens with normal chunks. The advantages of mmap
+ nearly always outweigh disadvantages for "large" chunks, but the
+ value of "large" may vary across systems. The default is an
+ empirically derived value that works well in most systems. You can
+ disable mmap by setting to MAX_SIZE_T.
+
+MAX_RELEASE_CHECK_RATE default: 4095 unless not HAVE_MMAP
+ The number of consolidated frees between checks to release
+ unused segments when freeing. When using non-contiguous segments,
+ especially with multiple mspaces, checking only for topmost space
+ doesn't always suffice to trigger trimming. To compensate for this,
+ free() will, with a period of MAX_RELEASE_CHECK_RATE (or the
+ current number of segments, if greater) try to release unused
+ segments to the OS when freeing chunks that result in
+ consolidation. The best value for this parameter is a compromise
+ between slowing down frees with relatively costly checks that
+ rarely trigger versus holding on to unused memory. To effectively
+ disable, set to MAX_SIZE_T. This may lead to a very slight speed
+ improvement at the expense of carrying around more memory.
+*/
+
+#define USE_DL_PREFIX
+//#define HAVE_USR_INCLUDE_MALLOC_H
+//#define MSPACES 1
+#define NO_SEGMENT_TRAVERSAL 1
+
+/* Version identifier to allow people to support multiple versions */
+#ifndef DLMALLOC_VERSION
+#define DLMALLOC_VERSION 20804
+#endif /* DLMALLOC_VERSION */
+
+#ifndef WIN32
+#ifdef _WIN32
+#define WIN32 1
+#endif /* _WIN32 */
+#ifdef _WIN32_WCE
+#define LACKS_FCNTL_H
+#define WIN32 1
+#endif /* _WIN32_WCE */
+#endif /* WIN32 */
+#ifdef WIN32
+#define WIN32_LEAN_AND_MEAN
+#include <windows.h>
+#define HAVE_MMAP 1
+#define HAVE_MORECORE 0
+#define LACKS_UNISTD_H
+#define LACKS_SYS_PARAM_H
+#define LACKS_SYS_MMAN_H
+#define LACKS_STRING_H
+#define LACKS_STRINGS_H
+#define LACKS_SYS_TYPES_H
+#define LACKS_ERRNO_H
+#ifndef MALLOC_FAILURE_ACTION
+#define MALLOC_FAILURE_ACTION
+#endif /* MALLOC_FAILURE_ACTION */
+#ifdef _WIN32_WCE /* WINCE reportedly does not clear */
+#define MMAP_CLEARS 0
+#else
+#define MMAP_CLEARS 1
+#endif /* _WIN32_WCE */
+#endif /* WIN32 */
+
+#if defined(DARWIN) || defined(_DARWIN)
+/* Mac OSX docs advise not to use sbrk; it seems better to use mmap */
+#ifndef HAVE_MORECORE
+#define HAVE_MORECORE 0
+#define HAVE_MMAP 1
+/* OSX allocators provide 16 byte alignment */
+#ifndef MALLOC_ALIGNMENT
+#define MALLOC_ALIGNMENT ((size_t)16U)
+#endif
+#endif /* HAVE_MORECORE */
+#endif /* DARWIN */
+
+#ifndef LACKS_SYS_TYPES_H
+#include <sys/types.h> /* For size_t */
+#endif /* LACKS_SYS_TYPES_H */
+
+#if (defined(__GNUC__) && ((defined(__i386__) || defined(__x86_64__)))) || (defined(_MSC_VER) && _MSC_VER>=1310)
+#define SPIN_LOCKS_AVAILABLE 1
+#else
+#define SPIN_LOCKS_AVAILABLE 0
+#endif
+
+/* The maximum possible size_t value has all bits set */
+#define MAX_SIZE_T (~(size_t)0)
+
+#ifndef ONLY_MSPACES
+#define ONLY_MSPACES 0 /* define to a value */
+#else
+#define ONLY_MSPACES 1
+#endif /* ONLY_MSPACES */
+#ifndef MSPACES
+#if ONLY_MSPACES
+#define MSPACES 1
+#else /* ONLY_MSPACES */
+#define MSPACES 0
+#endif /* ONLY_MSPACES */
+#endif /* MSPACES */
+#ifndef MALLOC_ALIGNMENT
+#define MALLOC_ALIGNMENT ((size_t)8U)
+#endif /* MALLOC_ALIGNMENT */
+#ifndef FOOTERS
+#define FOOTERS 0
+#endif /* FOOTERS */
+#ifndef ABORT
+#define ABORT abort()
+#endif /* ABORT */
+#ifndef ABORT_ON_ASSERT_FAILURE
+#define ABORT_ON_ASSERT_FAILURE 1
+#endif /* ABORT_ON_ASSERT_FAILURE */
+#ifndef PROCEED_ON_ERROR
+#define PROCEED_ON_ERROR 0
+#endif /* PROCEED_ON_ERROR */
+#ifndef USE_LOCKS
+#define USE_LOCKS 0
+#endif /* USE_LOCKS */
+#ifndef USE_SPIN_LOCKS
+#if USE_LOCKS && SPIN_LOCKS_AVAILABLE
+#define USE_SPIN_LOCKS 1
+#else
+#define USE_SPIN_LOCKS 0
+#endif /* USE_LOCKS && SPIN_LOCKS_AVAILABLE. */
+#endif /* USE_SPIN_LOCKS */
+#ifndef INSECURE
+#define INSECURE 0
+#endif /* INSECURE */
+#ifndef HAVE_MMAP
+#define HAVE_MMAP 1
+#endif /* HAVE_MMAP */
+#ifndef MMAP_CLEARS
+#define MMAP_CLEARS 1
+#endif /* MMAP_CLEARS */
+#ifndef HAVE_MREMAP
+#ifdef linux
+#define HAVE_MREMAP 1
+#else /* linux */
+#define HAVE_MREMAP 0
+#endif /* linux */
+#endif /* HAVE_MREMAP */
+#ifndef MALLOC_FAILURE_ACTION
+#define MALLOC_FAILURE_ACTION errno = ENOMEM;
+#endif /* MALLOC_FAILURE_ACTION */
+#ifndef HAVE_MORECORE
+#if ONLY_MSPACES
+#define HAVE_MORECORE 0
+#else /* ONLY_MSPACES */
+#define HAVE_MORECORE 1
+#endif /* ONLY_MSPACES */
+#endif /* HAVE_MORECORE */
+#if !HAVE_MORECORE
+#define MORECORE_CONTIGUOUS 0
+#else /* !HAVE_MORECORE */
+#define MORECORE_DEFAULT sbrk
+#ifndef MORECORE_CONTIGUOUS
+#define MORECORE_CONTIGUOUS 1
+#endif /* MORECORE_CONTIGUOUS */
+#endif /* HAVE_MORECORE */
+#ifndef DEFAULT_GRANULARITY
+#if (MORECORE_CONTIGUOUS || defined(WIN32))
+#define DEFAULT_GRANULARITY (0) /* 0 means to compute in init_mparams */
+#else /* MORECORE_CONTIGUOUS */
+#define DEFAULT_GRANULARITY ((size_t)64U * (size_t)1024U)
+#endif /* MORECORE_CONTIGUOUS */
+#endif /* DEFAULT_GRANULARITY */
+#ifndef DEFAULT_TRIM_THRESHOLD
+#ifndef MORECORE_CANNOT_TRIM
+#define DEFAULT_TRIM_THRESHOLD ((size_t)2U * (size_t)1024U * (size_t)1024U)
+#else /* MORECORE_CANNOT_TRIM */
+#define DEFAULT_TRIM_THRESHOLD MAX_SIZE_T
+#endif /* MORECORE_CANNOT_TRIM */
+#endif /* DEFAULT_TRIM_THRESHOLD */
+#ifndef DEFAULT_MMAP_THRESHOLD
+#if HAVE_MMAP
+#define DEFAULT_MMAP_THRESHOLD ((size_t)256U * (size_t)1024U)
+#else /* HAVE_MMAP */
+#define DEFAULT_MMAP_THRESHOLD MAX_SIZE_T
+#endif /* HAVE_MMAP */
+#endif /* DEFAULT_MMAP_THRESHOLD */
+#ifndef MAX_RELEASE_CHECK_RATE
+#if HAVE_MMAP
+#define MAX_RELEASE_CHECK_RATE 4095
+#else
+#define MAX_RELEASE_CHECK_RATE MAX_SIZE_T
+#endif /* HAVE_MMAP */
+#endif /* MAX_RELEASE_CHECK_RATE */
+#ifndef USE_BUILTIN_FFS
+#define USE_BUILTIN_FFS 0
+#endif /* USE_BUILTIN_FFS */
+#ifndef USE_DEV_RANDOM
+#define USE_DEV_RANDOM 0
+#endif /* USE_DEV_RANDOM */
+#ifndef NO_MALLINFO
+#define NO_MALLINFO 0
+#endif /* NO_MALLINFO */
+#ifndef MALLINFO_FIELD_TYPE
+#define MALLINFO_FIELD_TYPE size_t
+#endif /* MALLINFO_FIELD_TYPE */
+#ifndef NO_SEGMENT_TRAVERSAL
+#define NO_SEGMENT_TRAVERSAL 0
+#endif /* NO_SEGMENT_TRAVERSAL */
+
+/*
+ mallopt tuning options. SVID/XPG defines four standard parameter
+ numbers for mallopt, normally defined in malloc.h. None of these
+ are used in this malloc, so setting them has no effect. But this
+ malloc does support the following options.
+*/
+
+#define M_TRIM_THRESHOLD (-1)
+#define M_GRANULARITY (-2)
+#define M_MMAP_THRESHOLD (-3)
+
+/* ------------------------ Mallinfo declarations ------------------------ */
+
+#if !NO_MALLINFO
+/*
+ This version of malloc supports the standard SVID/XPG mallinfo
+ routine that returns a struct containing usage properties and
+ statistics. It should work on any system that has a
+ /usr/include/malloc.h defining struct mallinfo. The main
+ declaration needed is the mallinfo struct that is returned (by-copy)
+ by mallinfo(). The malloinfo struct contains a bunch of fields that
+ are not even meaningful in this version of malloc. These fields are
+ are instead filled by mallinfo() with other numbers that might be of
+ interest.
+
+ HAVE_USR_INCLUDE_MALLOC_H should be set if you have a
+ /usr/include/malloc.h file that includes a declaration of struct
+ mallinfo. If so, it is included; else a compliant version is
+ declared below. These must be precisely the same for mallinfo() to
+ work. The original SVID version of this struct, defined on most
+ systems with mallinfo, declares all fields as ints. But some others
+ define as unsigned long. If your system defines the fields using a
+ type of different width than listed here, you MUST #include your
+ system version and #define HAVE_USR_INCLUDE_MALLOC_H.
+*/
+
+/* #define HAVE_USR_INCLUDE_MALLOC_H */
+
+#ifdef HAVE_USR_INCLUDE_MALLOC_H
+#include "/usr/include/malloc.h"
+#else /* HAVE_USR_INCLUDE_MALLOC_H */
+#ifndef STRUCT_MALLINFO_DECLARED
+#define STRUCT_MALLINFO_DECLARED 1
+struct mallinfo {
+ MALLINFO_FIELD_TYPE arena; /* non-mmapped space allocated from system */
+ MALLINFO_FIELD_TYPE ordblks; /* number of free chunks */
+ MALLINFO_FIELD_TYPE smblks; /* always 0 */
+ MALLINFO_FIELD_TYPE hblks; /* always 0 */
+ MALLINFO_FIELD_TYPE hblkhd; /* space in mmapped regions */
+ MALLINFO_FIELD_TYPE usmblks; /* maximum total allocated space */
+ MALLINFO_FIELD_TYPE fsmblks; /* always 0 */
+ MALLINFO_FIELD_TYPE uordblks; /* total allocated space */
+ MALLINFO_FIELD_TYPE fordblks; /* total free space */
+ MALLINFO_FIELD_TYPE keepcost; /* releasable (via malloc_trim) space */
+};
+#endif /* STRUCT_MALLINFO_DECLARED */
+#endif /* HAVE_USR_INCLUDE_MALLOC_H */
+#endif /* NO_MALLINFO */
+
+/*
+ Try to persuade compilers to inline. The most critical functions for
+ inlining are defined as macros, so these aren't used for them.
+*/
+
+#ifndef FORCEINLINE
+ #if defined(__GNUC__)
+#define FORCEINLINE __inline __attribute__ ((always_inline))
+ #elif defined(_MSC_VER)
+ #define FORCEINLINE __forceinline
+ #endif
+#endif
+#ifndef NOINLINE
+ #if defined(__GNUC__)
+ #define NOINLINE __attribute__ ((noinline))
+ #elif defined(_MSC_VER)
+ #define NOINLINE __declspec(noinline)
+ #else
+ #define NOINLINE
+ #endif
+#endif
+
+#ifdef __cplusplus
+extern "C" {
+#ifndef FORCEINLINE
+ #define FORCEINLINE inline
+#endif
+#endif /* __cplusplus */
+#ifndef FORCEINLINE
+ #define FORCEINLINE
+#endif
+
+#if !ONLY_MSPACES
+
+/* ------------------- Declarations of public routines ------------------- */
+
+#ifndef USE_DL_PREFIX
+#define dlcalloc calloc
+#define dlfree free
+#define dlmalloc malloc
+#define dlmemalign memalign
+#define dlrealloc realloc
+#define dlvalloc valloc
+#define dlpvalloc pvalloc
+#define dlmallinfo mallinfo
+#define dlmallopt mallopt
+#define dlmalloc_trim malloc_trim
+#define dlmalloc_stats malloc_stats
+#define dlmalloc_usable_size malloc_usable_size
+#define dlmalloc_footprint malloc_footprint
+#define dlmalloc_max_footprint malloc_max_footprint
+#define dlindependent_calloc independent_calloc
+#define dlindependent_comalloc independent_comalloc
+#endif /* USE_DL_PREFIX */
+
+
+/*
+ malloc(size_t n)
+ Returns a pointer to a newly allocated chunk of at least n bytes, or
+ null if no space is available, in which case errno is set to ENOMEM
+ on ANSI C systems.
+
+ If n is zero, malloc returns a minimum-sized chunk. (The minimum
+ size is 16 bytes on most 32bit systems, and 32 bytes on 64bit
+ systems.) Note that size_t is an unsigned type, so calls with
+ arguments that would be negative if signed are interpreted as
+ requests for huge amounts of space, which will often fail. The
+ maximum supported value of n differs across systems, but is in all
+ cases less than the maximum representable value of a size_t.
+*/
+void* dlmalloc(size_t);
+
+/*
+ free(void* p)
+ Releases the chunk of memory pointed to by p, that had been previously
+ allocated using malloc or a related routine such as realloc.
+ It has no effect if p is null. If p was not malloced or already
+ freed, free(p) will by default cause the current program to abort.
+*/
+void dlfree(void*);
+
+/*
+ calloc(size_t n_elements, size_t element_size);
+ Returns a pointer to n_elements * element_size bytes, with all locations
+ set to zero.
+*/
+void* dlcalloc(size_t, size_t);
+
+/*
+ realloc(void* p, size_t n)
+ Returns a pointer to a chunk of size n that contains the same data
+ as does chunk p up to the minimum of (n, p's size) bytes, or null
+ if no space is available.
+
+ The returned pointer may or may not be the same as p. The algorithm
+ prefers extending p in most cases when possible, otherwise it
+ employs the equivalent of a malloc-copy-free sequence.
+
+ If p is null, realloc is equivalent to malloc.
+
+ If space is not available, realloc returns null, errno is set (if on
+ ANSI) and p is NOT freed.
+
+ if n is for fewer bytes than already held by p, the newly unused
+ space is lopped off and freed if possible. realloc with a size
+ argument of zero (re)allocates a minimum-sized chunk.
+
+ The old unix realloc convention of allowing the last-free'd chunk
+ to be used as an argument to realloc is not supported.
+*/
+
+void* dlrealloc(void*, size_t);
+
+/*
+ memalign(size_t alignment, size_t n);
+ Returns a pointer to a newly allocated chunk of n bytes, aligned
+ in accord with the alignment argument.
+
+ The alignment argument should be a power of two. If the argument is
+ not a power of two, the nearest greater power is used.
+ 8-byte alignment is guaranteed by normal malloc calls, so don't
+ bother calling memalign with an argument of 8 or less.
+
+ Overreliance on memalign is a sure way to fragment space.
+*/
+void* dlmemalign(size_t, size_t);
+
+/*
+ valloc(size_t n);
+ Equivalent to memalign(pagesize, n), where pagesize is the page
+ size of the system. If the pagesize is unknown, 4096 is used.
+*/
+void* dlvalloc(size_t);
+
+/*
+ mallopt(int parameter_number, int parameter_value)
+ Sets tunable parameters The format is to provide a
+ (parameter-number, parameter-value) pair. mallopt then sets the
+ corresponding parameter to the argument value if it can (i.e., so
+ long as the value is meaningful), and returns 1 if successful else
+ 0. To workaround the fact that mallopt is specified to use int,
+ not size_t parameters, the value -1 is specially treated as the
+ maximum unsigned size_t value.
+
+ SVID/XPG/ANSI defines four standard param numbers for mallopt,
+ normally defined in malloc.h. None of these are use in this malloc,
+ so setting them has no effect. But this malloc also supports other
+ options in mallopt. See below for details. Briefly, supported
+ parameters are as follows (listed defaults are for "typical"
+ configurations).
+
+ Symbol param # default allowed param values
+ M_TRIM_THRESHOLD -1 2*1024*1024 any (-1 disables)
+ M_GRANULARITY -2 page size any power of 2 >= page size
+ M_MMAP_THRESHOLD -3 256*1024 any (or 0 if no MMAP support)
+*/
+int dlmallopt(int, int);
+
+/*
+ malloc_footprint();
+ Returns the number of bytes obtained from the system. The total
+ number of bytes allocated by malloc, realloc etc., is less than this
+ value. Unlike mallinfo, this function returns only a precomputed
+ result, so can be called frequently to monitor memory consumption.
+ Even if locks are otherwise defined, this function does not use them,
+ so results might not be up to date.
+*/
+size_t dlmalloc_footprint(void);
+
+/*
+ malloc_max_footprint();
+ Returns the maximum number of bytes obtained from the system. This
+ value will be greater than current footprint if deallocated space
+ has been reclaimed by the system. The peak number of bytes allocated
+ by malloc, realloc etc., is less than this value. Unlike mallinfo,
+ this function returns only a precomputed result, so can be called
+ frequently to monitor memory consumption. Even if locks are
+ otherwise defined, this function does not use them, so results might
+ not be up to date.
+*/
+size_t dlmalloc_max_footprint(void);
+
+#if !NO_MALLINFO
+/*
+ mallinfo()
+ Returns (by copy) a struct containing various summary statistics:
+
+ arena: current total non-mmapped bytes allocated from system
+ ordblks: the number of free chunks
+ smblks: always zero.
+ hblks: current number of mmapped regions
+ hblkhd: total bytes held in mmapped regions
+ usmblks: the maximum total allocated space. This will be greater
+ than current total if trimming has occurred.
+ fsmblks: always zero
+ uordblks: current total allocated space (normal or mmapped)
+ fordblks: total free space
+ keepcost: the maximum number of bytes that could ideally be released
+ back to system via malloc_trim. ("ideally" means that
+ it ignores page restrictions etc.)
+
+ Because these fields are ints, but internal bookkeeping may
+ be kept as longs, the reported values may wrap around zero and
+ thus be inaccurate.
+*/
+struct mallinfo dlmallinfo(void);
+#endif /* NO_MALLINFO */
+
+/*
+ independent_calloc(size_t n_elements, size_t element_size, void* chunks[]);
+
+ independent_calloc is similar to calloc, but instead of returning a
+ single cleared space, it returns an array of pointers to n_elements
+ independent elements that can hold contents of size elem_size, each
+ of which starts out cleared, and can be independently freed,
+ realloc'ed etc. The elements are guaranteed to be adjacently
+ allocated (this is not guaranteed to occur with multiple callocs or
+ mallocs), which may also improve cache locality in some
+ applications.
+
+ The "chunks" argument is optional (i.e., may be null, which is
+ probably the most typical usage). If it is null, the returned array
+ is itself dynamically allocated and should also be freed when it is
+ no longer needed. Otherwise, the chunks array must be of at least
+ n_elements in length. It is filled in with the pointers to the
+ chunks.
+
+ In either case, independent_calloc returns this pointer array, or
+ null if the allocation failed. If n_elements is zero and "chunks"
+ is null, it returns a chunk representing an array with zero elements
+ (which should be freed if not wanted).
+
+ Each element must be individually freed when it is no longer
+ needed. If you'd like to instead be able to free all at once, you
+ should instead use regular calloc and assign pointers into this
+ space to represent elements. (In this case though, you cannot
+ independently free elements.)
+
+ independent_calloc simplifies and speeds up implementations of many
+ kinds of pools. It may also be useful when constructing large data
+ structures that initially have a fixed number of fixed-sized nodes,
+ but the number is not known at compile time, and some of the nodes
+ may later need to be freed. For example:
+
+ struct Node { int item; struct Node* next; };
+
+ struct Node* build_list() {
+ struct Node** pool;
+ int n = read_number_of_nodes_needed();
+ if (n <= 0) return 0;
+ pool = (struct Node**)(independent_calloc(n, sizeof(struct Node), 0);
+ if (pool == 0) die();
+ // organize into a linked list...
+ struct Node* first = pool[0];
+ for (i = 0; i < n-1; ++i)
+ pool[i]->next = pool[i+1];
+ free(pool); // Can now free the array (or not, if it is needed later)
+ return first;
+ }
+*/
+void** dlindependent_calloc(size_t, size_t, void**);
+
+/*
+ independent_comalloc(size_t n_elements, size_t sizes[], void* chunks[]);
+
+ independent_comalloc allocates, all at once, a set of n_elements
+ chunks with sizes indicated in the "sizes" array. It returns
+ an array of pointers to these elements, each of which can be
+ independently freed, realloc'ed etc. The elements are guaranteed to
+ be adjacently allocated (this is not guaranteed to occur with
+ multiple callocs or mallocs), which may also improve cache locality
+ in some applications.
+
+ The "chunks" argument is optional (i.e., may be null). If it is null
+ the returned array is itself dynamically allocated and should also
+ be freed when it is no longer needed. Otherwise, the chunks array
+ must be of at least n_elements in length. It is filled in with the
+ pointers to the chunks.
+
+ In either case, independent_comalloc returns this pointer array, or
+ null if the allocation failed. If n_elements is zero and chunks is
+ null, it returns a chunk representing an array with zero elements
+ (which should be freed if not wanted).
+
+ Each element must be individually freed when it is no longer
+ needed. If you'd like to instead be able to free all at once, you
+ should instead use a single regular malloc, and assign pointers at
+ particular offsets in the aggregate space. (In this case though, you
+ cannot independently free elements.)
+
+ independent_comallac differs from independent_calloc in that each
+ element may have a different size, and also that it does not
+ automatically clear elements.
+
+ independent_comalloc can be used to speed up allocation in cases
+ where several structs or objects must always be allocated at the
+ same time. For example:
+
+ struct Head { ... }
+ struct Foot { ... }
+
+ void send_message(char* msg) {
+ int msglen = strlen(msg);
+ size_t sizes[3] = { sizeof(struct Head), msglen, sizeof(struct Foot) };
+ void* chunks[3];
+ if (independent_comalloc(3, sizes, chunks) == 0)
+ die();
+ struct Head* head = (struct Head*)(chunks[0]);
+ char* body = (char*)(chunks[1]);
+ struct Foot* foot = (struct Foot*)(chunks[2]);
+ // ...
+ }
+
+ In general though, independent_comalloc is worth using only for
+ larger values of n_elements. For small values, you probably won't
+ detect enough difference from series of malloc calls to bother.
+
+ Overuse of independent_comalloc can increase overall memory usage,
+ since it cannot reuse existing noncontiguous small chunks that
+ might be available for some of the elements.
+*/
+void** dlindependent_comalloc(size_t, size_t*, void**);
+
+
+/*
+ pvalloc(size_t n);
+ Equivalent to valloc(minimum-page-that-holds(n)), that is,
+ round up n to nearest pagesize.
+ */
+void* dlpvalloc(size_t);
+
+/*
+ malloc_trim(size_t pad);
+
+ If possible, gives memory back to the system (via negative arguments
+ to sbrk) if there is unused memory at the `high' end of the malloc
+ pool or in unused MMAP segments. You can call this after freeing
+ large blocks of memory to potentially reduce the system-level memory
+ requirements of a program. However, it cannot guarantee to reduce
+ memory. Under some allocation patterns, some large free blocks of
+ memory will be locked between two used chunks, so they cannot be
+ given back to the system.
+
+ The `pad' argument to malloc_trim represents the amount of free
+ trailing space to leave untrimmed. If this argument is zero, only
+ the minimum amount of memory to maintain internal data structures
+ will be left. Non-zero arguments can be supplied to maintain enough
+ trailing space to service future expected allocations without having
+ to re-obtain memory from the system.
+
+ Malloc_trim returns 1 if it actually released any memory, else 0.
+*/
+int dlmalloc_trim(size_t);
+
+/*
+ malloc_stats();
+ Prints on stderr the amount of space obtained from the system (both
+ via sbrk and mmap), the maximum amount (which may be more than
+ current if malloc_trim and/or munmap got called), and the current
+ number of bytes allocated via malloc (or realloc, etc) but not yet
+ freed. Note that this is the number of bytes allocated, not the
+ number requested. It will be larger than the number requested
+ because of alignment and bookkeeping overhead. Because it includes
+ alignment wastage as being in use, this figure may be greater than
+ zero even when no user-level chunks are allocated.
+
+ The reported current and maximum system memory can be inaccurate if
+ a program makes other calls to system memory allocation functions
+ (normally sbrk) outside of malloc.
+
+ malloc_stats prints only the most commonly interesting statistics.
+ More information can be obtained by calling mallinfo.
+*/
+void dlmalloc_stats(void);
+
+#endif /* ONLY_MSPACES */
+
+/*
+ malloc_usable_size(void* p);
+
+ Returns the number of bytes you can actually use in
+ an allocated chunk, which may be more than you requested (although
+ often not) due to alignment and minimum size constraints.
+ You can use this many bytes without worrying about
+ overwriting other allocated objects. This is not a particularly great
+ programming practice. malloc_usable_size can be more useful in
+ debugging and assertions, for example:
+
+ p = malloc(n);
+ assert(malloc_usable_size(p) >= 256);
+*/
+size_t dlmalloc_usable_size(void*);
+
+
+#if MSPACES
+
+/*
+ mspace is an opaque type representing an independent
+ region of space that supports mspace_malloc, etc.
+*/
+typedef void* mspace;
+
+/*
+ create_mspace creates and returns a new independent space with the
+ given initial capacity, or, if 0, the default granularity size. It
+ returns null if there is no system memory available to create the
+ space. If argument locked is non-zero, the space uses a separate
+ lock to control access. The capacity of the space will grow
+ dynamically as needed to service mspace_malloc requests. You can
+ control the sizes of incremental increases of this space by
+ compiling with a different DEFAULT_GRANULARITY or dynamically
+ setting with mallopt(M_GRANULARITY, value).
+*/
+mspace create_mspace(size_t capacity, int locked);
+
+/*
+ destroy_mspace destroys the given space, and attempts to return all
+ of its memory back to the system, returning the total number of
+ bytes freed. After destruction, the results of access to all memory
+ used by the space become undefined.
+*/
+size_t destroy_mspace(mspace msp);
+
+/*
+ create_mspace_with_base uses the memory supplied as the initial base
+ of a new mspace. Part (less than 128*sizeof(size_t) bytes) of this
+ space is used for bookkeeping, so the capacity must be at least this
+ large. (Otherwise 0 is returned.) When this initial space is
+ exhausted, additional memory will be obtained from the system.
+ Destroying this space will deallocate all additionally allocated
+ space (if possible) but not the initial base.
+*/
+mspace create_mspace_with_base(void* base, size_t capacity, int locked);
+
+/*
+ mspace_track_large_chunks controls whether requests for large chunks
+ are allocated in their own untracked mmapped regions, separate from
+ others in this mspace. By default large chunks are not tracked,
+ which reduces fragmentation. However, such chunks are not
+ necessarily released to the system upon destroy_mspace. Enabling
+ tracking by setting to true may increase fragmentation, but avoids
+ leakage when relying on destroy_mspace to release all memory
+ allocated using this space. The function returns the previous
+ setting.
+*/
+int mspace_track_large_chunks(mspace msp, int enable);
+
+
+/*
+ mspace_malloc behaves as malloc, but operates within
+ the given space.
+*/
+void* mspace_malloc(mspace msp, size_t bytes);
+
+/*
+ mspace_free behaves as free, but operates within
+ the given space.
+
+ If compiled with FOOTERS==1, mspace_free is not actually needed.
+ free may be called instead of mspace_free because freed chunks from
+ any space are handled by their originating spaces.
+*/
+void mspace_free(mspace msp, void* mem);
+
+/*
+ mspace_realloc behaves as realloc, but operates within
+ the given space.
+
+ If compiled with FOOTERS==1, mspace_realloc is not actually
+ needed. realloc may be called instead of mspace_realloc because
+ realloced chunks from any space are handled by their originating
+ spaces.
+*/
+void* mspace_realloc(mspace msp, void* mem, size_t newsize);
+
+/*
+ mspace_calloc behaves as calloc, but operates within
+ the given space.
+*/
+void* mspace_calloc(mspace msp, size_t n_elements, size_t elem_size);
+
+/*
+ mspace_memalign behaves as memalign, but operates within
+ the given space.
+*/
+void* mspace_memalign(mspace msp, size_t alignment, size_t bytes);
+
+/*
+ mspace_independent_calloc behaves as independent_calloc, but
+ operates within the given space.
+*/
+void** mspace_independent_calloc(mspace msp, size_t n_elements,
+ size_t elem_size, void* chunks[]);
+
+/*
+ mspace_independent_comalloc behaves as independent_comalloc, but
+ operates within the given space.
+*/
+void** mspace_independent_comalloc(mspace msp, size_t n_elements,
+ size_t sizes[], void* chunks[]);
+
+/*
+ mspace_footprint() returns the number of bytes obtained from the
+ system for this space.
+*/
+size_t mspace_footprint(mspace msp);
+
+/*
+ mspace_max_footprint() returns the peak number of bytes obtained from the
+ system for this space.
+*/
+size_t mspace_max_footprint(mspace msp);
+
+
+#if !NO_MALLINFO
+/*
+ mspace_mallinfo behaves as mallinfo, but reports properties of
+ the given space.
+*/
+struct mallinfo mspace_mallinfo(mspace msp);
+#endif /* NO_MALLINFO */
+
+/*
+ malloc_usable_size(void* p) behaves the same as malloc_usable_size;
+*/
+ size_t mspace_usable_size(void* mem);
+
+/*
+ mspace_malloc_stats behaves as malloc_stats, but reports
+ properties of the given space.
+*/
+void mspace_malloc_stats(mspace msp);
+
+/*
+ mspace_trim behaves as malloc_trim, but
+ operates within the given space.
+*/
+int mspace_trim(mspace msp, size_t pad);
+
+/*
+ An alias for mallopt.
+*/
+int mspace_mallopt(int, int);
+
+#endif /* MSPACES */
+
+#ifdef __cplusplus
+} /* end of extern "C" */
+#endif /* __cplusplus */
+
+/*
+ ========================================================================
+ To make a fully customizable malloc.h header file, cut everything
+ above this line, put into file malloc.h, edit to suit, and #include it
+ on the next line, as well as in programs that use this malloc.
+ ========================================================================
+*/
+
+/* #include "malloc.h" */
+
+/*------------------------------ internal #includes ---------------------- */
+
+#ifdef WIN32
+#pragma warning( disable : 4146 ) /* no "unsigned" warnings */
+#endif /* WIN32 */
+
+#include <stdio.h> /* for printing in malloc_stats */
+
+#ifndef LACKS_ERRNO_H
+#include <errno.h> /* for MALLOC_FAILURE_ACTION */
+#endif /* LACKS_ERRNO_H */
+/*#if FOOTERS || DEBUG
+*/
+#include <time.h> /* for magic initialization */
+/*#endif*/ /* FOOTERS */
+#ifndef LACKS_STDLIB_H
+#include <stdlib.h> /* for abort() */
+#endif /* LACKS_STDLIB_H */
+#ifdef DEBUG
+#if ABORT_ON_ASSERT_FAILURE
+#undef assert
+#define assert(x) if(!(x)) ABORT
+#else /* ABORT_ON_ASSERT_FAILURE */
+#include <assert.h>
+#endif /* ABORT_ON_ASSERT_FAILURE */
+#else /* DEBUG */
+#ifndef assert
+#define assert(x)
+#endif
+#define DEBUG 0
+#endif /* DEBUG */
+#ifndef LACKS_STRING_H
+#include <string.h> /* for memset etc */
+#endif /* LACKS_STRING_H */
+#if USE_BUILTIN_FFS
+#ifndef LACKS_STRINGS_H
+#include <strings.h> /* for ffs */
+#endif /* LACKS_STRINGS_H */
+#endif /* USE_BUILTIN_FFS */
+#if HAVE_MMAP
+#ifndef LACKS_SYS_MMAN_H
+/* On some versions of linux, mremap decl in mman.h needs __USE_GNU set */
+#if (defined(linux) && !defined(__USE_GNU))
+#define __USE_GNU 1
+#include <sys/mman.h> /* for mmap */
+#undef __USE_GNU
+#else
+#include <sys/mman.h> /* for mmap */
+#endif /* linux */
+#endif /* LACKS_SYS_MMAN_H */
+#ifndef LACKS_FCNTL_H
+#include <fcntl.h>
+#endif /* LACKS_FCNTL_H */
+#endif /* HAVE_MMAP */
+#ifndef LACKS_UNISTD_H
+#include <unistd.h> /* for sbrk, sysconf */
+#else /* LACKS_UNISTD_H */
+#if !defined(__FreeBSD__) && !defined(__OpenBSD__) && !defined(__NetBSD__)
+extern void* sbrk(ptrdiff_t);
+#endif /* FreeBSD etc */
+#endif /* LACKS_UNISTD_H */
+
+/* Declarations for locking */
+#if USE_LOCKS
+#ifndef WIN32
+#include <pthread.h>
+#if defined (__SVR4) && defined (__sun) /* solaris */
+#include <thread.h>
+#endif /* solaris */
+#else
+#ifndef _M_AMD64
+/* These are already defined on AMD64 builds */
+#ifdef __cplusplus
+extern "C" {
+#endif /* __cplusplus */
+LONG __cdecl _InterlockedCompareExchange(LONG volatile *Dest, LONG Exchange, LONG Comp);
+LONG __cdecl _InterlockedExchange(LONG volatile *Target, LONG Value);
+#ifdef __cplusplus
+}
+#endif /* __cplusplus */
+#endif /* _M_AMD64 */
+#pragma intrinsic (_InterlockedCompareExchange)
+#pragma intrinsic (_InterlockedExchange)
+#define interlockedcompareexchange _InterlockedCompareExchange
+#define interlockedexchange _InterlockedExchange
+#endif /* Win32 */
+#endif /* USE_LOCKS */
+
+/* Declarations for bit scanning on win32 */
+#if defined(_MSC_VER) && _MSC_VER>=1300
+#ifndef BitScanForward /* Try to avoid pulling in WinNT.h */
+#ifdef __cplusplus
+extern "C" {
+#endif /* __cplusplus */
+unsigned char _BitScanForward(unsigned long *index, unsigned long mask);
+unsigned char _BitScanReverse(unsigned long *index, unsigned long mask);
+#ifdef __cplusplus
+}
+#endif /* __cplusplus */
+
+#define BitScanForward _BitScanForward
+#define BitScanReverse _BitScanReverse
+#pragma intrinsic(_BitScanForward)
+#pragma intrinsic(_BitScanReverse)
+#endif /* BitScanForward */
+#endif /* defined(_MSC_VER) && _MSC_VER>=1300 */
+
+#ifndef WIN32
+#ifndef malloc_getpagesize
+# ifdef _SC_PAGESIZE /* some SVR4 systems omit an underscore */
+# ifndef _SC_PAGE_SIZE
+# define _SC_PAGE_SIZE _SC_PAGESIZE
+# endif
+# endif
+# ifdef _SC_PAGE_SIZE
+# define malloc_getpagesize sysconf(_SC_PAGE_SIZE)
+# else
+# if defined(BSD) || defined(DGUX) || defined(HAVE_GETPAGESIZE)
+ extern size_t getpagesize();
+# define malloc_getpagesize getpagesize()
+# else
+# ifdef WIN32 /* use supplied emulation of getpagesize */
+# define malloc_getpagesize getpagesize()
+# else
+# ifndef LACKS_SYS_PARAM_H
+# include <sys/param.h>
+# endif
+# ifdef EXEC_PAGESIZE
+# define malloc_getpagesize EXEC_PAGESIZE
+# else
+# ifdef NBPG
+# ifndef CLSIZE
+# define malloc_getpagesize NBPG
+# else
+# define malloc_getpagesize (NBPG * CLSIZE)
+# endif
+# else
+# ifdef NBPC
+# define malloc_getpagesize NBPC
+# else
+# ifdef PAGESIZE
+# define malloc_getpagesize PAGESIZE
+# else /* just guess */
+# define malloc_getpagesize ((size_t)4096U)
+# endif
+# endif
+# endif
+# endif
+# endif
+# endif
+# endif
+#endif
+#endif
+
+
+
+/* ------------------- size_t and alignment properties -------------------- */
+
+/* The byte and bit size of a size_t */
+#define SIZE_T_SIZE (sizeof(size_t))
+#define SIZE_T_BITSIZE (sizeof(size_t) << 3)
+
+/* Some constants coerced to size_t */
+/* Annoying but necessary to avoid errors on some platforms */
+#define SIZE_T_ZERO ((size_t)0)
+#define SIZE_T_ONE ((size_t)1)
+#define SIZE_T_TWO ((size_t)2)
+#define SIZE_T_FOUR ((size_t)4)
+#define TWO_SIZE_T_SIZES (SIZE_T_SIZE<<1)
+#define FOUR_SIZE_T_SIZES (SIZE_T_SIZE<<2)
+#define SIX_SIZE_T_SIZES (FOUR_SIZE_T_SIZES+TWO_SIZE_T_SIZES)
+#define HALF_MAX_SIZE_T (MAX_SIZE_T / 2U)
+
+/* The bit mask value corresponding to MALLOC_ALIGNMENT */
+#define CHUNK_ALIGN_MASK (MALLOC_ALIGNMENT - SIZE_T_ONE)
+
+/* True if address a has acceptable alignment */
+#define is_aligned(A) (((size_t)((A)) & (CHUNK_ALIGN_MASK)) == 0)
+
+/* the number of bytes to offset an address to align it */
+#define align_offset(A)\
+ ((((size_t)(A) & CHUNK_ALIGN_MASK) == 0)? 0 :\
+ ((MALLOC_ALIGNMENT - ((size_t)(A) & CHUNK_ALIGN_MASK)) & CHUNK_ALIGN_MASK))
+
+/* -------------------------- MMAP preliminaries ------------------------- */
+
+/*
+ If HAVE_MORECORE or HAVE_MMAP are false, we just define calls and
+ checks to fail so compiler optimizer can delete code rather than
+ using so many "#if"s.
+*/
+
+
+/* MORECORE and MMAP must return MFAIL on failure */
+#define MFAIL ((void*)(MAX_SIZE_T))
+#define CMFAIL ((char*)(MFAIL)) /* defined for convenience */
+
+#if HAVE_MMAP
+
+#ifndef WIN32
+#define MUNMAP_DEFAULT(a, s) munmap((a), (s))
+#define MMAP_PROT (PROT_READ|PROT_WRITE)
+#if !defined(MAP_ANONYMOUS) && defined(MAP_ANON)
+#define MAP_ANONYMOUS MAP_ANON
+#endif /* MAP_ANON */
+#ifdef MAP_ANONYMOUS
+#define MMAP_FLAGS (MAP_PRIVATE|MAP_ANONYMOUS)
+#define MMAP_DEFAULT(s) mmap(0, (s), MMAP_PROT, MMAP_FLAGS, -1, 0)
+#else /* MAP_ANONYMOUS */
+/*
+ Nearly all versions of mmap support MAP_ANONYMOUS, so the following
+ is unlikely to be needed, but is supplied just in case.
+*/
+#define MMAP_FLAGS (MAP_PRIVATE)
+static int dev_zero_fd = -1; /* Cached file descriptor for /dev/zero. */
+#define MMAP_DEFAULT(s) ((dev_zero_fd < 0) ? \
+ (dev_zero_fd = open("/dev/zero", O_RDWR), \
+ mmap(0, (s), MMAP_PROT, MMAP_FLAGS, dev_zero_fd, 0)) : \
+ mmap(0, (s), MMAP_PROT, MMAP_FLAGS, dev_zero_fd, 0))
+#endif /* MAP_ANONYMOUS */
+
+#define DIRECT_MMAP_DEFAULT(s) MMAP_DEFAULT(s)
+
+#else /* WIN32 */
+
+/* Win32 MMAP via VirtualAlloc */
+static FORCEINLINE void* win32mmap(size_t size) {
+ void* ptr = VirtualAlloc(0, size, MEM_RESERVE|MEM_COMMIT, PAGE_READWRITE);
+ return (ptr != 0)? ptr: MFAIL;
+}
+
+/* For direct MMAP, use MEM_TOP_DOWN to minimize interference */
+static FORCEINLINE void* win32direct_mmap(size_t size) {
+ void* ptr = VirtualAlloc(0, size, MEM_RESERVE|MEM_COMMIT|MEM_TOP_DOWN,
+ PAGE_READWRITE);
+ return (ptr != 0)? ptr: MFAIL;
+}
+
+/* This function supports releasing coalesed segments */
+static FORCEINLINE int win32munmap(void* ptr, size_t size) {
+ MEMORY_BASIC_INFORMATION minfo;
+ char* cptr = (char*)ptr;
+ while (size) {
+ if (VirtualQuery(cptr, &minfo, sizeof(minfo)) == 0)
+ return -1;
+ if (minfo.BaseAddress != cptr || minfo.AllocationBase != cptr ||
+ minfo.State != MEM_COMMIT || minfo.RegionSize > size)
+ return -1;
+ if (VirtualFree(cptr, 0, MEM_RELEASE) == 0)
+ return -1;
+ cptr += minfo.RegionSize;
+ size -= minfo.RegionSize;
+ }
+ return 0;
+}
+
+#define MMAP_DEFAULT(s) win32mmap(s)
+#define MUNMAP_DEFAULT(a, s) win32munmap((a), (s))
+#define DIRECT_MMAP_DEFAULT(s) win32direct_mmap(s)
+#endif /* WIN32 */
+#endif /* HAVE_MMAP */
+
+#if HAVE_MREMAP
+#ifndef WIN32
+#define MREMAP_DEFAULT(addr, osz, nsz, mv) mremap((addr), (osz), (nsz), (mv))
+#endif /* WIN32 */
+#endif /* HAVE_MREMAP */
+
+
+/**
+ * Define CALL_MORECORE
+ */
+#if HAVE_MORECORE
+ #ifdef MORECORE
+ #define CALL_MORECORE(S) MORECORE(S)
+ #else /* MORECORE */
+ #define CALL_MORECORE(S) MORECORE_DEFAULT(S)
+ #endif /* MORECORE */
+#else /* HAVE_MORECORE */
+ #define CALL_MORECORE(S) MFAIL
+#endif /* HAVE_MORECORE */
+
+/**
+ * Define CALL_MMAP/CALL_MUNMAP/CALL_DIRECT_MMAP
+ */
+#if HAVE_MMAP
+ #define USE_MMAP_BIT (SIZE_T_ONE)
+
+ #ifdef MMAP
+ #define CALL_MMAP(s) MMAP(s)
+ #else /* MMAP */
+ #define CALL_MMAP(s) MMAP_DEFAULT(s)
+ #endif /* MMAP */
+ #ifdef MUNMAP
+ #define CALL_MUNMAP(a, s) MUNMAP((a), (s))
+ #else /* MUNMAP */
+ #define CALL_MUNMAP(a, s) MUNMAP_DEFAULT((a), (s))
+ #endif /* MUNMAP */
+ #ifdef DIRECT_MMAP
+ #define CALL_DIRECT_MMAP(s) DIRECT_MMAP(s)
+ #else /* DIRECT_MMAP */
+ #define CALL_DIRECT_MMAP(s) DIRECT_MMAP_DEFAULT(s)
+ #endif /* DIRECT_MMAP */
+#else /* HAVE_MMAP */
+ #define USE_MMAP_BIT (SIZE_T_ZERO)
+
+ #define MMAP(s) MFAIL
+ #define MUNMAP(a, s) (-1)
+ #define DIRECT_MMAP(s) MFAIL
+ #define CALL_DIRECT_MMAP(s) DIRECT_MMAP(s)
+ #define CALL_MMAP(s) MMAP(s)
+ #define CALL_MUNMAP(a, s) MUNMAP((a), (s))
+#endif /* HAVE_MMAP */
+
+/**
+ * Define CALL_MREMAP
+ */
+#if HAVE_MMAP && HAVE_MREMAP
+ #ifdef MREMAP
+ #define CALL_MREMAP(addr, osz, nsz, mv) MREMAP((addr), (osz), (nsz), (mv))
+ #else /* MREMAP */
+ #define CALL_MREMAP(addr, osz, nsz, mv) MREMAP_DEFAULT((addr), (osz), (nsz), (mv))
+ #endif /* MREMAP */
+#else /* HAVE_MMAP && HAVE_MREMAP */
+ #define CALL_MREMAP(addr, osz, nsz, mv) MFAIL
+#endif /* HAVE_MMAP && HAVE_MREMAP */
+
+/* mstate bit set if continguous morecore disabled or failed */
+#define USE_NONCONTIGUOUS_BIT (4U)
+
+/* segment bit set in create_mspace_with_base */
+#define EXTERN_BIT (8U)
+
+
+/* --------------------------- Lock preliminaries ------------------------ */
+
+/*
+ When locks are defined, there is one global lock, plus
+ one per-mspace lock.
+
+ The global lock_ensures that mparams.magic and other unique
+ mparams values are initialized only once. It also protects
+ sequences of calls to MORECORE. In many cases sys_alloc requires
+ two calls, that should not be interleaved with calls by other
+ threads. This does not protect against direct calls to MORECORE
+ by other threads not using this lock, so there is still code to
+ cope the best we can on interference.
+
+ Per-mspace locks surround calls to malloc, free, etc. To enable use
+ in layered extensions, per-mspace locks are reentrant.
+
+ Because lock-protected regions generally have bounded times, it is
+ OK to use the supplied simple spinlocks in the custom versions for
+ x86. Spinlocks are likely to improve performance for lightly
+ contended applications, but worsen performance under heavy
+ contention.
+
+ If USE_LOCKS is > 1, the definitions of lock routines here are
+ bypassed, in which case you will need to define the type MLOCK_T,
+ and at least INITIAL_LOCK, ACQUIRE_LOCK, RELEASE_LOCK and possibly
+ TRY_LOCK (which is not used in this malloc, but commonly needed in
+ extensions.) You must also declare a
+ static MLOCK_T malloc_global_mutex = { initialization values };.
+
+*/
+
+#if USE_LOCKS == 1
+
+#if USE_SPIN_LOCKS && SPIN_LOCKS_AVAILABLE
+#ifndef WIN32
+
+/* Custom pthread-style spin locks on x86 and x64 for gcc */
+struct pthread_mlock_t {
+ volatile unsigned int l;
+ unsigned int c;
+ pthread_t threadid;
+};
+#define MLOCK_T struct pthread_mlock_t
+#define CURRENT_THREAD pthread_self()
+#define INITIAL_LOCK(sl) ((sl)->threadid = 0, (sl)->l = (sl)->c = 0, 0)
+#define ACQUIRE_LOCK(sl) pthread_acquire_lock(sl)
+#define RELEASE_LOCK(sl) pthread_release_lock(sl)
+#define TRY_LOCK(sl) pthread_try_lock(sl)
+#define SPINS_PER_YIELD 63
+
+static MLOCK_T malloc_global_mutex = { 0, 0, 0};
+
+static FORCEINLINE int pthread_acquire_lock (MLOCK_T *sl) {
+ int spins = 0;
+ volatile unsigned int* lp = &sl->l;
+ for (;;) {
+ if (*lp != 0) {
+ if (sl->threadid == CURRENT_THREAD) {
+ ++sl->c;
+ return 0;
+ }
+ }
+ else {
+ /* place args to cmpxchgl in locals to evade oddities in some gccs */
+ int cmp = 0;
+ int val = 1;
+ int ret;
+ __asm__ __volatile__ ("lock; cmpxchgl %1, %2"
+ : "=a" (ret)
+ : "r" (val), "m" (*(lp)), "0"(cmp)
+ : "memory", "cc");
+ if (!ret) {
+ assert(!sl->threadid);
+ sl->threadid = CURRENT_THREAD;
+ sl->c = 1;
+ return 0;
+ }
+ }
+ if ((++spins & SPINS_PER_YIELD) == 0) {
+#if defined (__SVR4) && defined (__sun) /* solaris */
+ thr_yield();
+#else
+#if defined(__linux__) || defined(__FreeBSD__) || defined(__APPLE__)
+ sched_yield();
+#else /* no-op yield on unknown systems */
+ ;
+#endif /* __linux__ || __FreeBSD__ || __APPLE__ */
+#endif /* solaris */
+ }
+ }
+}
+
+static FORCEINLINE void pthread_release_lock (MLOCK_T *sl) {
+ volatile unsigned int* lp = &sl->l;
+ assert(*lp != 0);
+ assert(sl->threadid == CURRENT_THREAD);
+ if (--sl->c == 0) {
+ sl->threadid = 0;
+ int prev = 0;
+ int ret;
+ __asm__ __volatile__ ("lock; xchgl %0, %1"
+ : "=r" (ret)
+ : "m" (*(lp)), "0"(prev)
+ : "memory");
+ }
+}
+
+static FORCEINLINE int pthread_try_lock (MLOCK_T *sl) {
+ volatile unsigned int* lp = &sl->l;
+ if (*lp != 0) {
+ if (sl->threadid == CURRENT_THREAD) {
+ ++sl->c;
+ return 1;
+ }
+ }
+ else {
+ int cmp = 0;
+ int val = 1;
+ int ret;
+ __asm__ __volatile__ ("lock; cmpxchgl %1, %2"
+ : "=a" (ret)
+ : "r" (val), "m" (*(lp)), "0"(cmp)
+ : "memory", "cc");
+ if (!ret) {
+ assert(!sl->threadid);
+ sl->threadid = CURRENT_THREAD;
+ sl->c = 1;
+ return 1;
+ }
+ }
+ return 0;
+}
+
+
+#else /* WIN32 */
+/* Custom win32-style spin locks on x86 and x64 for MSC */
+struct win32_mlock_t {
+ volatile long l;
+ unsigned int c;
+ long threadid;
+};
+
+#define MLOCK_T struct win32_mlock_t
+#define CURRENT_THREAD GetCurrentThreadId()
+#define INITIAL_LOCK(sl) ((sl)->threadid = 0, (sl)->l = (sl)->c = 0, 0)
+#define ACQUIRE_LOCK(sl) win32_acquire_lock(sl)
+#define RELEASE_LOCK(sl) win32_release_lock(sl)
+#define TRY_LOCK(sl) win32_try_lock(sl)
+#define SPINS_PER_YIELD 63
+
+static MLOCK_T malloc_global_mutex = { 0, 0, 0};
+
+static FORCEINLINE int win32_acquire_lock (MLOCK_T *sl) {
+ int spins = 0;
+ for (;;) {
+ if (sl->l != 0) {
+ if (sl->threadid == CURRENT_THREAD) {
+ ++sl->c;
+ return 0;
+ }
+ }
+ else {
+ if (!interlockedexchange(&sl->l, 1)) {
+ assert(!sl->threadid);
+ sl->threadid = CURRENT_THREAD;
+ sl->c = 1;
+ return 0;
+ }
+ }
+ if ((++spins & SPINS_PER_YIELD) == 0)
+ SleepEx(0, FALSE);
+ }
+}
+
+static FORCEINLINE void win32_release_lock (MLOCK_T *sl) {
+ assert(sl->threadid == CURRENT_THREAD);
+ assert(sl->l != 0);
+ if (--sl->c == 0) {
+ sl->threadid = 0;
+ interlockedexchange (&sl->l, 0);
+ }
+}
+
+static FORCEINLINE int win32_try_lock (MLOCK_T *sl) {
+ if (sl->l != 0) {
+ if (sl->threadid == CURRENT_THREAD) {
+ ++sl->c;
+ return 1;
+ }
+ }
+ else {
+ if (!interlockedexchange(&sl->l, 1)){
+ assert(!sl->threadid);
+ sl->threadid = CURRENT_THREAD;
+ sl->c = 1;
+ return 1;
+ }
+ }
+ return 0;
+}
+
+#endif /* WIN32 */
+#else /* USE_SPIN_LOCKS */
+
+#ifndef WIN32
+/* pthreads-based locks */
+
+#define MLOCK_T pthread_mutex_t
+#define CURRENT_THREAD pthread_self()
+#define INITIAL_LOCK(sl) pthread_init_lock(sl)
+#define ACQUIRE_LOCK(sl) pthread_mutex_lock(sl)
+#define RELEASE_LOCK(sl) pthread_mutex_unlock(sl)
+#define TRY_LOCK(sl) (!pthread_mutex_trylock(sl))
+
+static MLOCK_T malloc_global_mutex = PTHREAD_MUTEX_INITIALIZER;
+
+/* Cope with old-style linux recursive lock initialization by adding */
+/* skipped internal declaration from pthread.h */
+#ifdef linux
+#ifndef PTHREAD_MUTEX_RECURSIVE
+extern int pthread_mutexattr_setkind_np __P ((pthread_mutexattr_t *__attr,
+ int __kind));
+#define PTHREAD_MUTEX_RECURSIVE PTHREAD_MUTEX_RECURSIVE_NP
+#define pthread_mutexattr_settype(x,y) pthread_mutexattr_setkind_np(x,y)
+#endif
+#endif
+
+static int pthread_init_lock (MLOCK_T *sl) {
+ pthread_mutexattr_t attr;
+ if (pthread_mutexattr_init(&attr)) return 1;
+ if (pthread_mutexattr_settype(&attr, PTHREAD_MUTEX_RECURSIVE)) return 1;
+ if (pthread_mutex_init(sl, &attr)) return 1;
+ if (pthread_mutexattr_destroy(&attr)) return 1;
+ return 0;
+}
+
+#else /* WIN32 */
+/* Win32 critical sections */
+#define MLOCK_T CRITICAL_SECTION
+#define CURRENT_THREAD GetCurrentThreadId()
+#define INITIAL_LOCK(s) (!InitializeCriticalSectionAndSpinCount((s), 0x80000000|4000))
+#define ACQUIRE_LOCK(s) (EnterCriticalSection(sl), 0)
+#define RELEASE_LOCK(s) LeaveCriticalSection(sl)
+#define TRY_LOCK(s) TryEnterCriticalSection(sl)
+#define NEED_GLOBAL_LOCK_INIT
+
+static MLOCK_T malloc_global_mutex;
+static volatile long malloc_global_mutex_status;
+
+/* Use spin loop to initialize global lock */
+static void init_malloc_global_mutex() {
+ for (;;) {
+ long stat = malloc_global_mutex_status;
+ if (stat > 0)
+ return;
+ /* transition to < 0 while initializing, then to > 0) */
+ if (stat == 0 &&
+ interlockedcompareexchange(&malloc_global_mutex_status, -1, 0) == 0) {
+ InitializeCriticalSection(&malloc_global_mutex);
+ interlockedexchange(&malloc_global_mutex_status,1);
+ return;
+ }
+ SleepEx(0, FALSE);
+ }
+}
+
+#endif /* WIN32 */
+#endif /* USE_SPIN_LOCKS */
+#endif /* USE_LOCKS == 1 */
+
+/* ----------------------- User-defined locks ------------------------ */
+
+#if USE_LOCKS > 1
+/* Define your own lock implementation here */
+/* #define INITIAL_LOCK(sl) ... */
+/* #define ACQUIRE_LOCK(sl) ... */
+/* #define RELEASE_LOCK(sl) ... */
+/* #define TRY_LOCK(sl) ... */
+/* static MLOCK_T malloc_global_mutex = ... */
+#endif /* USE_LOCKS > 1 */
+
+/* ----------------------- Lock-based state ------------------------ */
+
+#if USE_LOCKS
+#define USE_LOCK_BIT (2U)
+#else /* USE_LOCKS */
+#define USE_LOCK_BIT (0U)
+#define INITIAL_LOCK(l)
+#endif /* USE_LOCKS */
+
+#if USE_LOCKS
+#ifndef ACQUIRE_MALLOC_GLOBAL_LOCK
+#define ACQUIRE_MALLOC_GLOBAL_LOCK() ACQUIRE_LOCK(&malloc_global_mutex);
+#endif
+#ifndef RELEASE_MALLOC_GLOBAL_LOCK
+#define RELEASE_MALLOC_GLOBAL_LOCK() RELEASE_LOCK(&malloc_global_mutex);
+#endif
+#else /* USE_LOCKS */
+#define ACQUIRE_MALLOC_GLOBAL_LOCK()
+#define RELEASE_MALLOC_GLOBAL_LOCK()
+#endif /* USE_LOCKS */
+
+
+/* ----------------------- Chunk representations ------------------------ */
+
+/*
+ (The following includes lightly edited explanations by Colin Plumb.)
+
+ The malloc_chunk declaration below is misleading (but accurate and
+ necessary). It declares a "view" into memory allowing access to
+ necessary fields at known offsets from a given base.
+
+ Chunks of memory are maintained using a `boundary tag' method as
+ originally described by Knuth. (See the paper by Paul Wilson
+ ftp://ftp.cs.utexas.edu/pub/garbage/allocsrv.ps for a survey of such
+ techniques.) Sizes of free chunks are stored both in the front of
+ each chunk and at the end. This makes consolidating fragmented
+ chunks into bigger chunks fast. The head fields also hold bits
+ representing whether chunks are free or in use.
+
+ Here are some pictures to make it clearer. They are "exploded" to
+ show that the state of a chunk can be thought of as extending from
+ the high 31 bits of the head field of its header through the
+ prev_foot and PINUSE_BIT bit of the following chunk header.
+
+ A chunk that's in use looks like:
+
+ chunk-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Size of previous chunk (if P = 0) |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |P|
+ | Size of this chunk 1| +-+
+ mem-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | |
+ +- -+
+ | |
+ +- -+
+ | :
+ +- size - sizeof(size_t) available payload bytes -+
+ : |
+ chunk-> +- -+
+ | |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |1|
+ | Size of next chunk (may or may not be in use) | +-+
+ mem-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+
+ And if it's free, it looks like this:
+
+ chunk-> +- -+
+ | User payload (must be in use, or we would have merged!) |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |P|
+ | Size of this chunk 0| +-+
+ mem-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Next pointer |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Prev pointer |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | :
+ +- size - sizeof(struct chunk) unused bytes -+
+ : |
+ chunk-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Size of this chunk |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |0|
+ | Size of next chunk (must be in use, or we would have merged)| +-+
+ mem-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | :
+ +- User payload -+
+ : |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ |0|
+ +-+
+ Note that since we always merge adjacent free chunks, the chunks
+ adjacent to a free chunk must be in use.
+
+ Given a pointer to a chunk (which can be derived trivially from the
+ payload pointer) we can, in O(1) time, find out whether the adjacent
+ chunks are free, and if so, unlink them from the lists that they
+ are on and merge them with the current chunk.
+
+ Chunks always begin on even word boundaries, so the mem portion
+ (which is returned to the user) is also on an even word boundary, and
+ thus at least double-word aligned.
+
+ The P (PINUSE_BIT) bit, stored in the unused low-order bit of the
+ chunk size (which is always a multiple of two words), is an in-use
+ bit for the *previous* chunk. If that bit is *clear*, then the
+ word before the current chunk size contains the previous chunk
+ size, and can be used to find the front of the previous chunk.
+ The very first chunk allocated always has this bit set, preventing
+ access to non-existent (or non-owned) memory. If pinuse is set for
+ any given chunk, then you CANNOT determine the size of the
+ previous chunk, and might even get a memory addressing fault when
+ trying to do so.
+
+ The C (CINUSE_BIT) bit, stored in the unused second-lowest bit of
+ the chunk size redundantly records whether the current chunk is
+ inuse (unless the chunk is mmapped). This redundancy enables usage
+ checks within free and realloc, and reduces indirection when freeing
+ and consolidating chunks.
+
+ Each freshly allocated chunk must have both cinuse and pinuse set.
+ That is, each allocated chunk borders either a previously allocated
+ and still in-use chunk, or the base of its memory arena. This is
+ ensured by making all allocations from the the `lowest' part of any
+ found chunk. Further, no free chunk physically borders another one,
+ so each free chunk is known to be preceded and followed by either
+ inuse chunks or the ends of memory.
+
+ Note that the `foot' of the current chunk is actually represented
+ as the prev_foot of the NEXT chunk. This makes it easier to
+ deal with alignments etc but can be very confusing when trying
+ to extend or adapt this code.
+
+ The exceptions to all this are
+
+ 1. The special chunk `top' is the top-most available chunk (i.e.,
+ the one bordering the end of available memory). It is treated
+ specially. Top is never included in any bin, is used only if
+ no other chunk is available, and is released back to the
+ system if it is very large (see M_TRIM_THRESHOLD). In effect,
+ the top chunk is treated as larger (and thus less well
+ fitting) than any other available chunk. The top chunk
+ doesn't update its trailing size field since there is no next
+ contiguous chunk that would have to index off it. However,
+ space is still allocated for it (TOP_FOOT_SIZE) to enable
+ separation or merging when space is extended.
+
+ 3. Chunks allocated via mmap, have both cinuse and pinuse bits
+ cleared in their head fields. Because they are allocated
+ one-by-one, each must carry its own prev_foot field, which is
+ also used to hold the offset this chunk has within its mmapped
+ region, which is needed to preserve alignment. Each mmapped
+ chunk is trailed by the first two fields of a fake next-chunk
+ for sake of usage checks.
+
+*/
+
+struct malloc_chunk {
+ size_t prev_foot; /* Size of previous chunk (if free). */
+ size_t head; /* Size and inuse bits. */
+ struct malloc_chunk* fd; /* double links -- used only if free. */
+ struct malloc_chunk* bk;
+};
+
+typedef struct malloc_chunk mchunk;
+typedef struct malloc_chunk* mchunkptr;
+typedef struct malloc_chunk* sbinptr; /* The type of bins of chunks */
+typedef unsigned int bindex_t; /* Described below */
+typedef unsigned int binmap_t; /* Described below */
+typedef unsigned int flag_t; /* The type of various bit flag sets */
+
+/* ------------------- Chunks sizes and alignments ----------------------- */
+
+#define MCHUNK_SIZE (sizeof(mchunk))
+
+#if FOOTERS
+#define CHUNK_OVERHEAD (TWO_SIZE_T_SIZES)
+#else /* FOOTERS */
+#define CHUNK_OVERHEAD (SIZE_T_SIZE)
+#endif /* FOOTERS */
+
+/* MMapped chunks need a second word of overhead ... */
+#define MMAP_CHUNK_OVERHEAD (TWO_SIZE_T_SIZES)
+/* ... and additional padding for fake next-chunk at foot */
+#define MMAP_FOOT_PAD (FOUR_SIZE_T_SIZES)
+
+/* The smallest size we can malloc is an aligned minimal chunk */
+#define MIN_CHUNK_SIZE\
+ ((MCHUNK_SIZE + CHUNK_ALIGN_MASK) & ~CHUNK_ALIGN_MASK)
+
+/* conversion from malloc headers to user pointers, and back */
+#define chunk2mem(p) ((void*)((char*)(p) + TWO_SIZE_T_SIZES))
+#define mem2chunk(mem) ((mchunkptr)((char*)(mem) - TWO_SIZE_T_SIZES))
+/* chunk associated with aligned address A */
+#define align_as_chunk(A) (mchunkptr)((A) + align_offset(chunk2mem(A)))
+
+/* Bounds on request (not chunk) sizes. */
+#define MAX_REQUEST ((-MIN_CHUNK_SIZE) << 2)
+#define MIN_REQUEST (MIN_CHUNK_SIZE - CHUNK_OVERHEAD - SIZE_T_ONE)
+
+/* pad request bytes into a usable size */
+#define pad_request(req) \
+ (((req) + CHUNK_OVERHEAD + CHUNK_ALIGN_MASK) & ~CHUNK_ALIGN_MASK)
+
+/* pad request, checking for minimum (but not maximum) */
+#define request2size(req) \
+ (((req) < MIN_REQUEST)? MIN_CHUNK_SIZE : pad_request(req))
+
+
+/* ------------------ Operations on head and foot fields ----------------- */
+
+/*
+ The head field of a chunk is or'ed with PINUSE_BIT when previous
+ adjacent chunk in use, and or'ed with CINUSE_BIT if this chunk is in
+ use, unless mmapped, in which case both bits are cleared.
+
+ FLAG4_BIT is not used by this malloc, but might be useful in extensions.
+*/
+
+#define PINUSE_BIT (SIZE_T_ONE)
+#define CINUSE_BIT (SIZE_T_TWO)
+#define FLAG4_BIT (SIZE_T_FOUR)
+#define INUSE_BITS (PINUSE_BIT|CINUSE_BIT)
+#define FLAG_BITS (PINUSE_BIT|CINUSE_BIT|FLAG4_BIT)
+
+/* Head value for fenceposts */
+#define FENCEPOST_HEAD (INUSE_BITS|SIZE_T_SIZE)
+
+/* extraction of fields from head words */
+#define cinuse(p) ((p)->head & CINUSE_BIT)
+#define pinuse(p) ((p)->head & PINUSE_BIT)
+#define is_inuse(p) (((p)->head & INUSE_BITS) != PINUSE_BIT)
+#define is_mmapped(p) (((p)->head & INUSE_BITS) == 0)
+
+#define chunksize(p) ((p)->head & ~(FLAG_BITS))
+
+#define clear_pinuse(p) ((p)->head &= ~PINUSE_BIT)
+
+/* Treat space at ptr +/- offset as a chunk */
+#define chunk_plus_offset(p, s) ((mchunkptr)(((char*)(p)) + (s)))
+#define chunk_minus_offset(p, s) ((mchunkptr)(((char*)(p)) - (s)))
+
+/* Ptr to next or previous physical malloc_chunk. */
+#define next_chunk(p) ((mchunkptr)( ((char*)(p)) + ((p)->head & ~FLAG_BITS)))
+#define prev_chunk(p) ((mchunkptr)( ((char*)(p)) - ((p)->prev_foot) ))
+
+/* extract next chunk's pinuse bit */
+#define next_pinuse(p) ((next_chunk(p)->head) & PINUSE_BIT)
+
+/* Get/set size at footer */
+#define get_foot(p, s) (((mchunkptr)((char*)(p) + (s)))->prev_foot)
+#define set_foot(p, s) (((mchunkptr)((char*)(p) + (s)))->prev_foot = (s))
+
+/* Set size, pinuse bit, and foot */
+#define set_size_and_pinuse_of_free_chunk(p, s)\
+ ((p)->head = (s|PINUSE_BIT), set_foot(p, s))
+
+/* Set size, pinuse bit, foot, and clear next pinuse */
+#define set_free_with_pinuse(p, s, n)\
+ (clear_pinuse(n), set_size_and_pinuse_of_free_chunk(p, s))
+
+/* Get the internal overhead associated with chunk p */
+#define overhead_for(p)\
+ (is_mmapped(p)? MMAP_CHUNK_OVERHEAD : CHUNK_OVERHEAD)
+
+/* Return true if malloced space is not necessarily cleared */
+#if MMAP_CLEARS
+#define calloc_must_clear(p) (!is_mmapped(p))
+#else /* MMAP_CLEARS */
+#define calloc_must_clear(p) (1)
+#endif /* MMAP_CLEARS */
+
+/* ---------------------- Overlaid data structures ----------------------- */
+
+/*
+ When chunks are not in use, they are treated as nodes of either
+ lists or trees.
+
+ "Small" chunks are stored in circular doubly-linked lists, and look
+ like this:
+
+ chunk-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Size of previous chunk |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ `head:' | Size of chunk, in bytes |P|
+ mem-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Forward pointer to next chunk in list |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Back pointer to previous chunk in list |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Unused space (may be 0 bytes long) .
+ . .
+ . |
+nextchunk-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ `foot:' | Size of chunk, in bytes |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+
+ Larger chunks are kept in a form of bitwise digital trees (aka
+ tries) keyed on chunksizes. Because malloc_tree_chunks are only for
+ free chunks greater than 256 bytes, their size doesn't impose any
+ constraints on user chunk sizes. Each node looks like:
+
+ chunk-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Size of previous chunk |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ `head:' | Size of chunk, in bytes |P|
+ mem-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Forward pointer to next chunk of same size |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Back pointer to previous chunk of same size |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Pointer to left child (child[0]) |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Pointer to right child (child[1]) |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Pointer to parent |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | bin index of this chunk |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ | Unused space .
+ . |
+nextchunk-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+ `foot:' | Size of chunk, in bytes |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
+
+ Each tree holding treenodes is a tree of unique chunk sizes. Chunks
+ of the same size are arranged in a circularly-linked list, with only
+ the oldest chunk (the next to be used, in our FIFO ordering)
+ actually in the tree. (Tree members are distinguished by a non-null
+ parent pointer.) If a chunk with the same size an an existing node
+ is inserted, it is linked off the existing node using pointers that
+ work in the same way as fd/bk pointers of small chunks.
+
+ Each tree contains a power of 2 sized range of chunk sizes (the
+ smallest is 0x100 <= x < 0x180), which is is divided in half at each
+ tree level, with the chunks in the smaller half of the range (0x100
+ <= x < 0x140 for the top nose) in the left subtree and the larger
+ half (0x140 <= x < 0x180) in the right subtree. This is, of course,
+ done by inspecting individual bits.
+
+ Using these rules, each node's left subtree contains all smaller
+ sizes than its right subtree. However, the node at the root of each
+ subtree has no particular ordering relationship to either. (The
+ dividing line between the subtree sizes is based on trie relation.)
+ If we remove the last chunk of a given size from the interior of the
+ tree, we need to replace it with a leaf node. The tree ordering
+ rules permit a node to be replaced by any leaf below it.
+
+ The smallest chunk in a tree (a common operation in a best-fit
+ allocator) can be found by walking a path to the leftmost leaf in
+ the tree. Unlike a usual binary tree, where we follow left child
+ pointers until we reach a null, here we follow the right child
+ pointer any time the left one is null, until we reach a leaf with
+ both child pointers null. The smallest chunk in the tree will be
+ somewhere along that path.
+
+ The worst case number of steps to add, find, or remove a node is
+ bounded by the number of bits differentiating chunks within
+ bins. Under current bin calculations, this ranges from 6 up to 21
+ (for 32 bit sizes) or up to 53 (for 64 bit sizes). The typical case
+ is of course much better.
+*/
+
+struct malloc_tree_chunk {
+ /* The first four fields must be compatible with malloc_chunk */
+ size_t prev_foot;
+ size_t head;
+ struct malloc_tree_chunk* fd;
+ struct malloc_tree_chunk* bk;
+
+ struct malloc_tree_chunk* child[2];
+ struct malloc_tree_chunk* parent;
+ bindex_t index;
+};
+
+typedef struct malloc_tree_chunk tchunk;
+typedef struct malloc_tree_chunk* tchunkptr;
+typedef struct malloc_tree_chunk* tbinptr; /* The type of bins of trees */
+
+/* A little helper macro for trees */
+#define leftmost_child(t) ((t)->child[0] != 0? (t)->child[0] : (t)->child[1])
+
+/* ----------------------------- Segments -------------------------------- */
+
+/*
+ Each malloc space may include non-contiguous segments, held in a
+ list headed by an embedded malloc_segment record representing the
+ top-most space. Segments also include flags holding properties of
+ the space. Large chunks that are directly allocated by mmap are not
+ included in this list. They are instead independently created and
+ destroyed without otherwise keeping track of them.
+
+ Segment management mainly comes into play for spaces allocated by
+ MMAP. Any call to MMAP might or might not return memory that is
+ adjacent to an existing segment. MORECORE normally contiguously
+ extends the current space, so this space is almost always adjacent,
+ which is simpler and faster to deal with. (This is why MORECORE is
+ used preferentially to MMAP when both are available -- see
+ sys_alloc.) When allocating using MMAP, we don't use any of the
+ hinting mechanisms (inconsistently) supported in various
+ implementations of unix mmap, or distinguish reserving from
+ committing memory. Instead, we just ask for space, and exploit
+ contiguity when we get it. It is probably possible to do
+ better than this on some systems, but no general scheme seems
+ to be significantly better.
+
+ Management entails a simpler variant of the consolidation scheme
+ used for chunks to reduce fragmentation -- new adjacent memory is
+ normally prepended or appended to an existing segment. However,
+ there are limitations compared to chunk consolidation that mostly
+ reflect the fact that segment processing is relatively infrequent
+ (occurring only when getting memory from system) and that we
+ don't expect to have huge numbers of segments:
+
+ * Segments are not indexed, so traversal requires linear scans. (It
+ would be possible to index these, but is not worth the extra
+ overhead and complexity for most programs on most platforms.)
+ * New segments are only appended to old ones when holding top-most
+ memory; if they cannot be prepended to others, they are held in
+ different segments.
+
+ Except for the top-most segment of an mstate, each segment record
+ is kept at the tail of its segment. Segments are added by pushing
+ segment records onto the list headed by &mstate.seg for the
+ containing mstate.
+
+ Segment flags control allocation/merge/deallocation policies:
+ * If EXTERN_BIT set, then we did not allocate this segment,
+ and so should not try to deallocate or merge with others.
+ (This currently holds only for the initial segment passed
+ into create_mspace_with_base.)
+ * If USE_MMAP_BIT set, the segment may be merged with
+ other surrounding mmapped segments and trimmed/de-allocated
+ using munmap.
+ * If neither bit is set, then the segment was obtained using
+ MORECORE so can be merged with surrounding MORECORE'd segments
+ and deallocated/trimmed using MORECORE with negative arguments.
+*/
+
+struct malloc_segment {
+ char* base; /* base address */
+ size_t size; /* allocated size */
+ struct malloc_segment* next; /* ptr to next segment */
+ flag_t sflags; /* mmap and extern flag */
+};
+
+#define is_mmapped_segment(S) ((S)->sflags & USE_MMAP_BIT)
+#define is_extern_segment(S) ((S)->sflags & EXTERN_BIT)
+
+typedef struct malloc_segment msegment;
+typedef struct malloc_segment* msegmentptr;
+
+/* ---------------------------- malloc_state ----------------------------- */
+
+/*
+ A malloc_state holds all of the bookkeeping for a space.
+ The main fields are:
+
+ Top
+ The topmost chunk of the currently active segment. Its size is
+ cached in topsize. The actual size of topmost space is
+ topsize+TOP_FOOT_SIZE, which includes space reserved for adding
+ fenceposts and segment records if necessary when getting more
+ space from the system. The size at which to autotrim top is
+ cached from mparams in trim_check, except that it is disabled if
+ an autotrim fails.
+
+ Designated victim (dv)
+ This is the preferred chunk for servicing small requests that
+ don't have exact fits. It is normally the chunk split off most
+ recently to service another small request. Its size is cached in
+ dvsize. The link fields of this chunk are not maintained since it
+ is not kept in a bin.
+
+ SmallBins
+ An array of bin headers for free chunks. These bins hold chunks
+ with sizes less than MIN_LARGE_SIZE bytes. Each bin contains
+ chunks of all the same size, spaced 8 bytes apart. To simplify
+ use in double-linked lists, each bin header acts as a malloc_chunk
+ pointing to the real first node, if it exists (else pointing to
+ itself). This avoids special-casing for headers. But to avoid
+ waste, we allocate only the fd/bk pointers of bins, and then use
+ repositioning tricks to treat these as the fields of a chunk.
+
+ TreeBins
+ Treebins are pointers to the roots of trees holding a range of
+ sizes. There are 2 equally spaced treebins for each power of two
+ from TREE_SHIFT to TREE_SHIFT+16. The last bin holds anything
+ larger.
+
+ Bin maps
+ There is one bit map for small bins ("smallmap") and one for
+ treebins ("treemap). Each bin sets its bit when non-empty, and
+ clears the bit when empty. Bit operations are then used to avoid
+ bin-by-bin searching -- nearly all "search" is done without ever
+ looking at bins that won't be selected. The bit maps
+ conservatively use 32 bits per map word, even if on 64bit system.
+ For a good description of some of the bit-based techniques used
+ here, see Henry S. Warren Jr's book "Hacker's Delight" (and
+ supplement at http://hackersdelight.org/). Many of these are
+ intended to reduce the branchiness of paths through malloc etc, as
+ well as to reduce the number of memory locations read or written.
+
+ Segments
+ A list of segments headed by an embedded malloc_segment record
+ representing the initial space.
+
+ Address check support
+ The least_addr field is the least address ever obtained from
+ MORECORE or MMAP. Attempted frees and reallocs of any address less
+ than this are trapped (unless INSECURE is defined).
+
+ Magic tag
+ A cross-check field that should always hold same value as mparams.magic.
+
+ Flags
+ Bits recording whether to use MMAP, locks, or contiguous MORECORE
+
+ Statistics
+ Each space keeps track of current and maximum system memory
+ obtained via MORECORE or MMAP.
+
+ Trim support
+ Fields holding the amount of unused topmost memory that should trigger
+ timming, and a counter to force periodic scanning to release unused
+ non-topmost segments.
+
+ Locking
+ If USE_LOCKS is defined, the "mutex" lock is acquired and released
+ around every public call using this mspace.
+
+ Extension support
+ A void* pointer and a size_t field that can be used to help implement
+ extensions to this malloc.
+*/
+
+/* Bin types, widths and sizes */
+#define NSMALLBINS (32U)
+#define NTREEBINS (32U)
+#define SMALLBIN_SHIFT (3U)
+#define SMALLBIN_WIDTH (SIZE_T_ONE << SMALLBIN_SHIFT)
+#define TREEBIN_SHIFT (8U)
+#define MIN_LARGE_SIZE (SIZE_T_ONE << TREEBIN_SHIFT)
+#define MAX_SMALL_SIZE (MIN_LARGE_SIZE - SIZE_T_ONE)
+#define MAX_SMALL_REQUEST (MAX_SMALL_SIZE - CHUNK_ALIGN_MASK - CHUNK_OVERHEAD)
+
+struct malloc_state {
+ binmap_t smallmap;
+ binmap_t treemap;
+ size_t dvsize;
+ size_t topsize;
+ char* least_addr;
+ mchunkptr dv;
+ mchunkptr top;
+ size_t trim_check;
+ size_t release_checks;
+ size_t magic;
+ mchunkptr smallbins[(NSMALLBINS+1)*2];
+ tbinptr treebins[NTREEBINS];
+ size_t footprint;
+ size_t max_footprint;
+ flag_t mflags;
+#if USE_LOCKS
+ MLOCK_T mutex; /* locate lock among fields that rarely change */
+#endif /* USE_LOCKS */
+ msegment seg;
+ void* extp; /* Unused but available for extensions */
+ size_t exts;
+};
+
+typedef struct malloc_state* mstate;
+
+/* ------------- Global malloc_state and malloc_params ------------------- */
+
+/*
+ malloc_params holds global properties, including those that can be
+ dynamically set using mallopt. There is a single instance, mparams,
+ initialized in init_mparams. Note that the non-zeroness of "magic"
+ also serves as an initialization flag.
+*/
+
+struct malloc_params {
+ volatile size_t magic;
+ size_t page_size;
+ size_t granularity;
+ size_t mmap_threshold;
+ size_t trim_threshold;
+ flag_t default_mflags;
+};
+
+static struct malloc_params mparams;
+
+/* Ensure mparams initialized */
+#define ensure_initialization() (void)(mparams.magic != 0 || init_mparams())
+
+#if !ONLY_MSPACES
+
+/* The global malloc_state used for all non-"mspace" calls */
+static struct malloc_state _gm_;
+#define gm (&_gm_)
+#define is_global(M) ((M) == &_gm_)
+
+#endif /* !ONLY_MSPACES */
+
+#define is_initialized(M) ((M)->top != 0)
+
+/* -------------------------- system alloc setup ------------------------- */
+
+/* Operations on mflags */
+
+#define use_lock(M) ((M)->mflags & USE_LOCK_BIT)
+#define enable_lock(M) ((M)->mflags |= USE_LOCK_BIT)
+#define disable_lock(M) ((M)->mflags &= ~USE_LOCK_BIT)
+
+#define use_mmap(M) ((M)->mflags & USE_MMAP_BIT)
+#define enable_mmap(M) ((M)->mflags |= USE_MMAP_BIT)
+#define disable_mmap(M) ((M)->mflags &= ~USE_MMAP_BIT)
+
+#define use_noncontiguous(M) ((M)->mflags & USE_NONCONTIGUOUS_BIT)
+#define disable_contiguous(M) ((M)->mflags |= USE_NONCONTIGUOUS_BIT)
+
+#define set_lock(M,L)\
+ ((M)->mflags = (L)?\
+ ((M)->mflags | USE_LOCK_BIT) :\
+ ((M)->mflags & ~USE_LOCK_BIT))
+
+/* page-align a size */
+#define page_align(S)\
+ (((S) + (mparams.page_size - SIZE_T_ONE)) & ~(mparams.page_size - SIZE_T_ONE))
+
+/* granularity-align a size */
+#define granularity_align(S)\
+ (((S) + (mparams.granularity - SIZE_T_ONE))\
+ & ~(mparams.granularity - SIZE_T_ONE))
+
+
+/* For mmap, use granularity alignment on windows, else page-align */
+#ifdef WIN32
+#define mmap_align(S) granularity_align(S)
+#else
+#define mmap_align(S) page_align(S)
+#endif
+
+/* For sys_alloc, enough padding to ensure can malloc request on success */
+#define SYS_ALLOC_PADDING (TOP_FOOT_SIZE + MALLOC_ALIGNMENT)
+
+#define is_page_aligned(S)\
+ (((size_t)(S) & (mparams.page_size - SIZE_T_ONE)) == 0)
+#define is_granularity_aligned(S)\
+ (((size_t)(S) & (mparams.granularity - SIZE_T_ONE)) == 0)
+
+/* True if segment S holds address A */
+#define segment_holds(S, A)\
+ ((char*)(A) >= S->base && (char*)(A) < S->base + S->size)
+
+/* Return segment holding given address */
+static msegmentptr segment_holding(mstate m, char* addr) {
+ msegmentptr sp = &m->seg;
+ for (;;) {
+ if (addr >= sp->base && addr < sp->base + sp->size)
+ return sp;
+ if ((sp = sp->next) == 0)
+ return 0;
+ }
+}
+
+/* Return true if segment contains a segment link */
+static int has_segment_link(mstate m, msegmentptr ss) {
+ msegmentptr sp = &m->seg;
+ for (;;) {
+ if ((char*)sp >= ss->base && (char*)sp < ss->base + ss->size)
+ return 1;
+ if ((sp = sp->next) == 0)
+ return 0;
+ }
+}
+
+#ifndef MORECORE_CANNOT_TRIM
+#define should_trim(M,s) ((s) > (M)->trim_check)
+#else /* MORECORE_CANNOT_TRIM */
+#define should_trim(M,s) (0)
+#endif /* MORECORE_CANNOT_TRIM */
+
+/*
+ TOP_FOOT_SIZE is padding at the end of a segment, including space
+ that may be needed to place segment records and fenceposts when new
+ noncontiguous segments are added.
+*/
+#define TOP_FOOT_SIZE\
+ (align_offset(chunk2mem(0))+pad_request(sizeof(struct malloc_segment))+MIN_CHUNK_SIZE)
+
+
+/* ------------------------------- Hooks -------------------------------- */
+
+/*
+ PREACTION should be defined to return 0 on success, and nonzero on
+ failure. If you are not using locking, you can redefine these to do
+ anything you like.
+*/
+
+#if USE_LOCKS
+
+#define PREACTION(M) ((use_lock(M))? ACQUIRE_LOCK(&(M)->mutex) : 0)
+#define POSTACTION(M) { if (use_lock(M)) RELEASE_LOCK(&(M)->mutex); }
+#else /* USE_LOCKS */
+
+#ifndef PREACTION
+#define PREACTION(M) (0)
+#endif /* PREACTION */
+
+#ifndef POSTACTION
+#define POSTACTION(M)
+#endif /* POSTACTION */
+
+#endif /* USE_LOCKS */
+
+/*
+ CORRUPTION_ERROR_ACTION is triggered upon detected bad addresses.
+ USAGE_ERROR_ACTION is triggered on detected bad frees and
+ reallocs. The argument p is an address that might have triggered the
+ fault. It is ignored by the two predefined actions, but might be
+ useful in custom actions that try to help diagnose errors.
+*/
+
+#if PROCEED_ON_ERROR
+
+/* A count of the number of corruption errors causing resets */
+int malloc_corruption_error_count;
+
+/* default corruption action */
+static void reset_on_error(mstate m);
+
+#define CORRUPTION_ERROR_ACTION(m) reset_on_error(m)
+#define USAGE_ERROR_ACTION(m, p)
+
+#else /* PROCEED_ON_ERROR */
+
+#ifndef CORRUPTION_ERROR_ACTION
+#define CORRUPTION_ERROR_ACTION(m) ABORT
+#endif /* CORRUPTION_ERROR_ACTION */
+
+#ifndef USAGE_ERROR_ACTION
+#define USAGE_ERROR_ACTION(m,p) ABORT
+#endif /* USAGE_ERROR_ACTION */
+
+#endif /* PROCEED_ON_ERROR */
+
+/* -------------------------- Debugging setup ---------------------------- */
+
+#if ! DEBUG
+
+#define check_free_chunk(M,P)
+#define check_inuse_chunk(M,P)
+#define check_malloced_chunk(M,P,N)
+#define check_mmapped_chunk(M,P)
+#define check_malloc_state(M)
+#define check_top_chunk(M,P)
+
+#else /* DEBUG */
+#define check_free_chunk(M,P) do_check_free_chunk(M,P)
+#define check_inuse_chunk(M,P) do_check_inuse_chunk(M,P)
+#define check_top_chunk(M,P) do_check_top_chunk(M,P)
+#define check_malloced_chunk(M,P,N) do_check_malloced_chunk(M,P,N)
+#define check_mmapped_chunk(M,P) do_check_mmapped_chunk(M,P)
+#define check_malloc_state(M) do_check_malloc_state(M)
+
+static void do_check_any_chunk(mstate m, mchunkptr p);
+static void do_check_top_chunk(mstate m, mchunkptr p);
+static void do_check_mmapped_chunk(mstate m, mchunkptr p);
+static void do_check_inuse_chunk(mstate m, mchunkptr p);
+static void do_check_free_chunk(mstate m, mchunkptr p);
+static void do_check_malloced_chunk(mstate m, void* mem, size_t s);
+static void do_check_tree(mstate m, tchunkptr t);
+static void do_check_treebin(mstate m, bindex_t i);
+static void do_check_smallbin(mstate m, bindex_t i);
+static void do_check_malloc_state(mstate m);
+static int bin_find(mstate m, mchunkptr x);
+static size_t traverse_and_check(mstate m);
+#endif /* DEBUG */
+
+/* ---------------------------- Indexing Bins ---------------------------- */
+
+#define is_small(s) (((s) >> SMALLBIN_SHIFT) < NSMALLBINS)
+#define small_index(s) ((s) >> SMALLBIN_SHIFT)
+#define small_index2size(i) ((i) << SMALLBIN_SHIFT)
+#define MIN_SMALL_INDEX (small_index(MIN_CHUNK_SIZE))
+
+/* addressing by index. See above about smallbin repositioning */
+#define smallbin_at(M, i) ((sbinptr)((char*)&((M)->smallbins[(i)<<1])))
+#define treebin_at(M,i) (&((M)->treebins[i]))
+
+/* assign tree index for size S to variable I. Use x86 asm if possible */
+#if defined(__GNUC__) && (defined(__i386__) || defined(__x86_64__))
+#define compute_tree_index(S, I)\
+{\
+ unsigned int X = S >> TREEBIN_SHIFT;\
+ if (X == 0)\
+ I = 0;\
+ else if (X > 0xFFFF)\
+ I = NTREEBINS-1;\
+ else {\
+ unsigned int K;\
+ __asm__("bsrl\t%1, %0\n\t" : "=r" (K) : "g" (X));\
+ I = (bindex_t)((K << 1) + ((S >> (K + (TREEBIN_SHIFT-1)) & 1)));\
+ }\
+}
+
+#elif defined (__INTEL_COMPILER)
+#define compute_tree_index(S, I)\
+{\
+ size_t X = S >> TREEBIN_SHIFT;\
+ if (X == 0)\
+ I = 0;\
+ else if (X > 0xFFFF)\
+ I = NTREEBINS-1;\
+ else {\
+ unsigned int K = _bit_scan_reverse (X); \
+ I = (bindex_t)((K << 1) + ((S >> (K + (TREEBIN_SHIFT-1)) & 1)));\
+ }\
+}
+
+#elif defined(_MSC_VER) && _MSC_VER>=1300
+#define compute_tree_index(S, I)\
+{\
+ size_t X = S >> TREEBIN_SHIFT;\
+ if (X == 0)\
+ I = 0;\
+ else if (X > 0xFFFF)\
+ I = NTREEBINS-1;\
+ else {\
+ unsigned int K;\
+ _BitScanReverse((DWORD *) &K, X);\
+ I = (bindex_t)((K << 1) + ((S >> (K + (TREEBIN_SHIFT-1)) & 1)));\
+ }\
+}
+
+#else /* GNUC */
+#define compute_tree_index(S, I)\
+{\
+ size_t X = S >> TREEBIN_SHIFT;\
+ if (X == 0)\
+ I = 0;\
+ else if (X > 0xFFFF)\
+ I = NTREEBINS-1;\
+ else {\
+ unsigned int Y = (unsigned int)X;\
+ unsigned int N = ((Y - 0x100) >> 16) & 8;\
+ unsigned int K = (((Y <<= N) - 0x1000) >> 16) & 4;\
+ N += K;\
+ N += K = (((Y <<= K) - 0x4000) >> 16) & 2;\
+ K = 14 - N + ((Y <<= K) >> 15);\
+ I = (K << 1) + ((S >> (K + (TREEBIN_SHIFT-1)) & 1));\
+ }\
+}
+#endif /* GNUC */
+
+/* Bit representing maximum resolved size in a treebin at i */
+#define bit_for_tree_index(i) \
+ (i == NTREEBINS-1)? (SIZE_T_BITSIZE-1) : (((i) >> 1) + TREEBIN_SHIFT - 2)
+
+/* Shift placing maximum resolved bit in a treebin at i as sign bit */
+#define leftshift_for_tree_index(i) \
+ ((i == NTREEBINS-1)? 0 : \
+ ((SIZE_T_BITSIZE-SIZE_T_ONE) - (((i) >> 1) + TREEBIN_SHIFT - 2)))
+
+/* The size of the smallest chunk held in bin with index i */
+#define minsize_for_tree_index(i) \
+ ((SIZE_T_ONE << (((i) >> 1) + TREEBIN_SHIFT)) | \
+ (((size_t)((i) & SIZE_T_ONE)) << (((i) >> 1) + TREEBIN_SHIFT - 1)))
+
+
+/* ------------------------ Operations on bin maps ----------------------- */
+
+/* bit corresponding to given index */
+#define idx2bit(i) ((binmap_t)(1) << (i))
+
+/* Mark/Clear bits with given index */
+#define mark_smallmap(M,i) ((M)->smallmap |= idx2bit(i))
+#define clear_smallmap(M,i) ((M)->smallmap &= ~idx2bit(i))
+#define smallmap_is_marked(M,i) ((M)->smallmap & idx2bit(i))
+
+#define mark_treemap(M,i) ((M)->treemap |= idx2bit(i))
+#define clear_treemap(M,i) ((M)->treemap &= ~idx2bit(i))
+#define treemap_is_marked(M,i) ((M)->treemap & idx2bit(i))
+
+/* isolate the least set bit of a bitmap */
+#define least_bit(x) ((x) & -(x))
+
+/* mask with all bits to left of least bit of x on */
+#define left_bits(x) ((x<<1) | -(x<<1))
+
+/* mask with all bits to left of or equal to least bit of x on */
+#define same_or_left_bits(x) ((x) | -(x))
+
+/* index corresponding to given bit. Use x86 asm if possible */
+
+#if defined(__GNUC__) && (defined(__i386__) || defined(__x86_64__))
+#define compute_bit2idx(X, I)\
+{\
+ unsigned int J;\
+ __asm__("bsfl\t%1, %0\n\t" : "=r" (J) : "g" (X));\
+ I = (bindex_t)J;\
+}
+
+#elif defined (__INTEL_COMPILER)
+#define compute_bit2idx(X, I)\
+{\
+ unsigned int J;\
+ J = _bit_scan_forward (X); \
+ I = (bindex_t)J;\
+}
+
+#elif defined(_MSC_VER) && _MSC_VER>=1300
+#define compute_bit2idx(X, I)\
+{\
+ unsigned int J;\
+ _BitScanForward((DWORD *) &J, X);\
+ I = (bindex_t)J;\
+}
+
+#elif USE_BUILTIN_FFS
+#define compute_bit2idx(X, I) I = ffs(X)-1
+
+#else
+#define compute_bit2idx(X, I)\
+{\
+ unsigned int Y = X - 1;\
+ unsigned int K = Y >> (16-4) & 16;\
+ unsigned int N = K; Y >>= K;\
+ N += K = Y >> (8-3) & 8; Y >>= K;\
+ N += K = Y >> (4-2) & 4; Y >>= K;\
+ N += K = Y >> (2-1) & 2; Y >>= K;\
+ N += K = Y >> (1-0) & 1; Y >>= K;\
+ I = (bindex_t)(N + Y);\
+}
+#endif /* GNUC */
+
+
+/* ----------------------- Runtime Check Support ------------------------- */
+
+/*
+ For security, the main invariant is that malloc/free/etc never
+ writes to a static address other than malloc_state, unless static
+ malloc_state itself has been corrupted, which cannot occur via
+ malloc (because of these checks). In essence this means that we
+ believe all pointers, sizes, maps etc held in malloc_state, but
+ check all of those linked or offsetted from other embedded data
+ structures. These checks are interspersed with main code in a way
+ that tends to minimize their run-time cost.
+
+ When FOOTERS is defined, in addition to range checking, we also
+ verify footer fields of inuse chunks, which can be used guarantee
+ that the mstate controlling malloc/free is intact. This is a
+ streamlined version of the approach described by William Robertson
+ et al in "Run-time Detection of Heap-based Overflows" LISA'03
+ http://www.usenix.org/events/lisa03/tech/robertson.html The footer
+ of an inuse chunk holds the xor of its mstate and a random seed,
+ that is checked upon calls to free() and realloc(). This is
+ (probablistically) unguessable from outside the program, but can be
+ computed by any code successfully malloc'ing any chunk, so does not
+ itself provide protection against code that has already broken
+ security through some other means. Unlike Robertson et al, we
+ always dynamically check addresses of all offset chunks (previous,
+ next, etc). This turns out to be cheaper than relying on hashes.
+*/
+
+#if !INSECURE
+/* Check if address a is at least as high as any from MORECORE or MMAP */
+#define ok_address(M, a) ((char*)(a) >= (M)->least_addr)
+/* Check if address of next chunk n is higher than base chunk p */
+#define ok_next(p, n) ((char*)(p) < (char*)(n))
+/* Check if p has inuse status */
+#define ok_inuse(p) is_inuse(p)
+/* Check if p has its pinuse bit on */
+#define ok_pinuse(p) pinuse(p)
+
+#else /* !INSECURE */
+#define ok_address(M, a) (1)
+#define ok_next(b, n) (1)
+#define ok_inuse(p) (1)
+#define ok_pinuse(p) (1)
+#endif /* !INSECURE */
+
+#if (FOOTERS && !INSECURE)
+/* Check if (alleged) mstate m has expected magic field */
+#define ok_magic(M) ((M)->magic == mparams.magic)
+#else /* (FOOTERS && !INSECURE) */
+#define ok_magic(M) (1)
+#endif /* (FOOTERS && !INSECURE) */
+
+
+/* In gcc, use __builtin_expect to minimize impact of checks */
+#if !INSECURE
+#if defined(__GNUC__) && __GNUC__ >= 3
+#define RTCHECK(e) __builtin_expect(e, 1)
+#else /* GNUC */
+#define RTCHECK(e) (e)
+#endif /* GNUC */
+#else /* !INSECURE */
+#define RTCHECK(e) (1)
+#endif /* !INSECURE */
+
+/* macros to set up inuse chunks with or without footers */
+
+#if !FOOTERS
+
+#define mark_inuse_foot(M,p,s)
+
+/* Macros for setting head/foot of non-mmapped chunks */
+
+/* Set cinuse bit and pinuse bit of next chunk */
+#define set_inuse(M,p,s)\
+ ((p)->head = (((p)->head & PINUSE_BIT)|s|CINUSE_BIT),\
+ ((mchunkptr)(((char*)(p)) + (s)))->head |= PINUSE_BIT)
+
+/* Set cinuse and pinuse of this chunk and pinuse of next chunk */
+#define set_inuse_and_pinuse(M,p,s)\
+ ((p)->head = (s|PINUSE_BIT|CINUSE_BIT),\
+ ((mchunkptr)(((char*)(p)) + (s)))->head |= PINUSE_BIT)
+
+/* Set size, cinuse and pinuse bit of this chunk */
+#define set_size_and_pinuse_of_inuse_chunk(M, p, s)\
+ ((p)->head = (s|PINUSE_BIT|CINUSE_BIT))
+
+#else /* FOOTERS */
+
+/* Set foot of inuse chunk to be xor of mstate and seed */
+#define mark_inuse_foot(M,p,s)\
+ (((mchunkptr)((char*)(p) + (s)))->prev_foot = ((size_t)(M) ^ mparams.magic))
+
+#define get_mstate_for(p)\
+ ((mstate)(((mchunkptr)((char*)(p) +\
+ (chunksize(p))))->prev_foot ^ mparams.magic))
+
+#define set_inuse(M,p,s)\
+ ((p)->head = (((p)->head & PINUSE_BIT)|s|CINUSE_BIT),\
+ (((mchunkptr)(((char*)(p)) + (s)))->head |= PINUSE_BIT), \
+ mark_inuse_foot(M,p,s))
+
+#define set_inuse_and_pinuse(M,p,s)\
+ ((p)->head = (s|PINUSE_BIT|CINUSE_BIT),\
+ (((mchunkptr)(((char*)(p)) + (s)))->head |= PINUSE_BIT),\
+ mark_inuse_foot(M,p,s))
+
+#define set_size_and_pinuse_of_inuse_chunk(M, p, s)\
+ ((p)->head = (s|PINUSE_BIT|CINUSE_BIT),\
+ mark_inuse_foot(M, p, s))
+
+#endif /* !FOOTERS */
+
+/* ---------------------------- setting mparams -------------------------- */
+
+/* Initialize mparams */
+static int init_mparams(void) {
+#ifdef NEED_GLOBAL_LOCK_INIT
+ if (malloc_global_mutex_status <= 0)
+ init_malloc_global_mutex();
+#endif
+
+ ACQUIRE_MALLOC_GLOBAL_LOCK();
+ if (mparams.magic == 0) {
+ size_t magic;
+ size_t psize;
+ size_t gsize;
+
+#ifndef WIN32
+ psize = malloc_getpagesize;
+ gsize = ((DEFAULT_GRANULARITY != 0)? DEFAULT_GRANULARITY : psize);
+#else /* WIN32 */
+ {
+ SYSTEM_INFO system_info;
+ GetSystemInfo(&system_info);
+ psize = system_info.dwPageSize;
+ gsize = ((DEFAULT_GRANULARITY != 0)?
+ DEFAULT_GRANULARITY : system_info.dwAllocationGranularity);
+ }
+#endif /* WIN32 */
+
+ /* Sanity-check configuration:
+ size_t must be unsigned and as wide as pointer type.
+ ints must be at least 4 bytes.
+ alignment must be at least 8.
+ Alignment, min chunk size, and page size must all be powers of 2.
+ */
+ if ((sizeof(size_t) != sizeof(char*)) ||
+ (MAX_SIZE_T < MIN_CHUNK_SIZE) ||
+ (sizeof(int) < 4) ||
+ (MALLOC_ALIGNMENT < (size_t)8U) ||
+ ((MALLOC_ALIGNMENT & (MALLOC_ALIGNMENT-SIZE_T_ONE)) != 0) ||
+ ((MCHUNK_SIZE & (MCHUNK_SIZE-SIZE_T_ONE)) != 0) ||
+ ((gsize & (gsize-SIZE_T_ONE)) != 0) ||
+ ((psize & (psize-SIZE_T_ONE)) != 0))
+ ABORT;
+
+ mparams.granularity = gsize;
+ mparams.page_size = psize;
+ mparams.mmap_threshold = DEFAULT_MMAP_THRESHOLD;
+ mparams.trim_threshold = DEFAULT_TRIM_THRESHOLD;
+#if MORECORE_CONTIGUOUS
+ mparams.default_mflags = USE_LOCK_BIT|USE_MMAP_BIT;
+#else /* MORECORE_CONTIGUOUS */
+ mparams.default_mflags = USE_LOCK_BIT|USE_MMAP_BIT|USE_NONCONTIGUOUS_BIT;
+#endif /* MORECORE_CONTIGUOUS */
+
+#if !ONLY_MSPACES
+ /* Set up lock for main malloc area */
+ gm->mflags = mparams.default_mflags;
+ INITIAL_LOCK(&gm->mutex);
+#endif
+
+ {
+#if USE_DEV_RANDOM
+ int fd;
+ unsigned char buf[sizeof(size_t)];
+ /* Try to use /dev/urandom, else fall back on using time */
+ if ((fd = open("/dev/urandom", O_RDONLY)) >= 0 &&
+ read(fd, buf, sizeof(buf)) == sizeof(buf)) {
+ magic = *((size_t *) buf);
+ close(fd);
+ }
+ else
+#endif /* USE_DEV_RANDOM */
+#ifdef WIN32
+ magic = (size_t)(GetTickCount() ^ (size_t)0x55555555U);
+#else
+ magic = (size_t)(time(0) ^ (size_t)0x55555555U);
+#endif
+ magic |= (size_t)8U; /* ensure nonzero */
+ magic &= ~(size_t)7U; /* improve chances of fault for bad values */
+ mparams.magic = magic;
+ }
+ }
+
+ RELEASE_MALLOC_GLOBAL_LOCK();
+ return 1;
+}
+
+/* support for mallopt */
+static int change_mparam(int param_number, int value) {
+ size_t val;
+ ensure_initialization();
+ val = (value == -1)? MAX_SIZE_T : (size_t)value;
+ switch(param_number) {
+ case M_TRIM_THRESHOLD:
+ mparams.trim_threshold = val;
+ return 1;
+ case M_GRANULARITY:
+ if (val >= mparams.page_size && ((val & (val-1)) == 0)) {
+ mparams.granularity = val;
+ return 1;
+ }
+ else
+ return 0;
+ case M_MMAP_THRESHOLD:
+ mparams.mmap_threshold = val;
+ return 1;
+ default:
+ return 0;
+ }
+}
+
+#if DEBUG
+/* ------------------------- Debugging Support --------------------------- */
+
+/* Check properties of any chunk, whether free, inuse, mmapped etc */
+static void do_check_any_chunk(mstate m, mchunkptr p) {
+ assert((is_aligned(chunk2mem(p))) || (p->head == FENCEPOST_HEAD));
+ assert(ok_address(m, p));
+}
+
+/* Check properties of top chunk */
+static void do_check_top_chunk(mstate m, mchunkptr p) {
+ msegmentptr sp = segment_holding(m, (char*)p);
+ size_t sz = p->head & ~INUSE_BITS; /* third-lowest bit can be set! */
+ assert(sp != 0);
+ assert((is_aligned(chunk2mem(p))) || (p->head == FENCEPOST_HEAD));
+ assert(ok_address(m, p));
+ assert(sz == m->topsize);
+ assert(sz > 0);
+ assert(sz == ((sp->base + sp->size) - (char*)p) - TOP_FOOT_SIZE);
+ assert(pinuse(p));
+ assert(!pinuse(chunk_plus_offset(p, sz)));
+}
+
+/* Check properties of (inuse) mmapped chunks */
+static void do_check_mmapped_chunk(mstate m, mchunkptr p) {
+ size_t sz = chunksize(p);
+ size_t len = (sz + (p->prev_foot) + MMAP_FOOT_PAD);
+ assert(is_mmapped(p));
+ assert(use_mmap(m));
+ assert((is_aligned(chunk2mem(p))) || (p->head == FENCEPOST_HEAD));
+ assert(ok_address(m, p));
+ assert(!is_small(sz));
+ assert((len & (mparams.page_size-SIZE_T_ONE)) == 0);
+ assert(chunk_plus_offset(p, sz)->head == FENCEPOST_HEAD);
+ assert(chunk_plus_offset(p, sz+SIZE_T_SIZE)->head == 0);
+}
+
+/* Check properties of inuse chunks */
+static void do_check_inuse_chunk(mstate m, mchunkptr p) {
+ do_check_any_chunk(m, p);
+ assert(is_inuse(p));
+ assert(next_pinuse(p));
+ /* If not pinuse and not mmapped, previous chunk has OK offset */
+ assert(is_mmapped(p) || pinuse(p) || next_chunk(prev_chunk(p)) == p);
+ if (is_mmapped(p))
+ do_check_mmapped_chunk(m, p);
+}
+
+/* Check properties of free chunks */
+static void do_check_free_chunk(mstate m, mchunkptr p) {
+ size_t sz = chunksize(p);
+ mchunkptr next = chunk_plus_offset(p, sz);
+ do_check_any_chunk(m, p);
+ assert(!is_inuse(p));
+ assert(!next_pinuse(p));
+ assert (!is_mmapped(p));
+ if (p != m->dv && p != m->top) {
+ if (sz >= MIN_CHUNK_SIZE) {
+ assert((sz & CHUNK_ALIGN_MASK) == 0);
+ assert(is_aligned(chunk2mem(p)));
+ assert(next->prev_foot == sz);
+ assert(pinuse(p));
+ assert (next == m->top || is_inuse(next));
+ assert(p->fd->bk == p);
+ assert(p->bk->fd == p);
+ }
+ else /* markers are always of size SIZE_T_SIZE */
+ assert(sz == SIZE_T_SIZE);
+ }
+}
+
+/* Check properties of malloced chunks at the point they are malloced */
+static void do_check_malloced_chunk(mstate m, void* mem, size_t s) {
+ if (mem != 0) {
+ mchunkptr p = mem2chunk(mem);
+ size_t sz = p->head & ~INUSE_BITS;
+ do_check_inuse_chunk(m, p);
+ assert((sz & CHUNK_ALIGN_MASK) == 0);
+ assert(sz >= MIN_CHUNK_SIZE);
+ assert(sz >= s);
+ /* unless mmapped, size is less than MIN_CHUNK_SIZE more than request */
+ assert(is_mmapped(p) || sz < (s + MIN_CHUNK_SIZE));
+ }
+}
+
+/* Check a tree and its subtrees. */
+static void do_check_tree(mstate m, tchunkptr t) {
+ tchunkptr head = 0;
+ tchunkptr u = t;
+ bindex_t tindex = t->index;
+ size_t tsize = chunksize(t);
+ bindex_t idx;
+ compute_tree_index(tsize, idx);
+ assert(tindex == idx);
+ assert(tsize >= MIN_LARGE_SIZE);
+ assert(tsize >= minsize_for_tree_index(idx));
+ assert((idx == NTREEBINS-1) || (tsize < minsize_for_tree_index((idx+1))));
+
+ do { /* traverse through chain of same-sized nodes */
+ do_check_any_chunk(m, ((mchunkptr)u));
+ assert(u->index == tindex);
+ assert(chunksize(u) == tsize);
+ assert(!is_inuse(u));
+ assert(!next_pinuse(u));
+ assert(u->fd->bk == u);
+ assert(u->bk->fd == u);
+ if (u->parent == 0) {
+ assert(u->child[0] == 0);
+ assert(u->child[1] == 0);
+ }
+ else {
+ assert(head == 0); /* only one node on chain has parent */
+ head = u;
+ assert(u->parent != u);
+ assert (u->parent->child[0] == u ||
+ u->parent->child[1] == u ||
+ *((tbinptr*)(u->parent)) == u);
+ if (u->child[0] != 0) {
+ assert(u->child[0]->parent == u);
+ assert(u->child[0] != u);
+ do_check_tree(m, u->child[0]);
+ }
+ if (u->child[1] != 0) {
+ assert(u->child[1]->parent == u);
+ assert(u->child[1] != u);
+ do_check_tree(m, u->child[1]);
+ }
+ if (u->child[0] != 0 && u->child[1] != 0) {
+ assert(chunksize(u->child[0]) < chunksize(u->child[1]));
+ }
+ }
+ u = u->fd;
+ } while (u != t);
+ assert(head != 0);
+}
+
+/* Check all the chunks in a treebin. */
+static void do_check_treebin(mstate m, bindex_t i) {
+ tbinptr* tb = treebin_at(m, i);
+ tchunkptr t = *tb;
+ int empty = (m->treemap & (1U << i)) == 0;
+ if (t == 0)
+ assert(empty);
+ if (!empty)
+ do_check_tree(m, t);
+}
+
+/* Check all the chunks in a smallbin. */
+static void do_check_smallbin(mstate m, bindex_t i) {
+ sbinptr b = smallbin_at(m, i);
+ mchunkptr p = b->bk;
+ unsigned int empty = (m->smallmap & (1U << i)) == 0;
+ if (p == b)
+ assert(empty);
+ if (!empty) {
+ for (; p != b; p = p->bk) {
+ size_t size = chunksize(p);
+ mchunkptr q;
+ /* each chunk claims to be free */
+ do_check_free_chunk(m, p);
+ /* chunk belongs in bin */
+ assert(small_index(size) == i);
+ assert(p->bk == b || chunksize(p->bk) == chunksize(p));
+ /* chunk is followed by an inuse chunk */
+ q = next_chunk(p);
+ if (q->head != FENCEPOST_HEAD)
+ do_check_inuse_chunk(m, q);
+ }
+ }
+}
+
+/* Find x in a bin. Used in other check functions. */
+static int bin_find(mstate m, mchunkptr x) {
+ size_t size = chunksize(x);
+ if (is_small(size)) {
+ bindex_t sidx = small_index(size);
+ sbinptr b = smallbin_at(m, sidx);
+ if (smallmap_is_marked(m, sidx)) {
+ mchunkptr p = b;
+ do {
+ if (p == x)
+ return 1;
+ } while ((p = p->fd) != b);
+ }
+ }
+ else {
+ bindex_t tidx;
+ compute_tree_index(size, tidx);
+ if (treemap_is_marked(m, tidx)) {
+ tchunkptr t = *treebin_at(m, tidx);
+ size_t sizebits = size << leftshift_for_tree_index(tidx);
+ while (t != 0 && chunksize(t) != size) {
+ t = t->child[(sizebits >> (SIZE_T_BITSIZE-SIZE_T_ONE)) & 1];
+ sizebits <<= 1;
+ }
+ if (t != 0) {
+ tchunkptr u = t;
+ do {
+ if (u == (tchunkptr)x)
+ return 1;
+ } while ((u = u->fd) != t);
+ }
+ }
+ }
+ return 0;
+}
+
+/* Traverse each chunk and check it; return total */
+static size_t traverse_and_check(mstate m) {
+ size_t sum = 0;
+ if (is_initialized(m)) {
+ msegmentptr s = &m->seg;
+ sum += m->topsize + TOP_FOOT_SIZE;
+ while (s != 0) {
+ mchunkptr q = align_as_chunk(s->base);
+ mchunkptr lastq = 0;
+ assert(pinuse(q));
+ while (segment_holds(s, q) &&
+ q != m->top && q->head != FENCEPOST_HEAD) {
+ sum += chunksize(q);
+ if (is_inuse(q)) {
+ assert(!bin_find(m, q));
+ do_check_inuse_chunk(m, q);
+ }
+ else {
+ assert(q == m->dv || bin_find(m, q));
+ assert(lastq == 0 || is_inuse(lastq)); /* Not 2 consecutive free */
+ do_check_free_chunk(m, q);
+ }
+ lastq = q;
+ q = next_chunk(q);
+ }
+ s = s->next;
+ }
+ }
+ return sum;
+}
+
+/* Check all properties of malloc_state. */
+static void do_check_malloc_state(mstate m) {
+ bindex_t i;
+ size_t total;
+ /* check bins */
+ for (i = 0; i < NSMALLBINS; ++i)
+ do_check_smallbin(m, i);
+ for (i = 0; i < NTREEBINS; ++i)
+ do_check_treebin(m, i);
+
+ if (m->dvsize != 0) { /* check dv chunk */
+ do_check_any_chunk(m, m->dv);
+ assert(m->dvsize == chunksize(m->dv));
+ assert(m->dvsize >= MIN_CHUNK_SIZE);
+ assert(bin_find(m, m->dv) == 0);
+ }
+
+ if (m->top != 0) { /* check top chunk */
+ do_check_top_chunk(m, m->top);
+ /*assert(m->topsize == chunksize(m->top)); redundant */
+ assert(m->topsize > 0);
+ assert(bin_find(m, m->top) == 0);
+ }
+
+ total = traverse_and_check(m);
+ assert(total <= m->footprint);
+ assert(m->footprint <= m->max_footprint);
+}
+#endif /* DEBUG */
+
+/* ----------------------------- statistics ------------------------------ */
+
+#if !NO_MALLINFO
+static struct mallinfo internal_mallinfo(mstate m) {
+ struct mallinfo nm = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
+ ensure_initialization();
+ if (!PREACTION(m)) {
+ check_malloc_state(m);
+ if (is_initialized(m)) {
+ size_t nfree = SIZE_T_ONE; /* top always free */
+ size_t mfree = m->topsize + TOP_FOOT_SIZE;
+ size_t sum = mfree;
+ msegmentptr s = &m->seg;
+ while (s != 0) {
+ mchunkptr q = align_as_chunk(s->base);
+ while (segment_holds(s, q) &&
+ q != m->top && q->head != FENCEPOST_HEAD) {
+ size_t sz = chunksize(q);
+ sum += sz;
+ if (!is_inuse(q)) {
+ mfree += sz;
+ ++nfree;
+ }
+ q = next_chunk(q);
+ }
+ s = s->next;
+ }
+
+ nm.arena = sum;
+ nm.ordblks = nfree;
+ nm.hblkhd = m->footprint - sum;
+ nm.usmblks = m->max_footprint;
+ nm.uordblks = m->footprint - mfree;
+ nm.fordblks = mfree;
+ nm.keepcost = m->topsize;
+ }
+
+ POSTACTION(m);
+ }
+ return nm;
+}
+#endif /* !NO_MALLINFO */
+
+static void internal_malloc_stats(mstate m) {
+ ensure_initialization();
+ if (!PREACTION(m)) {
+ size_t maxfp = 0;
+ size_t fp = 0;
+ size_t used = 0;
+ check_malloc_state(m);
+ if (is_initialized(m)) {
+ msegmentptr s = &m->seg;
+ maxfp = m->max_footprint;
+ fp = m->footprint;
+ used = fp - (m->topsize + TOP_FOOT_SIZE);
+
+ while (s != 0) {
+ mchunkptr q = align_as_chunk(s->base);
+ while (segment_holds(s, q) &&
+ q != m->top && q->head != FENCEPOST_HEAD) {
+ if (!is_inuse(q))
+ used -= chunksize(q);
+ q = next_chunk(q);
+ }
+ s = s->next;
+ }
+ }
+
+ fprintf(stderr, "max system bytes = %10lu\n", (unsigned long)(maxfp));
+ fprintf(stderr, "system bytes = %10lu\n", (unsigned long)(fp));
+ fprintf(stderr, "in use bytes = %10lu\n", (unsigned long)(used));
+
+ POSTACTION(m);
+ }
+}
+
+/* ----------------------- Operations on smallbins ----------------------- */
+
+/*
+ Various forms of linking and unlinking are defined as macros. Even
+ the ones for trees, which are very long but have very short typical
+ paths. This is ugly but reduces reliance on inlining support of
+ compilers.
+*/
+
+/* Link a free chunk into a smallbin */
+#define insert_small_chunk(M, P, S) {\
+ bindex_t I = small_index(S);\
+ mchunkptr B = smallbin_at(M, I);\
+ mchunkptr F = B;\
+ assert(S >= MIN_CHUNK_SIZE);\
+ if (!smallmap_is_marked(M, I))\
+ mark_smallmap(M, I);\
+ else if (RTCHECK(ok_address(M, B->fd)))\
+ F = B->fd;\
+ else {\
+ CORRUPTION_ERROR_ACTION(M);\
+ }\
+ B->fd = P;\
+ F->bk = P;\
+ P->fd = F;\
+ P->bk = B;\
+}
+
+/* Unlink a chunk from a smallbin */
+#define unlink_small_chunk(M, P, S) {\
+ mchunkptr F = P->fd;\
+ mchunkptr B = P->bk;\
+ bindex_t I = small_index(S);\
+ assert(P != B);\
+ assert(P != F);\
+ assert(chunksize(P) == small_index2size(I));\
+ if (F == B)\
+ clear_smallmap(M, I);\
+ else if (RTCHECK((F == smallbin_at(M,I) || ok_address(M, F)) &&\
+ (B == smallbin_at(M,I) || ok_address(M, B)))) {\
+ F->bk = B;\
+ B->fd = F;\
+ }\
+ else {\
+ CORRUPTION_ERROR_ACTION(M);\
+ }\
+}
+
+/* Unlink the first chunk from a smallbin */
+#define unlink_first_small_chunk(M, B, P, I) {\
+ mchunkptr F = P->fd;\
+ assert(P != B);\
+ assert(P != F);\
+ assert(chunksize(P) == small_index2size(I));\
+ if (B == F)\
+ clear_smallmap(M, I);\
+ else if (RTCHECK(ok_address(M, F))) {\
+ B->fd = F;\
+ F->bk = B;\
+ }\
+ else {\
+ CORRUPTION_ERROR_ACTION(M);\
+ }\
+}
+
+
+
+/* Replace dv node, binning the old one */
+/* Used only when dvsize known to be small */
+#define replace_dv(M, P, S) {\
+ size_t DVS = M->dvsize;\
+ if (DVS != 0) {\
+ mchunkptr DV = M->dv;\
+ assert(is_small(DVS));\
+ insert_small_chunk(M, DV, DVS);\
+ }\
+ M->dvsize = S;\
+ M->dv = P;\
+}
+
+/* ------------------------- Operations on trees ------------------------- */
+
+/* Insert chunk into tree */
+#define insert_large_chunk(M, X, S) {\
+ tbinptr* H;\
+ bindex_t I;\
+ compute_tree_index(S, I);\
+ H = treebin_at(M, I);\
+ X->index = I;\
+ X->child[0] = X->child[1] = 0;\
+ if (!treemap_is_marked(M, I)) {\
+ mark_treemap(M, I);\
+ *H = X;\
+ X->parent = (tchunkptr)H;\
+ X->fd = X->bk = X;\
+ }\
+ else {\
+ tchunkptr T = *H;\
+ size_t K = S << leftshift_for_tree_index(I);\
+ for (;;) {\
+ if (chunksize(T) != S) {\
+ tchunkptr* C = &(T->child[(K >> (SIZE_T_BITSIZE-SIZE_T_ONE)) & 1]);\
+ K <<= 1;\
+ if (*C != 0)\
+ T = *C;\
+ else if (RTCHECK(ok_address(M, C))) {\
+ *C = X;\
+ X->parent = T;\
+ X->fd = X->bk = X;\
+ break;\
+ }\
+ else {\
+ CORRUPTION_ERROR_ACTION(M);\
+ break;\
+ }\
+ }\
+ else {\
+ tchunkptr F = T->fd;\
+ if (RTCHECK(ok_address(M, T) && ok_address(M, F))) {\
+ T->fd = F->bk = X;\
+ X->fd = F;\
+ X->bk = T;\
+ X->parent = 0;\
+ break;\
+ }\
+ else {\
+ CORRUPTION_ERROR_ACTION(M);\
+ break;\
+ }\
+ }\
+ }\
+ }\
+}
+
+/*
+ Unlink steps:
+
+ 1. If x is a chained node, unlink it from its same-sized fd/bk links
+ and choose its bk node as its replacement.
+ 2. If x was the last node of its size, but not a leaf node, it must
+ be replaced with a leaf node (not merely one with an open left or
+ right), to make sure that lefts and rights of descendents
+ correspond properly to bit masks. We use the rightmost descendent
+ of x. We could use any other leaf, but this is easy to locate and
+ tends to counteract removal of leftmosts elsewhere, and so keeps
+ paths shorter than minimally guaranteed. This doesn't loop much
+ because on average a node in a tree is near the bottom.
+ 3. If x is the base of a chain (i.e., has parent links) relink
+ x's parent and children to x's replacement (or null if none).
+*/
+
+#define unlink_large_chunk(M, X) {\
+ tchunkptr XP = X->parent;\
+ tchunkptr R;\
+ if (X->bk != X) {\
+ tchunkptr F = X->fd;\
+ R = X->bk;\
+ if (RTCHECK(ok_address(M, F))) {\
+ F->bk = R;\
+ R->fd = F;\
+ }\
+ else {\
+ CORRUPTION_ERROR_ACTION(M);\
+ }\
+ }\
+ else {\
+ tchunkptr* RP;\
+ if (((R = *(RP = &(X->child[1]))) != 0) ||\
+ ((R = *(RP = &(X->child[0]))) != 0)) {\
+ tchunkptr* CP;\
+ while ((*(CP = &(R->child[1])) != 0) ||\
+ (*(CP = &(R->child[0])) != 0)) {\
+ R = *(RP = CP);\
+ }\
+ if (RTCHECK(ok_address(M, RP)))\
+ *RP = 0;\
+ else {\
+ CORRUPTION_ERROR_ACTION(M);\
+ }\
+ }\
+ }\
+ if (XP != 0) {\
+ tbinptr* H = treebin_at(M, X->index);\
+ if (X == *H) {\
+ if ((*H = R) == 0) \
+ clear_treemap(M, X->index);\
+ }\
+ else if (RTCHECK(ok_address(M, XP))) {\
+ if (XP->child[0] == X) \
+ XP->child[0] = R;\
+ else \
+ XP->child[1] = R;\
+ }\
+ else\
+ CORRUPTION_ERROR_ACTION(M);\
+ if (R != 0) {\
+ if (RTCHECK(ok_address(M, R))) {\
+ tchunkptr C0, C1;\
+ R->parent = XP;\
+ if ((C0 = X->child[0]) != 0) {\
+ if (RTCHECK(ok_address(M, C0))) {\
+ R->child[0] = C0;\
+ C0->parent = R;\
+ }\
+ else\
+ CORRUPTION_ERROR_ACTION(M);\
+ }\
+ if ((C1 = X->child[1]) != 0) {\
+ if (RTCHECK(ok_address(M, C1))) {\
+ R->child[1] = C1;\
+ C1->parent = R;\
+ }\
+ else\
+ CORRUPTION_ERROR_ACTION(M);\
+ }\
+ }\
+ else\
+ CORRUPTION_ERROR_ACTION(M);\
+ }\
+ }\
+}
+
+/* Relays to large vs small bin operations */
+
+#define insert_chunk(M, P, S)\
+ if (is_small(S)) insert_small_chunk(M, P, S)\
+ else { tchunkptr TP = (tchunkptr)(P); insert_large_chunk(M, TP, S); }
+
+#define unlink_chunk(M, P, S)\
+ if (is_small(S)) unlink_small_chunk(M, P, S)\
+ else { tchunkptr TP = (tchunkptr)(P); unlink_large_chunk(M, TP); }
+
+
+/* Relays to internal calls to malloc/free from realloc, memalign etc */
+
+#if ONLY_MSPACES
+#define internal_malloc(m, b) mspace_malloc(m, b)
+#define internal_free(m, mem) mspace_free(m,mem);
+#else /* ONLY_MSPACES */
+#if MSPACES
+#define internal_malloc(m, b)\
+ (m == gm)? dlmalloc(b) : mspace_malloc(m, b)
+#define internal_free(m, mem)\
+ if (m == gm) dlfree(mem); else mspace_free(m,mem);
+#else /* MSPACES */
+#define internal_malloc(m, b) dlmalloc(b)
+#define internal_free(m, mem) dlfree(mem)
+#endif /* MSPACES */
+#endif /* ONLY_MSPACES */
+
+/* ----------------------- Direct-mmapping chunks ----------------------- */
+
+/*
+ Directly mmapped chunks are set up with an offset to the start of
+ the mmapped region stored in the prev_foot field of the chunk. This
+ allows reconstruction of the required argument to MUNMAP when freed,
+ and also allows adjustment of the returned chunk to meet alignment
+ requirements (especially in memalign).
+*/
+
+/* Malloc using mmap */
+static void* mmap_alloc(mstate m, size_t nb) {
+ size_t mmsize = mmap_align(nb + SIX_SIZE_T_SIZES + CHUNK_ALIGN_MASK);
+ if (mmsize > nb) { /* Check for wrap around 0 */
+ char* mm = (char*)(CALL_DIRECT_MMAP(mmsize));
+ if (mm != CMFAIL) {
+ size_t offset = align_offset(chunk2mem(mm));
+ size_t psize = mmsize - offset - MMAP_FOOT_PAD;
+ mchunkptr p = (mchunkptr)(mm + offset);
+ p->prev_foot = offset;
+ p->head = psize;
+ mark_inuse_foot(m, p, psize);
+ chunk_plus_offset(p, psize)->head = FENCEPOST_HEAD;
+ chunk_plus_offset(p, psize+SIZE_T_SIZE)->head = 0;
+
+ if (m->least_addr == 0 || mm < m->least_addr)
+ m->least_addr = mm;
+ if ((m->footprint += mmsize) > m->max_footprint)
+ m->max_footprint = m->footprint;
+ assert(is_aligned(chunk2mem(p)));
+ check_mmapped_chunk(m, p);
+ return chunk2mem(p);
+ }
+ }
+ return 0;
+}
+
+/* Realloc using mmap */
+static mchunkptr mmap_resize(mstate m, mchunkptr oldp, size_t nb) {
+ size_t oldsize = chunksize(oldp);
+ if (is_small(nb)) /* Can't shrink mmap regions below small size */
+ return 0;
+ /* Keep old chunk if big enough but not too big */
+ if (oldsize >= nb + SIZE_T_SIZE &&
+ (oldsize - nb) <= (mparams.granularity << 1))
+ return oldp;
+ else {
+ size_t offset = oldp->prev_foot;
+ size_t oldmmsize = oldsize + offset + MMAP_FOOT_PAD;
+ size_t newmmsize = mmap_align(nb + SIX_SIZE_T_SIZES + CHUNK_ALIGN_MASK);
+ char* cp = (char*)CALL_MREMAP((char*)oldp - offset,
+ oldmmsize, newmmsize, 1);
+ if (cp != CMFAIL) {
+ mchunkptr newp = (mchunkptr)(cp + offset);
+ size_t psize = newmmsize - offset - MMAP_FOOT_PAD;
+ newp->head = psize;
+ mark_inuse_foot(m, newp, psize);
+ chunk_plus_offset(newp, psize)->head = FENCEPOST_HEAD;
+ chunk_plus_offset(newp, psize+SIZE_T_SIZE)->head = 0;
+
+ if (cp < m->least_addr)
+ m->least_addr = cp;
+ if ((m->footprint += newmmsize - oldmmsize) > m->max_footprint)
+ m->max_footprint = m->footprint;
+ check_mmapped_chunk(m, newp);
+ return newp;
+ }
+ }
+ return 0;
+}
+
+/* -------------------------- mspace management -------------------------- */
+
+/* Initialize top chunk and its size */
+static void init_top(mstate m, mchunkptr p, size_t psize) {
+ /* Ensure alignment */
+ size_t offset = align_offset(chunk2mem(p));
+ p = (mchunkptr)((char*)p + offset);
+ psize -= offset;
+
+ m->top = p;
+ m->topsize = psize;
+ p->head = psize | PINUSE_BIT;
+ /* set size of fake trailing chunk holding overhead space only once */
+ chunk_plus_offset(p, psize)->head = TOP_FOOT_SIZE;
+ m->trim_check = mparams.trim_threshold; /* reset on each update */
+}
+
+/* Initialize bins for a new mstate that is otherwise zeroed out */
+static void init_bins(mstate m) {
+ /* Establish circular links for smallbins */
+ bindex_t i;
+ for (i = 0; i < NSMALLBINS; ++i) {
+ sbinptr bin = smallbin_at(m,i);
+ bin->fd = bin->bk = bin;
+ }
+}
+
+#if PROCEED_ON_ERROR
+
+/* default corruption action */
+static void reset_on_error(mstate m) {
+ int i;
+ ++malloc_corruption_error_count;
+ /* Reinitialize fields to forget about all memory */
+ m->smallbins = m->treebins = 0;
+ m->dvsize = m->topsize = 0;
+ m->seg.base = 0;
+ m->seg.size = 0;
+ m->seg.next = 0;
+ m->top = m->dv = 0;
+ for (i = 0; i < NTREEBINS; ++i)
+ *treebin_at(m, i) = 0;
+ init_bins(m);
+}
+#endif /* PROCEED_ON_ERROR */
+
+/* Allocate chunk and prepend remainder with chunk in successor base. */
+static void* prepend_alloc(mstate m, char* newbase, char* oldbase,
+ size_t nb) {
+ mchunkptr p = align_as_chunk(newbase);
+ mchunkptr oldfirst = align_as_chunk(oldbase);
+ size_t psize = (char*)oldfirst - (char*)p;
+ mchunkptr q = chunk_plus_offset(p, nb);
+ size_t qsize = psize - nb;
+ set_size_and_pinuse_of_inuse_chunk(m, p, nb);
+
+ assert((char*)oldfirst > (char*)q);
+ assert(pinuse(oldfirst));
+ assert(qsize >= MIN_CHUNK_SIZE);
+
+ /* consolidate remainder with first chunk of old base */
+ if (oldfirst == m->top) {
+ size_t tsize = m->topsize += qsize;
+ m->top = q;
+ q->head = tsize | PINUSE_BIT;
+ check_top_chunk(m, q);
+ }
+ else if (oldfirst == m->dv) {
+ size_t dsize = m->dvsize += qsize;
+ m->dv = q;
+ set_size_and_pinuse_of_free_chunk(q, dsize);
+ }
+ else {
+ if (!is_inuse(oldfirst)) {
+ size_t nsize = chunksize(oldfirst);
+ unlink_chunk(m, oldfirst, nsize);
+ oldfirst = chunk_plus_offset(oldfirst, nsize);
+ qsize += nsize;
+ }
+ set_free_with_pinuse(q, qsize, oldfirst);
+ insert_chunk(m, q, qsize);
+ check_free_chunk(m, q);
+ }
+
+ check_malloced_chunk(m, chunk2mem(p), nb);
+ return chunk2mem(p);
+}
+
+/* Add a segment to hold a new noncontiguous region */
+static void add_segment(mstate m, char* tbase, size_t tsize, flag_t mmapped) {
+ /* Determine locations and sizes of segment, fenceposts, old top */
+ char* old_top = (char*)m->top;
+ msegmentptr oldsp = segment_holding(m, old_top);
+ char* old_end = oldsp->base + oldsp->size;
+ size_t ssize = pad_request(sizeof(struct malloc_segment));
+ char* rawsp = old_end - (ssize + FOUR_SIZE_T_SIZES + CHUNK_ALIGN_MASK);
+ size_t offset = align_offset(chunk2mem(rawsp));
+ char* asp = rawsp + offset;
+ char* csp = (asp < (old_top + MIN_CHUNK_SIZE))? old_top : asp;
+ mchunkptr sp = (mchunkptr)csp;
+ msegmentptr ss = (msegmentptr)(chunk2mem(sp));
+ mchunkptr tnext = chunk_plus_offset(sp, ssize);
+ mchunkptr p = tnext;
+ int nfences = 0;
+
+ /* reset top to new space */
+ init_top(m, (mchunkptr)tbase, tsize - TOP_FOOT_SIZE);
+
+ /* Set up segment record */
+ assert(is_aligned(ss));
+ set_size_and_pinuse_of_inuse_chunk(m, sp, ssize);
+ *ss = m->seg; /* Push current record */
+ m->seg.base = tbase;
+ m->seg.size = tsize;
+ m->seg.sflags = mmapped;
+ m->seg.next = ss;
+
+ /* Insert trailing fenceposts */
+ for (;;) {
+ mchunkptr nextp = chunk_plus_offset(p, SIZE_T_SIZE);
+ p->head = FENCEPOST_HEAD;
+ ++nfences;
+ if ((char*)(&(nextp->head)) < old_end)
+ p = nextp;
+ else
+ break;
+ }
+ assert(nfences >= 2);
+
+ /* Insert the rest of old top into a bin as an ordinary free chunk */
+ if (csp != old_top) {
+ mchunkptr q = (mchunkptr)old_top;
+ size_t psize = csp - old_top;
+ mchunkptr tn = chunk_plus_offset(q, psize);
+ set_free_with_pinuse(q, psize, tn);
+ insert_chunk(m, q, psize);
+ }
+
+ check_top_chunk(m, m->top);
+}
+
+/* -------------------------- System allocation -------------------------- */
+
+/* Get memory from system using MORECORE or MMAP */
+static void* sys_alloc(mstate m, size_t nb) {
+ char* tbase = CMFAIL;
+ size_t tsize = 0;
+ flag_t mmap_flag = 0;
+
+ ensure_initialization();
+
+ /* Directly map large chunks, but only if already initialized */
+ if (use_mmap(m) && nb >= mparams.mmap_threshold && m->topsize != 0) {
+ void* mem = mmap_alloc(m, nb);
+ if (mem != 0)
+ return mem;
+ }
+
+ /*
+ Try getting memory in any of three ways (in most-preferred to
+ least-preferred order):
+ 1. A call to MORECORE that can normally contiguously extend memory.
+ (disabled if not MORECORE_CONTIGUOUS or not HAVE_MORECORE or
+ or main space is mmapped or a previous contiguous call failed)
+ 2. A call to MMAP new space (disabled if not HAVE_MMAP).
+ Note that under the default settings, if MORECORE is unable to
+ fulfill a request, and HAVE_MMAP is true, then mmap is
+ used as a noncontiguous system allocator. This is a useful backup
+ strategy for systems with holes in address spaces -- in this case
+ sbrk cannot contiguously expand the heap, but mmap may be able to
+ find space.
+ 3. A call to MORECORE that cannot usually contiguously extend memory.
+ (disabled if not HAVE_MORECORE)
+
+ In all cases, we need to request enough bytes from system to ensure
+ we can malloc nb bytes upon success, so pad with enough space for
+ top_foot, plus alignment-pad to make sure we don't lose bytes if
+ not on boundary, and round this up to a granularity unit.
+ */
+
+ if (MORECORE_CONTIGUOUS && !use_noncontiguous(m)) {
+ char* br = CMFAIL;
+ msegmentptr ss = (m->top == 0)? 0 : segment_holding(m, (char*)m->top);
+ size_t asize = 0;
+ ACQUIRE_MALLOC_GLOBAL_LOCK();
+
+ if (ss == 0) { /* First time through or recovery */
+ char* base = (char*)CALL_MORECORE(0);
+ if (base != CMFAIL) {
+ asize = granularity_align(nb + SYS_ALLOC_PADDING);
+ /* Adjust to end on a page boundary */
+ if (!is_page_aligned(base))
+ asize += (page_align((size_t)base) - (size_t)base);
+ /* Can't call MORECORE if size is negative when treated as signed */
+ if (asize < HALF_MAX_SIZE_T &&
+ (br = (char*)(CALL_MORECORE(asize))) == base) {
+ tbase = base;
+ tsize = asize;
+ }
+ }
+ }
+ else {
+ /* Subtract out existing available top space from MORECORE request. */
+ asize = granularity_align(nb - m->topsize + SYS_ALLOC_PADDING);
+ /* Use mem here only if it did continuously extend old space */
+ if (asize < HALF_MAX_SIZE_T &&
+ (br = (char*)(CALL_MORECORE(asize))) == ss->base+ss->size) {
+ tbase = br;
+ tsize = asize;
+ }
+ }
+
+ if (tbase == CMFAIL) { /* Cope with partial failure */
+ if (br != CMFAIL) { /* Try to use/extend the space we did get */
+ if (asize < HALF_MAX_SIZE_T &&
+ asize < nb + SYS_ALLOC_PADDING) {
+ size_t esize = granularity_align(nb + SYS_ALLOC_PADDING - asize);
+ if (esize < HALF_MAX_SIZE_T) {
+ char* end = (char*)CALL_MORECORE(esize);
+ if (end != CMFAIL)
+ asize += esize;
+ else { /* Can't use; try to release */
+ (void) CALL_MORECORE(-asize);
+ br = CMFAIL;
+ }
+ }
+ }
+ }
+ if (br != CMFAIL) { /* Use the space we did get */
+ tbase = br;
+ tsize = asize;
+ }
+ else
+ disable_contiguous(m); /* Don't try contiguous path in the future */
+ }
+
+ RELEASE_MALLOC_GLOBAL_LOCK();
+ }
+
+ if (HAVE_MMAP && tbase == CMFAIL) { /* Try MMAP */
+ size_t rsize = granularity_align(nb + SYS_ALLOC_PADDING);
+ if (rsize > nb) { /* Fail if wraps around zero */
+ char* mp = (char*)(CALL_MMAP(rsize));
+ if (mp != CMFAIL) {
+ tbase = mp;
+ tsize = rsize;
+ mmap_flag = USE_MMAP_BIT;
+ }
+ }
+ }
+
+ if (HAVE_MORECORE && tbase == CMFAIL) { /* Try noncontiguous MORECORE */
+ size_t asize = granularity_align(nb + SYS_ALLOC_PADDING);
+ if (asize < HALF_MAX_SIZE_T) {
+ char* br = CMFAIL;
+ char* end = CMFAIL;
+ ACQUIRE_MALLOC_GLOBAL_LOCK();
+ br = (char*)(CALL_MORECORE(asize));
+ end = (char*)(CALL_MORECORE(0));
+ RELEASE_MALLOC_GLOBAL_LOCK();
+ if (br != CMFAIL && end != CMFAIL && br < end) {
+ size_t ssize = end - br;
+ if (ssize > nb + TOP_FOOT_SIZE) {
+ tbase = br;
+ tsize = ssize;
+ }
+ }
+ }
+ }
+
+ if (tbase != CMFAIL) {
+
+ if ((m->footprint += tsize) > m->max_footprint)
+ m->max_footprint = m->footprint;
+
+ if (!is_initialized(m)) { /* first-time initialization */
+ if (m->least_addr == 0 || tbase < m->least_addr)
+ m->least_addr = tbase;
+ m->seg.base = tbase;
+ m->seg.size = tsize;
+ m->seg.sflags = mmap_flag;
+ m->magic = mparams.magic;
+ m->release_checks = MAX_RELEASE_CHECK_RATE;
+ init_bins(m);
+#if !ONLY_MSPACES
+ if (is_global(m))
+ init_top(m, (mchunkptr)tbase, tsize - TOP_FOOT_SIZE);
+ else
+#endif
+ {
+ /* Offset top by embedded malloc_state */
+ mchunkptr mn = next_chunk(mem2chunk(m));
+ init_top(m, mn, (size_t)((tbase + tsize) - (char*)mn) -TOP_FOOT_SIZE);
+ }
+ }
+
+ else {
+ /* Try to merge with an existing segment */
+ msegmentptr sp = &m->seg;
+ /* Only consider most recent segment if traversal suppressed */
+ while (sp != 0 && tbase != sp->base + sp->size)
+ sp = (NO_SEGMENT_TRAVERSAL) ? 0 : sp->next;
+ if (sp != 0 &&
+ !is_extern_segment(sp) &&
+ (sp->sflags & USE_MMAP_BIT) == mmap_flag &&
+ segment_holds(sp, m->top)) { /* append */
+ sp->size += tsize;
+ init_top(m, m->top, m->topsize + tsize);
+ }
+ else {
+ if (tbase < m->least_addr)
+ m->least_addr = tbase;
+ sp = &m->seg;
+ while (sp != 0 && sp->base != tbase + tsize)
+ sp = (NO_SEGMENT_TRAVERSAL) ? 0 : sp->next;
+ if (sp != 0 &&
+ !is_extern_segment(sp) &&
+ (sp->sflags & USE_MMAP_BIT) == mmap_flag) {
+ char* oldbase = sp->base;
+ sp->base = tbase;
+ sp->size += tsize;
+ return prepend_alloc(m, tbase, oldbase, nb);
+ }
+ else
+ add_segment(m, tbase, tsize, mmap_flag);
+ }
+ }
+
+ if (nb < m->topsize) { /* Allocate from new or extended top space */
+ size_t rsize = m->topsize -= nb;
+ mchunkptr p = m->top;
+ mchunkptr r = m->top = chunk_plus_offset(p, nb);
+ r->head = rsize | PINUSE_BIT;
+ set_size_and_pinuse_of_inuse_chunk(m, p, nb);
+ check_top_chunk(m, m->top);
+ check_malloced_chunk(m, chunk2mem(p), nb);
+ return chunk2mem(p);
+ }
+ }
+
+ MALLOC_FAILURE_ACTION;
+ return 0;
+}
+
+/* ----------------------- system deallocation -------------------------- */
+
+/* Unmap and unlink any mmapped segments that don't contain used chunks */
+static size_t release_unused_segments(mstate m) {
+ size_t released = 0;
+ int nsegs = 0;
+ msegmentptr pred = &m->seg;
+ msegmentptr sp = pred->next;
+ while (sp != 0) {
+ char* base = sp->base;
+ size_t size = sp->size;
+ msegmentptr next = sp->next;
+ ++nsegs;
+ if (is_mmapped_segment(sp) && !is_extern_segment(sp)) {
+ mchunkptr p = align_as_chunk(base);
+ size_t psize = chunksize(p);
+ /* Can unmap if first chunk holds entire segment and not pinned */
+ if (!is_inuse(p) && (char*)p + psize >= base + size - TOP_FOOT_SIZE) {
+ tchunkptr tp = (tchunkptr)p;
+ assert(segment_holds(sp, (char*)sp));
+ if (p == m->dv) {
+ m->dv = 0;
+ m->dvsize = 0;
+ }
+ else {
+ unlink_large_chunk(m, tp);
+ }
+ if (CALL_MUNMAP(base, size) == 0) {
+ released += size;
+ m->footprint -= size;
+ /* unlink obsoleted record */
+ sp = pred;
+ sp->next = next;
+ }
+ else { /* back out if cannot unmap */
+ insert_large_chunk(m, tp, psize);
+ }
+ }
+ }
+ if (NO_SEGMENT_TRAVERSAL) /* scan only first segment */
+ break;
+ pred = sp;
+ sp = next;
+ }
+ /* Reset check counter */
+ m->release_checks = ((nsegs > MAX_RELEASE_CHECK_RATE)?
+ nsegs : MAX_RELEASE_CHECK_RATE);
+ return released;
+}
+
+static int sys_trim(mstate m, size_t pad) {
+ size_t released = 0;
+ ensure_initialization();
+ if (pad < MAX_REQUEST && is_initialized(m)) {
+ pad += TOP_FOOT_SIZE; /* ensure enough room for segment overhead */
+
+ if (m->topsize > pad) {
+ /* Shrink top space in granularity-size units, keeping at least one */
+ size_t unit = mparams.granularity;
+ size_t extra = ((m->topsize - pad + (unit - SIZE_T_ONE)) / unit -
+ SIZE_T_ONE) * unit;
+ msegmentptr sp = segment_holding(m, (char*)m->top);
+
+ if (!is_extern_segment(sp)) {
+ if (is_mmapped_segment(sp)) {
+ if (HAVE_MMAP &&
+ sp->size >= extra &&
+ !has_segment_link(m, sp)) { /* can't shrink if pinned */
+ size_t newsize = sp->size - extra;
+ /* Prefer mremap, fall back to munmap */
+ if ((CALL_MREMAP(sp->base, sp->size, newsize, 0) != MFAIL) ||
+ (CALL_MUNMAP(sp->base + newsize, extra) == 0)) {
+ released = extra;
+ }
+ }
+ }
+ else if (HAVE_MORECORE) {
+ if (extra >= HALF_MAX_SIZE_T) /* Avoid wrapping negative */
+ extra = (HALF_MAX_SIZE_T) + SIZE_T_ONE - unit;
+ ACQUIRE_MALLOC_GLOBAL_LOCK();
+ {
+ /* Make sure end of memory is where we last set it. */
+ char* old_br = (char*)(CALL_MORECORE(0));
+ if (old_br == sp->base + sp->size) {
+ char* rel_br = (char*)(CALL_MORECORE(-extra));
+ char* new_br = (char*)(CALL_MORECORE(0));
+ if (rel_br != CMFAIL && new_br < old_br)
+ released = old_br - new_br;
+ }
+ }
+ RELEASE_MALLOC_GLOBAL_LOCK();
+ }
+ }
+
+ if (released != 0) {
+ sp->size -= released;
+ m->footprint -= released;
+ init_top(m, m->top, m->topsize - released);
+ check_top_chunk(m, m->top);
+ }
+ }
+
+ /* Unmap any unused mmapped segments */
+ if (HAVE_MMAP)
+ released += release_unused_segments(m);
+
+ /* On failure, disable autotrim to avoid repeated failed future calls */
+ if (released == 0 && m->topsize > m->trim_check)
+ m->trim_check = MAX_SIZE_T;
+ }
+
+ return (released != 0)? 1 : 0;
+}
+
+
+/* ---------------------------- malloc support --------------------------- */
+
+/* allocate a large request from the best fitting chunk in a treebin */
+static void* tmalloc_large(mstate m, size_t nb) {
+ tchunkptr v = 0;
+ size_t rsize = -nb; /* Unsigned negation */
+ tchunkptr t;
+ bindex_t idx;
+ compute_tree_index(nb, idx);
+ if ((t = *treebin_at(m, idx)) != 0) {
+ /* Traverse tree for this bin looking for node with size == nb */
+ size_t sizebits = nb << leftshift_for_tree_index(idx);
+ tchunkptr rst = 0; /* The deepest untaken right subtree */
+ for (;;) {
+ tchunkptr rt;
+ size_t trem = chunksize(t) - nb;
+ if (trem < rsize) {
+ v = t;
+ if ((rsize = trem) == 0)
+ break;
+ }
+ rt = t->child[1];
+ t = t->child[(sizebits >> (SIZE_T_BITSIZE-SIZE_T_ONE)) & 1];
+ if (rt != 0 && rt != t)
+ rst = rt;
+ if (t == 0) {
+ t = rst; /* set t to least subtree holding sizes > nb */
+ break;
+ }
+ sizebits <<= 1;
+ }
+ }
+ if (t == 0 && v == 0) { /* set t to root of next non-empty treebin */
+ binmap_t leftbits = left_bits(idx2bit(idx)) & m->treemap;
+ if (leftbits != 0) {
+ bindex_t i;
+ binmap_t leastbit = least_bit(leftbits);
+ compute_bit2idx(leastbit, i);
+ t = *treebin_at(m, i);
+ }
+ }
+
+ while (t != 0) { /* find smallest of tree or subtree */
+ size_t trem = chunksize(t) - nb;
+ if (trem < rsize) {
+ rsize = trem;
+ v = t;
+ }
+ t = leftmost_child(t);
+ }
+
+ /* If dv is a better fit, return 0 so malloc will use it */
+ if (v != 0 && rsize < (size_t)(m->dvsize - nb)) {
+ if (RTCHECK(ok_address(m, v))) { /* split */
+ mchunkptr r = chunk_plus_offset(v, nb);
+ assert(chunksize(v) == rsize + nb);
+ if (RTCHECK(ok_next(v, r))) {
+ unlink_large_chunk(m, v);
+ if (rsize < MIN_CHUNK_SIZE)
+ set_inuse_and_pinuse(m, v, (rsize + nb));
+ else {
+ set_size_and_pinuse_of_inuse_chunk(m, v, nb);
+ set_size_and_pinuse_of_free_chunk(r, rsize);
+ insert_chunk(m, r, rsize);
+ }
+ return chunk2mem(v);
+ }
+ }
+ CORRUPTION_ERROR_ACTION(m);
+ }
+ return 0;
+}
+
+/* allocate a small request from the best fitting chunk in a treebin */
+static void* tmalloc_small(mstate m, size_t nb) {
+ tchunkptr t, v;
+ size_t rsize;
+ bindex_t i;
+ binmap_t leastbit = least_bit(m->treemap);
+ compute_bit2idx(leastbit, i);
+ v = t = *treebin_at(m, i);
+ rsize = chunksize(t) - nb;
+
+ while ((t = leftmost_child(t)) != 0) {
+ size_t trem = chunksize(t) - nb;
+ if (trem < rsize) {
+ rsize = trem;
+ v = t;
+ }
+ }
+
+ if (RTCHECK(ok_address(m, v))) {
+ mchunkptr r = chunk_plus_offset(v, nb);
+ assert(chunksize(v) == rsize + nb);
+ if (RTCHECK(ok_next(v, r))) {
+ unlink_large_chunk(m, v);
+ if (rsize < MIN_CHUNK_SIZE)
+ set_inuse_and_pinuse(m, v, (rsize + nb));
+ else {
+ set_size_and_pinuse_of_inuse_chunk(m, v, nb);
+ set_size_and_pinuse_of_free_chunk(r, rsize);
+ replace_dv(m, r, rsize);
+ }
+ return chunk2mem(v);
+ }
+ }
+
+ CORRUPTION_ERROR_ACTION(m);
+ return 0;
+}
+
+/* --------------------------- realloc support --------------------------- */
+
+static void* internal_realloc(mstate m, void* oldmem, size_t bytes) {
+ if (bytes >= MAX_REQUEST) {
+ MALLOC_FAILURE_ACTION;
+ return 0;
+ }
+ if (!PREACTION(m)) {
+ mchunkptr oldp = mem2chunk(oldmem);
+ size_t oldsize = chunksize(oldp);
+ mchunkptr next = chunk_plus_offset(oldp, oldsize);
+ mchunkptr newp = 0;
+ void* extra = 0;
+
+ /* Try to either shrink or extend into top. Else malloc-copy-free */
+
+ if (RTCHECK(ok_address(m, oldp) && ok_inuse(oldp) &&
+ ok_next(oldp, next) && ok_pinuse(next))) {
+ size_t nb = request2size(bytes);
+ if (is_mmapped(oldp))
+ newp = mmap_resize(m, oldp, nb);
+ else if (oldsize >= nb) { /* already big enough */
+ size_t rsize = oldsize - nb;
+ newp = oldp;
+ if (rsize >= MIN_CHUNK_SIZE) {
+ mchunkptr remainder = chunk_plus_offset(newp, nb);
+ set_inuse(m, newp, nb);
+ set_inuse_and_pinuse(m, remainder, rsize);
+ extra = chunk2mem(remainder);
+ }
+ }
+ else if (next == m->top && oldsize + m->topsize > nb) {
+ /* Expand into top */
+ size_t newsize = oldsize + m->topsize;
+ size_t newtopsize = newsize - nb;
+ mchunkptr newtop = chunk_plus_offset(oldp, nb);
+ set_inuse(m, oldp, nb);
+ newtop->head = newtopsize |PINUSE_BIT;
+ m->top = newtop;
+ m->topsize = newtopsize;
+ newp = oldp;
+ }
+ }
+ else {
+ USAGE_ERROR_ACTION(m, oldmem);
+ POSTACTION(m);
+ return 0;
+ }
+#if DEBUG
+ if (newp != 0) {
+ check_inuse_chunk(m, newp); /* Check requires lock */
+ }
+#endif
+
+ POSTACTION(m);
+
+ if (newp != 0) {
+ if (extra != 0) {
+ internal_free(m, extra);
+ }
+ return chunk2mem(newp);
+ }
+ else {
+ void* newmem = internal_malloc(m, bytes);
+ if (newmem != 0) {
+ size_t oc = oldsize - overhead_for(oldp);
+ memcpy(newmem, oldmem, (oc < bytes)? oc : bytes);
+ internal_free(m, oldmem);
+ }
+ return newmem;
+ }
+ }
+ return 0;
+}
+
+/* --------------------------- memalign support -------------------------- */
+
+static void* internal_memalign(mstate m, size_t alignment, size_t bytes) {
+ if (alignment <= MALLOC_ALIGNMENT) /* Can just use malloc */
+ return internal_malloc(m, bytes);
+ if (alignment < MIN_CHUNK_SIZE) /* must be at least a minimum chunk size */
+ alignment = MIN_CHUNK_SIZE;
+ if ((alignment & (alignment-SIZE_T_ONE)) != 0) {/* Ensure a power of 2 */
+ size_t a = MALLOC_ALIGNMENT << 1;
+ while (a < alignment) a <<= 1;
+ alignment = a;
+ }
+
+ if (bytes >= MAX_REQUEST - alignment) {
+ if (m != 0) { /* Test isn't needed but avoids compiler warning */
+ MALLOC_FAILURE_ACTION;
+ }
+ }
+ else {
+ size_t nb = request2size(bytes);
+ size_t req = nb + alignment + MIN_CHUNK_SIZE - CHUNK_OVERHEAD;
+ char* mem = (char*)internal_malloc(m, req);
+ if (mem != 0) {
+ void* leader = 0;
+ void* trailer = 0;
+ mchunkptr p = mem2chunk(mem);
+
+ if (PREACTION(m)) return 0;
+ if ((((size_t)(mem)) % alignment) != 0) { /* misaligned */
+ /*
+ Find an aligned spot inside chunk. Since we need to give
+ back leading space in a chunk of at least MIN_CHUNK_SIZE, if
+ the first calculation places us at a spot with less than
+ MIN_CHUNK_SIZE leader, we can move to the next aligned spot.
+ We've allocated enough total room so that this is always
+ possible.
+ */
+ char* br = (char*)mem2chunk((size_t)(((size_t)(mem +
+ alignment -
+ SIZE_T_ONE)) &
+ -alignment));
+ char* pos = ((size_t)(br - (char*)(p)) >= MIN_CHUNK_SIZE)?
+ br : br+alignment;
+ mchunkptr newp = (mchunkptr)pos;
+ size_t leadsize = pos - (char*)(p);
+ size_t newsize = chunksize(p) - leadsize;
+
+ if (is_mmapped(p)) { /* For mmapped chunks, just adjust offset */
+ newp->prev_foot = p->prev_foot + leadsize;
+ newp->head = newsize;
+ }
+ else { /* Otherwise, give back leader, use the rest */
+ set_inuse(m, newp, newsize);
+ set_inuse(m, p, leadsize);
+ leader = chunk2mem(p);
+ }
+ p = newp;
+ }
+
+ /* Give back spare room at the end */
+ if (!is_mmapped(p)) {
+ size_t size = chunksize(p);
+ if (size > nb + MIN_CHUNK_SIZE) {
+ size_t remainder_size = size - nb;
+ mchunkptr remainder = chunk_plus_offset(p, nb);
+ set_inuse(m, p, nb);
+ set_inuse(m, remainder, remainder_size);
+ trailer = chunk2mem(remainder);
+ }
+ }
+
+ assert (chunksize(p) >= nb);
+ assert((((size_t)(chunk2mem(p))) % alignment) == 0);
+ check_inuse_chunk(m, p);
+ POSTACTION(m);
+ if (leader != 0) {
+ internal_free(m, leader);
+ }
+ if (trailer != 0) {
+ internal_free(m, trailer);
+ }
+ return chunk2mem(p);
+ }
+ }
+ return 0;
+}
+
+/* ------------------------ comalloc/coalloc support --------------------- */
+
+static void** ialloc(mstate m,
+ size_t n_elements,
+ size_t* sizes,
+ int opts,
+ void* chunks[]) {
+ /*
+ This provides common support for independent_X routines, handling
+ all of the combinations that can result.
+
+ The opts arg has:
+ bit 0 set if all elements are same size (using sizes[0])
+ bit 1 set if elements should be zeroed
+ */
+
+ size_t element_size; /* chunksize of each element, if all same */
+ size_t contents_size; /* total size of elements */
+ size_t array_size; /* request size of pointer array */
+ void* mem; /* malloced aggregate space */
+ mchunkptr p; /* corresponding chunk */
+ size_t remainder_size; /* remaining bytes while splitting */
+ void** marray; /* either "chunks" or malloced ptr array */
+ mchunkptr array_chunk; /* chunk for malloced ptr array */
+ flag_t was_enabled; /* to disable mmap */
+ size_t size;
+ size_t i;
+
+ ensure_initialization();
+ /* compute array length, if needed */
+ if (chunks != 0) {
+ if (n_elements == 0)
+ return chunks; /* nothing to do */
+ marray = chunks;
+ array_size = 0;
+ }
+ else {
+ /* if empty req, must still return chunk representing empty array */
+ if (n_elements == 0)
+ return (void**)internal_malloc(m, 0);
+ marray = 0;
+ array_size = request2size(n_elements * (sizeof(void*)));
+ }
+
+ /* compute total element size */
+ if (opts & 0x1) { /* all-same-size */
+ element_size = request2size(*sizes);
+ contents_size = n_elements * element_size;
+ }
+ else { /* add up all the sizes */
+ element_size = 0;
+ contents_size = 0;
+ for (i = 0; i != n_elements; ++i)
+ contents_size += request2size(sizes[i]);
+ }
+
+ size = contents_size + array_size;
+
+ /*
+ Allocate the aggregate chunk. First disable direct-mmapping so
+ malloc won't use it, since we would not be able to later
+ free/realloc space internal to a segregated mmap region.
+ */
+ was_enabled = use_mmap(m);
+ disable_mmap(m);
+ mem = internal_malloc(m, size - CHUNK_OVERHEAD);
+ if (was_enabled)
+ enable_mmap(m);
+ if (mem == 0)
+ return 0;
+
+ if (PREACTION(m)) return 0;
+ p = mem2chunk(mem);
+ remainder_size = chunksize(p);
+
+ assert(!is_mmapped(p));
+
+ if (opts & 0x2) { /* optionally clear the elements */
+ memset((size_t*)mem, 0, remainder_size - SIZE_T_SIZE - array_size);
+ }
+
+ /* If not provided, allocate the pointer array as final part of chunk */
+ if (marray == 0) {
+ size_t array_chunk_size;
+ array_chunk = chunk_plus_offset(p, contents_size);
+ array_chunk_size = remainder_size - contents_size;
+ marray = (void**) (chunk2mem(array_chunk));
+ set_size_and_pinuse_of_inuse_chunk(m, array_chunk, array_chunk_size);
+ remainder_size = contents_size;
+ }
+
+ /* split out elements */
+ for (i = 0; ; ++i) {
+ marray[i] = chunk2mem(p);
+ if (i != n_elements-1) {
+ if (element_size != 0)
+ size = element_size;
+ else
+ size = request2size(sizes[i]);
+ remainder_size -= size;
+ set_size_and_pinuse_of_inuse_chunk(m, p, size);
+ p = chunk_plus_offset(p, size);
+ }
+ else { /* the final element absorbs any overallocation slop */
+ set_size_and_pinuse_of_inuse_chunk(m, p, remainder_size);
+ break;
+ }
+ }
+
+#if DEBUG
+ if (marray != chunks) {
+ /* final element must have exactly exhausted chunk */
+ if (element_size != 0) {
+ assert(remainder_size == element_size);
+ }
+ else {
+ assert(remainder_size == request2size(sizes[i]));
+ }
+ check_inuse_chunk(m, mem2chunk(marray));
+ }
+ for (i = 0; i != n_elements; ++i)
+ check_inuse_chunk(m, mem2chunk(marray[i]));
+
+#endif /* DEBUG */
+
+ POSTACTION(m);
+ return marray;
+}
+
+
+/* -------------------------- public routines ---------------------------- */
+
+#if !ONLY_MSPACES
+
+void* dlmalloc(size_t bytes) {
+ /*
+ Basic algorithm:
+ If a small request (< 256 bytes minus per-chunk overhead):
+ 1. If one exists, use a remainderless chunk in associated smallbin.
+ (Remainderless means that there are too few excess bytes to
+ represent as a chunk.)
+ 2. If it is big enough, use the dv chunk, which is normally the
+ chunk adjacent to the one used for the most recent small request.
+ 3. If one exists, split the smallest available chunk in a bin,
+ saving remainder in dv.
+ 4. If it is big enough, use the top chunk.
+ 5. If available, get memory from system and use it
+ Otherwise, for a large request:
+ 1. Find the smallest available binned chunk that fits, and use it
+ if it is better fitting than dv chunk, splitting if necessary.
+ 2. If better fitting than any binned chunk, use the dv chunk.
+ 3. If it is big enough, use the top chunk.
+ 4. If request size >= mmap threshold, try to directly mmap this chunk.
+ 5. If available, get memory from system and use it
+
+ The ugly goto's here ensure that postaction occurs along all paths.
+ */
+
+#if USE_LOCKS
+ ensure_initialization(); /* initialize in sys_alloc if not using locks */
+#endif
+
+ if (!PREACTION(gm)) {
+ void* mem;
+ size_t nb;
+ if (bytes <= MAX_SMALL_REQUEST) {
+ bindex_t idx;
+ binmap_t smallbits;
+ nb = (bytes < MIN_REQUEST)? MIN_CHUNK_SIZE : pad_request(bytes);
+ idx = small_index(nb);
+ smallbits = gm->smallmap >> idx;
+
+ if ((smallbits & 0x3U) != 0) { /* Remainderless fit to a smallbin. */
+ mchunkptr b, p;
+ idx += ~smallbits & 1; /* Uses next bin if idx empty */
+ b = smallbin_at(gm, idx);
+ p = b->fd;
+ assert(chunksize(p) == small_index2size(idx));
+ unlink_first_small_chunk(gm, b, p, idx);
+ set_inuse_and_pinuse(gm, p, small_index2size(idx));
+ mem = chunk2mem(p);
+ check_malloced_chunk(gm, mem, nb);
+ goto postaction;
+ }
+
+ else if (nb > gm->dvsize) {
+ if (smallbits != 0) { /* Use chunk in next nonempty smallbin */
+ mchunkptr b, p, r;
+ size_t rsize;
+ bindex_t i;
+ binmap_t leftbits = (smallbits << idx) & left_bits(idx2bit(idx));
+ binmap_t leastbit = least_bit(leftbits);
+ compute_bit2idx(leastbit, i);
+ b = smallbin_at(gm, i);
+ p = b->fd;
+ assert(chunksize(p) == small_index2size(i));
+ unlink_first_small_chunk(gm, b, p, i);
+ rsize = small_index2size(i) - nb;
+ /* Fit here cannot be remainderless if 4byte sizes */
+ if (SIZE_T_SIZE != 4 && rsize < MIN_CHUNK_SIZE)
+ set_inuse_and_pinuse(gm, p, small_index2size(i));
+ else {
+ set_size_and_pinuse_of_inuse_chunk(gm, p, nb);
+ r = chunk_plus_offset(p, nb);
+ set_size_and_pinuse_of_free_chunk(r, rsize);
+ replace_dv(gm, r, rsize);
+ }
+ mem = chunk2mem(p);
+ check_malloced_chunk(gm, mem, nb);
+ goto postaction;
+ }
+
+ else if (gm->treemap != 0 && (mem = tmalloc_small(gm, nb)) != 0) {
+ check_malloced_chunk(gm, mem, nb);
+ goto postaction;
+ }
+ }
+ }
+ else if (bytes >= MAX_REQUEST)
+ nb = MAX_SIZE_T; /* Too big to allocate. Force failure (in sys alloc) */
+ else {
+ nb = pad_request(bytes);
+ if (gm->treemap != 0 && (mem = tmalloc_large(gm, nb)) != 0) {
+ check_malloced_chunk(gm, mem, nb);
+ goto postaction;
+ }
+ }
+
+ if (nb <= gm->dvsize) {
+ size_t rsize = gm->dvsize - nb;
+ mchunkptr p = gm->dv;
+ if (rsize >= MIN_CHUNK_SIZE) { /* split dv */
+ mchunkptr r = gm->dv = chunk_plus_offset(p, nb);
+ gm->dvsize = rsize;
+ set_size_and_pinuse_of_free_chunk(r, rsize);
+ set_size_and_pinuse_of_inuse_chunk(gm, p, nb);
+ }
+ else { /* exhaust dv */
+ size_t dvs = gm->dvsize;
+ gm->dvsize = 0;
+ gm->dv = 0;
+ set_inuse_and_pinuse(gm, p, dvs);
+ }
+ mem = chunk2mem(p);
+ check_malloced_chunk(gm, mem, nb);
+ goto postaction;
+ }
+
+ else if (nb < gm->topsize) { /* Split top */
+ size_t rsize = gm->topsize -= nb;
+ mchunkptr p = gm->top;
+ mchunkptr r = gm->top = chunk_plus_offset(p, nb);
+ r->head = rsize | PINUSE_BIT;
+ set_size_and_pinuse_of_inuse_chunk(gm, p, nb);
+ mem = chunk2mem(p);
+ check_top_chunk(gm, gm->top);
+ check_malloced_chunk(gm, mem, nb);
+ goto postaction;
+ }
+
+ mem = sys_alloc(gm, nb);
+
+ postaction:
+ POSTACTION(gm);
+ return mem;
+ }
+
+ return 0;
+}
+
+void dlfree(void* mem) {
+ /*
+ Consolidate freed chunks with preceeding or succeeding bordering
+ free chunks, if they exist, and then place in a bin. Intermixed
+ with special cases for top, dv, mmapped chunks, and usage errors.
+ */
+
+ if (mem != 0) {
+ mchunkptr p = mem2chunk(mem);
+#if FOOTERS
+ mstate fm = get_mstate_for(p);
+ if (!ok_magic(fm)) {
+ USAGE_ERROR_ACTION(fm, p);
+ return;
+ }
+#else /* FOOTERS */
+#define fm gm
+#endif /* FOOTERS */
+ if (!PREACTION(fm)) {
+ check_inuse_chunk(fm, p);
+ if (RTCHECK(ok_address(fm, p) && ok_inuse(p))) {
+ size_t psize = chunksize(p);
+ mchunkptr next = chunk_plus_offset(p, psize);
+ if (!pinuse(p)) {
+ size_t prevsize = p->prev_foot;
+ if (is_mmapped(p)) {
+ psize += prevsize + MMAP_FOOT_PAD;
+ if (CALL_MUNMAP((char*)p - prevsize, psize) == 0)
+ fm->footprint -= psize;
+ goto postaction;
+ }
+ else {
+ mchunkptr prev = chunk_minus_offset(p, prevsize);
+ psize += prevsize;
+ p = prev;
+ if (RTCHECK(ok_address(fm, prev))) { /* consolidate backward */
+ if (p != fm->dv) {
+ unlink_chunk(fm, p, prevsize);
+ }
+ else if ((next->head & INUSE_BITS) == INUSE_BITS) {
+ fm->dvsize = psize;
+ set_free_with_pinuse(p, psize, next);
+ goto postaction;
+ }
+ }
+ else
+ goto erroraction;
+ }
+ }
+
+ if (RTCHECK(ok_next(p, next) && ok_pinuse(next))) {
+ if (!cinuse(next)) { /* consolidate forward */
+ if (next == fm->top) {
+ size_t tsize = fm->topsize += psize;
+ fm->top = p;
+ p->head = tsize | PINUSE_BIT;
+ if (p == fm->dv) {
+ fm->dv = 0;
+ fm->dvsize = 0;
+ }
+ if (should_trim(fm, tsize))
+ sys_trim(fm, 0);
+ goto postaction;
+ }
+ else if (next == fm->dv) {
+ size_t dsize = fm->dvsize += psize;
+ fm->dv = p;
+ set_size_and_pinuse_of_free_chunk(p, dsize);
+ goto postaction;
+ }
+ else {
+ size_t nsize = chunksize(next);
+ psize += nsize;
+ unlink_chunk(fm, next, nsize);
+ set_size_and_pinuse_of_free_chunk(p, psize);
+ if (p == fm->dv) {
+ fm->dvsize = psize;
+ goto postaction;
+ }
+ }
+ }
+ else
+ set_free_with_pinuse(p, psize, next);
+
+ if (is_small(psize)) {
+ insert_small_chunk(fm, p, psize);
+ check_free_chunk(fm, p);
+ }
+ else {
+ tchunkptr tp = (tchunkptr)p;
+ insert_large_chunk(fm, tp, psize);
+ check_free_chunk(fm, p);
+ if (--fm->release_checks == 0)
+ release_unused_segments(fm);
+ }
+ goto postaction;
+ }
+ }
+ erroraction:
+ USAGE_ERROR_ACTION(fm, p);
+ postaction:
+ POSTACTION(fm);
+ }
+ }
+#if !FOOTERS
+#undef fm
+#endif /* FOOTERS */
+}
+
+void* dlcalloc(size_t n_elements, size_t elem_size) {
+ void* mem;
+ size_t req = 0;
+ if (n_elements != 0) {
+ req = n_elements * elem_size;
+ if (((n_elements | elem_size) & ~(size_t)0xffff) &&
+ (req / n_elements != elem_size))
+ req = MAX_SIZE_T; /* force downstream failure on overflow */
+ }
+ mem = dlmalloc(req);
+ if (mem != 0 && calloc_must_clear(mem2chunk(mem)))
+ memset(mem, 0, req);
+ return mem;
+}
+
+void* dlrealloc(void* oldmem, size_t bytes) {
+ if (oldmem == 0)
+ return dlmalloc(bytes);
+#ifdef REALLOC_ZERO_BYTES_FREES
+ if (bytes == 0) {
+ dlfree(oldmem);
+ return 0;
+ }
+#endif /* REALLOC_ZERO_BYTES_FREES */
+ else {
+#if ! FOOTERS
+ mstate m = gm;
+#else /* FOOTERS */
+ mstate m = get_mstate_for(mem2chunk(oldmem));
+ if (!ok_magic(m)) {
+ USAGE_ERROR_ACTION(m, oldmem);
+ return 0;
+ }
+#endif /* FOOTERS */
+ return internal_realloc(m, oldmem, bytes);
+ }
+}
+
+void* dlmemalign(size_t alignment, size_t bytes) {
+ return internal_memalign(gm, alignment, bytes);
+}
+
+void** dlindependent_calloc(size_t n_elements, size_t elem_size,
+ void* chunks[]) {
+ size_t sz = elem_size; /* serves as 1-element array */
+ return ialloc(gm, n_elements, &sz, 3, chunks);
+}
+
+void** dlindependent_comalloc(size_t n_elements, size_t sizes[],
+ void* chunks[]) {
+ return ialloc(gm, n_elements, sizes, 0, chunks);
+}
+
+void* dlvalloc(size_t bytes) {
+ size_t pagesz;
+ ensure_initialization();
+ pagesz = mparams.page_size;
+ return dlmemalign(pagesz, bytes);
+}
+
+void* dlpvalloc(size_t bytes) {
+ size_t pagesz;
+ ensure_initialization();
+ pagesz = mparams.page_size;
+ return dlmemalign(pagesz, (bytes + pagesz - SIZE_T_ONE) & ~(pagesz - SIZE_T_ONE));
+}
+
+int dlmalloc_trim(size_t pad) {
+ int result = 0;
+ ensure_initialization();
+ if (!PREACTION(gm)) {
+ result = sys_trim(gm, pad);
+ POSTACTION(gm);
+ }
+ return result;
+}
+
+size_t dlmalloc_footprint(void) {
+ return gm->footprint;
+}
+
+size_t dlmalloc_max_footprint(void) {
+ return gm->max_footprint;
+}
+
+#if !NO_MALLINFO
+struct mallinfo dlmallinfo(void) {
+ return internal_mallinfo(gm);
+}
+#endif /* NO_MALLINFO */
+
+void dlmalloc_stats() {
+ internal_malloc_stats(gm);
+}
+
+int dlmallopt(int param_number, int value) {
+ return change_mparam(param_number, value);
+}
+
+#endif /* !ONLY_MSPACES */
+
+size_t dlmalloc_usable_size(void* mem) {
+ if (mem != 0) {
+ mchunkptr p = mem2chunk(mem);
+ if (is_inuse(p))
+ return chunksize(p) - overhead_for(p);
+ }
+ return 0;
+}
+
+/* ----------------------------- user mspaces ---------------------------- */
+
+#if MSPACES
+
+static mstate init_user_mstate(char* tbase, size_t tsize) {
+ size_t msize = pad_request(sizeof(struct malloc_state));
+ mchunkptr mn;
+ mchunkptr msp = align_as_chunk(tbase);
+ mstate m = (mstate)(chunk2mem(msp));
+ memset(m, 0, msize);
+ INITIAL_LOCK(&m->mutex);
+ msp->head = (msize|INUSE_BITS);
+ m->seg.base = m->least_addr = tbase;
+ m->seg.size = m->footprint = m->max_footprint = tsize;
+ m->magic = mparams.magic;
+ m->release_checks = MAX_RELEASE_CHECK_RATE;
+ m->mflags = mparams.default_mflags;
+ m->extp = 0;
+ m->exts = 0;
+ disable_contiguous(m);
+ init_bins(m);
+ mn = next_chunk(mem2chunk(m));
+ init_top(m, mn, (size_t)((tbase + tsize) - (char*)mn) - TOP_FOOT_SIZE);
+ check_top_chunk(m, m->top);
+ return m;
+}
+
+mspace create_mspace(size_t capacity, int locked) {
+ mstate m = 0;
+ size_t msize;
+ ensure_initialization();
+ msize = pad_request(sizeof(struct malloc_state));
+ if (capacity < (size_t) -(msize + TOP_FOOT_SIZE + mparams.page_size)) {
+ size_t rs = ((capacity == 0)? mparams.granularity :
+ (capacity + TOP_FOOT_SIZE + msize));
+ size_t tsize = granularity_align(rs);
+ char* tbase = (char*)(CALL_MMAP(tsize));
+ if (tbase != CMFAIL) {
+ m = init_user_mstate(tbase, tsize);
+ m->seg.sflags = USE_MMAP_BIT;
+ set_lock(m, locked);
+ }
+ }
+ return (mspace)m;
+}
+
+mspace create_mspace_with_base(void* base, size_t capacity, int locked) {
+ mstate m = 0;
+ size_t msize;
+ ensure_initialization();
+ msize = pad_request(sizeof(struct malloc_state));
+ if (capacity > msize + TOP_FOOT_SIZE &&
+ capacity < (size_t) -(msize + TOP_FOOT_SIZE + mparams.page_size)) {
+ m = init_user_mstate((char*)base, capacity);
+ m->seg.sflags = EXTERN_BIT;
+ set_lock(m, locked);
+ }
+ return (mspace)m;
+}
+
+int mspace_track_large_chunks(mspace msp, int enable) {
+ int ret = 0;
+ mstate ms = (mstate)msp;
+ if (!PREACTION(ms)) {
+ if (!use_mmap(ms))
+ ret = 1;
+ if (!enable)
+ enable_mmap(ms);
+ else
+ disable_mmap(ms);
+ POSTACTION(ms);
+ }
+ return ret;
+}
+
+size_t destroy_mspace(mspace msp) {
+ size_t freed = 0;
+ mstate ms = (mstate)msp;
+ if (ok_magic(ms)) {
+ msegmentptr sp = &ms->seg;
+ while (sp != 0) {
+ char* base = sp->base;
+ size_t size = sp->size;
+ flag_t flag = sp->sflags;
+ sp = sp->next;
+ if ((flag & USE_MMAP_BIT) && !(flag & EXTERN_BIT) &&
+ CALL_MUNMAP(base, size) == 0)
+ freed += size;
+ }
+ }
+ else {
+ USAGE_ERROR_ACTION(ms,ms);
+ }
+ return freed;
+}
+
+/*
+ mspace versions of routines are near-clones of the global
+ versions. This is not so nice but better than the alternatives.
+*/
+
+
+void* mspace_malloc(mspace msp, size_t bytes) {
+ mstate ms = (mstate)msp;
+ if (!ok_magic(ms)) {
+ USAGE_ERROR_ACTION(ms,ms);
+ return 0;
+ }
+ if (!PREACTION(ms)) {
+ void* mem;
+ size_t nb;
+ if (bytes <= MAX_SMALL_REQUEST) {
+ bindex_t idx;
+ binmap_t smallbits;
+ nb = (bytes < MIN_REQUEST)? MIN_CHUNK_SIZE : pad_request(bytes);
+ idx = small_index(nb);
+ smallbits = ms->smallmap >> idx;
+
+ if ((smallbits & 0x3U) != 0) { /* Remainderless fit to a smallbin. */
+ mchunkptr b, p;
+ idx += ~smallbits & 1; /* Uses next bin if idx empty */
+ b = smallbin_at(ms, idx);
+ p = b->fd;
+ assert(chunksize(p) == small_index2size(idx));
+ unlink_first_small_chunk(ms, b, p, idx);
+ set_inuse_and_pinuse(ms, p, small_index2size(idx));
+ mem = chunk2mem(p);
+ check_malloced_chunk(ms, mem, nb);
+ goto postaction;
+ }
+
+ else if (nb > ms->dvsize) {
+ if (smallbits != 0) { /* Use chunk in next nonempty smallbin */
+ mchunkptr b, p, r;
+ size_t rsize;
+ bindex_t i;
+ binmap_t leftbits = (smallbits << idx) & left_bits(idx2bit(idx));
+ binmap_t leastbit = least_bit(leftbits);
+ compute_bit2idx(leastbit, i);
+ b = smallbin_at(ms, i);
+ p = b->fd;
+ assert(chunksize(p) == small_index2size(i));
+ unlink_first_small_chunk(ms, b, p, i);
+ rsize = small_index2size(i) - nb;
+ /* Fit here cannot be remainderless if 4byte sizes */
+ if (SIZE_T_SIZE != 4 && rsize < MIN_CHUNK_SIZE)
+ set_inuse_and_pinuse(ms, p, small_index2size(i));
+ else {
+ set_size_and_pinuse_of_inuse_chunk(ms, p, nb);
+ r = chunk_plus_offset(p, nb);
+ set_size_and_pinuse_of_free_chunk(r, rsize);
+ replace_dv(ms, r, rsize);
+ }
+ mem = chunk2mem(p);
+ check_malloced_chunk(ms, mem, nb);
+ goto postaction;
+ }
+
+ else if (ms->treemap != 0 && (mem = tmalloc_small(ms, nb)) != 0) {
+ check_malloced_chunk(ms, mem, nb);
+ goto postaction;
+ }
+ }
+ }
+ else if (bytes >= MAX_REQUEST)
+ nb = MAX_SIZE_T; /* Too big to allocate. Force failure (in sys alloc) */
+ else {
+ nb = pad_request(bytes);
+ if (ms->treemap != 0 && (mem = tmalloc_large(ms, nb)) != 0) {
+ check_malloced_chunk(ms, mem, nb);
+ goto postaction;
+ }
+ }
+
+ if (nb <= ms->dvsize) {
+ size_t rsize = ms->dvsize - nb;
+ mchunkptr p = ms->dv;
+ if (rsize >= MIN_CHUNK_SIZE) { /* split dv */
+ mchunkptr r = ms->dv = chunk_plus_offset(p, nb);
+ ms->dvsize = rsize;
+ set_size_and_pinuse_of_free_chunk(r, rsize);
+ set_size_and_pinuse_of_inuse_chunk(ms, p, nb);
+ }
+ else { /* exhaust dv */
+ size_t dvs = ms->dvsize;
+ ms->dvsize = 0;
+ ms->dv = 0;
+ set_inuse_and_pinuse(ms, p, dvs);
+ }
+ mem = chunk2mem(p);
+ check_malloced_chunk(ms, mem, nb);
+ goto postaction;
+ }
+
+ else if (nb < ms->topsize) { /* Split top */
+ size_t rsize = ms->topsize -= nb;
+ mchunkptr p = ms->top;
+ mchunkptr r = ms->top = chunk_plus_offset(p, nb);
+ r->head = rsize | PINUSE_BIT;
+ set_size_and_pinuse_of_inuse_chunk(ms, p, nb);
+ mem = chunk2mem(p);
+ check_top_chunk(ms, ms->top);
+ check_malloced_chunk(ms, mem, nb);
+ goto postaction;
+ }
+
+ mem = sys_alloc(ms, nb);
+
+ postaction:
+ POSTACTION(ms);
+ return mem;
+ }
+
+ return 0;
+}
+
+void mspace_free(mspace msp, void* mem) {
+ if (mem != 0) {
+ mchunkptr p = mem2chunk(mem);
+#if FOOTERS
+ mstate fm = get_mstate_for(p);
+ msp = msp; /* placate people compiling -Wunused */
+#else /* FOOTERS */
+ mstate fm = (mstate)msp;
+#endif /* FOOTERS */
+ if (!ok_magic(fm)) {
+ USAGE_ERROR_ACTION(fm, p);
+ return;
+ }
+ if (!PREACTION(fm)) {
+ check_inuse_chunk(fm, p);
+ if (RTCHECK(ok_address(fm, p) && ok_inuse(p))) {
+ size_t psize = chunksize(p);
+ mchunkptr next = chunk_plus_offset(p, psize);
+ if (!pinuse(p)) {
+ size_t prevsize = p->prev_foot;
+ if (is_mmapped(p)) {
+ psize += prevsize + MMAP_FOOT_PAD;
+ if (CALL_MUNMAP((char*)p - prevsize, psize) == 0)
+ fm->footprint -= psize;
+ goto postaction;
+ }
+ else {
+ mchunkptr prev = chunk_minus_offset(p, prevsize);
+ psize += prevsize;
+ p = prev;
+ if (RTCHECK(ok_address(fm, prev))) { /* consolidate backward */
+ if (p != fm->dv) {
+ unlink_chunk(fm, p, prevsize);
+ }
+ else if ((next->head & INUSE_BITS) == INUSE_BITS) {
+ fm->dvsize = psize;
+ set_free_with_pinuse(p, psize, next);
+ goto postaction;
+ }
+ }
+ else
+ goto erroraction;
+ }
+ }
+
+ if (RTCHECK(ok_next(p, next) && ok_pinuse(next))) {
+ if (!cinuse(next)) { /* consolidate forward */
+ if (next == fm->top) {
+ size_t tsize = fm->topsize += psize;
+ fm->top = p;
+ p->head = tsize | PINUSE_BIT;
+ if (p == fm->dv) {
+ fm->dv = 0;
+ fm->dvsize = 0;
+ }
+ if (should_trim(fm, tsize))
+ sys_trim(fm, 0);
+ goto postaction;
+ }
+ else if (next == fm->dv) {
+ size_t dsize = fm->dvsize += psize;
+ fm->dv = p;
+ set_size_and_pinuse_of_free_chunk(p, dsize);
+ goto postaction;
+ }
+ else {
+ size_t nsize = chunksize(next);
+ psize += nsize;
+ unlink_chunk(fm, next, nsize);
+ set_size_and_pinuse_of_free_chunk(p, psize);
+ if (p == fm->dv) {
+ fm->dvsize = psize;
+ goto postaction;
+ }
+ }
+ }
+ else
+ set_free_with_pinuse(p, psize, next);
+
+ if (is_small(psize)) {
+ insert_small_chunk(fm, p, psize);
+ check_free_chunk(fm, p);
+ }
+ else {
+ tchunkptr tp = (tchunkptr)p;
+ insert_large_chunk(fm, tp, psize);
+ check_free_chunk(fm, p);
+ if (--fm->release_checks == 0)
+ release_unused_segments(fm);
+ }
+ goto postaction;
+ }
+ }
+ erroraction:
+ USAGE_ERROR_ACTION(fm, p);
+ postaction:
+ POSTACTION(fm);
+ }
+ }
+}
+
+void* mspace_calloc(mspace msp, size_t n_elements, size_t elem_size) {
+ void* mem;
+ size_t req = 0;
+ mstate ms = (mstate)msp;
+ if (!ok_magic(ms)) {
+ USAGE_ERROR_ACTION(ms,ms);
+ return 0;
+ }
+ if (n_elements != 0) {
+ req = n_elements * elem_size;
+ if (((n_elements | elem_size) & ~(size_t)0xffff) &&
+ (req / n_elements != elem_size))
+ req = MAX_SIZE_T; /* force downstream failure on overflow */
+ }
+ mem = internal_malloc(ms, req);
+ if (mem != 0 && calloc_must_clear(mem2chunk(mem)))
+ memset(mem, 0, req);
+ return mem;
+}
+
+void* mspace_realloc(mspace msp, void* oldmem, size_t bytes) {
+ if (oldmem == 0)
+ return mspace_malloc(msp, bytes);
+#ifdef REALLOC_ZERO_BYTES_FREES
+ if (bytes == 0) {
+ mspace_free(msp, oldmem);
+ return 0;
+ }
+#endif /* REALLOC_ZERO_BYTES_FREES */
+ else {
+#if FOOTERS
+ mchunkptr p = mem2chunk(oldmem);
+ mstate ms = get_mstate_for(p);
+#else /* FOOTERS */
+ mstate ms = (mstate)msp;
+#endif /* FOOTERS */
+ if (!ok_magic(ms)) {
+ USAGE_ERROR_ACTION(ms,ms);
+ return 0;
+ }
+ return internal_realloc(ms, oldmem, bytes);
+ }
+}
+
+void* mspace_memalign(mspace msp, size_t alignment, size_t bytes) {
+ mstate ms = (mstate)msp;
+ if (!ok_magic(ms)) {
+ USAGE_ERROR_ACTION(ms,ms);
+ return 0;
+ }
+ return internal_memalign(ms, alignment, bytes);
+}
+
+void** mspace_independent_calloc(mspace msp, size_t n_elements,
+ size_t elem_size, void* chunks[]) {
+ size_t sz = elem_size; /* serves as 1-element array */
+ mstate ms = (mstate)msp;
+ if (!ok_magic(ms)) {
+ USAGE_ERROR_ACTION(ms,ms);
+ return 0;
+ }
+ return ialloc(ms, n_elements, &sz, 3, chunks);
+}
+
+void** mspace_independent_comalloc(mspace msp, size_t n_elements,
+ size_t sizes[], void* chunks[]) {
+ mstate ms = (mstate)msp;
+ if (!ok_magic(ms)) {
+ USAGE_ERROR_ACTION(ms,ms);
+ return 0;
+ }
+ return ialloc(ms, n_elements, sizes, 0, chunks);
+}
+
+int mspace_trim(mspace msp, size_t pad) {
+ int result = 0;
+ mstate ms = (mstate)msp;
+ if (ok_magic(ms)) {
+ if (!PREACTION(ms)) {
+ result = sys_trim(ms, pad);
+ POSTACTION(ms);
+ }
+ }
+ else {
+ USAGE_ERROR_ACTION(ms,ms);
+ }
+ return result;
+}
+
+void mspace_malloc_stats(mspace msp) {
+ mstate ms = (mstate)msp;
+ if (ok_magic(ms)) {
+ internal_malloc_stats(ms);
+ }
+ else {
+ USAGE_ERROR_ACTION(ms,ms);
+ }
+}
+
+size_t mspace_footprint(mspace msp) {
+ size_t result = 0;
+ mstate ms = (mstate)msp;
+ if (ok_magic(ms)) {
+ result = ms->footprint;
+ }
+ else {
+ USAGE_ERROR_ACTION(ms,ms);
+ }
+ return result;
+}
+
+
+size_t mspace_max_footprint(mspace msp) {
+ size_t result = 0;
+ mstate ms = (mstate)msp;
+ if (ok_magic(ms)) {
+ result = ms->max_footprint;
+ }
+ else {
+ USAGE_ERROR_ACTION(ms,ms);
+ }
+ return result;
+}
+
+
+#if !NO_MALLINFO
+struct mallinfo mspace_mallinfo(mspace msp) {
+ mstate ms = (mstate)msp;
+ if (!ok_magic(ms)) {
+ USAGE_ERROR_ACTION(ms,ms);
+ }
+ return internal_mallinfo(ms);
+}
+#endif /* NO_MALLINFO */
+
+size_t mspace_usable_size(void* mem) {
+ if (mem != 0) {
+ mchunkptr p = mem2chunk(mem);
+ if (is_inuse(p))
+ return chunksize(p) - overhead_for(p);
+ }
+ return 0;
+}
+
+int mspace_mallopt(int param_number, int value) {
+ return change_mparam(param_number, value);
+}
+
+#endif /* MSPACES */
+
+
+/* -------------------- Alternative MORECORE functions ------------------- */
+
+/*
+ Guidelines for creating a custom version of MORECORE:
+
+ * For best performance, MORECORE should allocate in multiples of pagesize.
+ * MORECORE may allocate more memory than requested. (Or even less,
+ but this will usually result in a malloc failure.)
+ * MORECORE must not allocate memory when given argument zero, but
+ instead return one past the end address of memory from previous
+ nonzero call.
+ * For best performance, consecutive calls to MORECORE with positive
+ arguments should return increasing addresses, indicating that
+ space has been contiguously extended.
+ * Even though consecutive calls to MORECORE need not return contiguous
+ addresses, it must be OK for malloc'ed chunks to span multiple
+ regions in those cases where they do happen to be contiguous.
+ * MORECORE need not handle negative arguments -- it may instead
+ just return MFAIL when given negative arguments.
+ Negative arguments are always multiples of pagesize. MORECORE
+ must not misinterpret negative args as large positive unsigned
+ args. You can suppress all such calls from even occurring by defining
+ MORECORE_CANNOT_TRIM,
+
+ As an example alternative MORECORE, here is a custom allocator
+ kindly contributed for pre-OSX macOS. It uses virtually but not
+ necessarily physically contiguous non-paged memory (locked in,
+ present and won't get swapped out). You can use it by uncommenting
+ this section, adding some #includes, and setting up the appropriate
+ defines above:
+
+ #define MORECORE osMoreCore
+
+ There is also a shutdown routine that should somehow be called for
+ cleanup upon program exit.
+
+ #define MAX_POOL_ENTRIES 100
+ #define MINIMUM_MORECORE_SIZE (64 * 1024U)
+ static int next_os_pool;
+ void *our_os_pools[MAX_POOL_ENTRIES];
+
+ void *osMoreCore(int size)
+ {
+ void *ptr = 0;
+ static void *sbrk_top = 0;
+
+ if (size > 0)
+ {
+ if (size < MINIMUM_MORECORE_SIZE)
+ size = MINIMUM_MORECORE_SIZE;
+ if (CurrentExecutionLevel() == kTaskLevel)
+ ptr = PoolAllocateResident(size + RM_PAGE_SIZE, 0);
+ if (ptr == 0)
+ {
+ return (void *) MFAIL;
+ }
+ // save ptrs so they can be freed during cleanup
+ our_os_pools[next_os_pool] = ptr;
+ next_os_pool++;
+ ptr = (void *) ((((size_t) ptr) + RM_PAGE_MASK) & ~RM_PAGE_MASK);
+ sbrk_top = (char *) ptr + size;
+ return ptr;
+ }
+ else if (size < 0)
+ {
+ // we don't currently support shrink behavior
+ return (void *) MFAIL;
+ }
+ else
+ {
+ return sbrk_top;
+ }
+ }
+
+ // cleanup any allocated memory pools
+ // called as last thing before shutting down driver
+
+ void osCleanupMem(void)
+ {
+ void **ptr;
+
+ for (ptr = our_os_pools; ptr < &our_os_pools[MAX_POOL_ENTRIES]; ptr++)
+ if (*ptr)
+ {
+ PoolDeallocate(*ptr);
+ *ptr = 0;
+ }
+ }
+
+*/
+
+
+/* -----------------------------------------------------------------------
+History:
+ V2.8.4 Wed May 27 09:56:23 2009 Doug Lea (dl at gee)
+ * Use zeros instead of prev foot for is_mmapped
+ * Add mspace_track_large_chunks; thanks to Jean Brouwers
+ * Fix set_inuse in internal_realloc; thanks to Jean Brouwers
+ * Fix insufficient sys_alloc padding when using 16byte alignment
+ * Fix bad error check in mspace_footprint
+ * Adaptations for ptmalloc; thanks to Wolfram Gloger.
+ * Reentrant spin locks; thanks to Earl Chew and others
+ * Win32 improvements; thanks to Niall Douglas and Earl Chew
+ * Add NO_SEGMENT_TRAVERSAL and MAX_RELEASE_CHECK_RATE options
+ * Extension hook in malloc_state
+ * Various small adjustments to reduce warnings on some compilers
+ * Various configuration extensions/changes for more platforms. Thanks
+ to all who contributed these.
+
+ V2.8.3 Thu Sep 22 11:16:32 2005 Doug Lea (dl at gee)
+ * Add max_footprint functions
+ * Ensure all appropriate literals are size_t
+ * Fix conditional compilation problem for some #define settings
+ * Avoid concatenating segments with the one provided
+ in create_mspace_with_base
+ * Rename some variables to avoid compiler shadowing warnings
+ * Use explicit lock initialization.
+ * Better handling of sbrk interference.
+ * Simplify and fix segment insertion, trimming and mspace_destroy
+ * Reinstate REALLOC_ZERO_BYTES_FREES option from 2.7.x
+ * Thanks especially to Dennis Flanagan for help on these.
+
+ V2.8.2 Sun Jun 12 16:01:10 2005 Doug Lea (dl at gee)
+ * Fix memalign brace error.
+
+ V2.8.1 Wed Jun 8 16:11:46 2005 Doug Lea (dl at gee)
+ * Fix improper #endif nesting in C++
+ * Add explicit casts needed for C++
+
+ V2.8.0 Mon May 30 14:09:02 2005 Doug Lea (dl at gee)
+ * Use trees for large bins
+ * Support mspaces
+ * Use segments to unify sbrk-based and mmap-based system allocation,
+ removing need for emulation on most platforms without sbrk.
+ * Default safety checks
+ * Optional footer checks. Thanks to William Robertson for the idea.
+ * Internal code refactoring
+ * Incorporate suggestions and platform-specific changes.
+ Thanks to Dennis Flanagan, Colin Plumb, Niall Douglas,
+ Aaron Bachmann, Emery Berger, and others.
+ * Speed up non-fastbin processing enough to remove fastbins.
+ * Remove useless cfree() to avoid conflicts with other apps.
+ * Remove internal memcpy, memset. Compilers handle builtins better.
+ * Remove some options that no one ever used and rename others.
+
+ V2.7.2 Sat Aug 17 09:07:30 2002 Doug Lea (dl at gee)
+ * Fix malloc_state bitmap array misdeclaration
+
+ V2.7.1 Thu Jul 25 10:58:03 2002 Doug Lea (dl at gee)
+ * Allow tuning of FIRST_SORTED_BIN_SIZE
+ * Use PTR_UINT as type for all ptr->int casts. Thanks to John Belmonte.
+ * Better detection and support for non-contiguousness of MORECORE.
+ Thanks to Andreas Mueller, Conal Walsh, and Wolfram Gloger
+ * Bypass most of malloc if no frees. Thanks To Emery Berger.
+ * Fix freeing of old top non-contiguous chunk im sysmalloc.
+ * Raised default trim and map thresholds to 256K.
+ * Fix mmap-related #defines. Thanks to Lubos Lunak.
+ * Fix copy macros; added LACKS_FCNTL_H. Thanks to Neal Walfield.
+ * Branch-free bin calculation
+ * Default trim and mmap thresholds now 256K.
+
+ V2.7.0 Sun Mar 11 14:14:06 2001 Doug Lea (dl at gee)
+ * Introduce independent_comalloc and independent_calloc.
+ Thanks to Michael Pachos for motivation and help.
+ * Make optional .h file available
+ * Allow > 2GB requests on 32bit systems.
+ * new WIN32 sbrk, mmap, munmap, lock code from <Walter@GeNeSys-e.de>.
+ Thanks also to Andreas Mueller <a.mueller at paradatec.de>,
+ and Anonymous.
+ * Allow override of MALLOC_ALIGNMENT (Thanks to Ruud Waij for
+ helping test this.)
+ * memalign: check alignment arg
+ * realloc: don't try to shift chunks backwards, since this
+ leads to more fragmentation in some programs and doesn't
+ seem to help in any others.
+ * Collect all cases in malloc requiring system memory into sysmalloc
+ * Use mmap as backup to sbrk
+ * Place all internal state in malloc_state
+ * Introduce fastbins (although similar to 2.5.1)
+ * Many minor tunings and cosmetic improvements
+ * Introduce USE_PUBLIC_MALLOC_WRAPPERS, USE_MALLOC_LOCK
+ * Introduce MALLOC_FAILURE_ACTION, MORECORE_CONTIGUOUS
+ Thanks to Tony E. Bennett <tbennett@nvidia.com> and others.
+ * Include errno.h to support default failure action.
+
+ V2.6.6 Sun Dec 5 07:42:19 1999 Doug Lea (dl at gee)
+ * return null for negative arguments
+ * Added Several WIN32 cleanups from Martin C. Fong <mcfong at yahoo.com>
+ * Add 'LACKS_SYS_PARAM_H' for those systems without 'sys/param.h'
+ (e.g. WIN32 platforms)
+ * Cleanup header file inclusion for WIN32 platforms
+ * Cleanup code to avoid Microsoft Visual C++ compiler complaints
+ * Add 'USE_DL_PREFIX' to quickly allow co-existence with existing
+ memory allocation routines
+ * Set 'malloc_getpagesize' for WIN32 platforms (needs more work)
+ * Use 'assert' rather than 'ASSERT' in WIN32 code to conform to
+ usage of 'assert' in non-WIN32 code
+ * Improve WIN32 'sbrk()' emulation's 'findRegion()' routine to
+ avoid infinite loop
+ * Always call 'fREe()' rather than 'free()'
+
+ V2.6.5 Wed Jun 17 15:57:31 1998 Doug Lea (dl at gee)
+ * Fixed ordering problem with boundary-stamping
+
+ V2.6.3 Sun May 19 08:17:58 1996 Doug Lea (dl at gee)
+ * Added pvalloc, as recommended by H.J. Liu
+ * Added 64bit pointer support mainly from Wolfram Gloger
+ * Added anonymously donated WIN32 sbrk emulation
+ * Malloc, calloc, getpagesize: add optimizations from Raymond Nijssen
+ * malloc_extend_top: fix mask error that caused wastage after
+ foreign sbrks
+ * Add linux mremap support code from HJ Liu
+
+ V2.6.2 Tue Dec 5 06:52:55 1995 Doug Lea (dl at gee)
+ * Integrated most documentation with the code.
+ * Add support for mmap, with help from
+ Wolfram Gloger (Gloger@lrz.uni-muenchen.de).
+ * Use last_remainder in more cases.
+ * Pack bins using idea from colin@nyx10.cs.du.edu
+ * Use ordered bins instead of best-fit threshhold
+ * Eliminate block-local decls to simplify tracing and debugging.
+ * Support another case of realloc via move into top
+ * Fix error occuring when initial sbrk_base not word-aligned.
+ * Rely on page size for units instead of SBRK_UNIT to
+ avoid surprises about sbrk alignment conventions.
+ * Add mallinfo, mallopt. Thanks to Raymond Nijssen
+ (raymond@es.ele.tue.nl) for the suggestion.
+ * Add `pad' argument to malloc_trim and top_pad mallopt parameter.
+ * More precautions for cases where other routines call sbrk,
+ courtesy of Wolfram Gloger (Gloger@lrz.uni-muenchen.de).
+ * Added macros etc., allowing use in linux libc from
+ H.J. Lu (hjl@gnu.ai.mit.edu)
+ * Inverted this history list
+
+ V2.6.1 Sat Dec 2 14:10:57 1995 Doug Lea (dl at gee)
+ * Re-tuned and fixed to behave more nicely with V2.6.0 changes.
+ * Removed all preallocation code since under current scheme
+ the work required to undo bad preallocations exceeds
+ the work saved in good cases for most test programs.
+ * No longer use return list or unconsolidated bins since
+ no scheme using them consistently outperforms those that don't
+ given above changes.
+ * Use best fit for very large chunks to prevent some worst-cases.
+ * Added some support for debugging
+
+ V2.6.0 Sat Nov 4 07:05:23 1995 Doug Lea (dl at gee)
+ * Removed footers when chunks are in use. Thanks to
+ Paul Wilson (wilson@cs.texas.edu) for the suggestion.
+
+ V2.5.4 Wed Nov 1 07:54:51 1995 Doug Lea (dl at gee)
+ * Added malloc_trim, with help from Wolfram Gloger
+ (wmglo@Dent.MED.Uni-Muenchen.DE).
+
+ V2.5.3 Tue Apr 26 10:16:01 1994 Doug Lea (dl at g)
+
+ V2.5.2 Tue Apr 5 16:20:40 1994 Doug Lea (dl at g)
+ * realloc: try to expand in both directions
+ * malloc: swap order of clean-bin strategy;
+ * realloc: only conditionally expand backwards
+ * Try not to scavenge used bins
+ * Use bin counts as a guide to preallocation
+ * Occasionally bin return list chunks in first scan
+ * Add a few optimizations from colin@nyx10.cs.du.edu
+
+ V2.5.1 Sat Aug 14 15:40:43 1993 Doug Lea (dl at g)
+ * faster bin computation & slightly different binning
+ * merged all consolidations to one part of malloc proper
+ (eliminating old malloc_find_space & malloc_clean_bin)
+ * Scan 2 returns chunks (not just 1)
+ * Propagate failure in realloc if malloc returns 0
+ * Add stuff to allow compilation on non-ANSI compilers
+ from kpv@research.att.com
+
+ V2.5 Sat Aug 7 07:41:59 1993 Doug Lea (dl at g.oswego.edu)
+ * removed potential for odd address access in prev_chunk
+ * removed dependency on getpagesize.h
+ * misc cosmetics and a bit more internal documentation
+ * anticosmetics: mangled names in macros to evade debugger strangeness
+ * tested on sparc, hp-700, dec-mips, rs6000
+ with gcc & native cc (hp, dec only) allowing
+ Detlefs & Zorn comparison study (in SIGPLAN Notices.)
+
+ Trial version Fri Aug 28 13:14:29 1992 Doug Lea (dl at g.oswego.edu)
+ * Based loosely on libg++-1.2X malloc. (It retains some of the overall
+ structure of old version, but most details differ.)
+
+*/
+
diff --git a/unsupported/test/mpreal/dlmalloc.h b/unsupported/test/mpreal/dlmalloc.h new file mode 100755 index 000000000..a90dcb6f5 --- /dev/null +++ b/unsupported/test/mpreal/dlmalloc.h @@ -0,0 +1,562 @@ +/*
+ Default header file for malloc-2.8.x, written by Doug Lea
+ and released to the public domain, as explained at
+ http://creativecommons.org/licenses/publicdomain.
+
+ last update: Wed May 27 14:25:17 2009 Doug Lea (dl at gee)
+
+ This header is for ANSI C/C++ only. You can set any of
+ the following #defines before including:
+
+ * If USE_DL_PREFIX is defined, it is assumed that malloc.c
+ was also compiled with this option, so all routines
+ have names starting with "dl".
+
+ * If HAVE_USR_INCLUDE_MALLOC_H is defined, it is assumed that this
+ file will be #included AFTER <malloc.h>. This is needed only if
+ your system defines a struct mallinfo that is incompatible with the
+ standard one declared here. Otherwise, you can include this file
+ INSTEAD of your system system <malloc.h>. At least on ANSI, all
+ declarations should be compatible with system versions
+
+ * If MSPACES is defined, declarations for mspace versions are included.
+*/
+
+#ifndef MALLOC_280_H
+#define MALLOC_280_H
+
+#define USE_DL_PREFIX
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <stddef.h> /* for size_t */
+
+#ifndef ONLY_MSPACES
+#define ONLY_MSPACES 0 /* define to a value */
+#endif /* ONLY_MSPACES */
+#ifndef NO_MALLINFO
+#define NO_MALLINFO 0
+#endif /* NO_MALLINFO */
+
+
+#if !ONLY_MSPACES
+
+#ifndef USE_DL_PREFIX
+#define dlcalloc calloc
+#define dlfree free
+#define dlmalloc malloc
+#define dlmemalign memalign
+#define dlrealloc realloc
+#define dlvalloc valloc
+#define dlpvalloc pvalloc
+#define dlmallinfo mallinfo
+#define dlmallopt mallopt
+#define dlmalloc_trim malloc_trim
+#define dlmalloc_stats malloc_stats
+#define dlmalloc_usable_size malloc_usable_size
+#define dlmalloc_footprint malloc_footprint
+#define dlindependent_calloc independent_calloc
+#define dlindependent_comalloc independent_comalloc
+#endif /* USE_DL_PREFIX */
+#if !NO_MALLINFO
+#ifndef HAVE_USR_INCLUDE_MALLOC_H
+#ifndef _MALLOC_H
+#ifndef MALLINFO_FIELD_TYPE
+#define MALLINFO_FIELD_TYPE size_t
+#endif /* MALLINFO_FIELD_TYPE */
+#ifndef STRUCT_MALLINFO_DECLARED
+#define STRUCT_MALLINFO_DECLARED 1
+struct mallinfo {
+ MALLINFO_FIELD_TYPE arena; /* non-mmapped space allocated from system */
+ MALLINFO_FIELD_TYPE ordblks; /* number of free chunks */
+ MALLINFO_FIELD_TYPE smblks; /* always 0 */
+ MALLINFO_FIELD_TYPE hblks; /* always 0 */
+ MALLINFO_FIELD_TYPE hblkhd; /* space in mmapped regions */
+ MALLINFO_FIELD_TYPE usmblks; /* maximum total allocated space */
+ MALLINFO_FIELD_TYPE fsmblks; /* always 0 */
+ MALLINFO_FIELD_TYPE uordblks; /* total allocated space */
+ MALLINFO_FIELD_TYPE fordblks; /* total free space */
+ MALLINFO_FIELD_TYPE keepcost; /* releasable (via malloc_trim) space */
+};
+#endif /* STRUCT_MALLINFO_DECLARED */
+#endif /* _MALLOC_H */
+#endif /* HAVE_USR_INCLUDE_MALLOC_H */
+#endif /* !NO_MALLINFO */
+
+/*
+ malloc(size_t n)
+ Returns a pointer to a newly allocated chunk of at least n bytes, or
+ null if no space is available, in which case errno is set to ENOMEM
+ on ANSI C systems.
+
+ If n is zero, malloc returns a minimum-sized chunk. (The minimum
+ size is 16 bytes on most 32bit systems, and 32 bytes on 64bit
+ systems.) Note that size_t is an unsigned type, so calls with
+ arguments that would be negative if signed are interpreted as
+ requests for huge amounts of space, which will often fail. The
+ maximum supported value of n differs across systems, but is in all
+ cases less than the maximum representable value of a size_t.
+*/
+void* dlmalloc(size_t);
+
+/*
+ free(void* p)
+ Releases the chunk of memory pointed to by p, that had been previously
+ allocated using malloc or a related routine such as realloc.
+ It has no effect if p is null. If p was not malloced or already
+ freed, free(p) will by default cuase the current program to abort.
+*/
+void dlfree(void*);
+
+/*
+ calloc(size_t n_elements, size_t element_size);
+ Returns a pointer to n_elements * element_size bytes, with all locations
+ set to zero.
+*/
+void* dlcalloc(size_t, size_t);
+
+/*
+ realloc(void* p, size_t n)
+ Returns a pointer to a chunk of size n that contains the same data
+ as does chunk p up to the minimum of (n, p's size) bytes, or null
+ if no space is available.
+
+ The returned pointer may or may not be the same as p. The algorithm
+ prefers extending p in most cases when possible, otherwise it
+ employs the equivalent of a malloc-copy-free sequence.
+
+ If p is null, realloc is equivalent to malloc.
+
+ If space is not available, realloc returns null, errno is set (if on
+ ANSI) and p is NOT freed.
+
+ if n is for fewer bytes than already held by p, the newly unused
+ space is lopped off and freed if possible. realloc with a size
+ argument of zero (re)allocates a minimum-sized chunk.
+
+ The old unix realloc convention of allowing the last-free'd chunk
+ to be used as an argument to realloc is not supported.
+*/
+
+void* dlrealloc(void*, size_t);
+
+/*
+ memalign(size_t alignment, size_t n);
+ Returns a pointer to a newly allocated chunk of n bytes, aligned
+ in accord with the alignment argument.
+
+ The alignment argument should be a power of two. If the argument is
+ not a power of two, the nearest greater power is used.
+ 8-byte alignment is guaranteed by normal malloc calls, so don't
+ bother calling memalign with an argument of 8 or less.
+
+ Overreliance on memalign is a sure way to fragment space.
+*/
+void* dlmemalign(size_t, size_t);
+
+/*
+ valloc(size_t n);
+ Equivalent to memalign(pagesize, n), where pagesize is the page
+ size of the system. If the pagesize is unknown, 4096 is used.
+*/
+void* dlvalloc(size_t);
+
+/*
+ mallopt(int parameter_number, int parameter_value)
+ Sets tunable parameters The format is to provide a
+ (parameter-number, parameter-value) pair. mallopt then sets the
+ corresponding parameter to the argument value if it can (i.e., so
+ long as the value is meaningful), and returns 1 if successful else
+ 0. SVID/XPG/ANSI defines four standard param numbers for mallopt,
+ normally defined in malloc.h. None of these are use in this malloc,
+ so setting them has no effect. But this malloc also supports other
+ options in mallopt:
+
+ Symbol param # default allowed param values
+ M_TRIM_THRESHOLD -1 2*1024*1024 any (-1U disables trimming)
+ M_GRANULARITY -2 page size any power of 2 >= page size
+ M_MMAP_THRESHOLD -3 256*1024 any (or 0 if no MMAP support)
+*/
+int dlmallopt(int, int);
+
+#define M_TRIM_THRESHOLD (-1)
+#define M_GRANULARITY (-2)
+#define M_MMAP_THRESHOLD (-3)
+
+
+/*
+ malloc_footprint();
+ Returns the number of bytes obtained from the system. The total
+ number of bytes allocated by malloc, realloc etc., is less than this
+ value. Unlike mallinfo, this function returns only a precomputed
+ result, so can be called frequently to monitor memory consumption.
+ Even if locks are otherwise defined, this function does not use them,
+ so results might not be up to date.
+*/
+size_t dlmalloc_footprint();
+
+#if !NO_MALLINFO
+/*
+ mallinfo()
+ Returns (by copy) a struct containing various summary statistics:
+
+ arena: current total non-mmapped bytes allocated from system
+ ordblks: the number of free chunks
+ smblks: always zero.
+ hblks: current number of mmapped regions
+ hblkhd: total bytes held in mmapped regions
+ usmblks: the maximum total allocated space. This will be greater
+ than current total if trimming has occurred.
+ fsmblks: always zero
+ uordblks: current total allocated space (normal or mmapped)
+ fordblks: total free space
+ keepcost: the maximum number of bytes that could ideally be released
+ back to system via malloc_trim. ("ideally" means that
+ it ignores page restrictions etc.)
+
+ Because these fields are ints, but internal bookkeeping may
+ be kept as longs, the reported values may wrap around zero and
+ thus be inaccurate.
+*/
+
+struct mallinfo dlmallinfo(void);
+#endif /* NO_MALLINFO */
+
+/*
+ independent_calloc(size_t n_elements, size_t element_size, void* chunks[]);
+
+ independent_calloc is similar to calloc, but instead of returning a
+ single cleared space, it returns an array of pointers to n_elements
+ independent elements that can hold contents of size elem_size, each
+ of which starts out cleared, and can be independently freed,
+ realloc'ed etc. The elements are guaranteed to be adjacently
+ allocated (this is not guaranteed to occur with multiple callocs or
+ mallocs), which may also improve cache locality in some
+ applications.
+
+ The "chunks" argument is optional (i.e., may be null, which is
+ probably the most typical usage). If it is null, the returned array
+ is itself dynamically allocated and should also be freed when it is
+ no longer needed. Otherwise, the chunks array must be of at least
+ n_elements in length. It is filled in with the pointers to the
+ chunks.
+
+ In either case, independent_calloc returns this pointer array, or
+ null if the allocation failed. If n_elements is zero and "chunks"
+ is null, it returns a chunk representing an array with zero elements
+ (which should be freed if not wanted).
+
+ Each element must be individually freed when it is no longer
+ needed. If you'd like to instead be able to free all at once, you
+ should instead use regular calloc and assign pointers into this
+ space to represent elements. (In this case though, you cannot
+ independently free elements.)
+
+ independent_calloc simplifies and speeds up implementations of many
+ kinds of pools. It may also be useful when constructing large data
+ structures that initially have a fixed number of fixed-sized nodes,
+ but the number is not known at compile time, and some of the nodes
+ may later need to be freed. For example:
+
+ struct Node { int item; struct Node* next; };
+
+ struct Node* build_list() {
+ struct Node** pool;
+ int n = read_number_of_nodes_needed();
+ if (n <= 0) return 0;
+ pool = (struct Node**)(independent_calloc(n, sizeof(struct Node), 0);
+ if (pool == 0) die();
+ // organize into a linked list...
+ struct Node* first = pool[0];
+ for (i = 0; i < n-1; ++i)
+ pool[i]->next = pool[i+1];
+ free(pool); // Can now free the array (or not, if it is needed later)
+ return first;
+ }
+*/
+void** dlindependent_calloc(size_t, size_t, void**);
+
+/*
+ independent_comalloc(size_t n_elements, size_t sizes[], void* chunks[]);
+
+ independent_comalloc allocates, all at once, a set of n_elements
+ chunks with sizes indicated in the "sizes" array. It returns
+ an array of pointers to these elements, each of which can be
+ independently freed, realloc'ed etc. The elements are guaranteed to
+ be adjacently allocated (this is not guaranteed to occur with
+ multiple callocs or mallocs), which may also improve cache locality
+ in some applications.
+
+ The "chunks" argument is optional (i.e., may be null). If it is null
+ the returned array is itself dynamically allocated and should also
+ be freed when it is no longer needed. Otherwise, the chunks array
+ must be of at least n_elements in length. It is filled in with the
+ pointers to the chunks.
+
+ In either case, independent_comalloc returns this pointer array, or
+ null if the allocation failed. If n_elements is zero and chunks is
+ null, it returns a chunk representing an array with zero elements
+ (which should be freed if not wanted).
+
+ Each element must be individually freed when it is no longer
+ needed. If you'd like to instead be able to free all at once, you
+ should instead use a single regular malloc, and assign pointers at
+ particular offsets in the aggregate space. (In this case though, you
+ cannot independently free elements.)
+
+ independent_comallac differs from independent_calloc in that each
+ element may have a different size, and also that it does not
+ automatically clear elements.
+
+ independent_comalloc can be used to speed up allocation in cases
+ where several structs or objects must always be allocated at the
+ same time. For example:
+
+ struct Head { ... }
+ struct Foot { ... }
+
+ void send_message(char* msg) {
+ int msglen = strlen(msg);
+ size_t sizes[3] = { sizeof(struct Head), msglen, sizeof(struct Foot) };
+ void* chunks[3];
+ if (independent_comalloc(3, sizes, chunks) == 0)
+ die();
+ struct Head* head = (struct Head*)(chunks[0]);
+ char* body = (char*)(chunks[1]);
+ struct Foot* foot = (struct Foot*)(chunks[2]);
+ // ...
+ }
+
+ In general though, independent_comalloc is worth using only for
+ larger values of n_elements. For small values, you probably won't
+ detect enough difference from series of malloc calls to bother.
+
+ Overuse of independent_comalloc can increase overall memory usage,
+ since it cannot reuse existing noncontiguous small chunks that
+ might be available for some of the elements.
+*/
+void** dlindependent_comalloc(size_t, size_t*, void**);
+
+
+/*
+ pvalloc(size_t n);
+ Equivalent to valloc(minimum-page-that-holds(n)), that is,
+ round up n to nearest pagesize.
+ */
+void* dlpvalloc(size_t);
+
+/*
+ malloc_trim(size_t pad);
+
+ If possible, gives memory back to the system (via negative arguments
+ to sbrk) if there is unused memory at the `high' end of the malloc
+ pool or in unused MMAP segments. You can call this after freeing
+ large blocks of memory to potentially reduce the system-level memory
+ requirements of a program. However, it cannot guarantee to reduce
+ memory. Under some allocation patterns, some large free blocks of
+ memory will be locked between two used chunks, so they cannot be
+ given back to the system.
+
+ The `pad' argument to malloc_trim represents the amount of free
+ trailing space to leave untrimmed. If this argument is zero, only
+ the minimum amount of memory to maintain internal data structures
+ will be left. Non-zero arguments can be supplied to maintain enough
+ trailing space to service future expected allocations without having
+ to re-obtain memory from the system.
+
+ Malloc_trim returns 1 if it actually released any memory, else 0.
+*/
+int dlmalloc_trim(size_t);
+
+/*
+ malloc_stats();
+ Prints on stderr the amount of space obtained from the system (both
+ via sbrk and mmap), the maximum amount (which may be more than
+ current if malloc_trim and/or munmap got called), and the current
+ number of bytes allocated via malloc (or realloc, etc) but not yet
+ freed. Note that this is the number of bytes allocated, not the
+ number requested. It will be larger than the number requested
+ because of alignment and bookkeeping overhead. Because it includes
+ alignment wastage as being in use, this figure may be greater than
+ zero even when no user-level chunks are allocated.
+
+ The reported current and maximum system memory can be inaccurate if
+ a program makes other calls to system memory allocation functions
+ (normally sbrk) outside of malloc.
+
+ malloc_stats prints only the most commonly interesting statistics.
+ More information can be obtained by calling mallinfo.
+*/
+void dlmalloc_stats();
+
+#endif /* !ONLY_MSPACES */
+
+/*
+ malloc_usable_size(void* p);
+
+ Returns the number of bytes you can actually use in
+ an allocated chunk, which may be more than you requested (although
+ often not) due to alignment and minimum size constraints.
+ You can use this many bytes without worrying about
+ overwriting other allocated objects. This is not a particularly great
+ programming practice. malloc_usable_size can be more useful in
+ debugging and assertions, for example:
+
+ p = malloc(n);
+ assert(malloc_usable_size(p) >= 256);
+*/
+size_t dlmalloc_usable_size(void*);
+
+
+#if MSPACES
+
+/*
+ mspace is an opaque type representing an independent
+ region of space that supports mspace_malloc, etc.
+*/
+typedef void* mspace;
+
+/*
+ create_mspace creates and returns a new independent space with the
+ given initial capacity, or, if 0, the default granularity size. It
+ returns null if there is no system memory available to create the
+ space. If argument locked is non-zero, the space uses a separate
+ lock to control access. The capacity of the space will grow
+ dynamically as needed to service mspace_malloc requests. You can
+ control the sizes of incremental increases of this space by
+ compiling with a different DEFAULT_GRANULARITY or dynamically
+ setting with mallopt(M_GRANULARITY, value).
+*/
+mspace create_mspace(size_t capacity, int locked);
+
+/*
+ destroy_mspace destroys the given space, and attempts to return all
+ of its memory back to the system, returning the total number of
+ bytes freed. After destruction, the results of access to all memory
+ used by the space become undefined.
+*/
+size_t destroy_mspace(mspace msp);
+
+/*
+ create_mspace_with_base uses the memory supplied as the initial base
+ of a new mspace. Part (less than 128*sizeof(size_t) bytes) of this
+ space is used for bookkeeping, so the capacity must be at least this
+ large. (Otherwise 0 is returned.) When this initial space is
+ exhausted, additional memory will be obtained from the system.
+ Destroying this space will deallocate all additionally allocated
+ space (if possible) but not the initial base.
+*/
+mspace create_mspace_with_base(void* base, size_t capacity, int locked);
+
+/*
+ mspace_track_large_chunks controls whether requests for large chunks
+ are allocated in their own untracked mmapped regions, separate from
+ others in this mspace. By default large chunks are not tracked,
+ which reduces fragmentation. However, such chunks are not
+ necessarily released to the system upon destroy_mspace. Enabling
+ tracking by setting to true may increase fragmentation, but avoids
+ leakage when relying on destroy_mspace to release all memory
+ allocated using this space. The function returns the previous
+ setting.
+*/
+int mspace_track_large_chunks(mspace msp, int enable);
+
+/*
+ mspace_malloc behaves as malloc, but operates within
+ the given space.
+*/
+void* mspace_malloc(mspace msp, size_t bytes);
+
+/*
+ mspace_free behaves as free, but operates within
+ the given space.
+
+ If compiled with FOOTERS==1, mspace_free is not actually needed.
+ free may be called instead of mspace_free because freed chunks from
+ any space are handled by their originating spaces.
+*/
+void mspace_free(mspace msp, void* mem);
+
+/*
+ mspace_realloc behaves as realloc, but operates within
+ the given space.
+
+ If compiled with FOOTERS==1, mspace_realloc is not actually
+ needed. realloc may be called instead of mspace_realloc because
+ realloced chunks from any space are handled by their originating
+ spaces.
+*/
+void* mspace_realloc(mspace msp, void* mem, size_t newsize);
+
+/*
+ mspace_calloc behaves as calloc, but operates within
+ the given space.
+*/
+void* mspace_calloc(mspace msp, size_t n_elements, size_t elem_size);
+
+/*
+ mspace_memalign behaves as memalign, but operates within
+ the given space.
+*/
+void* mspace_memalign(mspace msp, size_t alignment, size_t bytes);
+
+/*
+ mspace_independent_calloc behaves as independent_calloc, but
+ operates within the given space.
+*/
+void** mspace_independent_calloc(mspace msp, size_t n_elements,
+ size_t elem_size, void* chunks[]);
+
+/*
+ mspace_independent_comalloc behaves as independent_comalloc, but
+ operates within the given space.
+*/
+void** mspace_independent_comalloc(mspace msp, size_t n_elements,
+ size_t sizes[], void* chunks[]);
+
+/*
+ mspace_footprint() returns the number of bytes obtained from the
+ system for this space.
+*/
+size_t mspace_footprint(mspace msp);
+
+
+#if !NO_MALLINFO
+/*
+ mspace_mallinfo behaves as mallinfo, but reports properties of
+ the given space.
+*/
+struct mallinfo mspace_mallinfo(mspace msp);
+#endif /* NO_MALLINFO */
+
+/*
+ malloc_usable_size(void* p) behaves the same as malloc_usable_size;
+*/
+ size_t mspace_usable_size(void* mem);
+
+/*
+ mspace_malloc_stats behaves as malloc_stats, but reports
+ properties of the given space.
+*/
+void mspace_malloc_stats(mspace msp);
+
+/*
+ mspace_trim behaves as malloc_trim, but
+ operates within the given space.
+*/
+int mspace_trim(mspace msp, size_t pad);
+
+/*
+ An alias for mallopt.
+*/
+int mspace_mallopt(int, int);
+
+#endif /* MSPACES */
+
+#ifdef __cplusplus
+}; /* end of extern "C" */
+#endif
+
+#endif /* MALLOC_280_H */
diff --git a/unsupported/test/mpreal/mpreal.cpp b/unsupported/test/mpreal/mpreal.cpp new file mode 100644 index 000000000..5c23544ef --- /dev/null +++ b/unsupported/test/mpreal/mpreal.cpp @@ -0,0 +1,597 @@ +/*
+ Multi-precision real number class. C++ interface fo MPFR library.
+ Project homepage: http://www.holoborodko.com/pavel/
+ Contact e-mail: pavel@holoborodko.com
+
+ Copyright (c) 2008-2011 Pavel Holoborodko
+
+ Core Developers:
+ Pavel Holoborodko, Dmitriy Gubanov, Konstantin Holoborodko.
+
+ Contributors:
+ Brian Gladman, Helmut Jarausch, Fokko Beekhof, Ulrich Mutze,
+ Heinz van Saanen, Pere Constans, Peter van Hoof, Gael Guennebaud,
+ Tsai Chia Cheng, Alexei Zubanov.
+
+ ****************************************************************************
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
+
+ ****************************************************************************
+ ****************************************************************************
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+
+ 3. The name of the author may be used to endorse or promote products
+ derived from this software without specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ SUCH DAMAGE.
+*/
+#include <cstring>
+#include "mpreal.h"
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+#include "dlmalloc.h"
+#endif
+
+using std::ws;
+using std::cerr;
+using std::endl;
+using std::string;
+using std::ostream;
+using std::istream;
+
+namespace mpfr{
+
+mp_rnd_t mpreal::default_rnd = MPFR_RNDN; //(mpfr_get_default_rounding_mode)();
+mp_prec_t mpreal::default_prec = 64; //(mpfr_get_default_prec)();
+int mpreal::default_base = 10;
+int mpreal::double_bits = -1;
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+bool mpreal::is_custom_malloc = false;
+#endif
+
+// Default constructor: creates mp number and initializes it to 0.
+mpreal::mpreal()
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,default_prec);
+ mpfr_set_ui(mp,0,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+mpreal::mpreal(const mpreal& u)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,mpfr_get_prec(u.mp));
+ mpfr_set(mp,u.mp,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+mpreal::mpreal(const mpfr_t u)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,mpfr_get_prec(u));
+ mpfr_set(mp,u,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+mpreal::mpreal(const mpf_t u)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,(mp_prec_t) mpf_get_prec(u)); // (gmp: mp_bitcnt_t) unsigned long -> long (mpfr: mp_prec_t)
+ mpfr_set_f(mp,u,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+mpreal::mpreal(const mpz_t u, mp_prec_t prec, mp_rnd_t mode)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,prec);
+ mpfr_set_z(mp,u,mode);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+mpreal::mpreal(const mpq_t u, mp_prec_t prec, mp_rnd_t mode)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,prec);
+ mpfr_set_q(mp,u,mode);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+mpreal::mpreal(const double u, mp_prec_t prec, mp_rnd_t mode)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ if(double_bits == -1 || fits_in_bits(u, double_bits))
+ {
+ mpfr_init2(mp,prec);
+ mpfr_set_d(mp,u,mode);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ }
+ else
+ throw conversion_overflow();
+}
+
+mpreal::mpreal(const long double u, mp_prec_t prec, mp_rnd_t mode)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,prec);
+ mpfr_set_ld(mp,u,mode);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+mpreal::mpreal(const unsigned long int u, mp_prec_t prec, mp_rnd_t mode)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,prec);
+ mpfr_set_ui(mp,u,mode);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+mpreal::mpreal(const unsigned int u, mp_prec_t prec, mp_rnd_t mode)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,prec);
+ mpfr_set_ui(mp,u,mode);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+mpreal::mpreal(const long int u, mp_prec_t prec, mp_rnd_t mode)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,prec);
+ mpfr_set_si(mp,u,mode);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+mpreal::mpreal(const int u, mp_prec_t prec, mp_rnd_t mode)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,prec);
+ mpfr_set_si(mp,u,mode);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+#if defined (MPREAL_HAVE_INT64_SUPPORT)
+mpreal::mpreal(const uint64_t u, mp_prec_t prec, mp_rnd_t mode)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,prec);
+ mpfr_set_uj(mp, u, mode);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+mpreal::mpreal(const int64_t u, mp_prec_t prec, mp_rnd_t mode)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,prec);
+ mpfr_set_sj(mp, u, mode);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+#endif
+
+mpreal::mpreal(const char* s, mp_prec_t prec, int base, mp_rnd_t mode)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,prec);
+ mpfr_set_str(mp, s, base, mode);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+mpreal::mpreal(const std::string& s, mp_prec_t prec, int base, mp_rnd_t mode)
+{
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ mpfr_init2(mp,prec);
+ mpfr_set_str(mp, s.c_str(), base, mode);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+mpreal::~mpreal()
+{
+ mpfr_clear(mp);
+}
+
+// Operators - Assignment
+mpreal& mpreal::operator=(const char* s)
+{
+ mpfr_t t;
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ if(0==mpfr_init_set_str(t,s,default_base,default_rnd))
+ {
+ // We will rewrite mp anyway, so flash it and resize
+ mpfr_set_prec(mp,mpfr_get_prec(t));
+ mpfr_set(mp,t,mpreal::default_rnd);
+ mpfr_clear(t);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+
+ }else{
+ mpfr_clear(t);
+ }
+
+ return *this;
+}
+
+const mpreal fma (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode)
+{
+ mpreal a;
+ mp_prec_t p1, p2, p3;
+
+ p1 = v1.get_prec();
+ p2 = v2.get_prec();
+ p3 = v3.get_prec();
+
+ a.set_prec(p3>p2?(p3>p1?p3:p1):(p2>p1?p2:p1));
+
+ mpfr_fma(a.mp,v1.mp,v2.mp,v3.mp,rnd_mode);
+ return a;
+}
+
+const mpreal fms (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode)
+{
+ mpreal a;
+ mp_prec_t p1, p2, p3;
+
+ p1 = v1.get_prec();
+ p2 = v2.get_prec();
+ p3 = v3.get_prec();
+
+ a.set_prec(p3>p2?(p3>p1?p3:p1):(p2>p1?p2:p1));
+
+ mpfr_fms(a.mp,v1.mp,v2.mp,v3.mp,rnd_mode);
+ return a;
+}
+
+const mpreal agm (const mpreal& v1, const mpreal& v2, mp_rnd_t rnd_mode)
+{
+ mpreal a;
+ mp_prec_t p1, p2;
+
+ p1 = v1.get_prec();
+ p2 = v2.get_prec();
+
+ a.set_prec(p1>p2?p1:p2);
+
+ mpfr_agm(a.mp, v1.mp, v2.mp, rnd_mode);
+
+ return a;
+}
+
+const mpreal sum (const mpreal tab[], unsigned long int n, mp_rnd_t rnd_mode)
+{
+ mpreal x;
+ mpfr_ptr* t;
+ unsigned long int i;
+
+ t = new mpfr_ptr[n];
+ for (i=0;i<n;i++) t[i] = (mpfr_ptr)tab[i].mp;
+ mpfr_sum(x.mp,t,n,rnd_mode);
+ delete[] t;
+ return x;
+}
+
+const mpreal remquo (long* q, const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode)
+{
+ mpreal a;
+ mp_prec_t yp, xp;
+
+ yp = y.get_prec();
+ xp = x.get_prec();
+
+ a.set_prec(yp>xp?yp:xp);
+
+ mpfr_remquo(a.mp,q, x.mp, y.mp, rnd_mode);
+
+ return a;
+}
+
+template <class T>
+std::string toString(T t, std::ios_base & (*f)(std::ios_base&))
+{
+ std::ostringstream oss;
+ oss << f << t;
+ return oss.str();
+}
+
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+
+std::string mpreal::toString(const std::string& format) const
+{
+ char *s = NULL;
+ string out;
+
+ if( !format.empty() )
+ {
+ if(!(mpfr_asprintf(&s,format.c_str(),mp) < 0))
+ {
+ out = std::string(s);
+
+ mpfr_free_str(s);
+ }
+ }
+
+ return out;
+}
+
+#endif
+
+std::string mpreal::toString(int n, int b, mp_rnd_t mode) const
+{
+ (void)b;
+ (void)mode;
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+
+ // Use MPFR native function for output
+ char format[128];
+ int digits;
+
+ digits = n > 0 ? n : bits2digits(mpfr_get_prec(mp));
+
+ sprintf(format,"%%.%dRNg",digits); // Default format
+
+ return toString(std::string(format));
+
+#else
+
+ char *s, *ns = NULL;
+ size_t slen, nslen;
+ mp_exp_t exp;
+ string out;
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ set_custom_malloc();
+#endif
+
+ if(mpfr_inf_p(mp))
+ {
+ if(mpfr_sgn(mp)>0) return "+Inf";
+ else return "-Inf";
+ }
+
+ if(mpfr_zero_p(mp)) return "0";
+ if(mpfr_nan_p(mp)) return "NaN";
+
+ s = mpfr_get_str(NULL,&exp,b,0,mp,mode);
+ ns = mpfr_get_str(NULL,&exp,b,n,mp,mode);
+
+ if(s!=NULL && ns!=NULL)
+ {
+ slen = strlen(s);
+ nslen = strlen(ns);
+ if(nslen<=slen)
+ {
+ mpfr_free_str(s);
+ s = ns;
+ slen = nslen;
+ }
+ else {
+ mpfr_free_str(ns);
+ }
+
+ // Make human eye-friendly formatting if possible
+ if (exp>0 && static_cast<size_t>(exp)<slen)
+ {
+ if(s[0]=='-')
+ {
+ // Remove zeros starting from right end
+ char* ptr = s+slen-1;
+ while (*ptr=='0' && ptr>s+exp) ptr--;
+
+ if(ptr==s+exp) out = string(s,exp+1);
+ else out = string(s,exp+1)+'.'+string(s+exp+1,ptr-(s+exp+1)+1);
+
+ //out = string(s,exp+1)+'.'+string(s+exp+1);
+ }
+ else
+ {
+ // Remove zeros starting from right end
+ char* ptr = s+slen-1;
+ while (*ptr=='0' && ptr>s+exp-1) ptr--;
+
+ if(ptr==s+exp-1) out = string(s,exp);
+ else out = string(s,exp)+'.'+string(s+exp,ptr-(s+exp)+1);
+
+ //out = string(s,exp)+'.'+string(s+exp);
+ }
+
+ }else{ // exp<0 || exp>slen
+ if(s[0]=='-')
+ {
+ // Remove zeros starting from right end
+ char* ptr = s+slen-1;
+ while (*ptr=='0' && ptr>s+1) ptr--;
+
+ if(ptr==s+1) out = string(s,2);
+ else out = string(s,2)+'.'+string(s+2,ptr-(s+2)+1);
+
+ //out = string(s,2)+'.'+string(s+2);
+ }
+ else
+ {
+ // Remove zeros starting from right end
+ char* ptr = s+slen-1;
+ while (*ptr=='0' && ptr>s) ptr--;
+
+ if(ptr==s) out = string(s,1);
+ else out = string(s,1)+'.'+string(s+1,ptr-(s+1)+1);
+
+ //out = string(s,1)+'.'+string(s+1);
+ }
+
+ // Make final string
+ if(--exp)
+ {
+ if(exp>0) out += "e+"+mpfr::toString<mp_exp_t>(exp,std::dec);
+ else out += "e"+mpfr::toString<mp_exp_t>(exp,std::dec);
+ }
+ }
+
+ mpfr_free_str(s);
+ return out;
+ }else{
+ return "conversion error!";
+ }
+#endif
+}
+
+
+//////////////////////////////////////////////////////////////////////////
+// I/O
+ostream& operator<<(ostream& os, const mpreal& v)
+{
+ return os<<v.toString(static_cast<int>(os.precision()));
+}
+
+istream& operator>>(istream &is, mpreal& v)
+{
+ string tmp;
+ is >> tmp;
+ mpfr_set_str(v.mp, tmp.c_str(),mpreal::default_base,mpreal::default_rnd);
+ return is;
+}
+
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+ // Optimized dynamic memory allocation/(re-)deallocation.
+ void * mpreal::mpreal_allocate(size_t alloc_size)
+ {
+ return(dlmalloc(alloc_size));
+ }
+
+ void * mpreal::mpreal_reallocate(void *ptr, size_t old_size, size_t new_size)
+ {
+ return(dlrealloc(ptr,new_size));
+ }
+
+ void mpreal::mpreal_free(void *ptr, size_t size)
+ {
+ dlfree(ptr);
+ }
+
+ inline void mpreal::set_custom_malloc(void)
+ {
+ if(!is_custom_malloc)
+ {
+ mp_set_memory_functions(mpreal_allocate,mpreal_reallocate,mpreal_free);
+ is_custom_malloc = true;
+ }
+ }
+#endif
+
+}
+
diff --git a/unsupported/test/mpreal/mpreal.h b/unsupported/test/mpreal/mpreal.h new file mode 100644 index 000000000..c640af947 --- /dev/null +++ b/unsupported/test/mpreal/mpreal.h @@ -0,0 +1,2735 @@ +/*
+ Multi-precision real number class. C++ interface for MPFR library.
+ Project homepage: http://www.holoborodko.com/pavel/
+ Contact e-mail: pavel@holoborodko.com
+
+ Copyright (c) 2008-2012 Pavel Holoborodko
+
+ Core Developers:
+ Pavel Holoborodko, Dmitriy Gubanov, Konstantin Holoborodko.
+
+ Contributors:
+ Brian Gladman, Helmut Jarausch, Fokko Beekhof, Ulrich Mutze,
+ Heinz van Saanen, Pere Constans, Peter van Hoof, Gael Guennebaud,
+ Tsai Chia Cheng, Alexei Zubanov.
+
+ ****************************************************************************
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
+
+ ****************************************************************************
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+
+ 3. The name of the author may be used to endorse or promote products
+ derived from this software without specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ SUCH DAMAGE.
+*/
+
+#ifndef __MPREAL_H__
+#define __MPREAL_H__
+
+#include <string>
+#include <iostream>
+#include <sstream>
+#include <stdexcept>
+#include <cfloat>
+#include <cmath>
+
+// Options
+#define MPREAL_HAVE_INT64_SUPPORT // int64_t support: available only for MSVC 2010 & GCC
+#define MPREAL_HAVE_MSVC_DEBUGVIEW // Enable Debugger Visualizer (valid only for MSVC in "Debug" builds)
+
+// Detect compiler using signatures from http://predef.sourceforge.net/
+#if defined(__GNUC__) && defined(__INTEL_COMPILER)
+ #define IsInf(x) isinf(x) // Intel ICC compiler on Linux
+
+#elif defined(_MSC_VER) // Microsoft Visual C++
+ #define IsInf(x) (!_finite(x))
+
+#elif defined(__GNUC__)
+ #define IsInf(x) std::isinf(x) // GNU C/C++
+
+#else
+ #define IsInf(x) std::isinf(x) // Unknown compiler, just hope for C99 conformance
+#endif
+
+#if defined(MPREAL_HAVE_INT64_SUPPORT)
+
+ #define MPFR_USE_INTMAX_T // should be defined before mpfr.h
+
+ #if defined(_MSC_VER) // <stdint.h> is available only in msvc2010!
+ #if (_MSC_VER >= 1600)
+ #include <stdint.h>
+ #else // MPFR relies on intmax_t which is available only in msvc2010
+ #undef MPREAL_HAVE_INT64_SUPPORT // Besides, MPFR - MPIR have to be compiled with msvc2010
+ #undef MPFR_USE_INTMAX_T // Since we cannot detect this, disable x64 by default
+ // Someone should change this manually if needed.
+ #endif
+ #endif
+
+ #if defined (__MINGW32__) || defined(__MINGW64__)
+ #include <stdint.h> // equivalent to msvc2010
+ #elif defined (__GNUC__)
+ #if defined(__amd64__) || defined(__amd64) || defined(__x86_64__) || defined(__x86_64)
+ #undef MPREAL_HAVE_INT64_SUPPORT // remove all shaman dances for x64 builds since
+ #undef MPFR_USE_INTMAX_T // GCC already support x64 as of "long int" is 64-bit integer, nothing left to do
+ #else
+ #include <stdint.h> // use int64_t, uint64_t otherwise.
+ #endif
+ #endif
+
+#endif
+
+#if defined(MPREAL_HAVE_MSVC_DEBUGVIEW) && defined(_MSC_VER) && defined(_DEBUG)
+#define MPREAL_MSVC_DEBUGVIEW_CODE DebugView = toString()
+ #define MPREAL_MSVC_DEBUGVIEW_DATA std::string DebugView
+#else
+ #define MPREAL_MSVC_DEBUGVIEW_CODE
+ #define MPREAL_MSVC_DEBUGVIEW_DATA
+#endif
+
+#include <mpfr.h>
+
+#if (MPFR_VERSION < MPFR_VERSION_NUM(3,0,0))
+ #include <cstdlib> // needed for random()
+#endif
+
+namespace mpfr {
+
+class mpreal {
+private:
+ mpfr_t mp;
+
+public:
+ static mp_rnd_t default_rnd;
+ static mp_prec_t default_prec;
+ static int default_base;
+ static int double_bits;
+
+public:
+ // Constructors && type conversion
+ mpreal();
+ mpreal(const mpreal& u);
+ mpreal(const mpfr_t u);
+ mpreal(const mpf_t u);
+ mpreal(const mpz_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+ mpreal(const mpq_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+ mpreal(const double u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+ mpreal(const long double u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+ mpreal(const unsigned long int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+ mpreal(const unsigned int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+ mpreal(const long int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+ mpreal(const int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+
+#if defined (MPREAL_HAVE_INT64_SUPPORT)
+ mpreal(const uint64_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+ mpreal(const int64_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
+#endif
+
+ mpreal(const char* s, mp_prec_t prec = default_prec, int base = default_base, mp_rnd_t mode = default_rnd);
+ mpreal(const std::string& s, mp_prec_t prec = default_prec, int base = default_base, mp_rnd_t mode = default_rnd);
+
+ ~mpreal();
+
+ // Operations
+ // =
+ // +, -, *, /, ++, --, <<, >>
+ // *=, +=, -=, /=,
+ // <, >, ==, <=, >=
+
+ // =
+ mpreal& operator=(const mpreal& v);
+ mpreal& operator=(const mpf_t v);
+ mpreal& operator=(const mpz_t v);
+ mpreal& operator=(const mpq_t v);
+ mpreal& operator=(const long double v);
+ mpreal& operator=(const double v);
+ mpreal& operator=(const unsigned long int v);
+ mpreal& operator=(const unsigned int v);
+ mpreal& operator=(const long int v);
+ mpreal& operator=(const int v);
+ mpreal& operator=(const char* s);
+
+ // +
+ mpreal& operator+=(const mpreal& v);
+ mpreal& operator+=(const mpf_t v);
+ mpreal& operator+=(const mpz_t v);
+ mpreal& operator+=(const mpq_t v);
+ mpreal& operator+=(const long double u);
+ mpreal& operator+=(const double u);
+ mpreal& operator+=(const unsigned long int u);
+ mpreal& operator+=(const unsigned int u);
+ mpreal& operator+=(const long int u);
+ mpreal& operator+=(const int u);
+
+#if defined (MPREAL_HAVE_INT64_SUPPORT)
+ mpreal& operator+=(const int64_t u);
+ mpreal& operator+=(const uint64_t u);
+ mpreal& operator-=(const int64_t u);
+ mpreal& operator-=(const uint64_t u);
+ mpreal& operator*=(const int64_t u);
+ mpreal& operator*=(const uint64_t u);
+ mpreal& operator/=(const int64_t u);
+ mpreal& operator/=(const uint64_t u);
+#endif
+
+ const mpreal operator+() const;
+ mpreal& operator++ ();
+ const mpreal operator++ (int);
+
+ // -
+ mpreal& operator-=(const mpreal& v);
+ mpreal& operator-=(const mpz_t v);
+ mpreal& operator-=(const mpq_t v);
+ mpreal& operator-=(const long double u);
+ mpreal& operator-=(const double u);
+ mpreal& operator-=(const unsigned long int u);
+ mpreal& operator-=(const unsigned int u);
+ mpreal& operator-=(const long int u);
+ mpreal& operator-=(const int u);
+ const mpreal operator-() const;
+ friend const mpreal operator-(const unsigned long int b, const mpreal& a);
+ friend const mpreal operator-(const unsigned int b, const mpreal& a);
+ friend const mpreal operator-(const long int b, const mpreal& a);
+ friend const mpreal operator-(const int b, const mpreal& a);
+ friend const mpreal operator-(const double b, const mpreal& a);
+ mpreal& operator-- ();
+ const mpreal operator-- (int);
+
+ // *
+ mpreal& operator*=(const mpreal& v);
+ mpreal& operator*=(const mpz_t v);
+ mpreal& operator*=(const mpq_t v);
+ mpreal& operator*=(const long double v);
+ mpreal& operator*=(const double v);
+ mpreal& operator*=(const unsigned long int v);
+ mpreal& operator*=(const unsigned int v);
+ mpreal& operator*=(const long int v);
+ mpreal& operator*=(const int v);
+
+ // /
+ mpreal& operator/=(const mpreal& v);
+ mpreal& operator/=(const mpz_t v);
+ mpreal& operator/=(const mpq_t v);
+ mpreal& operator/=(const long double v);
+ mpreal& operator/=(const double v);
+ mpreal& operator/=(const unsigned long int v);
+ mpreal& operator/=(const unsigned int v);
+ mpreal& operator/=(const long int v);
+ mpreal& operator/=(const int v);
+ friend const mpreal operator/(const unsigned long int b, const mpreal& a);
+ friend const mpreal operator/(const unsigned int b, const mpreal& a);
+ friend const mpreal operator/(const long int b, const mpreal& a);
+ friend const mpreal operator/(const int b, const mpreal& a);
+ friend const mpreal operator/(const double b, const mpreal& a);
+
+ //<<= Fast Multiplication by 2^u
+ mpreal& operator<<=(const unsigned long int u);
+ mpreal& operator<<=(const unsigned int u);
+ mpreal& operator<<=(const long int u);
+ mpreal& operator<<=(const int u);
+
+ //>>= Fast Division by 2^u
+ mpreal& operator>>=(const unsigned long int u);
+ mpreal& operator>>=(const unsigned int u);
+ mpreal& operator>>=(const long int u);
+ mpreal& operator>>=(const int u);
+
+ // Boolean Operators
+ friend bool operator > (const mpreal& a, const mpreal& b);
+ friend bool operator >= (const mpreal& a, const mpreal& b);
+ friend bool operator < (const mpreal& a, const mpreal& b);
+ friend bool operator <= (const mpreal& a, const mpreal& b);
+ friend bool operator == (const mpreal& a, const mpreal& b);
+ friend bool operator != (const mpreal& a, const mpreal& b);
+
+ // Optimized specializations for boolean operators
+ friend bool operator == (const mpreal& a, const unsigned long int b);
+ friend bool operator == (const mpreal& a, const unsigned int b);
+ friend bool operator == (const mpreal& a, const long int b);
+ friend bool operator == (const mpreal& a, const int b);
+ friend bool operator == (const mpreal& a, const long double b);
+ friend bool operator == (const mpreal& a, const double b);
+
+ // Type Conversion operators
+ long toLong() const;
+ unsigned long toULong() const;
+ double toDouble() const;
+ long double toLDouble() const;
+
+#if defined (MPREAL_HAVE_INT64_SUPPORT)
+ int64_t toInt64() const;
+ uint64_t toUInt64() const;
+#endif
+
+ // Get raw pointers
+ ::mpfr_ptr mpfr_ptr();
+ ::mpfr_srcptr mpfr_srcptr() const;
+
+ // Convert mpreal to string with n significant digits in base b
+ // n = 0 -> convert with the maximum available digits
+ std::string toString(int n = 0, int b = default_base, mp_rnd_t mode = default_rnd) const;
+
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+ std::string toString(const std::string& format) const;
+#endif
+
+ // Math Functions
+ friend const mpreal sqr (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal pow (const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal pow (const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal pow (const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal pow (const mpreal& a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal pow (const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal pow (const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+ friend const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend int cmpabs(const mpreal& a,const mpreal& b);
+
+ friend const mpreal log (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal log2 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal exp (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal exp2 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal log1p(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal expm1(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+ friend const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+ friend const mpreal acos (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal asin (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal atan (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal acot (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal asec (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal acsc (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+ friend const mpreal cosh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal sinh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal tanh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal sech (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal csch (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal coth (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal acosh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal asinh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal atanh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal acoth (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal asech (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal acsch (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+ friend const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+ friend const mpreal fac_ui (unsigned long int v, mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal eint (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+ friend const mpreal gamma (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal lngamma (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal lgamma (const mpreal& v, int *signp = 0, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal zeta (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal erf (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal erfc (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal besselj0 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal besselj1 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal besseljn (long n, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal bessely0 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal bessely1 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal besselyn (long n, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal fma (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal fms (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal agm (const mpreal& v1, const mpreal& v2, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal sum (const mpreal tab[], unsigned long int n, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend int sgn(const mpreal& v); // -1 or +1
+
+// MPFR 2.4.0 Specifics
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+ friend int sinh_cosh(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal li2(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal rec_sqrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+#endif
+
+// MPFR 3.0.0 Specifics
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))
+ friend const mpreal digamma(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal ai(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal urandom (gmp_randstate_t& state,mp_rnd_t rnd_mode = mpreal::default_rnd); // use gmp_randinit_default() to init state, gmp_randclear() to clear
+ friend bool isregular(const mpreal& v);
+#endif
+
+ // Uniformly distributed random number generation in [0,1] using
+ // Mersenne-Twister algorithm by default.
+ // Use parameter to setup seed, e.g.: random((unsigned)time(NULL))
+ // Check urandom() for more precise control.
+ friend const mpreal random(unsigned int seed = 0);
+
+ // Exponent and mantissa manipulation
+ friend const mpreal frexp(const mpreal& v, mp_exp_t* exp);
+ friend const mpreal ldexp(const mpreal& v, mp_exp_t exp);
+
+ // Splits mpreal value into fractional and integer parts.
+ // Returns fractional part and stores integer part in n.
+ friend const mpreal modf(const mpreal& v, mpreal& n);
+
+ // Constants
+ // don't forget to call mpfr_free_cache() for every thread where you are using const-functions
+ friend const mpreal const_log2 (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal const_pi (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal const_euler (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal const_catalan (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ // returns +inf iff sign>=0 otherwise -inf
+ friend const mpreal const_infinity(int sign = 1, mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+ // Output/ Input
+ friend std::ostream& operator<<(std::ostream& os, const mpreal& v);
+ friend std::istream& operator>>(std::istream& is, mpreal& v);
+
+ // Integer Related Functions
+ friend const mpreal rint (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal ceil (const mpreal& v);
+ friend const mpreal floor(const mpreal& v);
+ friend const mpreal round(const mpreal& v);
+ friend const mpreal trunc(const mpreal& v);
+ friend const mpreal rint_ceil (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal rint_floor(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal rint_round(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal rint_trunc(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal frac (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal remainder (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
+ friend const mpreal remquo (long* q, const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+ // Miscellaneous Functions
+ friend const mpreal nexttoward (const mpreal& x, const mpreal& y);
+ friend const mpreal nextabove (const mpreal& x);
+ friend const mpreal nextbelow (const mpreal& x);
+
+ // use gmp_randinit_default() to init state, gmp_randclear() to clear
+ friend const mpreal urandomb (gmp_randstate_t& state);
+
+// MPFR < 2.4.2 Specifics
+#if (MPFR_VERSION <= MPFR_VERSION_NUM(2,4,2))
+ friend const mpreal random2 (mp_size_t size, mp_exp_t exp);
+#endif
+
+ // Instance Checkers
+ friend bool isnan (const mpreal& v);
+ friend bool isinf (const mpreal& v);
+ friend bool isfinite(const mpreal& v);
+
+ friend bool isnum(const mpreal& v);
+ friend bool iszero(const mpreal& v);
+ friend bool isint(const mpreal& v);
+
+ // Set/Get instance properties
+ inline mp_prec_t get_prec() const;
+ inline void set_prec(mp_prec_t prec, mp_rnd_t rnd_mode = default_rnd); // Change precision with rounding mode
+
+ // Aliases for get_prec(), set_prec() - needed for compatibility with std::complex<mpreal> interface
+ inline mpreal& setPrecision(int Precision, mp_rnd_t RoundingMode = (mpfr_get_default_rounding_mode)());
+ inline int getPrecision() const;
+
+ // Set mpreal to +/- inf, NaN, +/-0
+ mpreal& setInf (int Sign = +1);
+ mpreal& setNan ();
+ mpreal& setZero (int Sign = +1);
+ mpreal& setSign (int Sign, mp_rnd_t RoundingMode = (mpfr_get_default_rounding_mode)());
+
+ //Exponent
+ mp_exp_t get_exp();
+ int set_exp(mp_exp_t e);
+ int check_range (int t, mp_rnd_t rnd_mode = default_rnd);
+ int subnormalize (int t,mp_rnd_t rnd_mode = default_rnd);
+
+ // Inexact conversion from float
+ inline bool fits_in_bits(double x, int n);
+
+ // Set/Get global properties
+ static void set_default_prec(mp_prec_t prec);
+ static mp_prec_t get_default_prec();
+ static void set_default_base(int base);
+ static int get_default_base();
+ static void set_double_bits(int dbits);
+ static int get_double_bits();
+ static void set_default_rnd(mp_rnd_t rnd_mode);
+ static mp_rnd_t get_default_rnd();
+ static mp_exp_t get_emin (void);
+ static mp_exp_t get_emax (void);
+ static mp_exp_t get_emin_min (void);
+ static mp_exp_t get_emin_max (void);
+ static mp_exp_t get_emax_min (void);
+ static mp_exp_t get_emax_max (void);
+ static int set_emin (mp_exp_t exp);
+ static int set_emax (mp_exp_t exp);
+
+ // Efficient swapping of two mpreal values
+ friend void swap(mpreal& x, mpreal& y);
+
+ //Min Max - macros is evil. Needed for systems which defines max and min globally as macros (e.g. Windows)
+ //Hope that globally defined macros use > < operations only
+ friend const mpreal fmax(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = default_rnd);
+ friend const mpreal fmin(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = default_rnd);
+
+#if defined (MPREAL_HAVE_CUSTOM_MPFR_MALLOC)
+
+private:
+ // Optimized dynamic memory allocation/(re-)deallocation.
+ static bool is_custom_malloc;
+ static void *mpreal_allocate (size_t alloc_size);
+ static void *mpreal_reallocate (void *ptr, size_t old_size, size_t new_size);
+ static void mpreal_free (void *ptr, size_t size);
+ inline static void set_custom_malloc (void);
+
+#endif
+
+
+private:
+ // Human friendly Debug Preview in Visual Studio.
+ // Put one of these lines:
+ //
+ // mpfr::mpreal=<DebugView> ; Show value only
+ // mpfr::mpreal=<DebugView>, <mp[0]._mpfr_prec,u>bits ; Show value & precision
+ //
+ // at the beginning of
+ // [Visual Studio Installation Folder]\Common7\Packages\Debugger\autoexp.dat
+ MPREAL_MSVC_DEBUGVIEW_DATA
+};
+
+//////////////////////////////////////////////////////////////////////////
+// Exceptions
+class conversion_overflow : public std::exception {
+public:
+ std::string why() { return "inexact conversion from floating point"; }
+};
+
+namespace internal{
+
+ // Use SFINAE to restrict arithmetic operations instantiation only for numeric types
+ // This is needed for smooth integration with libraries based on expression templates
+ template <typename ArgumentType> struct result_type {};
+
+ template <> struct result_type<mpreal> {typedef mpreal type;};
+ template <> struct result_type<mpz_t> {typedef mpreal type;};
+ template <> struct result_type<mpq_t> {typedef mpreal type;};
+ template <> struct result_type<long double> {typedef mpreal type;};
+ template <> struct result_type<double> {typedef mpreal type;};
+ template <> struct result_type<unsigned long int> {typedef mpreal type;};
+ template <> struct result_type<unsigned int> {typedef mpreal type;};
+ template <> struct result_type<long int> {typedef mpreal type;};
+ template <> struct result_type<int> {typedef mpreal type;};
+
+#if defined (MPREAL_HAVE_INT64_SUPPORT)
+ template <> struct result_type<int64_t > {typedef mpreal type;};
+ template <> struct result_type<uint64_t > {typedef mpreal type;};
+#endif
+}
+
+// + Addition
+template <typename Rhs>
+inline const typename internal::result_type<Rhs>::type
+ operator+(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) += rhs; }
+
+template <typename Lhs>
+inline const typename internal::result_type<Lhs>::type
+ operator+(const Lhs& lhs, const mpreal& rhs){ return mpreal(rhs) += lhs; }
+
+// - Subtraction
+template <typename Rhs>
+inline const typename internal::result_type<Rhs>::type
+ operator-(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) -= rhs; }
+
+template <typename Lhs>
+inline const typename internal::result_type<Lhs>::type
+ operator-(const Lhs& lhs, const mpreal& rhs){ return mpreal(lhs) -= rhs; }
+
+// * Multiplication
+template <typename Rhs>
+inline const typename internal::result_type<Rhs>::type
+ operator*(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) *= rhs; }
+
+template <typename Lhs>
+inline const typename internal::result_type<Lhs>::type
+ operator*(const Lhs& lhs, const mpreal& rhs){ return mpreal(rhs) *= lhs; }
+
+// / Division
+template <typename Rhs>
+inline const typename internal::result_type<Rhs>::type
+ operator/(const mpreal& lhs, const Rhs& rhs){ return mpreal(lhs) /= rhs; }
+
+template <typename Lhs>
+inline const typename internal::result_type<Lhs>::type
+ operator/(const Lhs& lhs, const mpreal& rhs){ return mpreal(lhs) /= rhs; }
+
+//////////////////////////////////////////////////////////////////////////
+// sqrt
+const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal sqrt(const long int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal sqrt(const int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal sqrt(const long double v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal sqrt(const double v, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+//////////////////////////////////////////////////////////////////////////
+// pow
+const mpreal pow(const mpreal& a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const mpreal& a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const mpreal& a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const mpreal& a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+const mpreal pow(const unsigned int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+const mpreal pow(const unsigned long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned long int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned long int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned long int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned long int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+const mpreal pow(const unsigned int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const unsigned int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+const mpreal pow(const long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+const mpreal pow(const int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+const mpreal pow(const long double a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long double a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const long double a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+const mpreal pow(const double a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
+
+//////////////////////////////////////////////////////////////////////////
+// Estimate machine epsilon for the given precision
+// Returns smallest eps such that 1.0 + eps != 1.0
+inline const mpreal machine_epsilon(mp_prec_t prec = mpreal::get_default_prec());
+
+// Returns the positive distance from abs(x) to the next larger in magnitude floating point number of the same precision as x
+inline const mpreal machine_epsilon(const mpreal& x);
+
+inline const mpreal mpreal_min(mp_prec_t prec = mpreal::get_default_prec());
+inline const mpreal mpreal_max(mp_prec_t prec = mpreal::get_default_prec());
+inline bool isEqualFuzzy(const mpreal& a, const mpreal& b, const mpreal& eps);
+inline bool isEqualUlps(const mpreal& a, const mpreal& b, int maxUlps);
+
+//////////////////////////////////////////////////////////////////////////
+// Bits - decimal digits relation
+// bits = ceil(digits*log[2](10))
+// digits = floor(bits*log[10](2))
+
+inline mp_prec_t digits2bits(int d);
+inline int bits2digits(mp_prec_t b);
+
+//////////////////////////////////////////////////////////////////////////
+// min, max
+const mpreal (max)(const mpreal& x, const mpreal& y);
+const mpreal (min)(const mpreal& x, const mpreal& y);
+
+//////////////////////////////////////////////////////////////////////////
+// Implementation
+//////////////////////////////////////////////////////////////////////////
+
+//////////////////////////////////////////////////////////////////////////
+// Operators - Assignment
+inline mpreal& mpreal::operator=(const mpreal& v)
+{
+ if (this != &v)
+ {
+ mpfr_clear(mp);
+ mpfr_init2(mp,mpfr_get_prec(v.mp));
+ mpfr_set(mp,v.mp,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ }
+ return *this;
+}
+
+inline mpreal& mpreal::operator=(const mpf_t v)
+{
+ mpfr_set_f(mp,v,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator=(const mpz_t v)
+{
+ mpfr_set_z(mp,v,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator=(const mpq_t v)
+{
+ mpfr_set_q(mp,v,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator=(const long double v)
+{
+ mpfr_set_ld(mp,v,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator=(const double v)
+{
+ if(double_bits == -1 || fits_in_bits(v, double_bits))
+ {
+ mpfr_set_d(mp,v,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ }
+ else
+ throw conversion_overflow();
+
+ return *this;
+}
+
+inline mpreal& mpreal::operator=(const unsigned long int v)
+{
+ mpfr_set_ui(mp,v,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator=(const unsigned int v)
+{
+ mpfr_set_ui(mp,v,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator=(const long int v)
+{
+ mpfr_set_si(mp,v,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator=(const int v)
+{
+ mpfr_set_si(mp,v,default_rnd);
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// + Addition
+inline mpreal& mpreal::operator+=(const mpreal& v)
+{
+ mpfr_add(mp,mp,v.mp,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator+=(const mpf_t u)
+{
+ *this += mpreal(u);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator+=(const mpz_t u)
+{
+ mpfr_add_z(mp,mp,u,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator+=(const mpq_t u)
+{
+ mpfr_add_q(mp,mp,u,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator+= (const long double u)
+{
+ *this += mpreal(u);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator+= (const double u)
+{
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+ mpfr_add_d(mp,mp,u,default_rnd);
+#else
+ *this += mpreal(u);
+#endif
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator+=(const unsigned long int u)
+{
+ mpfr_add_ui(mp,mp,u,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator+=(const unsigned int u)
+{
+ mpfr_add_ui(mp,mp,u,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator+=(const long int u)
+{
+ mpfr_add_si(mp,mp,u,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator+=(const int u)
+{
+ mpfr_add_si(mp,mp,u,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+#if defined (MPREAL_HAVE_INT64_SUPPORT)
+inline mpreal& mpreal::operator+=(const int64_t u){ *this += mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
+inline mpreal& mpreal::operator+=(const uint64_t u){ *this += mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
+inline mpreal& mpreal::operator-=(const int64_t u){ *this -= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
+inline mpreal& mpreal::operator-=(const uint64_t u){ *this -= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
+inline mpreal& mpreal::operator*=(const int64_t u){ *this *= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
+inline mpreal& mpreal::operator*=(const uint64_t u){ *this *= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
+inline mpreal& mpreal::operator/=(const int64_t u){ *this /= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
+inline mpreal& mpreal::operator/=(const uint64_t u){ *this /= mpreal(u); MPREAL_MSVC_DEBUGVIEW_CODE; return *this; }
+#endif
+
+inline const mpreal mpreal::operator+()const { return mpreal(*this); }
+
+inline const mpreal operator+(const mpreal& a, const mpreal& b)
+{
+ // prec(a+b) = max(prec(a),prec(b))
+ if(a.get_prec()>b.get_prec()) return mpreal(a) += b;
+ else return mpreal(b) += a;
+}
+
+inline mpreal& mpreal::operator++()
+{
+ return *this += 1;
+}
+
+inline const mpreal mpreal::operator++ (int)
+{
+ mpreal x(*this);
+ *this += 1;
+ return x;
+}
+
+inline mpreal& mpreal::operator--()
+{
+ return *this -= 1;
+}
+
+inline const mpreal mpreal::operator-- (int)
+{
+ mpreal x(*this);
+ *this -= 1;
+ return x;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// - Subtraction
+inline mpreal& mpreal::operator-= (const mpreal& v)
+{
+ mpfr_sub(mp,mp,v.mp,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator-=(const mpz_t v)
+{
+ mpfr_sub_z(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator-=(const mpq_t v)
+{
+ mpfr_sub_q(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator-=(const long double v)
+{
+ *this -= mpreal(v);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator-=(const double v)
+{
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+ mpfr_sub_d(mp,mp,v,default_rnd);
+#else
+ *this -= mpreal(v);
+#endif
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator-=(const unsigned long int v)
+{
+ mpfr_sub_ui(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator-=(const unsigned int v)
+{
+ mpfr_sub_ui(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator-=(const long int v)
+{
+ mpfr_sub_si(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator-=(const int v)
+{
+ mpfr_sub_si(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline const mpreal mpreal::operator-()const
+{
+ mpreal u(*this);
+ mpfr_neg(u.mp,u.mp,default_rnd);
+ return u;
+}
+
+inline const mpreal operator-(const mpreal& a, const mpreal& b)
+{
+ // prec(a-b) = max(prec(a),prec(b))
+ if(a.getPrecision() >= b.getPrecision())
+ {
+ return mpreal(a) -= b;
+ }else{
+ mpreal x(a);
+ x.setPrecision(b.getPrecision());
+ return x -= b;
+ }
+}
+
+inline const mpreal operator-(const double b, const mpreal& a)
+{
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+ mpreal x(a);
+ mpfr_d_sub(x.mp,b,a.mp,mpreal::default_rnd);
+ return x;
+#else
+ return mpreal(b) -= a;
+#endif
+}
+
+inline const mpreal operator-(const unsigned long int b, const mpreal& a)
+{
+ mpreal x(a);
+ mpfr_ui_sub(x.mp,b,a.mp,mpreal::default_rnd);
+ return x;
+}
+
+inline const mpreal operator-(const unsigned int b, const mpreal& a)
+{
+ mpreal x(a);
+ mpfr_ui_sub(x.mp,b,a.mp,mpreal::default_rnd);
+ return x;
+}
+
+inline const mpreal operator-(const long int b, const mpreal& a)
+{
+ mpreal x(a);
+ mpfr_si_sub(x.mp,b,a.mp,mpreal::default_rnd);
+ return x;
+}
+
+inline const mpreal operator-(const int b, const mpreal& a)
+{
+ mpreal x(a);
+ mpfr_si_sub(x.mp,b,a.mp,mpreal::default_rnd);
+ return x;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// * Multiplication
+inline mpreal& mpreal::operator*= (const mpreal& v)
+{
+ mpfr_mul(mp,mp,v.mp,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator*=(const mpz_t v)
+{
+ mpfr_mul_z(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator*=(const mpq_t v)
+{
+ mpfr_mul_q(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator*=(const long double v)
+{
+ *this *= mpreal(v);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator*=(const double v)
+{
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+ mpfr_mul_d(mp,mp,v,default_rnd);
+#else
+ *this *= mpreal(v);
+#endif
+
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator*=(const unsigned long int v)
+{
+ mpfr_mul_ui(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator*=(const unsigned int v)
+{
+ mpfr_mul_ui(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator*=(const long int v)
+{
+ mpfr_mul_si(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator*=(const int v)
+{
+ mpfr_mul_si(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline const mpreal operator*(const mpreal& a, const mpreal& b)
+{
+ // prec(a*b) = max(prec(a),prec(b))
+ if(a.getPrecision() >= b.getPrecision()) return mpreal(a) *= b;
+ else return mpreal(b) *= a;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// / Division
+inline mpreal& mpreal::operator/=(const mpreal& v)
+{
+ mpfr_div(mp,mp,v.mp,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator/=(const mpz_t v)
+{
+ mpfr_div_z(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator/=(const mpq_t v)
+{
+ mpfr_div_q(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator/=(const long double v)
+{
+ *this /= mpreal(v);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator/=(const double v)
+{
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+ mpfr_div_d(mp,mp,v,default_rnd);
+#else
+ *this /= mpreal(v);
+#endif
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator/=(const unsigned long int v)
+{
+ mpfr_div_ui(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator/=(const unsigned int v)
+{
+ mpfr_div_ui(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator/=(const long int v)
+{
+ mpfr_div_si(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator/=(const int v)
+{
+ mpfr_div_si(mp,mp,v,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline const mpreal operator/(const mpreal& a, const mpreal& b)
+{
+ // prec(a/b) = max(prec(a),prec(b))
+ if(a.getPrecision() >= b.getPrecision())
+ {
+ return mpreal(a) /= b;
+ }else{
+
+ mpreal x(a);
+ x.setPrecision(b.getPrecision());
+ return x /= b;
+ }
+}
+
+inline const mpreal operator/(const unsigned long int b, const mpreal& a)
+{
+ mpreal x(a);
+ mpfr_ui_div(x.mp,b,a.mp,mpreal::default_rnd);
+ return x;
+}
+
+inline const mpreal operator/(const unsigned int b, const mpreal& a)
+{
+ mpreal x(a);
+ mpfr_ui_div(x.mp,b,a.mp,mpreal::default_rnd);
+ return x;
+}
+
+inline const mpreal operator/(const long int b, const mpreal& a)
+{
+ mpreal x(a);
+ mpfr_si_div(x.mp,b,a.mp,mpreal::default_rnd);
+ return x;
+}
+
+inline const mpreal operator/(const int b, const mpreal& a)
+{
+ mpreal x(a);
+ mpfr_si_div(x.mp,b,a.mp,mpreal::default_rnd);
+ return x;
+}
+
+inline const mpreal operator/(const double b, const mpreal& a)
+{
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+ mpreal x(a);
+ mpfr_d_div(x.mp,b,a.mp,mpreal::default_rnd);
+ return x;
+#else
+ return mpreal(b) /= a;
+#endif
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Shifts operators - Multiplication/Division by power of 2
+inline mpreal& mpreal::operator<<=(const unsigned long int u)
+{
+ mpfr_mul_2ui(mp,mp,u,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator<<=(const unsigned int u)
+{
+ mpfr_mul_2ui(mp,mp,static_cast<unsigned long int>(u),default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator<<=(const long int u)
+{
+ mpfr_mul_2si(mp,mp,u,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator<<=(const int u)
+{
+ mpfr_mul_2si(mp,mp,static_cast<long int>(u),default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator>>=(const unsigned long int u)
+{
+ mpfr_div_2ui(mp,mp,u,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator>>=(const unsigned int u)
+{
+ mpfr_div_2ui(mp,mp,static_cast<unsigned long int>(u),default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator>>=(const long int u)
+{
+ mpfr_div_2si(mp,mp,u,default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::operator>>=(const int u)
+{
+ mpfr_div_2si(mp,mp,static_cast<long int>(u),default_rnd);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline const mpreal operator<<(const mpreal& v, const unsigned long int k)
+{
+ return mul_2ui(v,k);
+}
+
+inline const mpreal operator<<(const mpreal& v, const unsigned int k)
+{
+ return mul_2ui(v,static_cast<unsigned long int>(k));
+}
+
+inline const mpreal operator<<(const mpreal& v, const long int k)
+{
+ return mul_2si(v,k);
+}
+
+inline const mpreal operator<<(const mpreal& v, const int k)
+{
+ return mul_2si(v,static_cast<long int>(k));
+}
+
+inline const mpreal operator>>(const mpreal& v, const unsigned long int k)
+{
+ return div_2ui(v,k);
+}
+
+inline const mpreal operator>>(const mpreal& v, const long int k)
+{
+ return div_2si(v,k);
+}
+
+inline const mpreal operator>>(const mpreal& v, const unsigned int k)
+{
+ return div_2ui(v,static_cast<unsigned long int>(k));
+}
+
+inline const mpreal operator>>(const mpreal& v, const int k)
+{
+ return div_2si(v,static_cast<long int>(k));
+}
+
+// mul_2ui
+inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_mul_2ui(x.mp,v.mp,k,rnd_mode);
+ return x;
+}
+
+// mul_2si
+inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_mul_2si(x.mp,v.mp,k,rnd_mode);
+ return x;
+}
+
+inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_div_2ui(x.mp,v.mp,k,rnd_mode);
+ return x;
+}
+
+inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_div_2si(x.mp,v.mp,k,rnd_mode);
+ return x;
+}
+
+//////////////////////////////////////////////////////////////////////////
+//Boolean operators
+inline bool operator > (const mpreal& a, const mpreal& b){ return (mpfr_greater_p(a.mp,b.mp) !=0); }
+inline bool operator >= (const mpreal& a, const mpreal& b){ return (mpfr_greaterequal_p(a.mp,b.mp) !=0); }
+inline bool operator < (const mpreal& a, const mpreal& b){ return (mpfr_less_p(a.mp,b.mp) !=0); }
+inline bool operator <= (const mpreal& a, const mpreal& b){ return (mpfr_lessequal_p(a.mp,b.mp) !=0); }
+inline bool operator == (const mpreal& a, const mpreal& b){ return (mpfr_equal_p(a.mp,b.mp) !=0); }
+inline bool operator != (const mpreal& a, const mpreal& b){ return (mpfr_lessgreater_p(a.mp,b.mp) !=0); }
+
+inline bool operator == (const mpreal& a, const unsigned long int b ){ return (mpfr_cmp_ui(a.mp,b) == 0); }
+inline bool operator == (const mpreal& a, const unsigned int b ){ return (mpfr_cmp_ui(a.mp,b) == 0); }
+inline bool operator == (const mpreal& a, const long int b ){ return (mpfr_cmp_si(a.mp,b) == 0); }
+inline bool operator == (const mpreal& a, const int b ){ return (mpfr_cmp_si(a.mp,b) == 0); }
+inline bool operator == (const mpreal& a, const long double b ){ return (mpfr_cmp_ld(a.mp,b) == 0); }
+inline bool operator == (const mpreal& a, const double b ){ return (mpfr_cmp_d(a.mp,b) == 0); }
+
+
+inline bool isnan (const mpreal& v){ return (mpfr_nan_p(v.mp) != 0); }
+inline bool isinf (const mpreal& v){ return (mpfr_inf_p(v.mp) != 0); }
+inline bool isfinite(const mpreal& v){ return (mpfr_number_p(v.mp) != 0); }
+inline bool iszero (const mpreal& v){ return (mpfr_zero_p(v.mp) != 0); }
+inline bool isint (const mpreal& v){ return (mpfr_integer_p(v.mp) != 0); }
+
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))
+inline bool isregular(const mpreal& v){ return (mpfr_regular_p(v.mp));}
+#endif
+
+//////////////////////////////////////////////////////////////////////////
+// Type Converters
+inline long mpreal::toLong() const { return mpfr_get_si(mp,GMP_RNDZ); }
+inline unsigned long mpreal::toULong() const { return mpfr_get_ui(mp,GMP_RNDZ); }
+inline double mpreal::toDouble() const { return mpfr_get_d(mp,default_rnd); }
+inline long double mpreal::toLDouble() const { return mpfr_get_ld(mp,default_rnd); }
+
+#if defined (MPREAL_HAVE_INT64_SUPPORT)
+inline int64_t mpreal::toInt64() const{ return mpfr_get_sj(mp,GMP_RNDZ); }
+inline uint64_t mpreal::toUInt64() const{ return mpfr_get_uj(mp,GMP_RNDZ); }
+#endif
+
+inline ::mpfr_ptr mpreal::mpfr_ptr() { return mp; }
+inline ::mpfr_srcptr mpreal::mpfr_srcptr() const { return const_cast< ::mpfr_srcptr >(mp); }
+
+//////////////////////////////////////////////////////////////////////////
+// Bits - decimal digits relation
+// bits = ceil(digits*log[2](10))
+// digits = floor(bits*log[10](2))
+
+inline mp_prec_t digits2bits(int d)
+{
+ const double LOG2_10 = 3.3219280948873624;
+
+ d = 10>d?10:d;
+
+ return (mp_prec_t)std::ceil((d)*LOG2_10);
+}
+
+inline int bits2digits(mp_prec_t b)
+{
+ const double LOG10_2 = 0.30102999566398119;
+
+ b = 34>b?34:b;
+
+ return (int)std::floor((b)*LOG10_2);
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Set/Get number properties
+inline int sgn(const mpreal& v)
+{
+ int r = mpfr_signbit(v.mp);
+ return (r>0?-1:1);
+}
+
+inline mpreal& mpreal::setSign(int sign, mp_rnd_t RoundingMode)
+{
+ mpfr_setsign(mp,mp,(sign<0?1:0),RoundingMode);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline int mpreal::getPrecision() const
+{
+ return mpfr_get_prec(mp);
+}
+
+inline mpreal& mpreal::setPrecision(int Precision, mp_rnd_t RoundingMode)
+{
+ mpfr_prec_round(mp,Precision, RoundingMode);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::setInf(int sign)
+{
+ mpfr_set_inf(mp,sign);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::setNan()
+{
+ mpfr_set_nan(mp);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mpreal& mpreal::setZero(int sign)
+{
+ mpfr_set_zero(mp,sign);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return *this;
+}
+
+inline mp_prec_t mpreal::get_prec() const
+{
+ return mpfr_get_prec(mp);
+}
+
+inline void mpreal::set_prec(mp_prec_t prec, mp_rnd_t rnd_mode)
+{
+ mpfr_prec_round(mp,prec,rnd_mode);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+}
+
+inline mp_exp_t mpreal::get_exp ()
+{
+ return mpfr_get_exp(mp);
+}
+
+inline int mpreal::set_exp (mp_exp_t e)
+{
+ int x = mpfr_set_exp(mp, e);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return x;
+}
+
+inline const mpreal frexp(const mpreal& v, mp_exp_t* exp)
+{
+ mpreal x(v);
+ *exp = x.get_exp();
+ x.set_exp(0);
+ return x;
+}
+
+inline const mpreal ldexp(const mpreal& v, mp_exp_t exp)
+{
+ mpreal x(v);
+
+ // rounding is not important since we just increasing the exponent
+ mpfr_mul_2si(x.mp,x.mp,exp,mpreal::default_rnd);
+ return x;
+}
+
+inline const mpreal machine_epsilon(mp_prec_t prec)
+{
+ // the smallest eps such that 1.0+eps != 1.0
+ // depends (of cause) on the precision
+ return machine_epsilon(mpreal(1,prec));
+}
+
+inline const mpreal machine_epsilon(const mpreal& x)
+{
+ if( x < 0)
+ {
+ return nextabove(-x)+x;
+ }else{
+ return nextabove(x)-x;
+ }
+}
+
+inline const mpreal mpreal_min(mp_prec_t prec)
+{
+ // min = 1/2*2^emin = 2^(emin-1)
+
+ return mpreal(1,prec) << mpreal::get_emin()-1;
+}
+
+inline const mpreal mpreal_max(mp_prec_t prec)
+{
+ // max = (1-eps)*2^emax, assume eps = 0?,
+ // and use emax-1 to prevent value to be +inf
+ // max = 2^(emax-1)
+
+ return mpreal(1,prec) << mpreal::get_emax()-1;
+}
+
+inline bool isEqualUlps(const mpreal& a, const mpreal& b, int maxUlps)
+{
+ /*
+ maxUlps - a and b can be apart by maxUlps binary numbers.
+ */
+ return abs(a - b) <= machine_epsilon((max)(abs(a), abs(b))) * maxUlps;
+}
+
+inline bool isEqualFuzzy(const mpreal& a, const mpreal& b, const mpreal& eps)
+{
+ return abs(a - b) <= (min)(abs(a), abs(b)) * eps;
+}
+
+inline bool isEqualFuzzy(const mpreal& a, const mpreal& b)
+{
+ return isEqualFuzzy(a,b,machine_epsilon((std::min)(abs(a), abs(b))));
+}
+
+inline const mpreal modf(const mpreal& v, mpreal& n)
+{
+ mpreal frac(v);
+
+ // rounding is not important since we are using the same number
+ mpfr_frac(frac.mp,frac.mp,mpreal::default_rnd);
+ mpfr_trunc(n.mp,v.mp);
+ return frac;
+}
+
+inline int mpreal::check_range (int t, mp_rnd_t rnd_mode)
+{
+ return mpfr_check_range(mp,t,rnd_mode);
+}
+
+inline int mpreal::subnormalize (int t,mp_rnd_t rnd_mode)
+{
+ int r = mpfr_subnormalize(mp,t,rnd_mode);
+ MPREAL_MSVC_DEBUGVIEW_CODE;
+ return r;
+}
+
+inline mp_exp_t mpreal::get_emin (void)
+{
+ return mpfr_get_emin();
+}
+
+inline int mpreal::set_emin (mp_exp_t exp)
+{
+ return mpfr_set_emin(exp);
+}
+
+inline mp_exp_t mpreal::get_emax (void)
+{
+ return mpfr_get_emax();
+}
+
+inline int mpreal::set_emax (mp_exp_t exp)
+{
+ return mpfr_set_emax(exp);
+}
+
+inline mp_exp_t mpreal::get_emin_min (void)
+{
+ return mpfr_get_emin_min();
+}
+
+inline mp_exp_t mpreal::get_emin_max (void)
+{
+ return mpfr_get_emin_max();
+}
+
+inline mp_exp_t mpreal::get_emax_min (void)
+{
+ return mpfr_get_emax_min();
+}
+
+inline mp_exp_t mpreal::get_emax_max (void)
+{
+ return mpfr_get_emax_max();
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Mathematical Functions
+//////////////////////////////////////////////////////////////////////////
+inline const mpreal sqr(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_sqr(x.mp,x.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_sqrt(x.mp,x.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode)
+{
+ mpreal x;
+ mpfr_sqrt_ui(x.mp,v,rnd_mode);
+ return x;
+}
+
+inline const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode)
+{
+ return sqrt(static_cast<unsigned long int>(v),rnd_mode);
+}
+
+inline const mpreal sqrt(const long int v, mp_rnd_t rnd_mode)
+{
+ if (v>=0) return sqrt(static_cast<unsigned long int>(v),rnd_mode);
+ else return mpreal().setNan(); // NaN
+}
+
+inline const mpreal sqrt(const int v, mp_rnd_t rnd_mode)
+{
+ if (v>=0) return sqrt(static_cast<unsigned long int>(v),rnd_mode);
+ else return mpreal().setNan(); // NaN
+}
+
+inline const mpreal sqrt(const long double v, mp_rnd_t rnd_mode)
+{
+ return sqrt(mpreal(v),rnd_mode);
+}
+
+inline const mpreal sqrt(const double v, mp_rnd_t rnd_mode)
+{
+ return sqrt(mpreal(v),rnd_mode);
+}
+
+inline const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_cbrt(x.mp,x.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_root(x.mp,x.mp,k,rnd_mode);
+ return x;
+}
+
+inline const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_abs(x.mp,x.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_abs(x.mp,x.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+ mpreal x(a);
+ mpfr_dim(x.mp,a.mp,b.mp,rnd_mode);
+ return x;
+}
+
+inline int cmpabs(const mpreal& a,const mpreal& b)
+{
+ return mpfr_cmpabs(a.mp,b.mp);
+}
+
+inline const mpreal log (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_log(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal log2(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_log2(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_log10(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal exp(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_exp(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal exp2(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_exp2(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_exp10(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_cos(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_sin(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_tan(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_sec(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_csc(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_cot(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode)
+{
+ return mpfr_sin_cos(s.mp,c.mp,v.mp,rnd_mode);
+}
+
+inline const mpreal acos (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_acos(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal asin (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_asin(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal atan (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_atan(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal acot (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ return atan(1/v, rnd_mode);
+}
+
+inline const mpreal asec (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ return acos(1/v, rnd_mode);
+}
+
+inline const mpreal acsc (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ return asin(1/v, rnd_mode);
+}
+
+inline const mpreal acoth (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ return atanh(1/v, rnd_mode);
+}
+
+inline const mpreal asech (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ return acosh(1/v, rnd_mode);
+}
+
+inline const mpreal acsch (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ return asinh(1/v, rnd_mode);
+}
+
+inline const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode)
+{
+ mpreal a;
+ mp_prec_t yp, xp;
+
+ yp = y.get_prec();
+ xp = x.get_prec();
+
+ a.set_prec(yp>xp?yp:xp);
+
+ mpfr_atan2(a.mp, y.mp, x.mp, rnd_mode);
+
+ return a;
+}
+
+inline const mpreal cosh (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_cosh(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal sinh (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_sinh(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal tanh (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_tanh(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal sech (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_sech(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal csch (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_csch(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal coth (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_coth(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal acosh (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_acosh(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal asinh (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_asinh(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal atanh (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_atanh(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode)
+{
+ mpreal a;
+ mp_prec_t yp, xp;
+
+ yp = y.get_prec();
+ xp = x.get_prec();
+
+ a.set_prec(yp>xp?yp:xp);
+
+ mpfr_hypot(a.mp, x.mp, y.mp, rnd_mode);
+
+ return a;
+}
+
+inline const mpreal remainder (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode)
+{
+ mpreal a;
+ mp_prec_t yp, xp;
+
+ yp = y.get_prec();
+ xp = x.get_prec();
+
+ a.set_prec(yp>xp?yp:xp);
+
+ mpfr_remainder(a.mp, x.mp, y.mp, rnd_mode);
+
+ return a;
+}
+
+inline const mpreal fac_ui (unsigned long int v, mp_prec_t prec, mp_rnd_t rnd_mode)
+{
+ mpreal x(0,prec);
+ mpfr_fac_ui(x.mp,v,rnd_mode);
+ return x;
+}
+
+inline const mpreal log1p (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_log1p(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal expm1 (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_expm1(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal eint (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_eint(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal gamma (const mpreal& x, mp_rnd_t rnd_mode)
+{
+ mpreal FunctionValue(x);
+
+ // x < 0: gamma(-x) = -pi/(x * gamma(x) * sin(pi*x))
+
+ mpfr_gamma(FunctionValue.mp, x.mp, rnd_mode);
+
+ return FunctionValue;
+}
+
+inline const mpreal lngamma (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_lngamma(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal lgamma (const mpreal& v, int *signp, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ int tsignp;
+
+ if(signp)
+ mpfr_lgamma(x.mp,signp,v.mp,rnd_mode);
+ else
+ mpfr_lgamma(x.mp,&tsignp,v.mp,rnd_mode);
+
+ return x;
+}
+
+inline const mpreal zeta (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_zeta(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal erf (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_erf(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal erfc (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_erfc(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal besselj0 (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_j0(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal besselj1 (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_j1(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal besseljn (long n, const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_jn(x.mp,n,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal bessely0 (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_y0(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal bessely1 (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_y1(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal besselyn (long n, const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_yn(x.mp,n,v.mp,rnd_mode);
+ return x;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// MPFR 2.4.0 Specifics
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
+
+inline int sinh_cosh(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode)
+{
+ return mpfr_sinh_cosh(s.mp,c.mp,v.mp,rnd_mode);
+}
+
+inline const mpreal li2(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_li2(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode)
+{
+ mpreal a;
+ mp_prec_t yp, xp;
+
+ yp = y.get_prec();
+ xp = x.get_prec();
+
+ a.set_prec(yp>xp?yp:xp);
+
+ mpfr_fmod(a.mp, x.mp, y.mp, rnd_mode);
+
+ return a;
+}
+
+inline const mpreal rec_sqrt(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_rec_sqrt(x.mp,v.mp,rnd_mode);
+ return x;
+}
+#endif // MPFR 2.4.0 Specifics
+
+//////////////////////////////////////////////////////////////////////////
+// MPFR 3.0.0 Specifics
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))
+
+inline const mpreal digamma(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_digamma(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal ai(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_ai(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+#endif // MPFR 3.0.0 Specifics
+
+//////////////////////////////////////////////////////////////////////////
+// Constants
+inline const mpreal const_log2 (mp_prec_t prec, mp_rnd_t rnd_mode)
+{
+ mpreal x;
+ x.set_prec(prec);
+ mpfr_const_log2(x.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal const_pi (mp_prec_t prec, mp_rnd_t rnd_mode)
+{
+ mpreal x;
+ x.set_prec(prec);
+ mpfr_const_pi(x.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal const_euler (mp_prec_t prec, mp_rnd_t rnd_mode)
+{
+ mpreal x;
+ x.set_prec(prec);
+ mpfr_const_euler(x.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal const_catalan (mp_prec_t prec, mp_rnd_t rnd_mode)
+{
+ mpreal x;
+ x.set_prec(prec);
+ mpfr_const_catalan(x.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal const_infinity (int sign, mp_prec_t prec, mp_rnd_t rnd_mode)
+{
+ mpreal x;
+ x.set_prec(prec,rnd_mode);
+ mpfr_set_inf(x.mp, sign);
+ return x;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Integer Related Functions
+inline const mpreal rint(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_rint(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal ceil(const mpreal& v)
+{
+ mpreal x(v);
+ mpfr_ceil(x.mp,v.mp);
+ return x;
+
+}
+
+inline const mpreal floor(const mpreal& v)
+{
+ mpreal x(v);
+ mpfr_floor(x.mp,v.mp);
+ return x;
+}
+
+inline const mpreal round(const mpreal& v)
+{
+ mpreal x(v);
+ mpfr_round(x.mp,v.mp);
+ return x;
+}
+
+inline const mpreal trunc(const mpreal& v)
+{
+ mpreal x(v);
+ mpfr_trunc(x.mp,v.mp);
+ return x;
+}
+
+inline const mpreal rint_ceil (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_rint_ceil(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal rint_floor(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_rint_floor(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal rint_round(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_rint_round(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal rint_trunc(const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_rint_trunc(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal frac (const mpreal& v, mp_rnd_t rnd_mode)
+{
+ mpreal x(v);
+ mpfr_frac(x.mp,v.mp,rnd_mode);
+ return x;
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Miscellaneous Functions
+inline void swap(mpreal& a, mpreal& b)
+{
+ mpfr_swap(a.mp,b.mp);
+}
+
+inline const mpreal (max)(const mpreal& x, const mpreal& y)
+{
+ return (x>y?x:y);
+}
+
+inline const mpreal (min)(const mpreal& x, const mpreal& y)
+{
+ return (x<y?x:y);
+}
+
+inline const mpreal fmax(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode)
+{
+ mpreal a;
+ mpfr_max(a.mp,x.mp,y.mp,rnd_mode);
+ return a;
+}
+
+inline const mpreal fmin(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode)
+{
+ mpreal a;
+ mpfr_min(a.mp,x.mp,y.mp,rnd_mode);
+ return a;
+}
+
+inline const mpreal nexttoward (const mpreal& x, const mpreal& y)
+{
+ mpreal a(x);
+ mpfr_nexttoward(a.mp,y.mp);
+ return a;
+}
+
+inline const mpreal nextabove (const mpreal& x)
+{
+ mpreal a(x);
+ mpfr_nextabove(a.mp);
+ return a;
+}
+
+inline const mpreal nextbelow (const mpreal& x)
+{
+ mpreal a(x);
+ mpfr_nextbelow(a.mp);
+ return a;
+}
+
+inline const mpreal urandomb (gmp_randstate_t& state)
+{
+ mpreal x;
+ mpfr_urandomb(x.mp,state);
+ return x;
+}
+
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))
+// use gmp_randinit_default() to init state, gmp_randclear() to clear
+inline const mpreal urandom (gmp_randstate_t& state, mp_rnd_t rnd_mode)
+{
+ mpreal x;
+ mpfr_urandom(x.mp,state,rnd_mode);
+ return x;
+}
+#endif
+
+#if (MPFR_VERSION <= MPFR_VERSION_NUM(2,4,2))
+inline const mpreal random2 (mp_size_t size, mp_exp_t exp)
+{
+ mpreal x;
+ mpfr_random2(x.mp,size,exp);
+ return x;
+}
+#endif
+
+// Uniformly distributed random number generation
+// a = random(seed); <- initialization & first random number generation
+// a = random(); <- next random numbers generation
+// seed != 0
+inline const mpreal random(unsigned int seed)
+{
+
+#if (MPFR_VERSION >= MPFR_VERSION_NUM(3,0,0))
+ static gmp_randstate_t state;
+ static bool isFirstTime = true;
+
+ if(isFirstTime)
+ {
+ gmp_randinit_default(state);
+ gmp_randseed_ui(state,0);
+ isFirstTime = false;
+ }
+
+ if(seed != 0) gmp_randseed_ui(state,seed);
+
+ return mpfr::urandom(state);
+#else
+ if(seed != 0) std::srand(seed);
+ return mpfr::mpreal(std::rand()/(double)RAND_MAX);
+#endif
+
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Set/Get global properties
+inline void mpreal::set_default_prec(mp_prec_t prec)
+{
+ default_prec = prec;
+ mpfr_set_default_prec(prec);
+}
+
+inline mp_prec_t mpreal::get_default_prec()
+{
+ return (mpfr_get_default_prec)();
+}
+
+inline void mpreal::set_default_base(int base)
+{
+ default_base = base;
+}
+
+inline int mpreal::get_default_base()
+{
+ return default_base;
+}
+
+inline void mpreal::set_default_rnd(mp_rnd_t rnd_mode)
+{
+ default_rnd = rnd_mode;
+ mpfr_set_default_rounding_mode(rnd_mode);
+}
+
+inline mp_rnd_t mpreal::get_default_rnd()
+{
+ return static_cast<mp_rnd_t>((mpfr_get_default_rounding_mode)());
+}
+
+inline void mpreal::set_double_bits(int dbits)
+{
+ double_bits = dbits;
+}
+
+inline int mpreal::get_double_bits()
+{
+ return double_bits;
+}
+
+inline bool mpreal::fits_in_bits(double x, int n)
+{
+ int i;
+ double t;
+ return IsInf(x) || (std::modf ( std::ldexp ( std::frexp ( x, &i ), n ), &t ) == 0.0);
+}
+
+inline const mpreal pow(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+ mpreal x(a);
+ mpfr_pow(x.mp,x.mp,b.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal pow(const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode)
+{
+ mpreal x(a);
+ mpfr_pow_z(x.mp,x.mp,b,rnd_mode);
+ return x;
+}
+
+inline const mpreal pow(const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+ mpreal x(a);
+ mpfr_pow_ui(x.mp,x.mp,b,rnd_mode);
+ return x;
+}
+
+inline const mpreal pow(const mpreal& a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+ return pow(a,static_cast<unsigned long int>(b),rnd_mode);
+}
+
+inline const mpreal pow(const mpreal& a, const long int b, mp_rnd_t rnd_mode)
+{
+ mpreal x(a);
+ mpfr_pow_si(x.mp,x.mp,b,rnd_mode);
+ return x;
+}
+
+inline const mpreal pow(const mpreal& a, const int b, mp_rnd_t rnd_mode)
+{
+ return pow(a,static_cast<long int>(b),rnd_mode);
+}
+
+inline const mpreal pow(const mpreal& a, const long double b, mp_rnd_t rnd_mode)
+{
+ return pow(a,mpreal(b),rnd_mode);
+}
+
+inline const mpreal pow(const mpreal& a, const double b, mp_rnd_t rnd_mode)
+{
+ return pow(a,mpreal(b),rnd_mode);
+}
+
+inline const mpreal pow(const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+ mpreal x(a);
+ mpfr_ui_pow(x.mp,a,b.mp,rnd_mode);
+ return x;
+}
+
+inline const mpreal pow(const unsigned int a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+ return pow(static_cast<unsigned long int>(a),b,rnd_mode);
+}
+
+inline const mpreal pow(const long int a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+ if (a>=0) return pow(static_cast<unsigned long int>(a),b,rnd_mode);
+ else return pow(mpreal(a),b,rnd_mode);
+}
+
+inline const mpreal pow(const int a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+ if (a>=0) return pow(static_cast<unsigned long int>(a),b,rnd_mode);
+ else return pow(mpreal(a),b,rnd_mode);
+}
+
+inline const mpreal pow(const long double a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+ return pow(mpreal(a),b,rnd_mode);
+}
+
+inline const mpreal pow(const double a, const mpreal& b, mp_rnd_t rnd_mode)
+{
+ return pow(mpreal(a),b,rnd_mode);
+}
+
+// pow unsigned long int
+inline const mpreal pow(const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+ mpreal x(a);
+ mpfr_ui_pow_ui(x.mp,a,b,rnd_mode);
+ return x;
+}
+
+inline const mpreal pow(const unsigned long int a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+ return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+}
+
+inline const mpreal pow(const unsigned long int a, const long int b, mp_rnd_t rnd_mode)
+{
+ if(b>0) return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+ else return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+inline const mpreal pow(const unsigned long int a, const int b, mp_rnd_t rnd_mode)
+{
+ if(b>0) return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+ else return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+inline const mpreal pow(const unsigned long int a, const long double b, mp_rnd_t rnd_mode)
+{
+ return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+inline const mpreal pow(const unsigned long int a, const double b, mp_rnd_t rnd_mode)
+{
+ return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+// pow unsigned int
+inline const mpreal pow(const unsigned int a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+ return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui
+}
+
+inline const mpreal pow(const unsigned int a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+ return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+}
+
+inline const mpreal pow(const unsigned int a, const long int b, mp_rnd_t rnd_mode)
+{
+ if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+ else return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+inline const mpreal pow(const unsigned int a, const int b, mp_rnd_t rnd_mode)
+{
+ if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+ else return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+inline const mpreal pow(const unsigned int a, const long double b, mp_rnd_t rnd_mode)
+{
+ return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+inline const mpreal pow(const unsigned int a, const double b, mp_rnd_t rnd_mode)
+{
+ return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+}
+
+// pow long int
+inline const mpreal pow(const long int a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+ if (a>0) return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui
+ else return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui
+}
+
+inline const mpreal pow(const long int a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+ if (a>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+ else return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui
+}
+
+inline const mpreal pow(const long int a, const long int b, mp_rnd_t rnd_mode)
+{
+ if (a>0)
+ {
+ if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+ else return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+ }else{
+ return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si
+ }
+}
+
+inline const mpreal pow(const long int a, const int b, mp_rnd_t rnd_mode)
+{
+ if (a>0)
+ {
+ if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+ else return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+ }else{
+ return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si
+ }
+}
+
+inline const mpreal pow(const long int a, const long double b, mp_rnd_t rnd_mode)
+{
+ if (a>=0) return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+ else return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow
+}
+
+inline const mpreal pow(const long int a, const double b, mp_rnd_t rnd_mode)
+{
+ if (a>=0) return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+ else return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow
+}
+
+// pow int
+inline const mpreal pow(const int a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+ if (a>0) return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui
+ else return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui
+}
+
+inline const mpreal pow(const int a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+ if (a>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+ else return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui
+}
+
+inline const mpreal pow(const int a, const long int b, mp_rnd_t rnd_mode)
+{
+ if (a>0)
+ {
+ if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+ else return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+ }else{
+ return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si
+ }
+}
+
+inline const mpreal pow(const int a, const int b, mp_rnd_t rnd_mode)
+{
+ if (a>0)
+ {
+ if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
+ else return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+ }else{
+ return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si
+ }
+}
+
+inline const mpreal pow(const int a, const long double b, mp_rnd_t rnd_mode)
+{
+ if (a>=0) return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+ else return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow
+}
+
+inline const mpreal pow(const int a, const double b, mp_rnd_t rnd_mode)
+{
+ if (a>=0) return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
+ else return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow
+}
+
+// pow long double
+inline const mpreal pow(const long double a, const long double b, mp_rnd_t rnd_mode)
+{
+ return pow(mpreal(a),mpreal(b),rnd_mode);
+}
+
+inline const mpreal pow(const long double a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+ return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui
+}
+
+inline const mpreal pow(const long double a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+ return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui
+}
+
+inline const mpreal pow(const long double a, const long int b, mp_rnd_t rnd_mode)
+{
+ return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si
+}
+
+inline const mpreal pow(const long double a, const int b, mp_rnd_t rnd_mode)
+{
+ return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si
+}
+
+inline const mpreal pow(const double a, const double b, mp_rnd_t rnd_mode)
+{
+ return pow(mpreal(a),mpreal(b),rnd_mode);
+}
+
+inline const mpreal pow(const double a, const unsigned long int b, mp_rnd_t rnd_mode)
+{
+ return pow(mpreal(a),b,rnd_mode); // mpfr_pow_ui
+}
+
+inline const mpreal pow(const double a, const unsigned int b, mp_rnd_t rnd_mode)
+{
+ return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); // mpfr_pow_ui
+}
+
+inline const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode)
+{
+ return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si
+}
+
+inline const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode)
+{
+ return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si
+}
+} // End of mpfr namespace
+
+// Explicit specialization of std::swap for mpreal numbers
+// Thus standard algorithms will use efficient version of swap (due to Koenig lookup)
+// Non-throwing swap C++ idiom: http://en.wikibooks.org/wiki/More_C%2B%2B_Idioms/Non-throwing_swap
+namespace std
+{
+ template <>
+ inline void swap(mpfr::mpreal& x, mpfr::mpreal& y)
+ {
+ return mpfr::swap(x, y);
+ }
+}
+
+#endif /* __MPREAL_H__ */
diff --git a/unsupported/test/mpreal_support.cpp b/unsupported/test/mpreal_support.cpp new file mode 100644 index 000000000..551af9db8 --- /dev/null +++ b/unsupported/test/mpreal_support.cpp @@ -0,0 +1,64 @@ +#include "main.h" +#include <Eigen/MPRealSupport> +#include <Eigen/LU> +#include <Eigen/Eigenvalues> +#include <sstream> + +using namespace mpfr; +using namespace std; +using namespace Eigen; + +void test_mpreal_support() +{ + // set precision to 256 bits (double has only 53 bits) + mpreal::set_default_prec(256); + typedef Matrix<mpreal,Eigen::Dynamic,Eigen::Dynamic> MatrixXmp; + + std::cerr << "epsilon = " << NumTraits<mpreal>::epsilon() << "\n"; + std::cerr << "dummy_precision = " << NumTraits<mpreal>::dummy_precision() << "\n"; + std::cerr << "highest = " << NumTraits<mpreal>::highest() << "\n"; + std::cerr << "lowest = " << NumTraits<mpreal>::lowest() << "\n"; + + for(int i = 0; i < g_repeat; i++) { + int s = Eigen::internal::random<int>(1,100); + MatrixXmp A = MatrixXmp::Random(s,s); + MatrixXmp B = MatrixXmp::Random(s,s); + MatrixXmp S = A.adjoint() * A; + MatrixXmp X; + + // Basic stuffs + VERIFY_IS_APPROX(A.real(), A); + VERIFY(Eigen::internal::isApprox(A.array().abs2().sum(), A.squaredNorm())); + VERIFY_IS_APPROX(A.array().exp(), exp(A.array())); + VERIFY_IS_APPROX(A.array().abs2().sqrt(), A.array().abs()); + VERIFY_IS_APPROX(A.array().sin(), sin(A.array())); + VERIFY_IS_APPROX(A.array().cos(), cos(A.array())); + + + // Cholesky + X = S.selfadjointView<Lower>().llt().solve(B); + VERIFY_IS_APPROX((S.selfadjointView<Lower>()*X).eval(),B); + + // partial LU + X = A.lu().solve(B); + VERIFY_IS_APPROX((A*X).eval(),B); + + // symmetric eigenvalues + SelfAdjointEigenSolver<MatrixXmp> eig(S); + VERIFY_IS_EQUAL(eig.info(), Success); + VERIFY_IS_APPROX((S.selfadjointView<Lower>() * eig.eigenvectors()), + eig.eigenvectors() * eig.eigenvalues().asDiagonal()); + } + + { + MatrixXmp A(8,3); A.setRandom(); + // test output (interesting things happen in this code) + std::stringstream stream; + stream << A; + } +} + +extern "C" { +#include "mpreal/dlmalloc.c" +} +#include "mpreal/mpreal.cpp" diff --git a/unsupported/test/openglsupport.cpp b/unsupported/test/openglsupport.cpp new file mode 100644 index 000000000..706a816f7 --- /dev/null +++ b/unsupported/test/openglsupport.cpp @@ -0,0 +1,337 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include <main.h> +#include <iostream> +#include <GL/glew.h> +#include <Eigen/OpenGLSupport> +#include <GL/glut.h> +using namespace Eigen; + + + + +#define VERIFY_MATRIX(CODE,REF) { \ + glLoadIdentity(); \ + CODE; \ + Matrix<float,4,4,ColMajor> m; m.setZero(); \ + glGet(GL_MODELVIEW_MATRIX, m); \ + if(!(REF).cast<float>().isApprox(m)) { \ + std::cerr << "Expected:\n" << ((REF).cast<float>()) << "\n" << "got\n" << m << "\n\n"; \ + } \ + VERIFY_IS_APPROX((REF).cast<float>(), m); \ + } + +#define VERIFY_UNIFORM(SUFFIX,NAME,TYPE) { \ + TYPE value; value.setRandom(); \ + TYPE data; \ + int loc = glGetUniformLocation(prg_id, #NAME); \ + VERIFY((loc!=-1) && "uniform not found"); \ + glUniform(loc,value); \ + EIGEN_CAT(glGetUniform,SUFFIX)(prg_id,loc,data.data()); \ + if(!value.isApprox(data)) { \ + std::cerr << "Expected:\n" << value << "\n" << "got\n" << data << "\n\n"; \ + } \ + VERIFY_IS_APPROX(value, data); \ + } + +#define VERIFY_UNIFORMi(NAME,TYPE) { \ + TYPE value = TYPE::Random().eval().cast<float>().cast<TYPE::Scalar>(); \ + TYPE data; \ + int loc = glGetUniformLocation(prg_id, #NAME); \ + VERIFY((loc!=-1) && "uniform not found"); \ + glUniform(loc,value); \ + glGetUniformiv(prg_id,loc,(GLint*)data.data()); \ + if(!value.isApprox(data)) { \ + std::cerr << "Expected:\n" << value << "\n" << "got\n" << data << "\n\n"; \ + } \ + VERIFY_IS_APPROX(value, data); \ + } + +void printInfoLog(GLuint objectID) +{ + int infologLength, charsWritten; + GLchar *infoLog; + glGetProgramiv(objectID,GL_INFO_LOG_LENGTH, &infologLength); + if(infologLength > 0) + { + infoLog = new GLchar[infologLength]; + glGetProgramInfoLog(objectID, infologLength, &charsWritten, infoLog); + if (charsWritten>0) + std::cerr << "Shader info : \n" << infoLog << std::endl; + delete[] infoLog; + } +} + +GLint createShader(const char* vtx, const char* frg) +{ + GLint prg_id = glCreateProgram(); + GLint vtx_id = glCreateShader(GL_VERTEX_SHADER); + GLint frg_id = glCreateShader(GL_FRAGMENT_SHADER); + GLint ok; + + glShaderSource(vtx_id, 1, &vtx, 0); + glCompileShader(vtx_id); + glGetShaderiv(vtx_id,GL_COMPILE_STATUS,&ok); + if(!ok) + { + std::cerr << "vtx compilation failed\n"; + } + + glShaderSource(frg_id, 1, &frg, 0); + glCompileShader(frg_id); + glGetShaderiv(frg_id,GL_COMPILE_STATUS,&ok); + if(!ok) + { + std::cerr << "frg compilation failed\n"; + } + + glAttachShader(prg_id, vtx_id); + glAttachShader(prg_id, frg_id); + glLinkProgram(prg_id); + glGetProgramiv(prg_id,GL_LINK_STATUS,&ok); + if(!ok) + { + std::cerr << "linking failed\n"; + } + printInfoLog(prg_id); + + glUseProgram(prg_id); + return prg_id; +} + +void test_openglsupport() +{ + int argc = 0; + glutInit(&argc, 0); + glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH); + glutInitWindowPosition (0,0); + glutInitWindowSize(10, 10); + + if(glutCreateWindow("Eigen") <= 0) + { + std::cerr << "Error: Unable to create GLUT Window.\n"; + exit(1); + } + + glewExperimental = GL_TRUE; + if(glewInit() != GLEW_OK) + { + std::cerr << "Warning: Failed to initialize GLEW\n"; + } + + Vector3f v3f; + Matrix3f rot; + glBegin(GL_POINTS); + + glVertex(v3f); + glVertex(2*v3f+v3f); + glVertex(rot*v3f); + + glEnd(); + + // 4x4 matrices + Matrix4f mf44; mf44.setRandom(); + VERIFY_MATRIX(glLoadMatrix(mf44), mf44); + VERIFY_MATRIX(glMultMatrix(mf44), mf44); + Matrix4d md44; md44.setRandom(); + VERIFY_MATRIX(glLoadMatrix(md44), md44); + VERIFY_MATRIX(glMultMatrix(md44), md44); + + // Quaternion + Quaterniond qd(AngleAxisd(internal::random<double>(), Vector3d::Random())); + VERIFY_MATRIX(glRotate(qd), Projective3d(qd).matrix()); + + Quaternionf qf(AngleAxisf(internal::random<double>(), Vector3f::Random())); + VERIFY_MATRIX(glRotate(qf), Projective3f(qf).matrix()); + + // 3D Transform + Transform<float,3,AffineCompact> acf3; acf3.matrix().setRandom(); + VERIFY_MATRIX(glLoadMatrix(acf3), Projective3f(acf3).matrix()); + VERIFY_MATRIX(glMultMatrix(acf3), Projective3f(acf3).matrix()); + + Transform<float,3,Affine> af3(acf3); + VERIFY_MATRIX(glLoadMatrix(af3), Projective3f(af3).matrix()); + VERIFY_MATRIX(glMultMatrix(af3), Projective3f(af3).matrix()); + + Transform<float,3,Projective> pf3; pf3.matrix().setRandom(); + VERIFY_MATRIX(glLoadMatrix(pf3), Projective3f(pf3).matrix()); + VERIFY_MATRIX(glMultMatrix(pf3), Projective3f(pf3).matrix()); + + Transform<double,3,AffineCompact> acd3; acd3.matrix().setRandom(); + VERIFY_MATRIX(glLoadMatrix(acd3), Projective3d(acd3).matrix()); + VERIFY_MATRIX(glMultMatrix(acd3), Projective3d(acd3).matrix()); + + Transform<double,3,Affine> ad3(acd3); + VERIFY_MATRIX(glLoadMatrix(ad3), Projective3d(ad3).matrix()); + VERIFY_MATRIX(glMultMatrix(ad3), Projective3d(ad3).matrix()); + + Transform<double,3,Projective> pd3; pd3.matrix().setRandom(); + VERIFY_MATRIX(glLoadMatrix(pd3), Projective3d(pd3).matrix()); + VERIFY_MATRIX(glMultMatrix(pd3), Projective3d(pd3).matrix()); + + // translations (2D and 3D) + { + Vector2f vf2; vf2.setRandom(); Vector3f vf23; vf23 << vf2, 0; + VERIFY_MATRIX(glTranslate(vf2), Projective3f(Translation3f(vf23)).matrix()); + Vector2d vd2; vd2.setRandom(); Vector3d vd23; vd23 << vd2, 0; + VERIFY_MATRIX(glTranslate(vd2), Projective3d(Translation3d(vd23)).matrix()); + + Vector3f vf3; vf3.setRandom(); + VERIFY_MATRIX(glTranslate(vf3), Projective3f(Translation3f(vf3)).matrix()); + Vector3d vd3; vd3.setRandom(); + VERIFY_MATRIX(glTranslate(vd3), Projective3d(Translation3d(vd3)).matrix()); + + Translation<float,3> tf3; tf3.vector().setRandom(); + VERIFY_MATRIX(glTranslate(tf3), Projective3f(tf3).matrix()); + + Translation<double,3> td3; td3.vector().setRandom(); + VERIFY_MATRIX(glTranslate(td3), Projective3d(td3).matrix()); + } + + // scaling (2D and 3D) + { + Vector2f vf2; vf2.setRandom(); Vector3f vf23; vf23 << vf2, 1; + VERIFY_MATRIX(glScale(vf2), Projective3f(Scaling(vf23)).matrix()); + Vector2d vd2; vd2.setRandom(); Vector3d vd23; vd23 << vd2, 1; + VERIFY_MATRIX(glScale(vd2), Projective3d(Scaling(vd23)).matrix()); + + Vector3f vf3; vf3.setRandom(); + VERIFY_MATRIX(glScale(vf3), Projective3f(Scaling(vf3)).matrix()); + Vector3d vd3; vd3.setRandom(); + VERIFY_MATRIX(glScale(vd3), Projective3d(Scaling(vd3)).matrix()); + + UniformScaling<float> usf(internal::random<float>()); + VERIFY_MATRIX(glScale(usf), Projective3f(usf).matrix()); + + UniformScaling<double> usd(internal::random<double>()); + VERIFY_MATRIX(glScale(usd), Projective3d(usd).matrix()); + } + + // uniform + { + const char* vtx = "void main(void) { gl_Position = gl_Vertex; }\n"; + + if(GLEW_VERSION_2_0) + { + #ifdef GL_VERSION_2_0 + const char* frg = "" + "uniform vec2 v2f;\n" + "uniform vec3 v3f;\n" + "uniform vec4 v4f;\n" + "uniform ivec2 v2i;\n" + "uniform ivec3 v3i;\n" + "uniform ivec4 v4i;\n" + "uniform mat2 m2f;\n" + "uniform mat3 m3f;\n" + "uniform mat4 m4f;\n" + "void main(void) { gl_FragColor = vec4(v2f[0]+v3f[0]+v4f[0])+vec4(v2i[0]+v3i[0]+v4i[0])+vec4(m2f[0][0]+m3f[0][0]+m4f[0][0]); }\n"; + + GLint prg_id = createShader(vtx,frg); + + VERIFY_UNIFORM(fv,v2f, Vector2f); + VERIFY_UNIFORM(fv,v3f, Vector3f); + VERIFY_UNIFORM(fv,v4f, Vector4f); + VERIFY_UNIFORMi(v2i, Vector2i); + VERIFY_UNIFORMi(v3i, Vector3i); + VERIFY_UNIFORMi(v4i, Vector4i); + VERIFY_UNIFORM(fv,m2f, Matrix2f); + VERIFY_UNIFORM(fv,m3f, Matrix3f); + VERIFY_UNIFORM(fv,m4f, Matrix4f); + #endif + } + else + std::cerr << "Warning: opengl 2.0 was not tested\n"; + + if(GLEW_VERSION_2_1) + { + #ifdef GL_VERSION_2_1 + const char* frg = "#version 120\n" + "uniform mat2x3 m23f;\n" + "uniform mat3x2 m32f;\n" + "uniform mat2x4 m24f;\n" + "uniform mat4x2 m42f;\n" + "uniform mat3x4 m34f;\n" + "uniform mat4x3 m43f;\n" + "void main(void) { gl_FragColor = vec4(m23f[0][0]+m32f[0][0]+m24f[0][0]+m42f[0][0]+m34f[0][0]+m43f[0][0]); }\n"; + + GLint prg_id = createShader(vtx,frg); + + typedef Matrix<float,2,3> Matrix23f; + typedef Matrix<float,3,2> Matrix32f; + typedef Matrix<float,2,4> Matrix24f; + typedef Matrix<float,4,2> Matrix42f; + typedef Matrix<float,3,4> Matrix34f; + typedef Matrix<float,4,3> Matrix43f; + + VERIFY_UNIFORM(fv,m23f, Matrix23f); + VERIFY_UNIFORM(fv,m32f, Matrix32f); + VERIFY_UNIFORM(fv,m24f, Matrix24f); + VERIFY_UNIFORM(fv,m42f, Matrix42f); + VERIFY_UNIFORM(fv,m34f, Matrix34f); + VERIFY_UNIFORM(fv,m43f, Matrix43f); + #endif + } + else + std::cerr << "Warning: opengl 2.1 was not tested\n"; + + if(GLEW_VERSION_3_0) + { + #ifdef GL_VERSION_3_0 + const char* frg = "#version 150\n" + "uniform uvec2 v2ui;\n" + "uniform uvec3 v3ui;\n" + "uniform uvec4 v4ui;\n" + "out vec4 data;\n" + "void main(void) { data = vec4(v2ui[0]+v3ui[0]+v4ui[0]); }\n"; + + GLint prg_id = createShader(vtx,frg); + + typedef Matrix<unsigned int,2,1> Vector2ui; + typedef Matrix<unsigned int,3,1> Vector3ui; + typedef Matrix<unsigned int,4,1> Vector4ui; + + VERIFY_UNIFORMi(v2ui, Vector2ui); + VERIFY_UNIFORMi(v3ui, Vector3ui); + VERIFY_UNIFORMi(v4ui, Vector4ui); + #endif + } + else + std::cerr << "Warning: opengl 3.0 was not tested\n"; + + #ifdef GLEW_ARB_gpu_shader_fp64 + if(GLEW_ARB_gpu_shader_fp64) + { + #ifdef GL_ARB_gpu_shader_fp64 + const char* frg = "#version 150\n" + "uniform dvec2 v2d;\n" + "uniform dvec3 v3d;\n" + "uniform dvec4 v4d;\n" + "out vec4 data;\n" + "void main(void) { data = vec4(v2d[0]+v3d[0]+v4d[0]); }\n"; + + GLint prg_id = createShader(vtx,frg); + + typedef Vector2d Vector2d; + typedef Vector3d Vector3d; + typedef Vector4d Vector4d; + + VERIFY_UNIFORM(dv,v2d, Vector2d); + VERIFY_UNIFORM(dv,v3d, Vector3d); + VERIFY_UNIFORM(dv,v4d, Vector4d); + #endif + } + else + std::cerr << "Warning: GLEW_ARB_gpu_shader_fp64 was not tested\n"; + #else + std::cerr << "Warning: GLEW_ARB_gpu_shader_fp64 was not tested\n"; + #endif + } + +} diff --git a/unsupported/test/polynomialsolver.cpp b/unsupported/test/polynomialsolver.cpp new file mode 100644 index 000000000..fefeaff01 --- /dev/null +++ b/unsupported/test/polynomialsolver.cpp @@ -0,0 +1,217 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include <unsupported/Eigen/Polynomials> +#include <iostream> +#include <algorithm> + +using namespace std; + +namespace Eigen { +namespace internal { +template<int Size> +struct increment_if_fixed_size +{ + enum { + ret = (Size == Dynamic) ? Dynamic : Size+1 + }; +}; +} +} + + +template<int Deg, typename POLYNOMIAL, typename SOLVER> +bool aux_evalSolver( const POLYNOMIAL& pols, SOLVER& psolve ) +{ + typedef typename POLYNOMIAL::Index Index; + typedef typename POLYNOMIAL::Scalar Scalar; + + typedef typename SOLVER::RootsType RootsType; + typedef Matrix<Scalar,Deg,1> EvalRootsType; + + const Index deg = pols.size()-1; + + psolve.compute( pols ); + const RootsType& roots( psolve.roots() ); + EvalRootsType evr( deg ); + for( int i=0; i<roots.size(); ++i ){ + evr[i] = std::abs( poly_eval( pols, roots[i] ) ); } + + bool evalToZero = evr.isZero( test_precision<Scalar>() ); + if( !evalToZero ) + { + cerr << "WRONG root: " << endl; + cerr << "Polynomial: " << pols.transpose() << endl; + cerr << "Roots found: " << roots.transpose() << endl; + cerr << "Abs value of the polynomial at the roots: " << evr.transpose() << endl; + cerr << endl; + } + + std::vector<Scalar> rootModuli( roots.size() ); + Map< EvalRootsType > aux( &rootModuli[0], roots.size() ); + aux = roots.array().abs(); + std::sort( rootModuli.begin(), rootModuli.end() ); + bool distinctModuli=true; + for( size_t i=1; i<rootModuli.size() && distinctModuli; ++i ) + { + if( internal::isApprox( rootModuli[i], rootModuli[i-1] ) ){ + distinctModuli = false; } + } + VERIFY( evalToZero || !distinctModuli ); + + return distinctModuli; +} + + + + + + + +template<int Deg, typename POLYNOMIAL> +void evalSolver( const POLYNOMIAL& pols ) +{ + typedef typename POLYNOMIAL::Scalar Scalar; + + typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType; + + PolynomialSolverType psolve; + aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve ); +} + + + + +template< int Deg, typename POLYNOMIAL, typename ROOTS, typename REAL_ROOTS > +void evalSolverSugarFunction( const POLYNOMIAL& pols, const ROOTS& roots, const REAL_ROOTS& real_roots ) +{ + typedef typename POLYNOMIAL::Scalar Scalar; + + typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType; + + PolynomialSolverType psolve; + if( aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve ) ) + { + //It is supposed that + // 1) the roots found are correct + // 2) the roots have distinct moduli + + typedef typename POLYNOMIAL::Scalar Scalar; + typedef typename REAL_ROOTS::Scalar Real; + + typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType; + typedef typename PolynomialSolverType::RootsType RootsType; + typedef Matrix<Scalar,Deg,1> EvalRootsType; + + //Test realRoots + std::vector< Real > calc_realRoots; + psolve.realRoots( calc_realRoots ); + VERIFY( calc_realRoots.size() == (size_t)real_roots.size() ); + + const Scalar psPrec = internal::sqrt( test_precision<Scalar>() ); + + for( size_t i=0; i<calc_realRoots.size(); ++i ) + { + bool found = false; + for( size_t j=0; j<calc_realRoots.size()&& !found; ++j ) + { + if( internal::isApprox( calc_realRoots[i], real_roots[j] ), psPrec ){ + found = true; } + } + VERIFY( found ); + } + + //Test greatestRoot + VERIFY( internal::isApprox( roots.array().abs().maxCoeff(), + internal::abs( psolve.greatestRoot() ), psPrec ) ); + + //Test smallestRoot + VERIFY( internal::isApprox( roots.array().abs().minCoeff(), + internal::abs( psolve.smallestRoot() ), psPrec ) ); + + bool hasRealRoot; + //Test absGreatestRealRoot + Real r = psolve.absGreatestRealRoot( hasRealRoot ); + VERIFY( hasRealRoot == (real_roots.size() > 0 ) ); + if( hasRealRoot ){ + VERIFY( internal::isApprox( real_roots.array().abs().maxCoeff(), internal::abs(r), psPrec ) ); } + + //Test absSmallestRealRoot + r = psolve.absSmallestRealRoot( hasRealRoot ); + VERIFY( hasRealRoot == (real_roots.size() > 0 ) ); + if( hasRealRoot ){ + VERIFY( internal::isApprox( real_roots.array().abs().minCoeff(), internal::abs( r ), psPrec ) ); } + + //Test greatestRealRoot + r = psolve.greatestRealRoot( hasRealRoot ); + VERIFY( hasRealRoot == (real_roots.size() > 0 ) ); + if( hasRealRoot ){ + VERIFY( internal::isApprox( real_roots.array().maxCoeff(), r, psPrec ) ); } + + //Test smallestRealRoot + r = psolve.smallestRealRoot( hasRealRoot ); + VERIFY( hasRealRoot == (real_roots.size() > 0 ) ); + if( hasRealRoot ){ + VERIFY( internal::isApprox( real_roots.array().minCoeff(), r, psPrec ) ); } + } +} + + +template<typename _Scalar, int _Deg> +void polynomialsolver(int deg) +{ + typedef internal::increment_if_fixed_size<_Deg> Dim; + typedef Matrix<_Scalar,Dim::ret,1> PolynomialType; + typedef Matrix<_Scalar,_Deg,1> EvalRootsType; + + cout << "Standard cases" << endl; + PolynomialType pols = PolynomialType::Random(deg+1); + evalSolver<_Deg,PolynomialType>( pols ); + + cout << "Hard cases" << endl; + _Scalar multipleRoot = internal::random<_Scalar>(); + EvalRootsType allRoots = EvalRootsType::Constant(deg,multipleRoot); + roots_to_monicPolynomial( allRoots, pols ); + evalSolver<_Deg,PolynomialType>( pols ); + + cout << "Test sugar" << endl; + EvalRootsType realRoots = EvalRootsType::Random(deg); + roots_to_monicPolynomial( realRoots, pols ); + evalSolverSugarFunction<_Deg>( + pols, + realRoots.template cast < + std::complex< + typename NumTraits<_Scalar>::Real + > + >(), + realRoots ); +} + +void test_polynomialsolver() +{ + for(int i = 0; i < g_repeat; i++) + { + CALL_SUBTEST_1( (polynomialsolver<float,1>(1)) ); + CALL_SUBTEST_2( (polynomialsolver<double,2>(2)) ); + CALL_SUBTEST_3( (polynomialsolver<double,3>(3)) ); + CALL_SUBTEST_4( (polynomialsolver<float,4>(4)) ); + CALL_SUBTEST_5( (polynomialsolver<double,5>(5)) ); + CALL_SUBTEST_6( (polynomialsolver<float,6>(6)) ); + CALL_SUBTEST_7( (polynomialsolver<float,7>(7)) ); + CALL_SUBTEST_8( (polynomialsolver<double,8>(8)) ); + + CALL_SUBTEST_9( (polynomialsolver<float,Dynamic>( + internal::random<int>(9,13) + )) ); + CALL_SUBTEST_10((polynomialsolver<double,Dynamic>( + internal::random<int>(9,13) + )) ); + } +} diff --git a/unsupported/test/polynomialutils.cpp b/unsupported/test/polynomialutils.cpp new file mode 100644 index 000000000..5fc968402 --- /dev/null +++ b/unsupported/test/polynomialutils.cpp @@ -0,0 +1,113 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include <unsupported/Eigen/Polynomials> +#include <iostream> + +using namespace std; + +namespace Eigen { +namespace internal { +template<int Size> +struct increment_if_fixed_size +{ + enum { + ret = (Size == Dynamic) ? Dynamic : Size+1 + }; +}; +} +} + +template<typename _Scalar, int _Deg> +void realRoots_to_monicPolynomial_test(int deg) +{ + typedef internal::increment_if_fixed_size<_Deg> Dim; + typedef Matrix<_Scalar,Dim::ret,1> PolynomialType; + typedef Matrix<_Scalar,_Deg,1> EvalRootsType; + + PolynomialType pols(deg+1); + EvalRootsType roots = EvalRootsType::Random(deg); + roots_to_monicPolynomial( roots, pols ); + + EvalRootsType evr( deg ); + for( int i=0; i<roots.size(); ++i ){ + evr[i] = std::abs( poly_eval( pols, roots[i] ) ); } + + bool evalToZero = evr.isZero( test_precision<_Scalar>() ); + if( !evalToZero ){ + cerr << evr.transpose() << endl; } + VERIFY( evalToZero ); +} + +template<typename _Scalar> void realRoots_to_monicPolynomial_scalar() +{ + CALL_SUBTEST_2( (realRoots_to_monicPolynomial_test<_Scalar,2>(2)) ); + CALL_SUBTEST_3( (realRoots_to_monicPolynomial_test<_Scalar,3>(3)) ); + CALL_SUBTEST_4( (realRoots_to_monicPolynomial_test<_Scalar,4>(4)) ); + CALL_SUBTEST_5( (realRoots_to_monicPolynomial_test<_Scalar,5>(5)) ); + CALL_SUBTEST_6( (realRoots_to_monicPolynomial_test<_Scalar,6>(6)) ); + CALL_SUBTEST_7( (realRoots_to_monicPolynomial_test<_Scalar,7>(7)) ); + CALL_SUBTEST_8( (realRoots_to_monicPolynomial_test<_Scalar,17>(17)) ); + + CALL_SUBTEST_9( (realRoots_to_monicPolynomial_test<_Scalar,Dynamic>( + internal::random<int>(18,26) )) ); +} + + + + +template<typename _Scalar, int _Deg> +void CauchyBounds(int deg) +{ + typedef internal::increment_if_fixed_size<_Deg> Dim; + typedef Matrix<_Scalar,Dim::ret,1> PolynomialType; + typedef Matrix<_Scalar,_Deg,1> EvalRootsType; + + PolynomialType pols(deg+1); + EvalRootsType roots = EvalRootsType::Random(deg); + roots_to_monicPolynomial( roots, pols ); + _Scalar M = cauchy_max_bound( pols ); + _Scalar m = cauchy_min_bound( pols ); + _Scalar Max = roots.array().abs().maxCoeff(); + _Scalar min = roots.array().abs().minCoeff(); + bool eval = (M >= Max) && (m <= min); + if( !eval ) + { + cerr << "Roots: " << roots << endl; + cerr << "Bounds: (" << m << ", " << M << ")" << endl; + cerr << "Min,Max: (" << min << ", " << Max << ")" << endl; + } + VERIFY( eval ); +} + +template<typename _Scalar> void CauchyBounds_scalar() +{ + CALL_SUBTEST_2( (CauchyBounds<_Scalar,2>(2)) ); + CALL_SUBTEST_3( (CauchyBounds<_Scalar,3>(3)) ); + CALL_SUBTEST_4( (CauchyBounds<_Scalar,4>(4)) ); + CALL_SUBTEST_5( (CauchyBounds<_Scalar,5>(5)) ); + CALL_SUBTEST_6( (CauchyBounds<_Scalar,6>(6)) ); + CALL_SUBTEST_7( (CauchyBounds<_Scalar,7>(7)) ); + CALL_SUBTEST_8( (CauchyBounds<_Scalar,17>(17)) ); + + CALL_SUBTEST_9( (CauchyBounds<_Scalar,Dynamic>( + internal::random<int>(18,26) )) ); +} + +void test_polynomialutils() +{ + for(int i = 0; i < g_repeat; i++) + { + realRoots_to_monicPolynomial_scalar<double>(); + realRoots_to_monicPolynomial_scalar<float>(); + CauchyBounds_scalar<double>(); + CauchyBounds_scalar<float>(); + } +} diff --git a/unsupported/test/sparse_extra.cpp b/unsupported/test/sparse_extra.cpp new file mode 100644 index 000000000..5dc333424 --- /dev/null +++ b/unsupported/test/sparse_extra.cpp @@ -0,0 +1,149 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2010 Gael Guennebaud <g.gael@free.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + + +// import basic and product tests for deprectaed DynamicSparseMatrix +#define EIGEN_NO_DEPRECATED_WARNING +#include "sparse_basic.cpp" +#include "sparse_product.cpp" +#include <Eigen/SparseExtra> + +template<typename SetterType,typename DenseType, typename Scalar, int Options> +bool test_random_setter(SparseMatrix<Scalar,Options>& sm, const DenseType& ref, const std::vector<Vector2i>& nonzeroCoords) +{ + typedef SparseMatrix<Scalar,Options> SparseType; + { + sm.setZero(); + SetterType w(sm); + std::vector<Vector2i> remaining = nonzeroCoords; + while(!remaining.empty()) + { + int i = internal::random<int>(0,static_cast<int>(remaining.size())-1); + w(remaining[i].x(),remaining[i].y()) = ref.coeff(remaining[i].x(),remaining[i].y()); + remaining[i] = remaining.back(); + remaining.pop_back(); + } + } + return sm.isApprox(ref); +} + +template<typename SetterType,typename DenseType, typename T> +bool test_random_setter(DynamicSparseMatrix<T>& sm, const DenseType& ref, const std::vector<Vector2i>& nonzeroCoords) +{ + sm.setZero(); + std::vector<Vector2i> remaining = nonzeroCoords; + while(!remaining.empty()) + { + int i = internal::random<int>(0,static_cast<int>(remaining.size())-1); + sm.coeffRef(remaining[i].x(),remaining[i].y()) = ref.coeff(remaining[i].x(),remaining[i].y()); + remaining[i] = remaining.back(); + remaining.pop_back(); + } + return sm.isApprox(ref); +} + +template<typename SparseMatrixType> void sparse_extra(const SparseMatrixType& ref) +{ + typedef typename SparseMatrixType::Index Index; + const Index rows = ref.rows(); + const Index cols = ref.cols(); + typedef typename SparseMatrixType::Scalar Scalar; + enum { Flags = SparseMatrixType::Flags }; + + double density = (std::max)(8./(rows*cols), 0.01); + typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; + typedef Matrix<Scalar,Dynamic,1> DenseVector; + Scalar eps = 1e-6; + + SparseMatrixType m(rows, cols); + DenseMatrix refMat = DenseMatrix::Zero(rows, cols); + DenseVector vec1 = DenseVector::Random(rows); + + std::vector<Vector2i> zeroCoords; + std::vector<Vector2i> nonzeroCoords; + initSparse<Scalar>(density, refMat, m, 0, &zeroCoords, &nonzeroCoords); + + if (zeroCoords.size()==0 || nonzeroCoords.size()==0) + return; + + // test coeff and coeffRef + for (int i=0; i<(int)zeroCoords.size(); ++i) + { + VERIFY_IS_MUCH_SMALLER_THAN( m.coeff(zeroCoords[i].x(),zeroCoords[i].y()), eps ); + if(internal::is_same<SparseMatrixType,SparseMatrix<Scalar,Flags> >::value) + VERIFY_RAISES_ASSERT( m.coeffRef(zeroCoords[0].x(),zeroCoords[0].y()) = 5 ); + } + VERIFY_IS_APPROX(m, refMat); + + m.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5); + refMat.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5); + + VERIFY_IS_APPROX(m, refMat); + + // random setter +// { +// m.setZero(); +// VERIFY_IS_NOT_APPROX(m, refMat); +// SparseSetter<SparseMatrixType, RandomAccessPattern> w(m); +// std::vector<Vector2i> remaining = nonzeroCoords; +// while(!remaining.empty()) +// { +// int i = internal::random<int>(0,remaining.size()-1); +// w->coeffRef(remaining[i].x(),remaining[i].y()) = refMat.coeff(remaining[i].x(),remaining[i].y()); +// remaining[i] = remaining.back(); +// remaining.pop_back(); +// } +// } +// VERIFY_IS_APPROX(m, refMat); + + VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, StdMapTraits> >(m,refMat,nonzeroCoords) )); + #ifdef EIGEN_UNORDERED_MAP_SUPPORT + VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, StdUnorderedMapTraits> >(m,refMat,nonzeroCoords) )); + #endif + #ifdef _DENSE_HASH_MAP_H_ + VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, GoogleDenseHashMapTraits> >(m,refMat,nonzeroCoords) )); + #endif + #ifdef _SPARSE_HASH_MAP_H_ + VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, GoogleSparseHashMapTraits> >(m,refMat,nonzeroCoords) )); + #endif + + + // test RandomSetter + /*{ + SparseMatrixType m1(rows,cols), m2(rows,cols); + DenseMatrix refM1 = DenseMatrix::Zero(rows, rows); + initSparse<Scalar>(density, refM1, m1); + { + Eigen::RandomSetter<SparseMatrixType > setter(m2); + for (int j=0; j<m1.outerSize(); ++j) + for (typename SparseMatrixType::InnerIterator i(m1,j); i; ++i) + setter(i.index(), j) = i.value(); + } + VERIFY_IS_APPROX(m1, m2); + }*/ + + +} + +void test_sparse_extra() +{ + for(int i = 0; i < g_repeat; i++) { + int s = Eigen::internal::random<int>(1,50); + CALL_SUBTEST_1( sparse_extra(SparseMatrix<double>(8, 8)) ); + CALL_SUBTEST_2( sparse_extra(SparseMatrix<std::complex<double> >(s, s)) ); + CALL_SUBTEST_1( sparse_extra(SparseMatrix<double>(s, s)) ); + + CALL_SUBTEST_3( sparse_extra(DynamicSparseMatrix<double>(s, s)) ); +// CALL_SUBTEST_3(( sparse_basic(DynamicSparseMatrix<double>(s, s)) )); +// CALL_SUBTEST_3(( sparse_basic(DynamicSparseMatrix<double,ColMajor,long int>(s, s)) )); + + CALL_SUBTEST_3( (sparse_product<DynamicSparseMatrix<float, ColMajor> >()) ); + CALL_SUBTEST_3( (sparse_product<DynamicSparseMatrix<float, RowMajor> >()) ); + } +} diff --git a/unsupported/test/splines.cpp b/unsupported/test/splines.cpp new file mode 100644 index 000000000..1043453dc --- /dev/null +++ b/unsupported/test/splines.cpp @@ -0,0 +1,240 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010-2011 Hauke Heibel <heibel@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +#include <unsupported/Eigen/Splines> + +// lets do some explicit instantiations and thus +// force the compilation of all spline functions... +template class Spline<double, 2, Dynamic>; +template class Spline<double, 3, Dynamic>; + +template class Spline<double, 2, 2>; +template class Spline<double, 2, 3>; +template class Spline<double, 2, 4>; +template class Spline<double, 2, 5>; + +template class Spline<float, 2, Dynamic>; +template class Spline<float, 3, Dynamic>; + +template class Spline<float, 3, 2>; +template class Spline<float, 3, 3>; +template class Spline<float, 3, 4>; +template class Spline<float, 3, 5>; + +Spline<double, 2, Dynamic> closed_spline2d() +{ + RowVectorXd knots(12); + knots << 0, + 0, + 0, + 0, + 0.867193179093898, + 1.660330955342408, + 2.605084834823134, + 3.484154586374428, + 4.252699478956276, + 4.252699478956276, + 4.252699478956276, + 4.252699478956276; + + MatrixXd ctrls(8,2); + ctrls << -0.370967741935484, 0.236842105263158, + -0.231401860693277, 0.442245185027632, + 0.344361228532831, 0.773369994120753, + 0.828990216203802, 0.106550882647595, + 0.407270163678382, -1.043452922172848, + -0.488467813584053, -0.390098582530090, + -0.494657189446427, 0.054804824897884, + -0.370967741935484, 0.236842105263158; + ctrls.transposeInPlace(); + + return Spline<double, 2, Dynamic>(knots, ctrls); +} + +/* create a reference spline */ +Spline<double, 3, Dynamic> spline3d() +{ + RowVectorXd knots(11); + knots << 0, + 0, + 0, + 0.118997681558377, + 0.162611735194631, + 0.498364051982143, + 0.655098003973841, + 0.679702676853675, + 1.000000000000000, + 1.000000000000000, + 1.000000000000000; + + MatrixXd ctrls(8,3); + ctrls << 0.959743958516081, 0.340385726666133, 0.585267750979777, + 0.223811939491137, 0.751267059305653, 0.255095115459269, + 0.505957051665142, 0.699076722656686, 0.890903252535799, + 0.959291425205444, 0.547215529963803, 0.138624442828679, + 0.149294005559057, 0.257508254123736, 0.840717255983663, + 0.254282178971531, 0.814284826068816, 0.243524968724989, + 0.929263623187228, 0.349983765984809, 0.196595250431208, + 0.251083857976031, 0.616044676146639, 0.473288848902729; + ctrls.transposeInPlace(); + + return Spline<double, 3, Dynamic>(knots, ctrls); +} + +/* compares evaluations against known results */ +void eval_spline3d() +{ + Spline3d spline = spline3d(); + + RowVectorXd u(10); + u << 0.351659507062997, + 0.830828627896291, + 0.585264091152724, + 0.549723608291140, + 0.917193663829810, + 0.285839018820374, + 0.757200229110721, + 0.753729094278495, + 0.380445846975357, + 0.567821640725221; + + MatrixXd pts(10,3); + pts << 0.707620811535916, 0.510258911240815, 0.417485437023409, + 0.603422256426978, 0.529498282727551, 0.270351549348981, + 0.228364197569334, 0.423745615677815, 0.637687289287490, + 0.275556796335168, 0.350856706427970, 0.684295784598905, + 0.514519311047655, 0.525077224890754, 0.351628308305896, + 0.724152914315666, 0.574461155457304, 0.469860285484058, + 0.529365063753288, 0.613328702656816, 0.237837040141739, + 0.522469395136878, 0.619099658652895, 0.237139665242069, + 0.677357023849552, 0.480655768435853, 0.422227610314397, + 0.247046593173758, 0.380604672404750, 0.670065791405019; + pts.transposeInPlace(); + + for (int i=0; i<u.size(); ++i) + { + Vector3d pt = spline(u(i)); + VERIFY( (pt - pts.col(i)).norm() < 1e-14 ); + } +} + +/* compares evaluations on corner cases */ +void eval_spline3d_onbrks() +{ + Spline3d spline = spline3d(); + + RowVectorXd u = spline.knots(); + + MatrixXd pts(11,3); + pts << 0.959743958516081, 0.340385726666133, 0.585267750979777, + 0.959743958516081, 0.340385726666133, 0.585267750979777, + 0.959743958516081, 0.340385726666133, 0.585267750979777, + 0.430282980289940, 0.713074680056118, 0.720373307943349, + 0.558074875553060, 0.681617921034459, 0.804417124839942, + 0.407076008291750, 0.349707710518163, 0.617275937419545, + 0.240037008286602, 0.738739390398014, 0.324554153129411, + 0.302434111480572, 0.781162443963899, 0.240177089094644, + 0.251083857976031, 0.616044676146639, 0.473288848902729, + 0.251083857976031, 0.616044676146639, 0.473288848902729, + 0.251083857976031, 0.616044676146639, 0.473288848902729; + pts.transposeInPlace(); + + for (int i=0; i<u.size(); ++i) + { + Vector3d pt = spline(u(i)); + VERIFY( (pt - pts.col(i)).norm() < 1e-14 ); + } +} + +void eval_closed_spline2d() +{ + Spline2d spline = closed_spline2d(); + + RowVectorXd u(12); + u << 0, + 0.332457030395796, + 0.356467130532952, + 0.453562180176215, + 0.648017921874804, + 0.973770235555003, + 1.882577647219307, + 2.289408593930498, + 3.511951429883045, + 3.884149321369450, + 4.236261590369414, + 4.252699478956276; + + MatrixXd pts(12,2); + pts << -0.370967741935484, 0.236842105263158, + -0.152576775123250, 0.448975001279334, + -0.133417538277668, 0.461615613865667, + -0.053199060826740, 0.507630360006299, + 0.114249591147281, 0.570414135097409, + 0.377810316891987, 0.560497102875315, + 0.665052120135908, -0.157557441109611, + 0.516006487053228, -0.559763292174825, + -0.379486035348887, -0.331959640488223, + -0.462034726249078, -0.039105670080824, + -0.378730600917982, 0.225127015099919, + -0.370967741935484, 0.236842105263158; + pts.transposeInPlace(); + + for (int i=0; i<u.size(); ++i) + { + Vector2d pt = spline(u(i)); + VERIFY( (pt - pts.col(i)).norm() < 1e-14 ); + } +} + +void check_global_interpolation2d() +{ + typedef Spline2d::PointType PointType; + typedef Spline2d::KnotVectorType KnotVectorType; + typedef Spline2d::ControlPointVectorType ControlPointVectorType; + + ControlPointVectorType points = ControlPointVectorType::Random(2,100); + + KnotVectorType chord_lengths; // knot parameters + Eigen::ChordLengths(points, chord_lengths); + + // interpolation without knot parameters + { + const Spline2d spline = SplineFitting<Spline2d>::Interpolate(points,3); + + for (Eigen::DenseIndex i=0; i<points.cols(); ++i) + { + PointType pt = spline( chord_lengths(i) ); + PointType ref = points.col(i); + VERIFY( (pt - ref).matrix().norm() < 1e-14 ); + } + } + + // interpolation with given knot parameters + { + const Spline2d spline = SplineFitting<Spline2d>::Interpolate(points,3,chord_lengths); + + for (Eigen::DenseIndex i=0; i<points.cols(); ++i) + { + PointType pt = spline( chord_lengths(i) ); + PointType ref = points.col(i); + VERIFY( (pt - ref).matrix().norm() < 1e-14 ); + } + } +} + + +void test_splines() +{ + CALL_SUBTEST( eval_spline3d() ); + CALL_SUBTEST( eval_spline3d_onbrks() ); + CALL_SUBTEST( eval_closed_spline2d() ); + CALL_SUBTEST( check_global_interpolation2d() ); +} |