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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011-2014 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_BASIC_PRECONDITIONERS_H
#define EIGEN_BASIC_PRECONDITIONERS_H
namespace Eigen {
/** \ingroup IterativeLinearSolvers_Module
* \brief A preconditioner based on the digonal entries
*
* This class allows to approximately solve for A.x = b problems assuming A is a diagonal matrix.
* In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:
\code
A.diagonal().asDiagonal() . x = b
\endcode
*
* \tparam _Scalar the type of the scalar.
*
* \implsparsesolverconcept
*
* This preconditioner is suitable for both selfadjoint and general problems.
* The diagonal entries are pre-inverted and stored into a dense vector.
*
* \note A variant that has yet to be implemented would attempt to preserve the norm of each column.
*
* \sa class LeastSquareDiagonalPreconditioner, class ConjugateGradient
*/
template <typename _Scalar>
class DiagonalPreconditioner
{
typedef _Scalar Scalar;
typedef Matrix<Scalar,Dynamic,1> Vector;
public:
typedef typename Vector::StorageIndex StorageIndex;
enum {
ColsAtCompileTime = Dynamic,
MaxColsAtCompileTime = Dynamic
};
DiagonalPreconditioner() : m_isInitialized(false) {}
template<typename MatType>
explicit DiagonalPreconditioner(const MatType& mat) : m_invdiag(mat.cols())
{
compute(mat);
}
Index rows() const { return m_invdiag.size(); }
Index cols() const { return m_invdiag.size(); }
template<typename MatType>
DiagonalPreconditioner& analyzePattern(const MatType& )
{
return *this;
}
template<typename MatType>
DiagonalPreconditioner& factorize(const MatType& mat)
{
m_invdiag.resize(mat.cols());
for(int j=0; j<mat.outerSize(); ++j)
{
typename MatType::InnerIterator it(mat,j);
while(it && it.index()!=j) ++it;
if(it && it.index()==j && it.value()!=Scalar(0))
m_invdiag(j) = Scalar(1)/it.value();
else
m_invdiag(j) = Scalar(1);
}
m_isInitialized = true;
return *this;
}
template<typename MatType>
DiagonalPreconditioner& compute(const MatType& mat)
{
return factorize(mat);
}
/** \internal */
template<typename Rhs, typename Dest>
void _solve_impl(const Rhs& b, Dest& x) const
{
x = m_invdiag.array() * b.array() ;
}
template<typename Rhs> inline const Solve<DiagonalPreconditioner, Rhs>
solve(const MatrixBase<Rhs>& b) const
{
eigen_assert(m_isInitialized && "DiagonalPreconditioner is not initialized.");
eigen_assert(m_invdiag.size()==b.rows()
&& "DiagonalPreconditioner::solve(): invalid number of rows of the right hand side matrix b");
return Solve<DiagonalPreconditioner, Rhs>(*this, b.derived());
}
ComputationInfo info() { return Success; }
protected:
Vector m_invdiag;
bool m_isInitialized;
};
/** \ingroup IterativeLinearSolvers_Module
* \brief Jacobi preconditioner for LeastSquaresConjugateGradient
*
* This class allows to approximately solve for A' A x = A' b problems assuming A' A is a diagonal matrix.
* In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:
\code
(A.adjoint() * A).diagonal().asDiagonal() * x = b
\endcode
*
* \tparam _Scalar the type of the scalar.
*
* \implsparsesolverconcept
*
* The diagonal entries are pre-inverted and stored into a dense vector.
*
* \sa class LeastSquaresConjugateGradient, class DiagonalPreconditioner
*/
template <typename _Scalar>
class LeastSquareDiagonalPreconditioner : public DiagonalPreconditioner<_Scalar>
{
typedef _Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef DiagonalPreconditioner<_Scalar> Base;
using Base::m_invdiag;
public:
LeastSquareDiagonalPreconditioner() : Base() {}
template<typename MatType>
explicit LeastSquareDiagonalPreconditioner(const MatType& mat) : Base()
{
compute(mat);
}
template<typename MatType>
LeastSquareDiagonalPreconditioner& analyzePattern(const MatType& )
{
return *this;
}
template<typename MatType>
LeastSquareDiagonalPreconditioner& factorize(const MatType& mat)
{
// Compute the inverse squared-norm of each column of mat
m_invdiag.resize(mat.cols());
for(Index j=0; j<mat.outerSize(); ++j)
{
RealScalar sum = mat.innerVector(j).squaredNorm();
if(sum>0)
m_invdiag(j) = RealScalar(1)/sum;
else
m_invdiag(j) = RealScalar(1);
}
Base::m_isInitialized = true;
return *this;
}
template<typename MatType>
LeastSquareDiagonalPreconditioner& compute(const MatType& mat)
{
return factorize(mat);
}
ComputationInfo info() { return Success; }
protected:
};
/** \ingroup IterativeLinearSolvers_Module
* \brief A naive preconditioner which approximates any matrix as the identity matrix
*
* \implsparsesolverconcept
*
* \sa class DiagonalPreconditioner
*/
class IdentityPreconditioner
{
public:
IdentityPreconditioner() {}
template<typename MatrixType>
explicit IdentityPreconditioner(const MatrixType& ) {}
template<typename MatrixType>
IdentityPreconditioner& analyzePattern(const MatrixType& ) { return *this; }
template<typename MatrixType>
IdentityPreconditioner& factorize(const MatrixType& ) { return *this; }
template<typename MatrixType>
IdentityPreconditioner& compute(const MatrixType& ) { return *this; }
template<typename Rhs>
inline const Rhs& solve(const Rhs& b) const { return b; }
ComputationInfo info() { return Success; }
};
} // end namespace Eigen
#endif // EIGEN_BASIC_PRECONDITIONERS_H
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