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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// 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_HOUSEHOLDER_H
#define EIGEN_HOUSEHOLDER_H
namespace Eigen {
namespace internal {
template<int n> struct decrement_size
{
enum {
ret = n==Dynamic ? n : n-1
};
};
}
/** Computes the elementary reflector H such that:
* \f$ H *this = [ beta 0 ... 0]^T \f$
* where the transformation H is:
* \f$ H = I - tau v v^*\f$
* and the vector v is:
* \f$ v^T = [1 essential^T] \f$
*
* The essential part of the vector \c v is stored in *this.
*
* On output:
* \param tau the scaling factor of the Householder transformation
* \param beta the result of H * \c *this
*
* \sa MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(),
* MatrixBase::applyHouseholderOnTheRight()
*/
template<typename Derived>
void MatrixBase<Derived>::makeHouseholderInPlace(Scalar& tau, RealScalar& beta)
{
VectorBlock<Derived, internal::decrement_size<Base::SizeAtCompileTime>::ret> essentialPart(derived(), 1, size()-1);
makeHouseholder(essentialPart, tau, beta);
}
/** Computes the elementary reflector H such that:
* \f$ H *this = [ beta 0 ... 0]^T \f$
* where the transformation H is:
* \f$ H = I - tau v v^*\f$
* and the vector v is:
* \f$ v^T = [1 essential^T] \f$
*
* On output:
* \param essential the essential part of the vector \c v
* \param tau the scaling factor of the Householder transformation
* \param beta the result of H * \c *this
*
* \sa MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(),
* MatrixBase::applyHouseholderOnTheRight()
*/
template<typename Derived>
template<typename EssentialPart>
void MatrixBase<Derived>::makeHouseholder(
EssentialPart& essential,
Scalar& tau,
RealScalar& beta) const
{
using std::sqrt;
using numext::conj;
EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);
RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm();
Scalar c0 = coeff(0);
const RealScalar tol = (std::numeric_limits<RealScalar>::min)();
if(tailSqNorm <= tol && numext::abs2(numext::imag(c0))<=tol)
{
tau = RealScalar(0);
beta = numext::real(c0);
essential.setZero();
}
else
{
beta = sqrt(numext::abs2(c0) + tailSqNorm);
if (numext::real(c0)>=RealScalar(0))
beta = -beta;
essential = tail / (c0 - beta);
tau = conj((beta - c0) / beta);
}
}
/** Apply the elementary reflector H given by
* \f$ H = I - tau v v^*\f$
* with
* \f$ v^T = [1 essential^T] \f$
* from the left to a vector or matrix.
*
* On input:
* \param essential the essential part of the vector \c v
* \param tau the scaling factor of the Householder transformation
* \param workspace a pointer to working space with at least
* this->cols() * essential.size() entries
*
* \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(),
* MatrixBase::applyHouseholderOnTheRight()
*/
template<typename Derived>
template<typename EssentialPart>
void MatrixBase<Derived>::applyHouseholderOnTheLeft(
const EssentialPart& essential,
const Scalar& tau,
Scalar* workspace)
{
if(rows() == 1)
{
*this *= Scalar(1)-tau;
}
else if(tau!=Scalar(0))
{
Map<typename internal::plain_row_type<PlainObject>::type> tmp(workspace,cols());
Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows()-1, cols());
tmp.noalias() = essential.adjoint() * bottom;
tmp += this->row(0);
this->row(0) -= tau * tmp;
bottom.noalias() -= tau * essential * tmp;
}
}
/** Apply the elementary reflector H given by
* \f$ H = I - tau v v^*\f$
* with
* \f$ v^T = [1 essential^T] \f$
* from the right to a vector or matrix.
*
* On input:
* \param essential the essential part of the vector \c v
* \param tau the scaling factor of the Householder transformation
* \param workspace a pointer to working space with at least
* this->cols() * essential.size() entries
*
* \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(),
* MatrixBase::applyHouseholderOnTheLeft()
*/
template<typename Derived>
template<typename EssentialPart>
void MatrixBase<Derived>::applyHouseholderOnTheRight(
const EssentialPart& essential,
const Scalar& tau,
Scalar* workspace)
{
if(cols() == 1)
{
*this *= Scalar(1)-tau;
}
else if(tau!=Scalar(0))
{
Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace,rows());
Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1);
tmp.noalias() = right * essential.conjugate();
tmp += this->col(0);
this->col(0) -= tau * tmp;
right.noalias() -= tau * tmp * essential.transpose();
}
}
} // end namespace Eigen
#endif // EIGEN_HOUSEHOLDER_H
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