// 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/.
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>
EIGEN_DEVICE_FUNC 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>
EIGEN_DEVICE_FUNC void MatrixBase<Derived>::makeHouseholder(
EssentialPart& essential,
Scalar& tau,
RealScalar& beta) const
{ using std::sqrt; using numext::conj;
/** 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() entries * * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), * MatrixBase::applyHouseholderOnTheRight()
*/ template<typename Derived> template<typename EssentialPart>
EIGEN_DEVICE_FUNC void MatrixBase<Derived>::applyHouseholderOnTheLeft( const EssentialPart& essential, const Scalar& tau,
Scalar* workspace)
{ if(rows() == 1)
{
*this *= Scalar(1)-tau;
} elseif(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->rows() entries * * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), * MatrixBase::applyHouseholderOnTheLeft()
*/ template<typename Derived> template<typename EssentialPart>
EIGEN_DEVICE_FUNC void MatrixBase<Derived>::applyHouseholderOnTheRight( const EssentialPart& essential, const Scalar& tau,
Scalar* workspace)
{ if(cols() == 1)
{
*this *= Scalar(1)-tau;
} elseif(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;
tmp += this->col(0);
this->col(0) -= tau * tmp;
right.noalias() -= tau * tmp * essential.adjoint();
}
}
} // end namespace Eigen
#endif// EIGEN_HOUSEHOLDER_H
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