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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// Eigen 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 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen 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 or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_HOUSEHOLDER_H
#define EIGEN_HOUSEHOLDER_H
template<int n> struct ei_decrement_size
{
enum {
ret = (n==1 || n==Dynamic) ? n : n-1
};
};
template<typename EssentialPart>
void makeTrivialHouseholder(
EssentialPart *essential,
typename EssentialPart::RealScalar *beta)
{
*beta = typename EssentialPart::RealScalar(0);
essential->setZero();
}
template<typename Derived>
template<typename EssentialPart>
void MatrixBase<Derived>::makeHouseholder(
EssentialPart *essential,
RealScalar *beta) const
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
RealScalar _squaredNorm = squaredNorm();
Scalar c0;
if(ei_abs2(coeff(0)) <= ei_abs2(precision<Scalar>()) * _squaredNorm)
{
c0 = ei_sqrt(_squaredNorm);
}
else
{
Scalar sign = coeff(0) / ei_abs(coeff(0));
c0 = coeff(0) + sign * ei_sqrt(_squaredNorm);
}
VectorBlock<Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);
*essential = tail / c0;
const RealScalar c0abs2 = ei_abs2(c0);
*beta = RealScalar(2) * c0abs2 / (c0abs2 + _squaredNorm - ei_abs2(coeff(0)));
}
template<typename Derived>
template<typename EssentialPart>
void MatrixBase<Derived>::applyHouseholderOnTheLeft(
const EssentialPart& essential,
const RealScalar& beta)
{
Matrix<Scalar, 1, ColsAtCompileTime, PlainMatrixType::Options, 1, MaxColsAtCompileTime> tmp(cols());
Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows()-1, cols());
tmp = (essential.adjoint() * bottom).lazy();
tmp += row(0);
row(0) -= beta * tmp;
bottom -= beta * essential * tmp;
}
template<typename Derived>
template<typename EssentialPart>
void MatrixBase<Derived>::applyHouseholderOnTheRight(
const EssentialPart& essential,
const RealScalar& beta)
{
Matrix<Scalar, RowsAtCompileTime, 1, PlainMatrixType::Options, MaxRowsAtCompileTime, 1> tmp(rows());
Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1);
tmp = (right * essential.conjugate()).lazy();
tmp += col(0);
col(0) -= beta * tmp;
right -= beta * tmp * essential.transpose();
}
#endif // EIGEN_HOUSEHOLDER_H
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