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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>
//
// 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_BIDIAGONALIZATION_H
#define EIGEN_BIDIAGONALIZATION_H
template<typename _MatrixType> class UpperBidiagonalization
{
public:
typedef _MatrixType MatrixType;
enum {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
ColsAtCompileTimeMinusOne = ei_decrement_size<ColsAtCompileTime>::ret
};
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::Index Index;
typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;
typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;
typedef BandMatrix<RealScalar, ColsAtCompileTime, ColsAtCompileTime, 1, 0> BidiagonalType;
typedef Matrix<Scalar, ColsAtCompileTime, 1> DiagVectorType;
typedef Matrix<Scalar, ColsAtCompileTimeMinusOne, 1> SuperDiagVectorType;
typedef HouseholderSequence<
MatrixType,
CwiseUnaryOp<ei_scalar_conjugate_op<Scalar>, Diagonal<MatrixType,0> >
> HouseholderUSequenceType;
typedef HouseholderSequence<
MatrixType,
Diagonal<MatrixType,1>,
OnTheRight
> HouseholderVSequenceType;
/**
* \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via Bidiagonalization::compute(const MatrixType&).
*/
UpperBidiagonalization() : m_householder(), m_bidiagonal(), m_isInitialized(false) {}
UpperBidiagonalization(const MatrixType& matrix)
: m_householder(matrix.rows(), matrix.cols()),
m_bidiagonal(matrix.cols(), matrix.cols()),
m_isInitialized(false)
{
compute(matrix);
}
UpperBidiagonalization& compute(const MatrixType& matrix);
const MatrixType& householder() const { return m_householder; }
const BidiagonalType& bidiagonal() const { return m_bidiagonal; }
HouseholderUSequenceType householderU() const
{
ei_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
return HouseholderUSequenceType(m_householder, m_householder.diagonal().conjugate());
}
HouseholderVSequenceType householderV() // const here gives nasty errors and i'm lazy
{
ei_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
return HouseholderVSequenceType(m_householder, m_householder.template diagonal<1>(),
false, m_householder.cols()-1, 1);
}
protected:
MatrixType m_householder;
BidiagonalType m_bidiagonal;
bool m_isInitialized;
};
template<typename _MatrixType>
UpperBidiagonalization<_MatrixType>& UpperBidiagonalization<_MatrixType>::compute(const _MatrixType& matrix)
{
Index rows = matrix.rows();
Index cols = matrix.cols();
ei_assert(rows >= cols && "UpperBidiagonalization is only for matrices satisfying rows>=cols.");
m_householder = matrix;
ColVectorType temp(rows);
for (Index k = 0; /* breaks at k==cols-1 below */ ; ++k)
{
Index remainingRows = rows - k;
Index remainingCols = cols - k - 1;
// construct left householder transform in-place in m_householder
m_householder.col(k).tail(remainingRows)
.makeHouseholderInPlace(m_householder.coeffRef(k,k),
m_bidiagonal.template diagonal<0>().coeffRef(k));
// apply householder transform to remaining part of m_householder on the left
m_householder.bottomRightCorner(remainingRows, remainingCols)
.applyHouseholderOnTheLeft(m_householder.col(k).tail(remainingRows-1),
m_householder.coeff(k,k),
temp.data());
if(k == cols-1) break;
// construct right householder transform in-place in m_householder
m_householder.row(k).tail(remainingCols)
.makeHouseholderInPlace(m_householder.coeffRef(k,k+1),
m_bidiagonal.template diagonal<1>().coeffRef(k));
// apply householder transform to remaining part of m_householder on the left
m_householder.bottomRightCorner(remainingRows-1, remainingCols)
.applyHouseholderOnTheRight(m_householder.row(k).tail(remainingCols-1).transpose(),
m_householder.coeff(k,k+1),
temp.data());
}
m_isInitialized = true;
return *this;
}
#if 0
/** \return the Householder QR decomposition of \c *this.
*
* \sa class Bidiagonalization
*/
template<typename Derived>
const UpperBidiagonalization<typename MatrixBase<Derived>::PlainObject>
MatrixBase<Derived>::bidiagonalization() const
{
return UpperBidiagonalization<PlainObject>(eval());
}
#endif
#endif // EIGEN_BIDIAGONALIZATION_H
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