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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_JACOBISQUARESVD_H
#define EIGEN_JACOBISQUARESVD_H
/** \ingroup SVD_Module
* \nonstableyet
*
* \class JacobiSquareSVD
*
* \brief Jacobi SVD decomposition of a square matrix
*
* \param MatrixType the type of the matrix of which we are computing the SVD decomposition
* \param ComputeU whether the U matrix should be computed
* \param ComputeV whether the V matrix should be computed
*
* \sa MatrixBase::jacobiSvd()
*/
template<typename MatrixType, bool ComputeU, bool ComputeV> class JacobiSquareSVD
{
private:
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
enum {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
Options = MatrixType::Options
};
typedef Matrix<Scalar, Dynamic, Dynamic, Options> DummyMatrixType;
typedef typename ei_meta_if<ComputeU,
Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
Options, MaxRowsAtCompileTime, MaxRowsAtCompileTime>,
DummyMatrixType>::ret MatrixUType;
typedef typename Diagonal<MatrixType,0>::PlainMatrixType SingularValuesType;
typedef Matrix<Scalar, 1, RowsAtCompileTime, Options, 1, MaxRowsAtCompileTime> RowType;
typedef Matrix<Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1> ColType;
public:
JacobiSquareSVD() : m_isInitialized(false) {}
JacobiSquareSVD(const MatrixType& matrix) : m_isInitialized(false)
{
compute(matrix);
}
void compute(const MatrixType& matrix);
const MatrixUType& matrixU() const
{
ei_assert(m_isInitialized && "SVD is not initialized.");
return m_matrixU;
}
const SingularValuesType& singularValues() const
{
ei_assert(m_isInitialized && "SVD is not initialized.");
return m_singularValues;
}
const MatrixUType& matrixV() const
{
ei_assert(m_isInitialized && "SVD is not initialized.");
return m_matrixV;
}
protected:
MatrixUType m_matrixU;
MatrixUType m_matrixV;
SingularValuesType m_singularValues;
bool m_isInitialized;
};
template<typename MatrixType, bool ComputeU, bool ComputeV>
void JacobiSquareSVD<MatrixType, ComputeU, ComputeV>::compute(const MatrixType& matrix)
{
MatrixType work_matrix(matrix);
int size = matrix.rows();
if(ComputeU) m_matrixU = MatrixUType::Identity(size,size);
if(ComputeV) m_matrixV = MatrixUType::Identity(size,size);
m_singularValues.resize(size);
sweep_again:
for(int p = 1; p < size; ++p)
{
for(int q = 0; q < p; ++q)
{
Scalar c, s;
while(std::max(ei_abs(work_matrix.coeff(p,q)),ei_abs(work_matrix.coeff(q,p)))
> std::max(ei_abs(work_matrix.coeff(p,p)),ei_abs(work_matrix.coeff(q,q)))*machine_epsilon<Scalar>())
{
if(work_matrix.makeJacobiForAtA(p,q,&c,&s))
{
work_matrix.applyJacobiOnTheRight(p,q,c,s);
if(ComputeV) m_matrixV.applyJacobiOnTheRight(p,q,c,s);
}
if(work_matrix.makeJacobiForAAt(p,q,&c,&s))
{
Scalar x = ei_abs2(work_matrix.coeff(p,p)) + ei_abs2(work_matrix.coeff(p,q));
Scalar y = ei_conj(work_matrix.coeff(q,p))*work_matrix.coeff(p,p) + ei_conj(work_matrix.coeff(q,q))*work_matrix.coeff(p,q);
Scalar z = ei_abs2(work_matrix.coeff(q,p)) + ei_abs2(work_matrix.coeff(q,q));
work_matrix.applyJacobiOnTheLeft(p,q,c,s);
if(ComputeU) m_matrixU.applyJacobiOnTheRight(p,q,c,s);
if(std::max(ei_abs(work_matrix.coeff(p,q)),ei_abs(work_matrix.coeff(q,p)))
> std::max(ei_abs(work_matrix.coeff(p,p)),ei_abs(work_matrix.coeff(q,q))) )
{
work_matrix.row(p).swap(work_matrix.row(q));
if(ComputeU) m_matrixU.col(p).swap(m_matrixU.col(q));
}
}
}
}
}
RealScalar biggestOnDiag = work_matrix.diagonal().cwise().abs().maxCoeff();
RealScalar maxAllowedOffDiag = biggestOnDiag * machine_epsilon<Scalar>();
for(int p = 0; p < size; ++p)
{
for(int q = 0; q < p; ++q)
if(ei_abs(work_matrix.coeff(p,q)) > maxAllowedOffDiag)
goto sweep_again;
for(int q = p+1; q < size; ++q)
if(ei_abs(work_matrix.coeff(p,q)) > maxAllowedOffDiag)
goto sweep_again;
}
m_singularValues = work_matrix.diagonal().cwise().abs();
RealScalar biggestSingularValue = m_singularValues.maxCoeff();
for(int i = 0; i < size; ++i)
{
RealScalar a = ei_abs(work_matrix.coeff(i,i));
m_singularValues.coeffRef(i) = a;
if(ComputeU && !ei_isMuchSmallerThan(a, biggestSingularValue)) m_matrixU.col(i) *= work_matrix.coeff(i,i)/a;
}
for(int i = 0; i < size; i++)
{
int pos;
m_singularValues.end(size-i).maxCoeff(&pos);
if(pos)
{
pos += i;
std::swap(m_singularValues.coeffRef(i), m_singularValues.coeffRef(pos));
if(ComputeU) m_matrixU.col(pos).swap(m_matrixU.col(i));
if(ComputeV) m_matrixV.col(pos).swap(m_matrixV.col(i));
}
}
m_isInitialized = true;
}
#endif // EIGEN_JACOBISQUARESVD_H
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