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* JacobiSVD:
- support complex numbers - big rewrite of the 2x2 kernel, much more robust * Jacobi: - fix weirdness in initial design, e.g. applyJacobiOnTheRight actually did the inverse transformation - fully support complex numbers - fix logic to decide whether to vectorize - remove several clumsy methods fix for complex numbers
This commit is contained in:
Benoit Jacob
258
Eigen/src/SVD/JacobiSVD.h
Normal file
258
Eigen/src/SVD/JacobiSVD.h
Normal file
@@ -0,0 +1,258 @@
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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||||
// License as published by the Free Software Foundation; either
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||||
// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// 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.
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||||
//
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||||
// 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.
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||||
//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#ifndef EIGEN_JACOBISVD_H
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#define EIGEN_JACOBISVD_H
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/** \ingroup SVD_Module
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* \nonstableyet
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*
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* \class JacobiSVD
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*
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* \brief Jacobi SVD decomposition of a square matrix
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*
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* \param MatrixType the type of the matrix of which we are computing the SVD decomposition
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* \param ComputeU whether the U matrix should be computed
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* \param ComputeV whether the V matrix should be computed
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*
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* \sa MatrixBase::jacobiSvd()
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*/
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template<typename MatrixType, unsigned int Options> class JacobiSVD
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{
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private:
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typedef typename MatrixType::Scalar Scalar;
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typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
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enum {
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ComputeU = 1,
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ComputeV = 1,
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RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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ColsAtCompileTime = MatrixType::ColsAtCompileTime,
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DiagSizeAtCompileTime = EIGEN_ENUM_MIN(RowsAtCompileTime,ColsAtCompileTime),
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MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
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MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
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MaxDiagSizeAtCompileTime = EIGEN_ENUM_MIN(MaxRowsAtCompileTime,MaxColsAtCompileTime),
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MatrixOptions = MatrixType::Options
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};
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typedef Matrix<Scalar, Dynamic, Dynamic, MatrixOptions> DummyMatrixType;
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typedef typename ei_meta_if<ComputeU,
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Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
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MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>,
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DummyMatrixType>::ret MatrixUType;
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typedef typename ei_meta_if<ComputeV,
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Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
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MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>,
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DummyMatrixType>::ret MatrixVType;
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typedef Matrix<RealScalar, DiagSizeAtCompileTime, 1,
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Options, MaxDiagSizeAtCompileTime, 1> SingularValuesType;
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typedef Matrix<Scalar, 1, RowsAtCompileTime, MatrixOptions, 1, MaxRowsAtCompileTime> RowType;
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typedef Matrix<Scalar, RowsAtCompileTime, 1, MatrixOptions, MaxRowsAtCompileTime, 1> ColType;
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public:
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JacobiSVD() : m_isInitialized(false) {}
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JacobiSVD(const MatrixType& matrix) : m_isInitialized(false)
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{
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compute(matrix);
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}
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JacobiSVD& compute(const MatrixType& matrix);
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const MatrixUType& matrixU() const
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{
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ei_assert(m_isInitialized && "JacobiSVD is not initialized.");
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return m_matrixU;
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}
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const SingularValuesType& singularValues() const
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{
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ei_assert(m_isInitialized && "JacobiSVD is not initialized.");
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return m_singularValues;
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}
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const MatrixUType& matrixV() const
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{
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ei_assert(m_isInitialized && "JacobiSVD is not initialized.");
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return m_matrixV;
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}
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protected:
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MatrixUType m_matrixU;
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MatrixVType m_matrixV;
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SingularValuesType m_singularValues;
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bool m_isInitialized;
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template<typename _MatrixType, unsigned int _Options, bool _IsComplex>
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friend struct ei_svd_precondition_2x2_block_to_be_real;
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};
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template<typename MatrixType, unsigned int Options, bool IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex>
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struct ei_svd_precondition_2x2_block_to_be_real
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{
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static void run(MatrixType&, JacobiSVD<MatrixType, Options>&, int, int) {}
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};
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template<typename MatrixType, unsigned int Options>
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struct ei_svd_precondition_2x2_block_to_be_real<MatrixType, Options, true>
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{
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typedef JacobiSVD<MatrixType, Options> SVD;
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::RealScalar RealScalar;
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enum { ComputeU = SVD::ComputeU, ComputeV = SVD::ComputeV };
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static void run(MatrixType& work_matrix, JacobiSVD<MatrixType, Options>& svd, int p, int q)
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{
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Scalar c, s, z;
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RealScalar n = ei_sqrt(ei_abs2(work_matrix.coeff(p,p)) + ei_abs2(work_matrix.coeff(q,p)));
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if(n==0)
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{
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z = ei_abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
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work_matrix.row(p) *= z;
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if(ComputeU) svd.m_matrixU.col(p) *= ei_conj(z);
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z = ei_abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
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work_matrix.row(q) *= z;
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if(ComputeU) svd.m_matrixU.col(q) *= ei_conj(z);
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}
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else
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{
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c = ei_conj(work_matrix.coeff(p,p)) / n;
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s = work_matrix.coeff(q,p) / n;
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work_matrix.applyJacobiOnTheLeft(p,q,c,s);
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if(ComputeU) svd.m_matrixU.applyJacobiOnTheRight(p,q,ei_conj(c),-s);
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if(work_matrix.coeff(p,q) != Scalar(0))
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{
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Scalar z = ei_abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
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work_matrix.col(q) *= z;
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if(ComputeV) svd.m_matrixV.col(q) *= z;
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}
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if(work_matrix.coeff(q,q) != Scalar(0))
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{
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z = ei_abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
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work_matrix.row(q) *= z;
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if(ComputeU) svd.m_matrixU.col(q) *= ei_conj(z);
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}
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}
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}
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};
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template<typename MatrixType, typename RealScalar>
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void ei_real_2x2_jacobi_svd(const MatrixType& matrix, int p, int q,
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RealScalar *c_left, RealScalar *s_left,
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RealScalar *c_right, RealScalar *s_right)
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{
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Matrix<RealScalar,2,2> m;
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m << ei_real(matrix.coeff(p,p)), ei_real(matrix.coeff(p,q)),
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ei_real(matrix.coeff(q,p)), ei_real(matrix.coeff(q,q));
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RealScalar c1, s1;
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RealScalar t = m.coeff(0,0) + m.coeff(1,1);
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RealScalar d = m.coeff(1,0) - m.coeff(0,1);
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if(t == RealScalar(0))
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{
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c1 = 0;
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s1 = d > 0 ? 1 : -1;
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}
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else
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{
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RealScalar u = d / t;
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c1 = RealScalar(1) / ei_sqrt(1 + ei_abs2(u));
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s1 = c1 * u;
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}
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m.applyJacobiOnTheLeft(0,1,c1,s1);
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RealScalar c2, s2;
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m.makeJacobi(0,1,&c2,&s2);
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*c_left = c1*c2 + s1*s2;
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*s_left = s1*c2 - c1*s2;
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*c_right = c2;
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*s_right = s2;
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}
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template<typename MatrixType, unsigned int Options>
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JacobiSVD<MatrixType, Options>& JacobiSVD<MatrixType, Options>::compute(const MatrixType& matrix)
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{
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MatrixType work_matrix(matrix);
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int size = matrix.rows();
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if(ComputeU) m_matrixU = MatrixUType::Identity(size,size);
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if(ComputeV) m_matrixV = MatrixUType::Identity(size,size);
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m_singularValues.resize(size);
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const RealScalar precision = 2 * epsilon<Scalar>();
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sweep_again:
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for(int p = 1; p < size; ++p)
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{
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for(int q = 0; q < p; ++q)
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{
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if(std::max(ei_abs(work_matrix.coeff(p,q)),ei_abs(work_matrix.coeff(q,p)))
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> std::max(ei_abs(work_matrix.coeff(p,p)),ei_abs(work_matrix.coeff(q,q)))*precision)
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{
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ei_svd_precondition_2x2_block_to_be_real<MatrixType, Options>::run(work_matrix, *this, p, q);
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RealScalar c_left, s_left, c_right, s_right;
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ei_real_2x2_jacobi_svd(work_matrix, p, q, &c_left, &s_left, &c_right, &s_right);
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work_matrix.applyJacobiOnTheLeft(p,q,c_left,s_left);
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if(ComputeU) m_matrixU.applyJacobiOnTheRight(p,q,c_left,-s_left);
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work_matrix.applyJacobiOnTheRight(p,q,c_right,s_right);
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if(ComputeV) m_matrixV.applyJacobiOnTheRight(p,q,c_right,s_right);
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}
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}
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}
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RealScalar biggestOnDiag = work_matrix.diagonal().cwise().abs().maxCoeff();
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RealScalar maxAllowedOffDiag = biggestOnDiag * precision;
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for(int p = 0; p < size; ++p)
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{
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for(int q = 0; q < p; ++q)
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if(ei_abs(work_matrix.coeff(p,q)) > maxAllowedOffDiag)
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goto sweep_again;
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for(int q = p+1; q < size; ++q)
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if(ei_abs(work_matrix.coeff(p,q)) > maxAllowedOffDiag)
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goto sweep_again;
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}
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for(int i = 0; i < size; ++i)
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{
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RealScalar a = ei_abs(work_matrix.coeff(i,i));
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m_singularValues.coeffRef(i) = a;
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if(ComputeU && (a!=RealScalar(0))) m_matrixU.col(i) *= work_matrix.coeff(i,i)/a;
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}
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for(int i = 0; i < size; i++)
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{
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int pos;
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m_singularValues.end(size-i).maxCoeff(&pos);
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if(pos)
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{
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pos += i;
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std::swap(m_singularValues.coeffRef(i), m_singularValues.coeffRef(pos));
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if(ComputeU) m_matrixU.col(pos).swap(m_matrixU.col(i));
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if(ComputeV) m_matrixV.col(pos).swap(m_matrixV.col(i));
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}
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}
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m_isInitialized = true;
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return *this;
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}
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#endif // EIGEN_JACOBISVD_H
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@@ -1,169 +0,0 @@
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// This file is part of Eigen, a lightweight C++ template library
|
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// 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
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#define EIGEN_JACOBISQUARESVD_H
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/** \ingroup SVD_Module
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* \nonstableyet
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*
|
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* \class JacobiSquareSVD
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*
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* \brief Jacobi SVD decomposition of a square matrix
|
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*
|
||||
* \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);
|
||||
}
|
||||
|
||||
JacobiSquareSVD& 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>
|
||||
JacobiSquareSVD<MatrixType, ComputeU, ComputeV>& 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);
|
||||
const RealScalar precision = 2 * epsilon<Scalar>();
|
||||
|
||||
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)))*precision)
|
||||
{
|
||||
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))
|
||||
{
|
||||
ei_normalizeJacobi(&c, &s, work_matrix.coeff(p,p), work_matrix.coeff(q,p)),
|
||||
work_matrix.applyJacobiOnTheLeft(p,q,c,s);
|
||||
if(ComputeU) m_matrixU.applyJacobiOnTheRight(p,q,c,s);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
RealScalar biggestOnDiag = work_matrix.diagonal().cwise().abs().maxCoeff();
|
||||
RealScalar maxAllowedOffDiag = biggestOnDiag * precision;
|
||||
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;
|
||||
return *this;
|
||||
}
|
||||
#endif // EIGEN_JACOBISQUARESVD_H
|
||||
Reference in New Issue
Block a user