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Yousef Khadadeh
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1453
include/Eigen/src/SVD/BDCSVD.h
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1453
include/Eigen/src/SVD/BDCSVD.h
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File diff suppressed because it is too large
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172
include/Eigen/src/SVD/BDCSVD_LAPACKE.h
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172
include/Eigen/src/SVD/BDCSVD_LAPACKE.h
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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) 2022 Melven Roehrig-Zoellner <Melven.Roehrig-Zoellner@DLR.de>
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// Copyright (c) 2011, Intel Corporation. All rights reserved.
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//
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// This file is based on the JacobiSVD_LAPACKE.h originally from Intel -
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// see license notice below:
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/*
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Redistribution and use in source and binary forms, with or without modification,
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are permitted provided that the following conditions are met:
|
||||
|
||||
* Redistributions of source code must retain the above copyright notice, this
|
||||
list of conditions and the following disclaimer.
|
||||
* Redistributions in binary form must reproduce the above copyright notice,
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||||
this list of conditions and the following disclaimer in the documentation
|
||||
and/or other materials provided with the distribution.
|
||||
* Neither the name of Intel Corporation nor the names of its contributors may
|
||||
be used to endorse or promote products derived from this software without
|
||||
specific prior written permission.
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||||
|
||||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
||||
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
||||
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
||||
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
|
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ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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||||
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
||||
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
|
||||
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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||||
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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********************************************************************************
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* Content : Eigen bindings to LAPACKe
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* Singular Value Decomposition - SVD (divide and conquer variant)
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********************************************************************************
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*/
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#ifndef EIGEN_BDCSVD_LAPACKE_H
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#define EIGEN_BDCSVD_LAPACKE_H
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namespace Eigen {
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namespace internal {
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namespace lapacke_helpers {
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/** \internal Specialization for the data types supported by LAPACKe */
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// defining a derived class to allow access to protected members
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template <typename MatrixType_, int Options>
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class BDCSVD_LAPACKE : public BDCSVD<MatrixType_, Options> {
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typedef BDCSVD<MatrixType_, Options> SVD;
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typedef typename SVD::MatrixType MatrixType;
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typedef typename SVD::Scalar Scalar;
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typedef typename SVD::RealScalar RealScalar;
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public:
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// construct this by moving from a parent object
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BDCSVD_LAPACKE(SVD&& svd) : SVD(std::move(svd)) {}
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void compute_impl_lapacke(const MatrixType& matrix, unsigned int computationOptions) {
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SVD::allocate(matrix.rows(), matrix.cols(), computationOptions);
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SVD::m_nonzeroSingularValues = SVD::m_diagSize;
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// prepare arguments to ?gesdd
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const lapack_int matrix_order = lapack_storage_of(matrix);
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const char jobz = (SVD::m_computeFullU || SVD::m_computeFullV) ? 'A'
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: (SVD::m_computeThinU || SVD::m_computeThinV) ? 'S'
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: 'N';
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const lapack_int u_cols = (jobz == 'A') ? to_lapack(SVD::rows()) : (jobz == 'S') ? to_lapack(SVD::diagSize()) : 1;
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const lapack_int vt_rows = (jobz == 'A') ? to_lapack(SVD::cols()) : (jobz == 'S') ? to_lapack(SVD::diagSize()) : 1;
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lapack_int ldu, ldvt;
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Scalar *u, *vt, dummy;
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MatrixType localU;
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if (SVD::computeU() && !(SVD::m_computeThinU && SVD::m_computeFullV)) {
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ldu = to_lapack(SVD::m_matrixU.outerStride());
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u = SVD::m_matrixU.data();
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} else if (SVD::computeV()) {
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localU.resize(SVD::rows(), u_cols);
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ldu = to_lapack(localU.outerStride());
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u = localU.data();
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} else {
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ldu = 1;
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u = &dummy;
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}
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MatrixType localV;
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if (SVD::computeU() || SVD::computeV()) {
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localV.resize(vt_rows, SVD::cols());
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ldvt = to_lapack(localV.outerStride());
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vt = localV.data();
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} else {
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ldvt = 1;
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vt = &dummy;
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}
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MatrixType temp;
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temp = matrix;
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// actual call to ?gesdd
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lapack_int info = gesdd(matrix_order, jobz, to_lapack(SVD::rows()), to_lapack(SVD::cols()), to_lapack(temp.data()),
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to_lapack(temp.outerStride()), (RealScalar*)SVD::m_singularValues.data(), to_lapack(u), ldu,
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to_lapack(vt), ldvt);
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// Check the result of the LAPACK call
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if (info < 0 || !SVD::m_singularValues.allFinite()) {
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// this includes info == -4 => NaN entry in A
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SVD::m_info = InvalidInput;
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} else if (info > 0) {
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SVD::m_info = NoConvergence;
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} else {
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SVD::m_info = Success;
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if (SVD::m_computeThinU && SVD::m_computeFullV) {
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SVD::m_matrixU = localU.leftCols(SVD::m_matrixU.cols());
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}
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if (SVD::computeV()) {
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SVD::m_matrixV = localV.adjoint().leftCols(SVD::m_matrixV.cols());
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}
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}
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SVD::m_isInitialized = true;
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}
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};
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template <typename MatrixType_, int Options>
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BDCSVD<MatrixType_, Options>& BDCSVD_wrapper(BDCSVD<MatrixType_, Options>& svd, const MatrixType_& matrix,
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int computationOptions) {
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// we need to move to the wrapper type and back
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BDCSVD_LAPACKE<MatrixType_, Options> tmpSvd(std::move(svd));
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tmpSvd.compute_impl_lapacke(matrix, computationOptions);
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svd = std::move(tmpSvd);
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return svd;
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}
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} // end namespace lapacke_helpers
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} // end namespace internal
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#define EIGEN_LAPACKE_SDD(EIGTYPE, EIGCOLROW, OPTIONS) \
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template <> \
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inline BDCSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>& \
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BDCSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>::compute_impl( \
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const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>& matrix, unsigned int computationOptions) { \
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return internal::lapacke_helpers::BDCSVD_wrapper(*this, matrix, computationOptions); \
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}
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#define EIGEN_LAPACK_SDD_OPTIONS(OPTIONS) \
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EIGEN_LAPACKE_SDD(double, ColMajor, OPTIONS) \
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EIGEN_LAPACKE_SDD(float, ColMajor, OPTIONS) \
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EIGEN_LAPACKE_SDD(dcomplex, ColMajor, OPTIONS) \
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EIGEN_LAPACKE_SDD(scomplex, ColMajor, OPTIONS) \
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\
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EIGEN_LAPACKE_SDD(double, RowMajor, OPTIONS) \
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EIGEN_LAPACKE_SDD(float, RowMajor, OPTIONS) \
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EIGEN_LAPACKE_SDD(dcomplex, RowMajor, OPTIONS) \
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EIGEN_LAPACKE_SDD(scomplex, RowMajor, OPTIONS)
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EIGEN_LAPACK_SDD_OPTIONS(0)
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EIGEN_LAPACK_SDD_OPTIONS(ComputeThinU)
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EIGEN_LAPACK_SDD_OPTIONS(ComputeThinV)
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EIGEN_LAPACK_SDD_OPTIONS(ComputeFullU)
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EIGEN_LAPACK_SDD_OPTIONS(ComputeFullV)
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EIGEN_LAPACK_SDD_OPTIONS(ComputeThinU | ComputeThinV)
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EIGEN_LAPACK_SDD_OPTIONS(ComputeFullU | ComputeFullV)
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EIGEN_LAPACK_SDD_OPTIONS(ComputeThinU | ComputeFullV)
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EIGEN_LAPACK_SDD_OPTIONS(ComputeFullU | ComputeThinV)
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#undef EIGEN_LAPACK_SDD_OPTIONS
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#undef EIGEN_LAPACKE_SDD
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} // end namespace Eigen
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#endif // EIGEN_BDCSVD_LAPACKE_H
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3
include/Eigen/src/SVD/InternalHeaderCheck.h
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3
include/Eigen/src/SVD/InternalHeaderCheck.h
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@ -0,0 +1,3 @@
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#ifndef EIGEN_SVD_MODULE_H
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#error "Please include Eigen/SVD instead of including headers inside the src directory directly."
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#endif
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807
include/Eigen/src/SVD/JacobiSVD.h
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807
include/Eigen/src/SVD/JacobiSVD.h
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@ -0,0 +1,807 @@
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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) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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// Copyright (C) 2013-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
|
||||
// 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/.
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#ifndef EIGEN_JACOBISVD_H
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#define EIGEN_JACOBISVD_H
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// IWYU pragma: private
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#include "./InternalHeaderCheck.h"
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namespace Eigen {
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namespace internal {
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// forward declaration (needed by ICC)
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// the empty body is required by MSVC
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template <typename MatrixType, int Options, bool IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex>
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struct svd_precondition_2x2_block_to_be_real {};
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/*** QR preconditioners (R-SVD)
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***
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*** Their role is to reduce the problem of computing the SVD to the case of a square matrix.
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*** This approach, known as R-SVD, is an optimization for rectangular-enough matrices, and is a requirement for
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*** JacobiSVD which by itself is only able to work on square matrices.
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***/
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enum { PreconditionIfMoreColsThanRows, PreconditionIfMoreRowsThanCols };
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template <typename MatrixType, int QRPreconditioner, int Case>
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struct qr_preconditioner_should_do_anything {
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enum {
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a = MatrixType::RowsAtCompileTime != Dynamic && MatrixType::ColsAtCompileTime != Dynamic &&
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MatrixType::ColsAtCompileTime <= MatrixType::RowsAtCompileTime,
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b = MatrixType::RowsAtCompileTime != Dynamic && MatrixType::ColsAtCompileTime != Dynamic &&
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MatrixType::RowsAtCompileTime <= MatrixType::ColsAtCompileTime,
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ret = !((QRPreconditioner == NoQRPreconditioner) || (Case == PreconditionIfMoreColsThanRows && bool(a)) ||
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(Case == PreconditionIfMoreRowsThanCols && bool(b)))
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};
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};
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template <typename MatrixType, int Options, int QRPreconditioner, int Case,
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bool DoAnything = qr_preconditioner_should_do_anything<MatrixType, QRPreconditioner, Case>::ret>
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struct qr_preconditioner_impl {};
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template <typename MatrixType, int Options, int QRPreconditioner, int Case>
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class qr_preconditioner_impl<MatrixType, Options, QRPreconditioner, Case, false> {
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public:
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void allocate(const JacobiSVD<MatrixType, Options>&) {}
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template <typename Xpr>
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bool run(JacobiSVD<MatrixType, Options>&, const Xpr&) {
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return false;
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}
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};
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/*** preconditioner using FullPivHouseholderQR ***/
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template <typename MatrixType, int Options>
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class qr_preconditioner_impl<MatrixType, Options, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols,
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true> {
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public:
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typedef typename MatrixType::Scalar Scalar;
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typedef JacobiSVD<MatrixType, Options> SVDType;
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enum { WorkspaceSize = MatrixType::RowsAtCompileTime, MaxWorkspaceSize = MatrixType::MaxRowsAtCompileTime };
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typedef Matrix<Scalar, 1, WorkspaceSize, RowMajor, 1, MaxWorkspaceSize> WorkspaceType;
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void allocate(const SVDType& svd) {
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if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols()) {
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internal::destroy_at(&m_qr);
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internal::construct_at(&m_qr, svd.rows(), svd.cols());
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}
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if (svd.m_computeFullU) m_workspace.resize(svd.rows());
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}
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template <typename Xpr>
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bool run(SVDType& svd, const Xpr& matrix) {
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if (matrix.rows() > matrix.cols()) {
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m_qr.compute(matrix);
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svd.m_workMatrix = m_qr.matrixQR().block(0, 0, matrix.cols(), matrix.cols()).template triangularView<Upper>();
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if (svd.m_computeFullU) m_qr.matrixQ().evalTo(svd.m_matrixU, m_workspace);
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if (svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
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return true;
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}
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return false;
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}
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private:
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typedef FullPivHouseholderQR<MatrixType> QRType;
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QRType m_qr;
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WorkspaceType m_workspace;
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};
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template <typename MatrixType, int Options>
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class qr_preconditioner_impl<MatrixType, Options, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows,
|
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true> {
|
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public:
|
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typedef typename MatrixType::Scalar Scalar;
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typedef JacobiSVD<MatrixType, Options> SVDType;
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|
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enum {
|
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RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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ColsAtCompileTime = MatrixType::ColsAtCompileTime,
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MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
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MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
|
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MatrixOptions = traits<MatrixType>::Options
|
||||
};
|
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|
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typedef typename internal::make_proper_matrix_type<Scalar, ColsAtCompileTime, RowsAtCompileTime, MatrixOptions,
|
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MaxColsAtCompileTime, MaxRowsAtCompileTime>::type
|
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TransposeTypeWithSameStorageOrder;
|
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|
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void allocate(const SVDType& svd) {
|
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if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols()) {
|
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internal::destroy_at(&m_qr);
|
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internal::construct_at(&m_qr, svd.cols(), svd.rows());
|
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}
|
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if (svd.m_computeFullV) m_workspace.resize(svd.cols());
|
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}
|
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template <typename Xpr>
|
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bool run(SVDType& svd, const Xpr& matrix) {
|
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if (matrix.cols() > matrix.rows()) {
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m_qr.compute(matrix.adjoint());
|
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svd.m_workMatrix =
|
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m_qr.matrixQR().block(0, 0, matrix.rows(), matrix.rows()).template triangularView<Upper>().adjoint();
|
||||
if (svd.m_computeFullV) m_qr.matrixQ().evalTo(svd.m_matrixV, m_workspace);
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if (svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
|
||||
return true;
|
||||
} else
|
||||
return false;
|
||||
}
|
||||
|
||||
private:
|
||||
typedef FullPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
|
||||
QRType m_qr;
|
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typename plain_row_type<MatrixType>::type m_workspace;
|
||||
};
|
||||
|
||||
/*** preconditioner using ColPivHouseholderQR ***/
|
||||
|
||||
template <typename MatrixType, int Options>
|
||||
class qr_preconditioner_impl<MatrixType, Options, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols,
|
||||
true> {
|
||||
public:
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef JacobiSVD<MatrixType, Options> SVDType;
|
||||
|
||||
enum {
|
||||
WorkspaceSize = internal::traits<SVDType>::MatrixUColsAtCompileTime,
|
||||
MaxWorkspaceSize = internal::traits<SVDType>::MatrixUMaxColsAtCompileTime
|
||||
};
|
||||
|
||||
typedef Matrix<Scalar, 1, WorkspaceSize, RowMajor, 1, MaxWorkspaceSize> WorkspaceType;
|
||||
|
||||
void allocate(const SVDType& svd) {
|
||||
if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols()) {
|
||||
internal::destroy_at(&m_qr);
|
||||
internal::construct_at(&m_qr, svd.rows(), svd.cols());
|
||||
}
|
||||
if (svd.m_computeFullU)
|
||||
m_workspace.resize(svd.rows());
|
||||
else if (svd.m_computeThinU)
|
||||
m_workspace.resize(svd.cols());
|
||||
}
|
||||
template <typename Xpr>
|
||||
bool run(SVDType& svd, const Xpr& matrix) {
|
||||
if (matrix.rows() > matrix.cols()) {
|
||||
m_qr.compute(matrix);
|
||||
svd.m_workMatrix = m_qr.matrixQR().block(0, 0, matrix.cols(), matrix.cols()).template triangularView<Upper>();
|
||||
if (svd.m_computeFullU)
|
||||
m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
|
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else if (svd.m_computeThinU) {
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||||
svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
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m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
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}
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if (svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
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return true;
|
||||
}
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||||
return false;
|
||||
}
|
||||
|
||||
private:
|
||||
typedef ColPivHouseholderQR<MatrixType> QRType;
|
||||
QRType m_qr;
|
||||
WorkspaceType m_workspace;
|
||||
};
|
||||
|
||||
template <typename MatrixType, int Options>
|
||||
class qr_preconditioner_impl<MatrixType, Options, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows,
|
||||
true> {
|
||||
public:
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef JacobiSVD<MatrixType, Options> SVDType;
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
|
||||
MatrixOptions = internal::traits<MatrixType>::Options,
|
||||
WorkspaceSize = internal::traits<SVDType>::MatrixVColsAtCompileTime,
|
||||
MaxWorkspaceSize = internal::traits<SVDType>::MatrixVMaxColsAtCompileTime
|
||||
};
|
||||
|
||||
typedef Matrix<Scalar, WorkspaceSize, 1, ColMajor, MaxWorkspaceSize, 1> WorkspaceType;
|
||||
|
||||
typedef typename internal::make_proper_matrix_type<Scalar, ColsAtCompileTime, RowsAtCompileTime, MatrixOptions,
|
||||
MaxColsAtCompileTime, MaxRowsAtCompileTime>::type
|
||||
TransposeTypeWithSameStorageOrder;
|
||||
|
||||
void allocate(const SVDType& svd) {
|
||||
if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols()) {
|
||||
internal::destroy_at(&m_qr);
|
||||
internal::construct_at(&m_qr, svd.cols(), svd.rows());
|
||||
}
|
||||
if (svd.m_computeFullV)
|
||||
m_workspace.resize(svd.cols());
|
||||
else if (svd.m_computeThinV)
|
||||
m_workspace.resize(svd.rows());
|
||||
}
|
||||
template <typename Xpr>
|
||||
bool run(SVDType& svd, const Xpr& matrix) {
|
||||
if (matrix.cols() > matrix.rows()) {
|
||||
m_qr.compute(matrix.adjoint());
|
||||
|
||||
svd.m_workMatrix =
|
||||
m_qr.matrixQR().block(0, 0, matrix.rows(), matrix.rows()).template triangularView<Upper>().adjoint();
|
||||
if (svd.m_computeFullV)
|
||||
m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
|
||||
else if (svd.m_computeThinV) {
|
||||
svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
|
||||
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
|
||||
}
|
||||
if (svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
|
||||
return true;
|
||||
} else
|
||||
return false;
|
||||
}
|
||||
|
||||
private:
|
||||
typedef ColPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
|
||||
QRType m_qr;
|
||||
WorkspaceType m_workspace;
|
||||
};
|
||||
|
||||
/*** preconditioner using HouseholderQR ***/
|
||||
|
||||
template <typename MatrixType, int Options>
|
||||
class qr_preconditioner_impl<MatrixType, Options, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true> {
|
||||
public:
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef JacobiSVD<MatrixType, Options> SVDType;
|
||||
|
||||
enum {
|
||||
WorkspaceSize = internal::traits<SVDType>::MatrixUColsAtCompileTime,
|
||||
MaxWorkspaceSize = internal::traits<SVDType>::MatrixUMaxColsAtCompileTime
|
||||
};
|
||||
|
||||
typedef Matrix<Scalar, 1, WorkspaceSize, RowMajor, 1, MaxWorkspaceSize> WorkspaceType;
|
||||
|
||||
void allocate(const SVDType& svd) {
|
||||
if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols()) {
|
||||
internal::destroy_at(&m_qr);
|
||||
internal::construct_at(&m_qr, svd.rows(), svd.cols());
|
||||
}
|
||||
if (svd.m_computeFullU)
|
||||
m_workspace.resize(svd.rows());
|
||||
else if (svd.m_computeThinU)
|
||||
m_workspace.resize(svd.cols());
|
||||
}
|
||||
template <typename Xpr>
|
||||
bool run(SVDType& svd, const Xpr& matrix) {
|
||||
if (matrix.rows() > matrix.cols()) {
|
||||
m_qr.compute(matrix);
|
||||
svd.m_workMatrix = m_qr.matrixQR().block(0, 0, matrix.cols(), matrix.cols()).template triangularView<Upper>();
|
||||
if (svd.m_computeFullU)
|
||||
m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
|
||||
else if (svd.m_computeThinU) {
|
||||
svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
|
||||
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
|
||||
}
|
||||
if (svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols());
|
||||
return true;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
private:
|
||||
typedef HouseholderQR<MatrixType> QRType;
|
||||
QRType m_qr;
|
||||
WorkspaceType m_workspace;
|
||||
};
|
||||
|
||||
template <typename MatrixType, int Options>
|
||||
class qr_preconditioner_impl<MatrixType, Options, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true> {
|
||||
public:
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef JacobiSVD<MatrixType, Options> SVDType;
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
|
||||
MatrixOptions = internal::traits<MatrixType>::Options,
|
||||
WorkspaceSize = internal::traits<SVDType>::MatrixVColsAtCompileTime,
|
||||
MaxWorkspaceSize = internal::traits<SVDType>::MatrixVMaxColsAtCompileTime
|
||||
};
|
||||
|
||||
typedef Matrix<Scalar, WorkspaceSize, 1, ColMajor, MaxWorkspaceSize, 1> WorkspaceType;
|
||||
|
||||
typedef typename internal::make_proper_matrix_type<Scalar, ColsAtCompileTime, RowsAtCompileTime, MatrixOptions,
|
||||
MaxColsAtCompileTime, MaxRowsAtCompileTime>::type
|
||||
TransposeTypeWithSameStorageOrder;
|
||||
|
||||
void allocate(const SVDType& svd) {
|
||||
if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols()) {
|
||||
internal::destroy_at(&m_qr);
|
||||
internal::construct_at(&m_qr, svd.cols(), svd.rows());
|
||||
}
|
||||
if (svd.m_computeFullV)
|
||||
m_workspace.resize(svd.cols());
|
||||
else if (svd.m_computeThinV)
|
||||
m_workspace.resize(svd.rows());
|
||||
}
|
||||
|
||||
template <typename Xpr>
|
||||
bool run(SVDType& svd, const Xpr& matrix) {
|
||||
if (matrix.cols() > matrix.rows()) {
|
||||
m_qr.compute(matrix.adjoint());
|
||||
|
||||
svd.m_workMatrix =
|
||||
m_qr.matrixQR().block(0, 0, matrix.rows(), matrix.rows()).template triangularView<Upper>().adjoint();
|
||||
if (svd.m_computeFullV)
|
||||
m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
|
||||
else if (svd.m_computeThinV) {
|
||||
svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
|
||||
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
|
||||
}
|
||||
if (svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows());
|
||||
return true;
|
||||
} else
|
||||
return false;
|
||||
}
|
||||
|
||||
private:
|
||||
typedef HouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
|
||||
QRType m_qr;
|
||||
WorkspaceType m_workspace;
|
||||
};
|
||||
|
||||
/*** 2x2 SVD implementation
|
||||
***
|
||||
*** JacobiSVD consists in performing a series of 2x2 SVD subproblems
|
||||
***/
|
||||
|
||||
template <typename MatrixType, int Options>
|
||||
struct svd_precondition_2x2_block_to_be_real<MatrixType, Options, false> {
|
||||
typedef JacobiSVD<MatrixType, Options> SVD;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
static bool run(typename SVD::WorkMatrixType&, SVD&, Index, Index, RealScalar&) { return true; }
|
||||
};
|
||||
|
||||
template <typename MatrixType, int Options>
|
||||
struct svd_precondition_2x2_block_to_be_real<MatrixType, Options, true> {
|
||||
typedef JacobiSVD<MatrixType, Options> SVD;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
static bool run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q, RealScalar& maxDiagEntry) {
|
||||
using std::abs;
|
||||
using std::sqrt;
|
||||
Scalar z;
|
||||
JacobiRotation<Scalar> rot;
|
||||
RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p, p)) + numext::abs2(work_matrix.coeff(q, p)));
|
||||
|
||||
const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();
|
||||
const RealScalar precision = NumTraits<Scalar>::epsilon();
|
||||
|
||||
if (numext::is_exactly_zero(n)) {
|
||||
// make sure first column is zero
|
||||
work_matrix.coeffRef(p, p) = work_matrix.coeffRef(q, p) = Scalar(0);
|
||||
|
||||
if (abs(numext::imag(work_matrix.coeff(p, q))) > considerAsZero) {
|
||||
// work_matrix.coeff(p,q) can be zero if work_matrix.coeff(q,p) is not zero but small enough to underflow when
|
||||
// computing n
|
||||
z = abs(work_matrix.coeff(p, q)) / work_matrix.coeff(p, q);
|
||||
work_matrix.row(p) *= z;
|
||||
if (svd.computeU()) svd.m_matrixU.col(p) *= conj(z);
|
||||
}
|
||||
if (abs(numext::imag(work_matrix.coeff(q, q))) > considerAsZero) {
|
||||
z = abs(work_matrix.coeff(q, q)) / work_matrix.coeff(q, q);
|
||||
work_matrix.row(q) *= z;
|
||||
if (svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
|
||||
}
|
||||
// otherwise the second row is already zero, so we have nothing to do.
|
||||
} else {
|
||||
rot.c() = conj(work_matrix.coeff(p, p)) / n;
|
||||
rot.s() = work_matrix.coeff(q, p) / n;
|
||||
work_matrix.applyOnTheLeft(p, q, rot);
|
||||
if (svd.computeU()) svd.m_matrixU.applyOnTheRight(p, q, rot.adjoint());
|
||||
if (abs(numext::imag(work_matrix.coeff(p, q))) > considerAsZero) {
|
||||
z = abs(work_matrix.coeff(p, q)) / work_matrix.coeff(p, q);
|
||||
work_matrix.col(q) *= z;
|
||||
if (svd.computeV()) svd.m_matrixV.col(q) *= z;
|
||||
}
|
||||
if (abs(numext::imag(work_matrix.coeff(q, q))) > considerAsZero) {
|
||||
z = abs(work_matrix.coeff(q, q)) / work_matrix.coeff(q, q);
|
||||
work_matrix.row(q) *= z;
|
||||
if (svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
|
||||
}
|
||||
}
|
||||
|
||||
// update largest diagonal entry
|
||||
maxDiagEntry = numext::maxi<RealScalar>(
|
||||
maxDiagEntry, numext::maxi<RealScalar>(abs(work_matrix.coeff(p, p)), abs(work_matrix.coeff(q, q))));
|
||||
// and check whether the 2x2 block is already diagonal
|
||||
RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, precision * maxDiagEntry);
|
||||
return abs(work_matrix.coeff(p, q)) > threshold || abs(work_matrix.coeff(q, p)) > threshold;
|
||||
}
|
||||
};
|
||||
|
||||
template <typename MatrixType_, int Options>
|
||||
struct traits<JacobiSVD<MatrixType_, Options> > : svd_traits<MatrixType_, Options> {
|
||||
typedef MatrixType_ MatrixType;
|
||||
};
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
/** \ingroup SVD_Module
|
||||
*
|
||||
*
|
||||
* \class JacobiSVD
|
||||
*
|
||||
* \brief Two-sided Jacobi SVD decomposition of a rectangular matrix
|
||||
*
|
||||
* \tparam MatrixType_ the type of the matrix of which we are computing the SVD decomposition
|
||||
* \tparam Options this optional parameter allows one to specify the type of QR decomposition that will be used
|
||||
* internally for the R-SVD step for non-square matrices. Additionally, it allows one to specify whether to compute thin
|
||||
* or full unitaries \a U and \a V. See discussion of possible values below.
|
||||
*
|
||||
* SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
|
||||
* \f[ A = U S V^* \f]
|
||||
* where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero
|
||||
* outside of its main diagonal; the diagonal entries of S are known as the \em singular \em values of \a A and the
|
||||
* columns of \a U and \a V are known as the left and right \em singular \em vectors of \a A respectively.
|
||||
*
|
||||
* Singular values are always sorted in decreasing order.
|
||||
*
|
||||
* This JacobiSVD decomposition computes only the singular values by default. If you want \a U or \a V, you need to ask
|
||||
* for them explicitly.
|
||||
*
|
||||
* You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p
|
||||
* matrix, letting \a m be the smaller value among \a n and \a p, there are only \a m singular vectors; the remaining
|
||||
* columns of \a U and \a V do not correspond to actual singular vectors. Asking for \em thin \a U or \a V means asking
|
||||
* for only their \a m first columns to be formed. So \a U is then a n-by-m matrix, and \a V is then a p-by-m matrix.
|
||||
* Notice that thin \a U and \a V are all you need for (least squares) solving.
|
||||
*
|
||||
* Here's an example demonstrating basic usage:
|
||||
* \include JacobiSVD_basic.cpp
|
||||
* Output: \verbinclude JacobiSVD_basic.out
|
||||
*
|
||||
* This JacobiSVD class is a two-sided Jacobi R-SVD decomposition, ensuring optimal reliability and accuracy. The
|
||||
* downside is that it's slower than bidiagonalizing SVD algorithms for large square matrices; however its complexity is
|
||||
* still \f$ O(n^2p) \f$ where \a n is the smaller dimension and \a p is the greater dimension, meaning that it is still
|
||||
* of the same order of complexity as the faster bidiagonalizing R-SVD algorithms. In particular, like any R-SVD, it
|
||||
* takes advantage of non-squareness in that its complexity is only linear in the greater dimension.
|
||||
*
|
||||
* If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is
|
||||
* guaranteed to terminate in finite (and reasonable) time.
|
||||
*
|
||||
* The possible QR preconditioners that can be set with Options template parameter are:
|
||||
* \li ColPivHouseholderQRPreconditioner is the default. In practice it's very safe. It uses column-pivoting QR.
|
||||
* \li FullPivHouseholderQRPreconditioner, is the safest and slowest. It uses full-pivoting QR.
|
||||
* Contrary to other QRs, it doesn't allow computing thin unitaries.
|
||||
* \li HouseholderQRPreconditioner is the fastest, and less safe and accurate than the pivoting variants. It uses
|
||||
* non-pivoting QR. This is very similar in safety and accuracy to the bidiagonalization process used by bidiagonalizing
|
||||
* SVD algorithms (since bidiagonalization is inherently non-pivoting). However the resulting SVD is still more reliable
|
||||
* than bidiagonalizing SVDs because the Jacobi-based iterarive process is more reliable than the optimized bidiagonal
|
||||
* SVD iterations. \li NoQRPreconditioner allows not to use a QR preconditioner at all. This is useful if you know that
|
||||
* you will only be computing JacobiSVD decompositions of square matrices. Non-square matrices require a QR
|
||||
* preconditioner. Using this option will result in faster compilation and smaller executable code. It won't
|
||||
* significantly speed up computation, since JacobiSVD is always checking if QR preconditioning is needed before
|
||||
* applying it anyway.
|
||||
*
|
||||
* One may also use the Options template parameter to specify how the unitaries should be computed. The options are
|
||||
* #ComputeThinU, #ComputeThinV, #ComputeFullU, #ComputeFullV. It is not possible to request both the thin and full
|
||||
* versions of a unitary. By default, unitaries will not be computed.
|
||||
*
|
||||
* You can set the QRPreconditioner and unitary options together: JacobiSVD<MatrixType,
|
||||
* ColPivHouseholderQRPreconditioner | ComputeThinU | ComputeFullV>
|
||||
*
|
||||
* \sa MatrixBase::jacobiSvd()
|
||||
*/
|
||||
template <typename MatrixType_, int Options_>
|
||||
class JacobiSVD : public SVDBase<JacobiSVD<MatrixType_, Options_> > {
|
||||
typedef SVDBase<JacobiSVD> Base;
|
||||
|
||||
public:
|
||||
typedef MatrixType_ MatrixType;
|
||||
typedef typename Base::Scalar Scalar;
|
||||
typedef typename Base::RealScalar RealScalar;
|
||||
enum : int {
|
||||
Options = Options_,
|
||||
QRPreconditioner = internal::get_qr_preconditioner(Options),
|
||||
RowsAtCompileTime = Base::RowsAtCompileTime,
|
||||
ColsAtCompileTime = Base::ColsAtCompileTime,
|
||||
DiagSizeAtCompileTime = Base::DiagSizeAtCompileTime,
|
||||
MaxRowsAtCompileTime = Base::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = Base::MaxColsAtCompileTime,
|
||||
MaxDiagSizeAtCompileTime = Base::MaxDiagSizeAtCompileTime,
|
||||
MatrixOptions = Base::MatrixOptions
|
||||
};
|
||||
|
||||
typedef typename Base::MatrixUType MatrixUType;
|
||||
typedef typename Base::MatrixVType MatrixVType;
|
||||
typedef typename Base::SingularValuesType SingularValuesType;
|
||||
typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, MatrixOptions, MaxDiagSizeAtCompileTime,
|
||||
MaxDiagSizeAtCompileTime>
|
||||
WorkMatrixType;
|
||||
|
||||
/** \brief Default Constructor.
|
||||
*
|
||||
* The default constructor is useful in cases in which the user intends to
|
||||
* perform decompositions via JacobiSVD::compute(const MatrixType&).
|
||||
*/
|
||||
JacobiSVD() {}
|
||||
|
||||
/** \brief Default Constructor with memory preallocation
|
||||
*
|
||||
* Like the default constructor but with preallocation of the internal data
|
||||
* according to the specified problem size and \a Options template parameter.
|
||||
*
|
||||
* \sa JacobiSVD()
|
||||
*/
|
||||
JacobiSVD(Index rows, Index cols) { allocate(rows, cols, internal::get_computation_options(Options)); }
|
||||
|
||||
/** \brief Default Constructor with memory preallocation
|
||||
*
|
||||
* Like the default constructor but with preallocation of the internal data
|
||||
* according to the specified problem size.
|
||||
*
|
||||
* One \b cannot request unitaries using both the \a Options template parameter
|
||||
* and the constructor. If possible, prefer using the \a Options template parameter.
|
||||
*
|
||||
* \param computationOptions specify whether to compute Thin/Full unitaries U/V
|
||||
* \sa JacobiSVD()
|
||||
*
|
||||
* \deprecated Will be removed in the next major Eigen version. Options should
|
||||
* be specified in the \a Options template parameter.
|
||||
*/
|
||||
EIGEN_DEPRECATED JacobiSVD(Index rows, Index cols, unsigned int computationOptions) {
|
||||
internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, rows, cols);
|
||||
allocate(rows, cols, computationOptions);
|
||||
}
|
||||
|
||||
/** \brief Constructor performing the decomposition of given matrix, using the custom options specified
|
||||
* with the \a Options template parameter.
|
||||
*
|
||||
* \param matrix the matrix to decompose
|
||||
*/
|
||||
explicit JacobiSVD(const MatrixType& matrix) { compute_impl(matrix, internal::get_computation_options(Options)); }
|
||||
|
||||
/** \brief Constructor performing the decomposition of given matrix using specified options
|
||||
* for computing unitaries.
|
||||
*
|
||||
* One \b cannot request unitiaries using both the \a Options template parameter
|
||||
* and the constructor. If possible, prefer using the \a Options template parameter.
|
||||
*
|
||||
* \param matrix the matrix to decompose
|
||||
* \param computationOptions specify whether to compute Thin/Full unitaries U/V
|
||||
*
|
||||
* \deprecated Will be removed in the next major Eigen version. Options should
|
||||
* be specified in the \a Options template parameter.
|
||||
*/
|
||||
// EIGEN_DEPRECATED // TODO(cantonios): re-enable after fixing a few 3p libraries that error on deprecation warnings.
|
||||
JacobiSVD(const MatrixType& matrix, unsigned int computationOptions) {
|
||||
internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, matrix.rows(), matrix.cols());
|
||||
compute_impl(matrix, computationOptions);
|
||||
}
|
||||
|
||||
/** \brief Method performing the decomposition of given matrix. Computes Thin/Full unitaries U/V if specified
|
||||
* using the \a Options template parameter or the class constructor.
|
||||
*
|
||||
* \param matrix the matrix to decompose
|
||||
*/
|
||||
JacobiSVD& compute(const MatrixType& matrix) { return compute_impl(matrix, m_computationOptions); }
|
||||
|
||||
/** \brief Method performing the decomposition of given matrix, as specified by
|
||||
* the `computationOptions` parameter.
|
||||
*
|
||||
* \param matrix the matrix to decompose
|
||||
* \param computationOptions specify whether to compute Thin/Full unitaries U/V
|
||||
*
|
||||
* \deprecated Will be removed in the next major Eigen version. Options should
|
||||
* be specified in the \a Options template parameter.
|
||||
*/
|
||||
EIGEN_DEPRECATED JacobiSVD& compute(const MatrixType& matrix, unsigned int computationOptions) {
|
||||
internal::check_svd_options_assertions<MatrixType, Options>(m_computationOptions, matrix.rows(), matrix.cols());
|
||||
return compute_impl(matrix, computationOptions);
|
||||
}
|
||||
|
||||
using Base::cols;
|
||||
using Base::computeU;
|
||||
using Base::computeV;
|
||||
using Base::diagSize;
|
||||
using Base::rank;
|
||||
using Base::rows;
|
||||
|
||||
void allocate(Index rows_, Index cols_, unsigned int computationOptions) {
|
||||
if (Base::allocate(rows_, cols_, computationOptions)) return;
|
||||
eigen_assert(!(ShouldComputeThinU && int(QRPreconditioner) == int(FullPivHouseholderQRPreconditioner)) &&
|
||||
!(ShouldComputeThinU && int(QRPreconditioner) == int(FullPivHouseholderQRPreconditioner)) &&
|
||||
"JacobiSVD: can't compute thin U or thin V with the FullPivHouseholderQR preconditioner. "
|
||||
"Use the ColPivHouseholderQR preconditioner instead.");
|
||||
|
||||
m_workMatrix.resize(diagSize(), diagSize());
|
||||
if (cols() > rows()) m_qr_precond_morecols.allocate(*this);
|
||||
if (rows() > cols()) m_qr_precond_morerows.allocate(*this);
|
||||
}
|
||||
|
||||
private:
|
||||
JacobiSVD& compute_impl(const MatrixType& matrix, unsigned int computationOptions);
|
||||
|
||||
protected:
|
||||
using Base::m_computationOptions;
|
||||
using Base::m_computeFullU;
|
||||
using Base::m_computeFullV;
|
||||
using Base::m_computeThinU;
|
||||
using Base::m_computeThinV;
|
||||
using Base::m_info;
|
||||
using Base::m_isAllocated;
|
||||
using Base::m_isInitialized;
|
||||
using Base::m_matrixU;
|
||||
using Base::m_matrixV;
|
||||
using Base::m_nonzeroSingularValues;
|
||||
using Base::m_prescribedThreshold;
|
||||
using Base::m_singularValues;
|
||||
using Base::m_usePrescribedThreshold;
|
||||
using Base::ShouldComputeThinU;
|
||||
using Base::ShouldComputeThinV;
|
||||
|
||||
EIGEN_STATIC_ASSERT(!(ShouldComputeThinU && int(QRPreconditioner) == int(FullPivHouseholderQRPreconditioner)) &&
|
||||
!(ShouldComputeThinU && int(QRPreconditioner) == int(FullPivHouseholderQRPreconditioner)),
|
||||
"JacobiSVD: can't compute thin U or thin V with the FullPivHouseholderQR preconditioner. "
|
||||
"Use the ColPivHouseholderQR preconditioner instead.")
|
||||
|
||||
template <typename MatrixType__, int Options__, bool IsComplex_>
|
||||
friend struct internal::svd_precondition_2x2_block_to_be_real;
|
||||
template <typename MatrixType__, int Options__, int QRPreconditioner_, int Case_, bool DoAnything_>
|
||||
friend struct internal::qr_preconditioner_impl;
|
||||
|
||||
internal::qr_preconditioner_impl<MatrixType, Options, QRPreconditioner, internal::PreconditionIfMoreColsThanRows>
|
||||
m_qr_precond_morecols;
|
||||
internal::qr_preconditioner_impl<MatrixType, Options, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols>
|
||||
m_qr_precond_morerows;
|
||||
WorkMatrixType m_workMatrix;
|
||||
};
|
||||
|
||||
template <typename MatrixType, int Options>
|
||||
JacobiSVD<MatrixType, Options>& JacobiSVD<MatrixType, Options>::compute_impl(const MatrixType& matrix,
|
||||
unsigned int computationOptions) {
|
||||
using std::abs;
|
||||
|
||||
allocate(matrix.rows(), matrix.cols(), computationOptions);
|
||||
|
||||
// currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number
|
||||
// of iterations, only worsening the precision of U and V as we accumulate more rotations
|
||||
const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();
|
||||
|
||||
// limit for denormal numbers to be considered zero in order to avoid infinite loops (see bug 286)
|
||||
const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();
|
||||
|
||||
// Scaling factor to reduce over/under-flows
|
||||
RealScalar scale = matrix.cwiseAbs().template maxCoeff<PropagateNaN>();
|
||||
if (!(numext::isfinite)(scale)) {
|
||||
m_isInitialized = true;
|
||||
m_info = InvalidInput;
|
||||
m_nonzeroSingularValues = 0;
|
||||
return *this;
|
||||
}
|
||||
if (numext::is_exactly_zero(scale)) scale = RealScalar(1);
|
||||
|
||||
/*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */
|
||||
|
||||
if (rows() != cols()) {
|
||||
m_qr_precond_morecols.run(*this, matrix / scale);
|
||||
m_qr_precond_morerows.run(*this, matrix / scale);
|
||||
} else {
|
||||
m_workMatrix =
|
||||
matrix.template topLeftCorner<DiagSizeAtCompileTime, DiagSizeAtCompileTime>(diagSize(), diagSize()) / scale;
|
||||
if (m_computeFullU) m_matrixU.setIdentity(rows(), rows());
|
||||
if (m_computeThinU) m_matrixU.setIdentity(rows(), diagSize());
|
||||
if (m_computeFullV) m_matrixV.setIdentity(cols(), cols());
|
||||
if (m_computeThinV) m_matrixV.setIdentity(cols(), diagSize());
|
||||
}
|
||||
|
||||
/*** step 2. The main Jacobi SVD iteration. ***/
|
||||
RealScalar maxDiagEntry = m_workMatrix.cwiseAbs().diagonal().maxCoeff();
|
||||
|
||||
bool finished = false;
|
||||
while (!finished) {
|
||||
finished = true;
|
||||
|
||||
// do a sweep: for all index pairs (p,q), perform SVD of the corresponding 2x2 sub-matrix
|
||||
|
||||
for (Index p = 1; p < diagSize(); ++p) {
|
||||
for (Index q = 0; q < p; ++q) {
|
||||
// if this 2x2 sub-matrix is not diagonal already...
|
||||
// notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't
|
||||
// keep us iterating forever. Similarly, small denormal numbers are considered zero.
|
||||
RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, precision * maxDiagEntry);
|
||||
if (abs(m_workMatrix.coeff(p, q)) > threshold || abs(m_workMatrix.coeff(q, p)) > threshold) {
|
||||
finished = false;
|
||||
// perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal
|
||||
// the complex to real operation returns true if the updated 2x2 block is not already diagonal
|
||||
if (internal::svd_precondition_2x2_block_to_be_real<MatrixType, Options>::run(m_workMatrix, *this, p, q,
|
||||
maxDiagEntry)) {
|
||||
JacobiRotation<RealScalar> j_left, j_right;
|
||||
internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right);
|
||||
|
||||
// accumulate resulting Jacobi rotations
|
||||
m_workMatrix.applyOnTheLeft(p, q, j_left);
|
||||
if (computeU()) m_matrixU.applyOnTheRight(p, q, j_left.transpose());
|
||||
|
||||
m_workMatrix.applyOnTheRight(p, q, j_right);
|
||||
if (computeV()) m_matrixV.applyOnTheRight(p, q, j_right);
|
||||
|
||||
// keep track of the largest diagonal coefficient
|
||||
maxDiagEntry = numext::maxi<RealScalar>(
|
||||
maxDiagEntry, numext::maxi<RealScalar>(abs(m_workMatrix.coeff(p, p)), abs(m_workMatrix.coeff(q, q))));
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/*** step 3. The work matrix is now diagonal, so ensure it's positive so its diagonal entries are the singular values
|
||||
* ***/
|
||||
|
||||
for (Index i = 0; i < diagSize(); ++i) {
|
||||
// For a complex matrix, some diagonal coefficients might note have been
|
||||
// treated by svd_precondition_2x2_block_to_be_real, and the imaginary part
|
||||
// of some diagonal entry might not be null.
|
||||
if (NumTraits<Scalar>::IsComplex && abs(numext::imag(m_workMatrix.coeff(i, i))) > considerAsZero) {
|
||||
RealScalar a = abs(m_workMatrix.coeff(i, i));
|
||||
m_singularValues.coeffRef(i) = abs(a);
|
||||
if (computeU()) m_matrixU.col(i) *= m_workMatrix.coeff(i, i) / a;
|
||||
} else {
|
||||
// m_workMatrix.coeff(i,i) is already real, no difficulty:
|
||||
RealScalar a = numext::real(m_workMatrix.coeff(i, i));
|
||||
m_singularValues.coeffRef(i) = abs(a);
|
||||
if (computeU() && (a < RealScalar(0))) m_matrixU.col(i) = -m_matrixU.col(i);
|
||||
}
|
||||
}
|
||||
|
||||
m_singularValues *= scale;
|
||||
|
||||
/*** step 4. Sort singular values in descending order and compute the number of nonzero singular values ***/
|
||||
|
||||
m_nonzeroSingularValues = diagSize();
|
||||
for (Index i = 0; i < diagSize(); i++) {
|
||||
Index pos;
|
||||
RealScalar maxRemainingSingularValue = m_singularValues.tail(diagSize() - i).maxCoeff(&pos);
|
||||
if (numext::is_exactly_zero(maxRemainingSingularValue)) {
|
||||
m_nonzeroSingularValues = i;
|
||||
break;
|
||||
}
|
||||
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;
|
||||
}
|
||||
|
||||
/** \svd_module
|
||||
*
|
||||
* \return the singular value decomposition of \c *this computed by two-sided
|
||||
* Jacobi transformations.
|
||||
*
|
||||
* \sa class JacobiSVD
|
||||
*/
|
||||
template <typename Derived>
|
||||
template <int Options>
|
||||
JacobiSVD<typename MatrixBase<Derived>::PlainObject, Options> MatrixBase<Derived>::jacobiSvd() const {
|
||||
return JacobiSVD<PlainObject, Options>(*this);
|
||||
}
|
||||
|
||||
template <typename Derived>
|
||||
template <int Options>
|
||||
JacobiSVD<typename MatrixBase<Derived>::PlainObject, Options> MatrixBase<Derived>::jacobiSvd(
|
||||
unsigned int computationOptions) const {
|
||||
return JacobiSVD<PlainObject, Options>(*this, computationOptions);
|
||||
}
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_JACOBISVD_H
|
||||
127
include/Eigen/src/SVD/JacobiSVD_LAPACKE.h
Normal file
127
include/Eigen/src/SVD/JacobiSVD_LAPACKE.h
Normal file
|
|
@ -0,0 +1,127 @@
|
|||
/*
|
||||
Copyright (c) 2011, Intel Corporation. All rights reserved.
|
||||
|
||||
Redistribution and use in source and binary forms, with or without modification,
|
||||
are permitted provided that the following conditions are met:
|
||||
|
||||
* Redistributions of source code must retain the above copyright notice, this
|
||||
list of conditions and the following disclaimer.
|
||||
* Redistributions in binary form must reproduce the above copyright notice,
|
||||
this list of conditions and the following disclaimer in the documentation
|
||||
and/or other materials provided with the distribution.
|
||||
* Neither the name of Intel Corporation nor the names of its contributors may
|
||||
be used to endorse or promote products derived from this software without
|
||||
specific prior written permission.
|
||||
|
||||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
||||
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
||||
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
||||
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
|
||||
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
|
||||
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
||||
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
|
||||
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
||||
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
||||
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
|
||||
********************************************************************************
|
||||
* Content : Eigen bindings to LAPACKe
|
||||
* Singular Value Decomposition - SVD.
|
||||
********************************************************************************
|
||||
*/
|
||||
|
||||
#ifndef EIGEN_JACOBISVD_LAPACKE_H
|
||||
#define EIGEN_JACOBISVD_LAPACKE_H
|
||||
|
||||
// IWYU pragma: private
|
||||
#include "./InternalHeaderCheck.h"
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
/** \internal Specialization for the data types supported by LAPACKe */
|
||||
|
||||
#define EIGEN_LAPACKE_SVD(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_PREFIX, EIGCOLROW, LAPACKE_COLROW, OPTIONS) \
|
||||
template <> \
|
||||
inline JacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>& \
|
||||
JacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>::compute_impl( \
|
||||
const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>& matrix, unsigned int computationOptions) { \
|
||||
typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> MatrixType; \
|
||||
/*typedef MatrixType::Scalar Scalar;*/ \
|
||||
/*typedef MatrixType::RealScalar RealScalar;*/ \
|
||||
allocate(matrix.rows(), matrix.cols(), computationOptions); \
|
||||
\
|
||||
/*const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();*/ \
|
||||
m_nonzeroSingularValues = diagSize(); \
|
||||
\
|
||||
lapack_int lda = internal::convert_index<lapack_int>(matrix.outerStride()), ldu, ldvt; \
|
||||
lapack_int matrix_order = LAPACKE_COLROW; \
|
||||
char jobu, jobvt; \
|
||||
LAPACKE_TYPE *u, *vt, dummy; \
|
||||
jobu = (m_computeFullU) ? 'A' : (m_computeThinU) ? 'S' : 'N'; \
|
||||
jobvt = (m_computeFullV) ? 'A' : (m_computeThinV) ? 'S' : 'N'; \
|
||||
if (computeU()) { \
|
||||
ldu = internal::convert_index<lapack_int>(m_matrixU.outerStride()); \
|
||||
u = (LAPACKE_TYPE*)m_matrixU.data(); \
|
||||
} else { \
|
||||
ldu = 1; \
|
||||
u = &dummy; \
|
||||
} \
|
||||
MatrixType localV; \
|
||||
lapack_int vt_rows = (m_computeFullV) ? internal::convert_index<lapack_int>(cols()) \
|
||||
: (m_computeThinV) ? internal::convert_index<lapack_int>(diagSize()) \
|
||||
: 1; \
|
||||
if (computeV()) { \
|
||||
localV.resize(vt_rows, cols()); \
|
||||
ldvt = internal::convert_index<lapack_int>(localV.outerStride()); \
|
||||
vt = (LAPACKE_TYPE*)localV.data(); \
|
||||
} else { \
|
||||
ldvt = 1; \
|
||||
vt = &dummy; \
|
||||
} \
|
||||
Matrix<LAPACKE_RTYPE, Dynamic, Dynamic> superb; \
|
||||
superb.resize(diagSize(), 1); \
|
||||
MatrixType m_temp; \
|
||||
m_temp = matrix; \
|
||||
lapack_int info = LAPACKE_##LAPACKE_PREFIX##gesvd( \
|
||||
matrix_order, jobu, jobvt, internal::convert_index<lapack_int>(rows()), \
|
||||
internal::convert_index<lapack_int>(cols()), (LAPACKE_TYPE*)m_temp.data(), lda, \
|
||||
(LAPACKE_RTYPE*)m_singularValues.data(), u, ldu, vt, ldvt, superb.data()); \
|
||||
/* Check the result of the LAPACK call */ \
|
||||
if (info < 0 || !m_singularValues.allFinite()) { \
|
||||
m_info = InvalidInput; \
|
||||
} else if (info > 0) { \
|
||||
m_info = NoConvergence; \
|
||||
} else { \
|
||||
m_info = Success; \
|
||||
if (computeV()) m_matrixV = localV.adjoint(); \
|
||||
} \
|
||||
/* for(int i=0;i<diagSize();i++) if (m_singularValues.coeffRef(i) < precision) { m_nonzeroSingularValues--; \
|
||||
* m_singularValues.coeffRef(i)=RealScalar(0);}*/ \
|
||||
m_isInitialized = true; \
|
||||
return *this; \
|
||||
}
|
||||
|
||||
#define EIGEN_LAPACK_SVD_OPTIONS(OPTIONS) \
|
||||
EIGEN_LAPACKE_SVD(double, double, double, d, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
|
||||
EIGEN_LAPACKE_SVD(float, float, float, s, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
|
||||
EIGEN_LAPACKE_SVD(dcomplex, lapack_complex_double, double, z, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
|
||||
EIGEN_LAPACKE_SVD(scomplex, lapack_complex_float, float, c, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
|
||||
\
|
||||
EIGEN_LAPACKE_SVD(double, double, double, d, RowMajor, LAPACK_ROW_MAJOR, OPTIONS) \
|
||||
EIGEN_LAPACKE_SVD(float, float, float, s, RowMajor, LAPACK_ROW_MAJOR, OPTIONS) \
|
||||
EIGEN_LAPACKE_SVD(dcomplex, lapack_complex_double, double, z, RowMajor, LAPACK_ROW_MAJOR, OPTIONS) \
|
||||
EIGEN_LAPACKE_SVD(scomplex, lapack_complex_float, float, c, RowMajor, LAPACK_ROW_MAJOR, OPTIONS)
|
||||
|
||||
EIGEN_LAPACK_SVD_OPTIONS(0)
|
||||
EIGEN_LAPACK_SVD_OPTIONS(ComputeThinU)
|
||||
EIGEN_LAPACK_SVD_OPTIONS(ComputeThinV)
|
||||
EIGEN_LAPACK_SVD_OPTIONS(ComputeFullU)
|
||||
EIGEN_LAPACK_SVD_OPTIONS(ComputeFullV)
|
||||
EIGEN_LAPACK_SVD_OPTIONS(ComputeThinU | ComputeThinV)
|
||||
EIGEN_LAPACK_SVD_OPTIONS(ComputeFullU | ComputeFullV)
|
||||
EIGEN_LAPACK_SVD_OPTIONS(ComputeThinU | ComputeFullV)
|
||||
EIGEN_LAPACK_SVD_OPTIONS(ComputeFullU | ComputeThinV)
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_JACOBISVD_LAPACKE_H
|
||||
436
include/Eigen/src/SVD/SVDBase.h
Normal file
436
include/Eigen/src/SVD/SVDBase.h
Normal file
|
|
@ -0,0 +1,436 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
|
||||
// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
//
|
||||
// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
|
||||
// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
|
||||
// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
|
||||
// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.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/.
|
||||
|
||||
#ifndef EIGEN_SVDBASE_H
|
||||
#define EIGEN_SVDBASE_H
|
||||
|
||||
// IWYU pragma: private
|
||||
#include "./InternalHeaderCheck.h"
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
namespace internal {
|
||||
|
||||
enum OptionsMasks {
|
||||
QRPreconditionerBits = NoQRPreconditioner | HouseholderQRPreconditioner | ColPivHouseholderQRPreconditioner |
|
||||
FullPivHouseholderQRPreconditioner,
|
||||
ComputationOptionsBits = ComputeThinU | ComputeFullU | ComputeThinV | ComputeFullV
|
||||
};
|
||||
|
||||
constexpr int get_qr_preconditioner(int options) { return options & QRPreconditionerBits; }
|
||||
|
||||
constexpr int get_computation_options(int options) { return options & ComputationOptionsBits; }
|
||||
|
||||
constexpr bool should_svd_compute_thin_u(int options) { return (options & ComputeThinU) != 0; }
|
||||
constexpr bool should_svd_compute_full_u(int options) { return (options & ComputeFullU) != 0; }
|
||||
constexpr bool should_svd_compute_thin_v(int options) { return (options & ComputeThinV) != 0; }
|
||||
constexpr bool should_svd_compute_full_v(int options) { return (options & ComputeFullV) != 0; }
|
||||
|
||||
template <typename MatrixType, int Options>
|
||||
void check_svd_options_assertions(unsigned int computationOptions, Index rows, Index cols) {
|
||||
EIGEN_STATIC_ASSERT((Options & ComputationOptionsBits) == 0,
|
||||
"SVDBase: Cannot request U or V using both static and runtime options, even if they match. "
|
||||
"Requesting unitaries at runtime is DEPRECATED: "
|
||||
"Prefer requesting unitaries statically, using the Options template parameter.");
|
||||
eigen_assert(
|
||||
!(should_svd_compute_thin_u(computationOptions) && cols < rows && MatrixType::RowsAtCompileTime != Dynamic) &&
|
||||
!(should_svd_compute_thin_v(computationOptions) && rows < cols && MatrixType::ColsAtCompileTime != Dynamic) &&
|
||||
"SVDBase: If thin U is requested at runtime, your matrix must have more rows than columns or a dynamic number of "
|
||||
"rows."
|
||||
"Similarly, if thin V is requested at runtime, you matrix must have more columns than rows or a dynamic number "
|
||||
"of columns.");
|
||||
(void)computationOptions;
|
||||
(void)rows;
|
||||
(void)cols;
|
||||
}
|
||||
|
||||
template <typename Derived>
|
||||
struct traits<SVDBase<Derived> > : traits<Derived> {
|
||||
typedef MatrixXpr XprKind;
|
||||
typedef SolverStorage StorageKind;
|
||||
typedef int StorageIndex;
|
||||
enum { Flags = 0 };
|
||||
};
|
||||
|
||||
template <typename MatrixType, int Options_>
|
||||
struct svd_traits : traits<MatrixType> {
|
||||
static constexpr int Options = Options_;
|
||||
static constexpr bool ShouldComputeFullU = internal::should_svd_compute_full_u(Options);
|
||||
static constexpr bool ShouldComputeThinU = internal::should_svd_compute_thin_u(Options);
|
||||
static constexpr bool ShouldComputeFullV = internal::should_svd_compute_full_v(Options);
|
||||
static constexpr bool ShouldComputeThinV = internal::should_svd_compute_thin_v(Options);
|
||||
enum {
|
||||
DiagSizeAtCompileTime =
|
||||
internal::min_size_prefer_dynamic(MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime),
|
||||
MaxDiagSizeAtCompileTime =
|
||||
internal::min_size_prefer_dynamic(MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime),
|
||||
MatrixUColsAtCompileTime = ShouldComputeThinU ? DiagSizeAtCompileTime : MatrixType::RowsAtCompileTime,
|
||||
MatrixVColsAtCompileTime = ShouldComputeThinV ? DiagSizeAtCompileTime : MatrixType::ColsAtCompileTime,
|
||||
MatrixUMaxColsAtCompileTime = ShouldComputeThinU ? MaxDiagSizeAtCompileTime : MatrixType::MaxRowsAtCompileTime,
|
||||
MatrixVMaxColsAtCompileTime = ShouldComputeThinV ? MaxDiagSizeAtCompileTime : MatrixType::MaxColsAtCompileTime
|
||||
};
|
||||
};
|
||||
} // namespace internal
|
||||
|
||||
/** \ingroup SVD_Module
|
||||
*
|
||||
*
|
||||
* \class SVDBase
|
||||
*
|
||||
* \brief Base class of SVD algorithms
|
||||
*
|
||||
* \tparam Derived the type of the actual SVD decomposition
|
||||
*
|
||||
* SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
|
||||
* \f[ A = U S V^* \f]
|
||||
* where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero
|
||||
* outside of its main diagonal; the diagonal entries of S are known as the \em singular \em values of \a A and the
|
||||
* columns of \a U and \a V are known as the left and right \em singular \em vectors of \a A respectively.
|
||||
*
|
||||
* Singular values are always sorted in decreasing order.
|
||||
*
|
||||
*
|
||||
* You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p
|
||||
* matrix, letting \a m be the smaller value among \a n and \a p, there are only \a m singular vectors; the remaining
|
||||
* columns of \a U and \a V do not correspond to actual singular vectors. Asking for \em thin \a U or \a V means asking
|
||||
* for only their \a m first columns to be formed. So \a U is then a n-by-m matrix, and \a V is then a p-by-m matrix.
|
||||
* Notice that thin \a U and \a V are all you need for (least squares) solving.
|
||||
*
|
||||
* The status of the computation can be retrieved using the \a info() method. Unless \a info() returns \a Success, the
|
||||
* results should be not considered well defined.
|
||||
*
|
||||
* If the input matrix has inf or nan coefficients, the result of the computation is undefined, and \a info() will
|
||||
* return \a InvalidInput, but the computation is guaranteed to terminate in finite (and reasonable) time. \sa class
|
||||
* BDCSVD, class JacobiSVD
|
||||
*/
|
||||
template <typename Derived>
|
||||
class SVDBase : public SolverBase<SVDBase<Derived> > {
|
||||
public:
|
||||
template <typename Derived_>
|
||||
friend struct internal::solve_assertion;
|
||||
|
||||
typedef typename internal::traits<Derived>::MatrixType MatrixType;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
|
||||
typedef typename Eigen::internal::traits<SVDBase>::StorageIndex StorageIndex;
|
||||
|
||||
static constexpr bool ShouldComputeFullU = internal::traits<Derived>::ShouldComputeFullU;
|
||||
static constexpr bool ShouldComputeThinU = internal::traits<Derived>::ShouldComputeThinU;
|
||||
static constexpr bool ShouldComputeFullV = internal::traits<Derived>::ShouldComputeFullV;
|
||||
static constexpr bool ShouldComputeThinV = internal::traits<Derived>::ShouldComputeThinV;
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
DiagSizeAtCompileTime = internal::min_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime),
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
|
||||
MaxDiagSizeAtCompileTime = internal::min_size_prefer_fixed(MaxRowsAtCompileTime, MaxColsAtCompileTime),
|
||||
MatrixOptions = internal::traits<MatrixType>::Options,
|
||||
MatrixUColsAtCompileTime = internal::traits<Derived>::MatrixUColsAtCompileTime,
|
||||
MatrixVColsAtCompileTime = internal::traits<Derived>::MatrixVColsAtCompileTime,
|
||||
MatrixUMaxColsAtCompileTime = internal::traits<Derived>::MatrixUMaxColsAtCompileTime,
|
||||
MatrixVMaxColsAtCompileTime = internal::traits<Derived>::MatrixVMaxColsAtCompileTime
|
||||
};
|
||||
|
||||
EIGEN_STATIC_ASSERT(!(ShouldComputeFullU && ShouldComputeThinU), "SVDBase: Cannot request both full and thin U")
|
||||
EIGEN_STATIC_ASSERT(!(ShouldComputeFullV && ShouldComputeThinV), "SVDBase: Cannot request both full and thin V")
|
||||
|
||||
typedef
|
||||
typename internal::make_proper_matrix_type<Scalar, RowsAtCompileTime, MatrixUColsAtCompileTime, MatrixOptions,
|
||||
MaxRowsAtCompileTime, MatrixUMaxColsAtCompileTime>::type MatrixUType;
|
||||
typedef
|
||||
typename internal::make_proper_matrix_type<Scalar, ColsAtCompileTime, MatrixVColsAtCompileTime, MatrixOptions,
|
||||
MaxColsAtCompileTime, MatrixVMaxColsAtCompileTime>::type MatrixVType;
|
||||
|
||||
typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
|
||||
|
||||
Derived& derived() { return *static_cast<Derived*>(this); }
|
||||
const Derived& derived() const { return *static_cast<const Derived*>(this); }
|
||||
|
||||
/** \returns the \a U matrix.
|
||||
*
|
||||
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
|
||||
* the U matrix is n-by-n if you asked for \link Eigen::ComputeFullU ComputeFullU \endlink, and is n-by-m if you asked
|
||||
* for \link Eigen::ComputeThinU ComputeThinU \endlink.
|
||||
*
|
||||
* The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
|
||||
*
|
||||
* This method asserts that you asked for \a U to be computed.
|
||||
*/
|
||||
const MatrixUType& matrixU() const {
|
||||
_check_compute_assertions();
|
||||
eigen_assert(computeU() && "This SVD decomposition didn't compute U. Did you ask for it?");
|
||||
return m_matrixU;
|
||||
}
|
||||
|
||||
/** \returns the \a V matrix.
|
||||
*
|
||||
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
|
||||
* the V matrix is p-by-p if you asked for \link Eigen::ComputeFullV ComputeFullV \endlink, and is p-by-m if you asked
|
||||
* for \link Eigen::ComputeThinV ComputeThinV \endlink.
|
||||
*
|
||||
* The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
|
||||
*
|
||||
* This method asserts that you asked for \a V to be computed.
|
||||
*/
|
||||
const MatrixVType& matrixV() const {
|
||||
_check_compute_assertions();
|
||||
eigen_assert(computeV() && "This SVD decomposition didn't compute V. Did you ask for it?");
|
||||
return m_matrixV;
|
||||
}
|
||||
|
||||
/** \returns the vector of singular values.
|
||||
*
|
||||
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
|
||||
* returned vector has size \a m. Singular values are always sorted in decreasing order.
|
||||
*/
|
||||
const SingularValuesType& singularValues() const {
|
||||
_check_compute_assertions();
|
||||
return m_singularValues;
|
||||
}
|
||||
|
||||
/** \returns the number of singular values that are not exactly 0 */
|
||||
Index nonzeroSingularValues() const {
|
||||
_check_compute_assertions();
|
||||
return m_nonzeroSingularValues;
|
||||
}
|
||||
|
||||
/** \returns the rank of the matrix of which \c *this is the SVD.
|
||||
*
|
||||
* \note This method has to determine which singular values should be considered nonzero.
|
||||
* For that, it uses the threshold value that you can control by calling
|
||||
* setThreshold(const RealScalar&).
|
||||
*/
|
||||
inline Index rank() const {
|
||||
using std::abs;
|
||||
_check_compute_assertions();
|
||||
if (m_singularValues.size() == 0) return 0;
|
||||
RealScalar premultiplied_threshold =
|
||||
numext::maxi<RealScalar>(m_singularValues.coeff(0) * threshold(), (std::numeric_limits<RealScalar>::min)());
|
||||
Index i = m_nonzeroSingularValues - 1;
|
||||
while (i >= 0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
|
||||
return i + 1;
|
||||
}
|
||||
|
||||
/** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
|
||||
* which need to determine when singular values are to be considered nonzero.
|
||||
* This is not used for the SVD decomposition itself.
|
||||
*
|
||||
* When it needs to get the threshold value, Eigen calls threshold().
|
||||
* The default is \c NumTraits<Scalar>::epsilon()
|
||||
*
|
||||
* \param threshold The new value to use as the threshold.
|
||||
*
|
||||
* A singular value will be considered nonzero if its value is strictly greater than
|
||||
* \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
|
||||
*
|
||||
* If you want to come back to the default behavior, call setThreshold(Default_t)
|
||||
*/
|
||||
Derived& setThreshold(const RealScalar& threshold) {
|
||||
m_usePrescribedThreshold = true;
|
||||
m_prescribedThreshold = threshold;
|
||||
return derived();
|
||||
}
|
||||
|
||||
/** Allows to come back to the default behavior, letting Eigen use its default formula for
|
||||
* determining the threshold.
|
||||
*
|
||||
* You should pass the special object Eigen::Default as parameter here.
|
||||
* \code svd.setThreshold(Eigen::Default); \endcode
|
||||
*
|
||||
* See the documentation of setThreshold(const RealScalar&).
|
||||
*/
|
||||
Derived& setThreshold(Default_t) {
|
||||
m_usePrescribedThreshold = false;
|
||||
return derived();
|
||||
}
|
||||
|
||||
/** Returns the threshold that will be used by certain methods such as rank().
|
||||
*
|
||||
* See the documentation of setThreshold(const RealScalar&).
|
||||
*/
|
||||
RealScalar threshold() const {
|
||||
eigen_assert(m_isInitialized || m_usePrescribedThreshold);
|
||||
// this temporary is needed to workaround a MSVC issue
|
||||
Index diagSize = (std::max<Index>)(1, m_diagSize);
|
||||
return m_usePrescribedThreshold ? m_prescribedThreshold : RealScalar(diagSize) * NumTraits<Scalar>::epsilon();
|
||||
}
|
||||
|
||||
/** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
|
||||
inline bool computeU() const { return m_computeFullU || m_computeThinU; }
|
||||
/** \returns true if \a V (full or thin) is asked for in this SVD decomposition */
|
||||
inline bool computeV() const { return m_computeFullV || m_computeThinV; }
|
||||
|
||||
inline Index rows() const { return m_rows.value(); }
|
||||
inline Index cols() const { return m_cols.value(); }
|
||||
inline Index diagSize() const { return m_diagSize.value(); }
|
||||
|
||||
#ifdef EIGEN_PARSED_BY_DOXYGEN
|
||||
/** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
|
||||
*
|
||||
* \param b the right-hand-side of the equation to solve.
|
||||
*
|
||||
* \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.
|
||||
*
|
||||
* \note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and
|
||||
* least-squares solving. In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert
|
||||
* A x - b \Vert \f$.
|
||||
*/
|
||||
template <typename Rhs>
|
||||
inline const Solve<Derived, Rhs> solve(const MatrixBase<Rhs>& b) const;
|
||||
#endif
|
||||
|
||||
/** \brief Reports whether previous computation was successful.
|
||||
*
|
||||
* \returns \c Success if computation was successful.
|
||||
*/
|
||||
EIGEN_DEVICE_FUNC ComputationInfo info() const {
|
||||
eigen_assert(m_isInitialized && "SVD is not initialized.");
|
||||
return m_info;
|
||||
}
|
||||
|
||||
#ifndef EIGEN_PARSED_BY_DOXYGEN
|
||||
template <typename RhsType, typename DstType>
|
||||
void _solve_impl(const RhsType& rhs, DstType& dst) const;
|
||||
|
||||
template <bool Conjugate, typename RhsType, typename DstType>
|
||||
void _solve_impl_transposed(const RhsType& rhs, DstType& dst) const;
|
||||
#endif
|
||||
|
||||
protected:
|
||||
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
|
||||
|
||||
void _check_compute_assertions() const { eigen_assert(m_isInitialized && "SVD is not initialized."); }
|
||||
|
||||
template <bool Transpose_, typename Rhs>
|
||||
void _check_solve_assertion(const Rhs& b) const {
|
||||
EIGEN_ONLY_USED_FOR_DEBUG(b);
|
||||
_check_compute_assertions();
|
||||
eigen_assert(computeU() && computeV() &&
|
||||
"SVDBase::solve(): Both unitaries U and V are required to be computed (thin unitaries suffice).");
|
||||
eigen_assert((Transpose_ ? cols() : rows()) == b.rows() &&
|
||||
"SVDBase::solve(): invalid number of rows of the right hand side matrix b");
|
||||
}
|
||||
|
||||
// return true if already allocated
|
||||
bool allocate(Index rows, Index cols, unsigned int computationOptions);
|
||||
|
||||
MatrixUType m_matrixU;
|
||||
MatrixVType m_matrixV;
|
||||
SingularValuesType m_singularValues;
|
||||
ComputationInfo m_info;
|
||||
bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;
|
||||
bool m_computeFullU, m_computeThinU;
|
||||
bool m_computeFullV, m_computeThinV;
|
||||
unsigned int m_computationOptions;
|
||||
Index m_nonzeroSingularValues;
|
||||
internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
|
||||
internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
|
||||
internal::variable_if_dynamic<Index, DiagSizeAtCompileTime> m_diagSize;
|
||||
RealScalar m_prescribedThreshold;
|
||||
|
||||
/** \brief Default Constructor.
|
||||
*
|
||||
* Default constructor of SVDBase
|
||||
*/
|
||||
SVDBase()
|
||||
: m_matrixU(MatrixUType()),
|
||||
m_matrixV(MatrixVType()),
|
||||
m_singularValues(SingularValuesType()),
|
||||
m_info(Success),
|
||||
m_isInitialized(false),
|
||||
m_isAllocated(false),
|
||||
m_usePrescribedThreshold(false),
|
||||
m_computeFullU(ShouldComputeFullU),
|
||||
m_computeThinU(ShouldComputeThinU),
|
||||
m_computeFullV(ShouldComputeFullV),
|
||||
m_computeThinV(ShouldComputeThinV),
|
||||
m_computationOptions(internal::traits<Derived>::Options),
|
||||
m_nonzeroSingularValues(0),
|
||||
m_rows(RowsAtCompileTime),
|
||||
m_cols(ColsAtCompileTime),
|
||||
m_diagSize(DiagSizeAtCompileTime),
|
||||
m_prescribedThreshold(0) {}
|
||||
};
|
||||
|
||||
#ifndef EIGEN_PARSED_BY_DOXYGEN
|
||||
template <typename Derived>
|
||||
template <typename RhsType, typename DstType>
|
||||
void SVDBase<Derived>::_solve_impl(const RhsType& rhs, DstType& dst) const {
|
||||
// A = U S V^*
|
||||
// So A^{-1} = V S^{-1} U^*
|
||||
|
||||
Matrix<typename RhsType::Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime,
|
||||
RhsType::MaxColsAtCompileTime>
|
||||
tmp;
|
||||
Index l_rank = rank();
|
||||
tmp.noalias() = m_matrixU.leftCols(l_rank).adjoint() * rhs;
|
||||
tmp = m_singularValues.head(l_rank).asDiagonal().inverse() * tmp;
|
||||
dst = m_matrixV.leftCols(l_rank) * tmp;
|
||||
}
|
||||
|
||||
template <typename Derived>
|
||||
template <bool Conjugate, typename RhsType, typename DstType>
|
||||
void SVDBase<Derived>::_solve_impl_transposed(const RhsType& rhs, DstType& dst) const {
|
||||
// A = U S V^*
|
||||
// So A^{-*} = U S^{-1} V^*
|
||||
// And A^{-T} = U_conj S^{-1} V^T
|
||||
Matrix<typename RhsType::Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime,
|
||||
RhsType::MaxColsAtCompileTime>
|
||||
tmp;
|
||||
Index l_rank = rank();
|
||||
|
||||
tmp.noalias() = m_matrixV.leftCols(l_rank).transpose().template conjugateIf<Conjugate>() * rhs;
|
||||
tmp = m_singularValues.head(l_rank).asDiagonal().inverse() * tmp;
|
||||
dst = m_matrixU.template conjugateIf<!Conjugate>().leftCols(l_rank) * tmp;
|
||||
}
|
||||
#endif
|
||||
|
||||
template <typename Derived>
|
||||
bool SVDBase<Derived>::allocate(Index rows, Index cols, unsigned int computationOptions) {
|
||||
eigen_assert(rows >= 0 && cols >= 0);
|
||||
|
||||
if (m_isAllocated && rows == m_rows.value() && cols == m_cols.value() && computationOptions == m_computationOptions) {
|
||||
return true;
|
||||
}
|
||||
|
||||
m_rows.setValue(rows);
|
||||
m_cols.setValue(cols);
|
||||
m_info = Success;
|
||||
m_isInitialized = false;
|
||||
m_isAllocated = true;
|
||||
m_computationOptions = computationOptions;
|
||||
m_computeFullU = ShouldComputeFullU || internal::should_svd_compute_full_u(computationOptions);
|
||||
m_computeThinU = ShouldComputeThinU || internal::should_svd_compute_thin_u(computationOptions);
|
||||
m_computeFullV = ShouldComputeFullV || internal::should_svd_compute_full_v(computationOptions);
|
||||
m_computeThinV = ShouldComputeThinV || internal::should_svd_compute_thin_v(computationOptions);
|
||||
|
||||
eigen_assert(!(m_computeFullU && m_computeThinU) && "SVDBase: you can't ask for both full and thin U");
|
||||
eigen_assert(!(m_computeFullV && m_computeThinV) && "SVDBase: you can't ask for both full and thin V");
|
||||
|
||||
m_diagSize.setValue(numext::mini(m_rows.value(), m_cols.value()));
|
||||
m_singularValues.resize(m_diagSize.value());
|
||||
if (RowsAtCompileTime == Dynamic)
|
||||
m_matrixU.resize(m_rows.value(), m_computeFullU ? m_rows.value() : m_computeThinU ? m_diagSize.value() : 0);
|
||||
if (ColsAtCompileTime == Dynamic)
|
||||
m_matrixV.resize(m_cols.value(), m_computeFullV ? m_cols.value() : m_computeThinV ? m_diagSize.value() : 0);
|
||||
|
||||
return false;
|
||||
}
|
||||
|
||||
} // namespace Eigen
|
||||
|
||||
#endif // EIGEN_SVDBASE_H
|
||||
379
include/Eigen/src/SVD/UpperBidiagonalization.h
Normal file
379
include/Eigen/src/SVD/UpperBidiagonalization.h
Normal file
|
|
@ -0,0 +1,379 @@
|
|||
// 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) 2013-2014 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/.
|
||||
|
||||
#ifndef EIGEN_BIDIAGONALIZATION_H
|
||||
#define EIGEN_BIDIAGONALIZATION_H
|
||||
|
||||
// IWYU pragma: private
|
||||
#include "./InternalHeaderCheck.h"
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
namespace internal {
|
||||
// UpperBidiagonalization will probably be replaced by a Bidiagonalization class, don't want to make it stable API.
|
||||
// At the same time, it's useful to keep for now as it's about the only thing that is testing the BandMatrix class.
|
||||
|
||||
template <typename MatrixType_>
|
||||
class UpperBidiagonalization {
|
||||
public:
|
||||
typedef MatrixType_ MatrixType;
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
ColsAtCompileTimeMinusOne = internal::decrement_size<ColsAtCompileTime>::ret
|
||||
};
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
|
||||
typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;
|
||||
typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;
|
||||
typedef BandMatrix<RealScalar, ColsAtCompileTime, ColsAtCompileTime, 1, 0, RowMajor> BidiagonalType;
|
||||
typedef Matrix<Scalar, ColsAtCompileTime, 1> DiagVectorType;
|
||||
typedef Matrix<Scalar, ColsAtCompileTimeMinusOne, 1> SuperDiagVectorType;
|
||||
typedef HouseholderSequence<
|
||||
const MatrixType, const internal::remove_all_t<typename Diagonal<const MatrixType, 0>::ConjugateReturnType> >
|
||||
HouseholderUSequenceType;
|
||||
typedef HouseholderSequence<const internal::remove_all_t<typename MatrixType::ConjugateReturnType>,
|
||||
Diagonal<const 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(0, 0), m_isInitialized(false) {}
|
||||
|
||||
explicit UpperBidiagonalization(const MatrixType& matrix)
|
||||
: m_householder(matrix.rows(), matrix.cols()),
|
||||
m_bidiagonal(matrix.cols(), matrix.cols()),
|
||||
m_isInitialized(false) {
|
||||
compute(matrix);
|
||||
}
|
||||
|
||||
UpperBidiagonalization(Index rows, Index cols)
|
||||
: m_householder(rows, cols), m_bidiagonal(cols, cols), m_isInitialized(false) {}
|
||||
|
||||
UpperBidiagonalization& compute(const MatrixType& matrix);
|
||||
UpperBidiagonalization& computeUnblocked(const MatrixType& matrix);
|
||||
|
||||
const MatrixType& householder() const { return m_householder; }
|
||||
const BidiagonalType& bidiagonal() const { return m_bidiagonal; }
|
||||
|
||||
const HouseholderUSequenceType householderU() const {
|
||||
eigen_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
|
||||
return HouseholderUSequenceType(m_householder, m_householder.diagonal().conjugate());
|
||||
}
|
||||
|
||||
const HouseholderVSequenceType householderV() // const here gives nasty errors and i'm lazy
|
||||
{
|
||||
eigen_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
|
||||
return HouseholderVSequenceType(m_householder.conjugate(), m_householder.const_derived().template diagonal<1>())
|
||||
.setLength(m_householder.cols() - 1)
|
||||
.setShift(1);
|
||||
}
|
||||
|
||||
protected:
|
||||
MatrixType m_householder;
|
||||
BidiagonalType m_bidiagonal;
|
||||
bool m_isInitialized;
|
||||
};
|
||||
|
||||
// Standard upper bidiagonalization without fancy optimizations
|
||||
// This version should be faster for small matrix size
|
||||
template <typename MatrixType>
|
||||
void upperbidiagonalization_inplace_unblocked(MatrixType& mat, typename MatrixType::RealScalar* diagonal,
|
||||
typename MatrixType::RealScalar* upper_diagonal,
|
||||
typename MatrixType::Scalar* tempData = 0) {
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
|
||||
Index rows = mat.rows();
|
||||
Index cols = mat.cols();
|
||||
|
||||
typedef Matrix<Scalar, Dynamic, 1, ColMajor, MatrixType::MaxRowsAtCompileTime, 1> TempType;
|
||||
TempType tempVector;
|
||||
if (tempData == 0) {
|
||||
tempVector.resize(rows);
|
||||
tempData = tempVector.data();
|
||||
}
|
||||
|
||||
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 A
|
||||
mat.col(k).tail(remainingRows).makeHouseholderInPlace(mat.coeffRef(k, k), diagonal[k]);
|
||||
// apply householder transform to remaining part of A on the left
|
||||
mat.bottomRightCorner(remainingRows, remainingCols)
|
||||
.applyHouseholderOnTheLeft(mat.col(k).tail(remainingRows - 1), mat.coeff(k, k), tempData);
|
||||
|
||||
if (k == cols - 1) break;
|
||||
|
||||
// construct right householder transform in-place in mat
|
||||
mat.row(k).tail(remainingCols).makeHouseholderInPlace(mat.coeffRef(k, k + 1), upper_diagonal[k]);
|
||||
// apply householder transform to remaining part of mat on the left
|
||||
mat.bottomRightCorner(remainingRows - 1, remainingCols)
|
||||
.applyHouseholderOnTheRight(mat.row(k).tail(remainingCols - 1).adjoint(), mat.coeff(k, k + 1), tempData);
|
||||
}
|
||||
}
|
||||
|
||||
/** \internal
|
||||
* Helper routine for the block reduction to upper bidiagonal form.
|
||||
*
|
||||
* Let's partition the matrix A:
|
||||
*
|
||||
* | A00 A01 |
|
||||
* A = | |
|
||||
* | A10 A11 |
|
||||
*
|
||||
* This function reduces to bidiagonal form the left \c rows x \a blockSize vertical panel [A00/A10]
|
||||
* and the \a blockSize x \c cols horizontal panel [A00 A01] of the matrix \a A. The bottom-right block A11
|
||||
* is updated using matrix-matrix products:
|
||||
* A22 -= V * Y^T - X * U^T
|
||||
* where V and U contains the left and right Householder vectors. U and V are stored in A10, and A01
|
||||
* respectively, and the update matrices X and Y are computed during the reduction.
|
||||
*
|
||||
*/
|
||||
template <typename MatrixType>
|
||||
void upperbidiagonalization_blocked_helper(
|
||||
MatrixType& A, typename MatrixType::RealScalar* diagonal, typename MatrixType::RealScalar* upper_diagonal, Index bs,
|
||||
Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic, traits<MatrixType>::Flags & RowMajorBit> > X,
|
||||
Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic, traits<MatrixType>::Flags & RowMajorBit> > Y) {
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef typename NumTraits<RealScalar>::Literal Literal;
|
||||
static constexpr int StorageOrder = (traits<MatrixType>::Flags & RowMajorBit) ? RowMajor : ColMajor;
|
||||
typedef InnerStride<StorageOrder == ColMajor ? 1 : Dynamic> ColInnerStride;
|
||||
typedef InnerStride<StorageOrder == ColMajor ? Dynamic : 1> RowInnerStride;
|
||||
typedef Ref<Matrix<Scalar, Dynamic, 1>, 0, ColInnerStride> SubColumnType;
|
||||
typedef Ref<Matrix<Scalar, 1, Dynamic>, 0, RowInnerStride> SubRowType;
|
||||
typedef Ref<Matrix<Scalar, Dynamic, Dynamic, StorageOrder> > SubMatType;
|
||||
|
||||
Index brows = A.rows();
|
||||
Index bcols = A.cols();
|
||||
|
||||
Scalar tau_u, tau_u_prev(0), tau_v;
|
||||
|
||||
for (Index k = 0; k < bs; ++k) {
|
||||
Index remainingRows = brows - k;
|
||||
Index remainingCols = bcols - k - 1;
|
||||
|
||||
SubMatType X_k1(X.block(k, 0, remainingRows, k));
|
||||
SubMatType V_k1(A.block(k, 0, remainingRows, k));
|
||||
|
||||
// 1 - update the k-th column of A
|
||||
SubColumnType v_k = A.col(k).tail(remainingRows);
|
||||
v_k -= V_k1 * Y.row(k).head(k).adjoint();
|
||||
if (k) v_k -= X_k1 * A.col(k).head(k);
|
||||
|
||||
// 2 - construct left Householder transform in-place
|
||||
v_k.makeHouseholderInPlace(tau_v, diagonal[k]);
|
||||
|
||||
if (k + 1 < bcols) {
|
||||
SubMatType Y_k(Y.block(k + 1, 0, remainingCols, k + 1));
|
||||
SubMatType U_k1(A.block(0, k + 1, k, remainingCols));
|
||||
|
||||
// this eases the application of Householder transforAions
|
||||
// A(k,k) will store tau_v later
|
||||
A(k, k) = Scalar(1);
|
||||
|
||||
// 3 - Compute y_k^T = tau_v * ( A^T*v_k - Y_k-1*V_k-1^T*v_k - U_k-1*X_k-1^T*v_k )
|
||||
{
|
||||
SubColumnType y_k(Y.col(k).tail(remainingCols));
|
||||
|
||||
// let's use the beginning of column k of Y as a temporary vector
|
||||
SubColumnType tmp(Y.col(k).head(k));
|
||||
y_k.noalias() = A.block(k, k + 1, remainingRows, remainingCols).adjoint() * v_k; // bottleneck
|
||||
tmp.noalias() = V_k1.adjoint() * v_k;
|
||||
y_k.noalias() -= Y_k.leftCols(k) * tmp;
|
||||
tmp.noalias() = X_k1.adjoint() * v_k;
|
||||
y_k.noalias() -= U_k1.adjoint() * tmp;
|
||||
y_k *= numext::conj(tau_v);
|
||||
}
|
||||
|
||||
// 4 - update k-th row of A (it will become u_k)
|
||||
SubRowType u_k(A.row(k).tail(remainingCols));
|
||||
u_k = u_k.conjugate();
|
||||
{
|
||||
u_k -= Y_k * A.row(k).head(k + 1).adjoint();
|
||||
if (k) u_k -= U_k1.adjoint() * X.row(k).head(k).adjoint();
|
||||
}
|
||||
|
||||
// 5 - construct right Householder transform in-place
|
||||
u_k.makeHouseholderInPlace(tau_u, upper_diagonal[k]);
|
||||
|
||||
// this eases the application of Householder transformations
|
||||
// A(k,k+1) will store tau_u later
|
||||
A(k, k + 1) = Scalar(1);
|
||||
|
||||
// 6 - Compute x_k = tau_u * ( A*u_k - X_k-1*U_k-1^T*u_k - V_k*Y_k^T*u_k )
|
||||
{
|
||||
SubColumnType x_k(X.col(k).tail(remainingRows - 1));
|
||||
|
||||
// let's use the beginning of column k of X as a temporary vectors
|
||||
// note that tmp0 and tmp1 overlaps
|
||||
SubColumnType tmp0(X.col(k).head(k)), tmp1(X.col(k).head(k + 1));
|
||||
|
||||
x_k.noalias() = A.block(k + 1, k + 1, remainingRows - 1, remainingCols) * u_k.transpose(); // bottleneck
|
||||
tmp0.noalias() = U_k1 * u_k.transpose();
|
||||
x_k.noalias() -= X_k1.bottomRows(remainingRows - 1) * tmp0;
|
||||
tmp1.noalias() = Y_k.adjoint() * u_k.transpose();
|
||||
x_k.noalias() -= A.block(k + 1, 0, remainingRows - 1, k + 1) * tmp1;
|
||||
x_k *= numext::conj(tau_u);
|
||||
tau_u = numext::conj(tau_u);
|
||||
u_k = u_k.conjugate();
|
||||
}
|
||||
|
||||
if (k > 0) A.coeffRef(k - 1, k) = tau_u_prev;
|
||||
tau_u_prev = tau_u;
|
||||
} else
|
||||
A.coeffRef(k - 1, k) = tau_u_prev;
|
||||
|
||||
A.coeffRef(k, k) = tau_v;
|
||||
}
|
||||
|
||||
if (bs < bcols) A.coeffRef(bs - 1, bs) = tau_u_prev;
|
||||
|
||||
// update A22
|
||||
if (bcols > bs && brows > bs) {
|
||||
SubMatType A11(A.bottomRightCorner(brows - bs, bcols - bs));
|
||||
SubMatType A10(A.block(bs, 0, brows - bs, bs));
|
||||
SubMatType A01(A.block(0, bs, bs, bcols - bs));
|
||||
Scalar tmp = A01(bs - 1, 0);
|
||||
A01(bs - 1, 0) = Literal(1);
|
||||
A11.noalias() -= A10 * Y.topLeftCorner(bcols, bs).bottomRows(bcols - bs).adjoint();
|
||||
A11.noalias() -= X.topLeftCorner(brows, bs).bottomRows(brows - bs) * A01;
|
||||
A01(bs - 1, 0) = tmp;
|
||||
}
|
||||
}
|
||||
|
||||
/** \internal
|
||||
*
|
||||
* Implementation of a block-bidiagonal reduction.
|
||||
* It is based on the following paper:
|
||||
* The Design of a Parallel Dense Linear Algebra Software Library: Reduction to Hessenberg, Tridiagonal, and
|
||||
* Bidiagonal Form. by Jaeyoung Choi, Jack J. Dongarra, David W. Walker. (1995) section 3.3
|
||||
*/
|
||||
template <typename MatrixType, typename BidiagType>
|
||||
void upperbidiagonalization_inplace_blocked(MatrixType& A, BidiagType& bidiagonal, Index maxBlockSize = 32,
|
||||
typename MatrixType::Scalar* /*tempData*/ = 0) {
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef Block<MatrixType, Dynamic, Dynamic> BlockType;
|
||||
|
||||
Index rows = A.rows();
|
||||
Index cols = A.cols();
|
||||
Index size = (std::min)(rows, cols);
|
||||
|
||||
// X and Y are work space
|
||||
static constexpr int StorageOrder = (traits<MatrixType>::Flags & RowMajorBit) ? RowMajor : ColMajor;
|
||||
Matrix<Scalar, MatrixType::RowsAtCompileTime, Dynamic, StorageOrder, MatrixType::MaxRowsAtCompileTime> X(
|
||||
rows, maxBlockSize);
|
||||
Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic, StorageOrder, MatrixType::MaxColsAtCompileTime> Y(
|
||||
cols, maxBlockSize);
|
||||
Index blockSize = (std::min)(maxBlockSize, size);
|
||||
|
||||
Index k = 0;
|
||||
for (k = 0; k < size; k += blockSize) {
|
||||
Index bs = (std::min)(size - k, blockSize); // actual size of the block
|
||||
Index brows = rows - k; // rows of the block
|
||||
Index bcols = cols - k; // columns of the block
|
||||
|
||||
// partition the matrix A:
|
||||
//
|
||||
// | A00 A01 A02 |
|
||||
// | |
|
||||
// A = | A10 A11 A12 |
|
||||
// | |
|
||||
// | A20 A21 A22 |
|
||||
//
|
||||
// where A11 is a bs x bs diagonal block,
|
||||
// and let:
|
||||
// | A11 A12 |
|
||||
// B = | |
|
||||
// | A21 A22 |
|
||||
|
||||
BlockType B = A.block(k, k, brows, bcols);
|
||||
|
||||
// This stage performs the bidiagonalization of A11, A21, A12, and updating of A22.
|
||||
// Finally, the algorithm continue on the updated A22.
|
||||
//
|
||||
// However, if B is too small, or A22 empty, then let's use an unblocked strategy
|
||||
|
||||
auto upper_diagonal = bidiagonal.template diagonal<1>();
|
||||
typename MatrixType::RealScalar* upper_diagonal_ptr =
|
||||
upper_diagonal.size() > 0 ? &upper_diagonal.coeffRef(k) : nullptr;
|
||||
|
||||
if (k + bs == cols || bcols < 48) // somewhat arbitrary threshold
|
||||
{
|
||||
upperbidiagonalization_inplace_unblocked(B, &(bidiagonal.template diagonal<0>().coeffRef(k)), upper_diagonal_ptr,
|
||||
X.data());
|
||||
break; // We're done
|
||||
} else {
|
||||
upperbidiagonalization_blocked_helper<BlockType>(B, &(bidiagonal.template diagonal<0>().coeffRef(k)),
|
||||
upper_diagonal_ptr, bs, X.topLeftCorner(brows, bs),
|
||||
Y.topLeftCorner(bcols, bs));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
template <typename MatrixType_>
|
||||
UpperBidiagonalization<MatrixType_>& UpperBidiagonalization<MatrixType_>::computeUnblocked(const MatrixType_& matrix) {
|
||||
Index rows = matrix.rows();
|
||||
Index cols = matrix.cols();
|
||||
EIGEN_ONLY_USED_FOR_DEBUG(cols);
|
||||
|
||||
eigen_assert(rows >= cols && "UpperBidiagonalization is only for Arices satisfying rows>=cols.");
|
||||
|
||||
m_householder = matrix;
|
||||
|
||||
ColVectorType temp(rows);
|
||||
|
||||
upperbidiagonalization_inplace_unblocked(m_householder, &(m_bidiagonal.template diagonal<0>().coeffRef(0)),
|
||||
&(m_bidiagonal.template diagonal<1>().coeffRef(0)), temp.data());
|
||||
|
||||
m_isInitialized = true;
|
||||
return *this;
|
||||
}
|
||||
|
||||
template <typename MatrixType_>
|
||||
UpperBidiagonalization<MatrixType_>& UpperBidiagonalization<MatrixType_>::compute(const MatrixType_& matrix) {
|
||||
Index rows = matrix.rows();
|
||||
Index cols = matrix.cols();
|
||||
EIGEN_ONLY_USED_FOR_DEBUG(rows);
|
||||
EIGEN_ONLY_USED_FOR_DEBUG(cols);
|
||||
|
||||
eigen_assert(rows >= cols && "UpperBidiagonalization is only for Arices satisfying rows>=cols.");
|
||||
|
||||
m_householder = matrix;
|
||||
upperbidiagonalization_inplace_blocked(m_householder, m_bidiagonal);
|
||||
|
||||
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
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_BIDIAGONALIZATION_H
|
||||
Loading…
Add table
Add a link
Reference in a new issue