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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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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// 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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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 QRPreconditioner,
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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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{
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enum { a = MatrixType::RowsAtCompileTime != Dynamic &&
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MatrixType::ColsAtCompileTime != Dynamic &&
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MatrixType::ColsAtCompileTime <= MatrixType::RowsAtCompileTime,
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b = MatrixType::RowsAtCompileTime != Dynamic &&
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MatrixType::ColsAtCompileTime != Dynamic &&
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MatrixType::RowsAtCompileTime <= MatrixType::ColsAtCompileTime,
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ret = !( (QRPreconditioner == NoQRPreconditioner) ||
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(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 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 QRPreconditioner, int Case>
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class qr_preconditioner_impl<MatrixType, QRPreconditioner, Case, false>
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{
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public:
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typedef typename MatrixType::Index Index;
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void allocate(const JacobiSVD<MatrixType, QRPreconditioner>&) {}
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bool run(JacobiSVD<MatrixType, QRPreconditioner>&, const MatrixType&)
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{
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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>
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class qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
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{
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public:
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typedef typename MatrixType::Index Index;
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typedef typename MatrixType::Scalar Scalar;
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enum
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{
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RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime
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};
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typedef Matrix<Scalar, 1, RowsAtCompileTime, RowMajor, 1, MaxRowsAtCompileTime> WorkspaceType;
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void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)
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{
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if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
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{
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m_qr.~QRType();
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::new (&m_qr) QRType(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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bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
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{
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if(matrix.rows() > matrix.cols())
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{
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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>
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class qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
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{
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public:
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typedef typename MatrixType::Index Index;
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typedef typename MatrixType::Scalar Scalar;
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enum
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{
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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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Options = MatrixType::Options
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};
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typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
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TransposeTypeWithSameStorageOrder;
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void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)
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{
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if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
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{
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m_qr.~QRType();
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::new (&m_qr) QRType(svd.cols(), svd.rows());
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}
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m_adjoint.resize(svd.cols(), svd.rows());
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if (svd.m_computeFullV) m_workspace.resize(svd.cols());
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}
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bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
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{
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if(matrix.cols() > matrix.rows())
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{
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m_adjoint = matrix.adjoint();
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m_qr.compute(m_adjoint);
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svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
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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();
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return true;
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}
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else return false;
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}
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private:
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typedef FullPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
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QRType m_qr;
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TransposeTypeWithSameStorageOrder m_adjoint;
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typename internal::plain_row_type<MatrixType>::type m_workspace;
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};
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/*** preconditioner using ColPivHouseholderQR ***/
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template<typename MatrixType>
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class qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
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{
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public:
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typedef typename MatrixType::Index Index;
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void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)
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{
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if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
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{
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m_qr.~QRType();
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::new (&m_qr) QRType(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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else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
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}
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bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
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{
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if(matrix.rows() > matrix.cols())
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{
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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.householderQ().evalTo(svd.m_matrixU, m_workspace);
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else if(svd.m_computeThinU)
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{
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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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}
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return false;
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}
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private:
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typedef ColPivHouseholderQR<MatrixType> QRType;
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QRType m_qr;
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typename internal::plain_col_type<MatrixType>::type m_workspace;
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};
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195
|
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template<typename MatrixType>
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class qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
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{
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public:
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typedef typename MatrixType::Index Index;
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typedef typename MatrixType::Scalar Scalar;
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enum
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203
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{
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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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Options = MatrixType::Options
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};
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typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
|
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TransposeTypeWithSameStorageOrder;
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213
|
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214
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void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)
|
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215
|
{
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216
|
if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
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217
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{
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m_qr.~QRType();
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::new (&m_qr) QRType(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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else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
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m_adjoint.resize(svd.cols(), svd.rows());
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224
|
}
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225
|
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|
bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
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227
|
{
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0:13a5d365ba16
|
228
|
if(matrix.cols() > matrix.rows())
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229
|
{
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230
|
m_adjoint = matrix.adjoint();
|
| ykuroda |
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231
|
m_qr.compute(m_adjoint);
|
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0:13a5d365ba16
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232
|
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233
|
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
|
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234
|
if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
|
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235
|
else if(svd.m_computeThinV)
|
| ykuroda |
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236
|
{
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|
237
|
svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
|
| ykuroda |
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238
|
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
|
| ykuroda |
0:13a5d365ba16
|
239
|
}
|
| ykuroda |
0:13a5d365ba16
|
240
|
if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
|
| ykuroda |
0:13a5d365ba16
|
241
|
return true;
|
| ykuroda |
0:13a5d365ba16
|
242
|
}
|
| ykuroda |
0:13a5d365ba16
|
243
|
else return false;
|
| ykuroda |
0:13a5d365ba16
|
244
|
}
|
| ykuroda |
0:13a5d365ba16
|
245
|
|
| ykuroda |
0:13a5d365ba16
|
246
|
private:
|
| ykuroda |
0:13a5d365ba16
|
247
|
typedef ColPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
|
| ykuroda |
0:13a5d365ba16
|
248
|
QRType m_qr;
|
| ykuroda |
0:13a5d365ba16
|
249
|
TransposeTypeWithSameStorageOrder m_adjoint;
|
| ykuroda |
0:13a5d365ba16
|
250
|
typename internal::plain_row_type<MatrixType>::type m_workspace;
|
| ykuroda |
0:13a5d365ba16
|
251
|
};
|
| ykuroda |
0:13a5d365ba16
|
252
|
|
| ykuroda |
0:13a5d365ba16
|
253
|
/*** preconditioner using HouseholderQR ***/
|
| ykuroda |
0:13a5d365ba16
|
254
|
|
| ykuroda |
0:13a5d365ba16
|
255
|
template<typename MatrixType>
|
| ykuroda |
0:13a5d365ba16
|
256
|
class qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
|
| ykuroda |
0:13a5d365ba16
|
257
|
{
|
| ykuroda |
0:13a5d365ba16
|
258
|
public:
|
| ykuroda |
0:13a5d365ba16
|
259
|
typedef typename MatrixType::Index Index;
|
| ykuroda |
0:13a5d365ba16
|
260
|
|
| ykuroda |
0:13a5d365ba16
|
261
|
void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)
|
| ykuroda |
0:13a5d365ba16
|
262
|
{
|
| ykuroda |
0:13a5d365ba16
|
263
|
if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
|
| ykuroda |
0:13a5d365ba16
|
264
|
{
|
| ykuroda |
0:13a5d365ba16
|
265
|
m_qr.~QRType();
|
| ykuroda |
0:13a5d365ba16
|
266
|
::new (&m_qr) QRType(svd.rows(), svd.cols());
|
| ykuroda |
0:13a5d365ba16
|
267
|
}
|
| ykuroda |
0:13a5d365ba16
|
268
|
if (svd.m_computeFullU) m_workspace.resize(svd.rows());
|
| ykuroda |
0:13a5d365ba16
|
269
|
else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
|
| ykuroda |
0:13a5d365ba16
|
270
|
}
|
| ykuroda |
0:13a5d365ba16
|
271
|
|
| ykuroda |
0:13a5d365ba16
|
272
|
bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)
|
| ykuroda |
0:13a5d365ba16
|
273
|
{
|
| ykuroda |
0:13a5d365ba16
|
274
|
if(matrix.rows() > matrix.cols())
|
| ykuroda |
0:13a5d365ba16
|
275
|
{
|
| ykuroda |
0:13a5d365ba16
|
276
|
m_qr.compute(matrix);
|
| ykuroda |
0:13a5d365ba16
|
277
|
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
|
| ykuroda |
0:13a5d365ba16
|
278
|
if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
|
| ykuroda |
0:13a5d365ba16
|
279
|
else if(svd.m_computeThinU)
|
| ykuroda |
0:13a5d365ba16
|
280
|
{
|
| ykuroda |
0:13a5d365ba16
|
281
|
svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
|
| ykuroda |
0:13a5d365ba16
|
282
|
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
|
| ykuroda |
0:13a5d365ba16
|
283
|
}
|
| ykuroda |
0:13a5d365ba16
|
284
|
if(svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols());
|
| ykuroda |
0:13a5d365ba16
|
285
|
return true;
|
| ykuroda |
0:13a5d365ba16
|
286
|
}
|
| ykuroda |
0:13a5d365ba16
|
287
|
return false;
|
| ykuroda |
0:13a5d365ba16
|
288
|
}
|
| ykuroda |
0:13a5d365ba16
|
289
|
private:
|
| ykuroda |
0:13a5d365ba16
|
290
|
typedef HouseholderQR<MatrixType> QRType;
|
| ykuroda |
0:13a5d365ba16
|
291
|
QRType m_qr;
|
| ykuroda |
0:13a5d365ba16
|
292
|
typename internal::plain_col_type<MatrixType>::type m_workspace;
|
| ykuroda |
0:13a5d365ba16
|
293
|
};
|
| ykuroda |
0:13a5d365ba16
|
294
|
|
| ykuroda |
0:13a5d365ba16
|
295
|
template<typename MatrixType>
|
| ykuroda |
0:13a5d365ba16
|
296
|
class qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
|
| ykuroda |
0:13a5d365ba16
|
297
|
{
|
| ykuroda |
0:13a5d365ba16
|
298
|
public:
|
| ykuroda |
0:13a5d365ba16
|
299
|
typedef typename MatrixType::Index Index;
|
| ykuroda |
0:13a5d365ba16
|
300
|
typedef typename MatrixType::Scalar Scalar;
|
| ykuroda |
0:13a5d365ba16
|
301
|
enum
|
| ykuroda |
0:13a5d365ba16
|
302
|
{
|
| ykuroda |
0:13a5d365ba16
|
303
|
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
| ykuroda |
0:13a5d365ba16
|
304
|
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
| ykuroda |
0:13a5d365ba16
|
305
|
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
| ykuroda |
0:13a5d365ba16
|
306
|
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
|
| ykuroda |
0:13a5d365ba16
|
307
|
Options = MatrixType::Options
|
| ykuroda |
0:13a5d365ba16
|
308
|
};
|
| ykuroda |
0:13a5d365ba16
|
309
|
|
| ykuroda |
0:13a5d365ba16
|
310
|
typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
|
| ykuroda |
0:13a5d365ba16
|
311
|
TransposeTypeWithSameStorageOrder;
|
| ykuroda |
0:13a5d365ba16
|
312
|
|
| ykuroda |
0:13a5d365ba16
|
313
|
void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)
|
| ykuroda |
0:13a5d365ba16
|
314
|
{
|
| ykuroda |
0:13a5d365ba16
|
315
|
if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
|
| ykuroda |
0:13a5d365ba16
|
316
|
{
|
| ykuroda |
0:13a5d365ba16
|
317
|
m_qr.~QRType();
|
| ykuroda |
0:13a5d365ba16
|
318
|
::new (&m_qr) QRType(svd.cols(), svd.rows());
|
| ykuroda |
0:13a5d365ba16
|
319
|
}
|
| ykuroda |
0:13a5d365ba16
|
320
|
if (svd.m_computeFullV) m_workspace.resize(svd.cols());
|
| ykuroda |
0:13a5d365ba16
|
321
|
else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
|
| ykuroda |
0:13a5d365ba16
|
322
|
m_adjoint.resize(svd.cols(), svd.rows());
|
| ykuroda |
0:13a5d365ba16
|
323
|
}
|
| ykuroda |
0:13a5d365ba16
|
324
|
|
| ykuroda |
0:13a5d365ba16
|
325
|
bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)
|
| ykuroda |
0:13a5d365ba16
|
326
|
{
|
| ykuroda |
0:13a5d365ba16
|
327
|
if(matrix.cols() > matrix.rows())
|
| ykuroda |
0:13a5d365ba16
|
328
|
{
|
| ykuroda |
0:13a5d365ba16
|
329
|
m_adjoint = matrix.adjoint();
|
| ykuroda |
0:13a5d365ba16
|
330
|
m_qr.compute(m_adjoint);
|
| ykuroda |
0:13a5d365ba16
|
331
|
|
| ykuroda |
0:13a5d365ba16
|
332
|
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
|
| ykuroda |
0:13a5d365ba16
|
333
|
if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
|
| ykuroda |
0:13a5d365ba16
|
334
|
else if(svd.m_computeThinV)
|
| ykuroda |
0:13a5d365ba16
|
335
|
{
|
| ykuroda |
0:13a5d365ba16
|
336
|
svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
|
| ykuroda |
0:13a5d365ba16
|
337
|
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
|
| ykuroda |
0:13a5d365ba16
|
338
|
}
|
| ykuroda |
0:13a5d365ba16
|
339
|
if(svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows());
|
| ykuroda |
0:13a5d365ba16
|
340
|
return true;
|
| ykuroda |
0:13a5d365ba16
|
341
|
}
|
| ykuroda |
0:13a5d365ba16
|
342
|
else return false;
|
| ykuroda |
0:13a5d365ba16
|
343
|
}
|
| ykuroda |
0:13a5d365ba16
|
344
|
|
| ykuroda |
0:13a5d365ba16
|
345
|
private:
|
| ykuroda |
0:13a5d365ba16
|
346
|
typedef HouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
|
| ykuroda |
0:13a5d365ba16
|
347
|
QRType m_qr;
|
| ykuroda |
0:13a5d365ba16
|
348
|
TransposeTypeWithSameStorageOrder m_adjoint;
|
| ykuroda |
0:13a5d365ba16
|
349
|
typename internal::plain_row_type<MatrixType>::type m_workspace;
|
| ykuroda |
0:13a5d365ba16
|
350
|
};
|
| ykuroda |
0:13a5d365ba16
|
351
|
|
| ykuroda |
0:13a5d365ba16
|
352
|
/*** 2x2 SVD implementation
|
| ykuroda |
0:13a5d365ba16
|
353
|
***
|
| ykuroda |
0:13a5d365ba16
|
354
|
*** JacobiSVD consists in performing a series of 2x2 SVD subproblems
|
| ykuroda |
0:13a5d365ba16
|
355
|
***/
|
| ykuroda |
0:13a5d365ba16
|
356
|
|
| ykuroda |
0:13a5d365ba16
|
357
|
template<typename MatrixType, int QRPreconditioner>
|
| ykuroda |
0:13a5d365ba16
|
358
|
struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, false>
|
| ykuroda |
0:13a5d365ba16
|
359
|
{
|
| ykuroda |
0:13a5d365ba16
|
360
|
typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
|
| ykuroda |
0:13a5d365ba16
|
361
|
typedef typename SVD::Index Index;
|
| ykuroda |
0:13a5d365ba16
|
362
|
static void run(typename SVD::WorkMatrixType&, SVD&, Index, Index) {}
|
| ykuroda |
0:13a5d365ba16
|
363
|
};
|
| ykuroda |
0:13a5d365ba16
|
364
|
|
| ykuroda |
0:13a5d365ba16
|
365
|
template<typename MatrixType, int QRPreconditioner>
|
| ykuroda |
0:13a5d365ba16
|
366
|
struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
|
| ykuroda |
0:13a5d365ba16
|
367
|
{
|
| ykuroda |
0:13a5d365ba16
|
368
|
typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
|
| ykuroda |
0:13a5d365ba16
|
369
|
typedef typename MatrixType::Scalar Scalar;
|
| ykuroda |
0:13a5d365ba16
|
370
|
typedef typename MatrixType::RealScalar RealScalar;
|
| ykuroda |
0:13a5d365ba16
|
371
|
typedef typename SVD::Index Index;
|
| ykuroda |
0:13a5d365ba16
|
372
|
static void run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q)
|
| ykuroda |
0:13a5d365ba16
|
373
|
{
|
| ykuroda |
0:13a5d365ba16
|
374
|
using std::sqrt;
|
| ykuroda |
0:13a5d365ba16
|
375
|
Scalar z;
|
| ykuroda |
0:13a5d365ba16
|
376
|
JacobiRotation<Scalar> rot;
|
| ykuroda |
0:13a5d365ba16
|
377
|
RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));
|
| ykuroda |
0:13a5d365ba16
|
378
|
|
| ykuroda |
0:13a5d365ba16
|
379
|
if(n==0)
|
| ykuroda |
0:13a5d365ba16
|
380
|
{
|
| ykuroda |
0:13a5d365ba16
|
381
|
z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
|
| ykuroda |
0:13a5d365ba16
|
382
|
work_matrix.row(p) *= z;
|
| ykuroda |
0:13a5d365ba16
|
383
|
if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z);
|
| ykuroda |
0:13a5d365ba16
|
384
|
if(work_matrix.coeff(q,q)!=Scalar(0))
|
| ykuroda |
0:13a5d365ba16
|
385
|
{
|
| ykuroda |
0:13a5d365ba16
|
386
|
z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
|
| ykuroda |
0:13a5d365ba16
|
387
|
work_matrix.row(q) *= z;
|
| ykuroda |
0:13a5d365ba16
|
388
|
if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
|
| ykuroda |
0:13a5d365ba16
|
389
|
}
|
| ykuroda |
0:13a5d365ba16
|
390
|
// otherwise the second row is already zero, so we have nothing to do.
|
| ykuroda |
0:13a5d365ba16
|
391
|
}
|
| ykuroda |
0:13a5d365ba16
|
392
|
else
|
| ykuroda |
0:13a5d365ba16
|
393
|
{
|
| ykuroda |
0:13a5d365ba16
|
394
|
rot.c() = conj(work_matrix.coeff(p,p)) / n;
|
| ykuroda |
0:13a5d365ba16
|
395
|
rot.s() = work_matrix.coeff(q,p) / n;
|
| ykuroda |
0:13a5d365ba16
|
396
|
work_matrix.applyOnTheLeft(p,q,rot);
|
| ykuroda |
0:13a5d365ba16
|
397
|
if(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());
|
| ykuroda |
0:13a5d365ba16
|
398
|
if(work_matrix.coeff(p,q) != Scalar(0))
|
| ykuroda |
0:13a5d365ba16
|
399
|
{
|
| ykuroda |
0:13a5d365ba16
|
400
|
Scalar z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
|
| ykuroda |
0:13a5d365ba16
|
401
|
work_matrix.col(q) *= z;
|
| ykuroda |
0:13a5d365ba16
|
402
|
if(svd.computeV()) svd.m_matrixV.col(q) *= z;
|
| ykuroda |
0:13a5d365ba16
|
403
|
}
|
| ykuroda |
0:13a5d365ba16
|
404
|
if(work_matrix.coeff(q,q) != Scalar(0))
|
| ykuroda |
0:13a5d365ba16
|
405
|
{
|
| ykuroda |
0:13a5d365ba16
|
406
|
z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
|
| ykuroda |
0:13a5d365ba16
|
407
|
work_matrix.row(q) *= z;
|
| ykuroda |
0:13a5d365ba16
|
408
|
if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
|
| ykuroda |
0:13a5d365ba16
|
409
|
}
|
| ykuroda |
0:13a5d365ba16
|
410
|
}
|
| ykuroda |
0:13a5d365ba16
|
411
|
}
|
| ykuroda |
0:13a5d365ba16
|
412
|
};
|
| ykuroda |
0:13a5d365ba16
|
413
|
|
| ykuroda |
0:13a5d365ba16
|
414
|
template<typename MatrixType, typename RealScalar, typename Index>
|
| ykuroda |
0:13a5d365ba16
|
415
|
void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
|
| ykuroda |
0:13a5d365ba16
|
416
|
JacobiRotation<RealScalar> *j_left,
|
| ykuroda |
0:13a5d365ba16
|
417
|
JacobiRotation<RealScalar> *j_right)
|
| ykuroda |
0:13a5d365ba16
|
418
|
{
|
| ykuroda |
0:13a5d365ba16
|
419
|
using std::sqrt;
|
| ykuroda |
0:13a5d365ba16
|
420
|
using std::abs;
|
| ykuroda |
0:13a5d365ba16
|
421
|
Matrix<RealScalar,2,2> m;
|
| ykuroda |
0:13a5d365ba16
|
422
|
m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
|
| ykuroda |
0:13a5d365ba16
|
423
|
numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));
|
| ykuroda |
0:13a5d365ba16
|
424
|
JacobiRotation<RealScalar> rot1;
|
| ykuroda |
0:13a5d365ba16
|
425
|
RealScalar t = m.coeff(0,0) + m.coeff(1,1);
|
| ykuroda |
0:13a5d365ba16
|
426
|
RealScalar d = m.coeff(1,0) - m.coeff(0,1);
|
| ykuroda |
0:13a5d365ba16
|
427
|
if(t == RealScalar(0))
|
| ykuroda |
0:13a5d365ba16
|
428
|
{
|
| ykuroda |
0:13a5d365ba16
|
429
|
rot1.c() = RealScalar(0);
|
| ykuroda |
0:13a5d365ba16
|
430
|
rot1.s() = d > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
|
| ykuroda |
0:13a5d365ba16
|
431
|
}
|
| ykuroda |
0:13a5d365ba16
|
432
|
else
|
| ykuroda |
0:13a5d365ba16
|
433
|
{
|
| ykuroda |
0:13a5d365ba16
|
434
|
RealScalar t2d2 = numext::hypot(t,d);
|
| ykuroda |
0:13a5d365ba16
|
435
|
rot1.c() = abs(t)/t2d2;
|
| ykuroda |
0:13a5d365ba16
|
436
|
rot1.s() = d/t2d2;
|
| ykuroda |
0:13a5d365ba16
|
437
|
if(t<RealScalar(0))
|
| ykuroda |
0:13a5d365ba16
|
438
|
rot1.s() = -rot1.s();
|
| ykuroda |
0:13a5d365ba16
|
439
|
}
|
| ykuroda |
0:13a5d365ba16
|
440
|
m.applyOnTheLeft(0,1,rot1);
|
| ykuroda |
0:13a5d365ba16
|
441
|
j_right->makeJacobi(m,0,1);
|
| ykuroda |
0:13a5d365ba16
|
442
|
*j_left = rot1 * j_right->transpose();
|
| ykuroda |
0:13a5d365ba16
|
443
|
}
|
| ykuroda |
0:13a5d365ba16
|
444
|
|
| ykuroda |
0:13a5d365ba16
|
445
|
} // end namespace internal
|
| ykuroda |
0:13a5d365ba16
|
446
|
|
| ykuroda |
0:13a5d365ba16
|
447
|
/** \ingroup SVD_Module
|
| ykuroda |
0:13a5d365ba16
|
448
|
*
|
| ykuroda |
0:13a5d365ba16
|
449
|
*
|
| ykuroda |
0:13a5d365ba16
|
450
|
* \class JacobiSVD
|
| ykuroda |
0:13a5d365ba16
|
451
|
*
|
| ykuroda |
0:13a5d365ba16
|
452
|
* \brief Two-sided Jacobi SVD decomposition of a rectangular matrix
|
| ykuroda |
0:13a5d365ba16
|
453
|
*
|
| ykuroda |
0:13a5d365ba16
|
454
|
* \param MatrixType the type of the matrix of which we are computing the SVD decomposition
|
| ykuroda |
0:13a5d365ba16
|
455
|
* \param QRPreconditioner this optional parameter allows to specify the type of QR decomposition that will be used internally
|
| ykuroda |
0:13a5d365ba16
|
456
|
* for the R-SVD step for non-square matrices. See discussion of possible values below.
|
| ykuroda |
0:13a5d365ba16
|
457
|
*
|
| ykuroda |
0:13a5d365ba16
|
458
|
* SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
|
| ykuroda |
0:13a5d365ba16
|
459
|
* \f[ A = U S V^* \f]
|
| ykuroda |
0:13a5d365ba16
|
460
|
* 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;
|
| ykuroda |
0:13a5d365ba16
|
461
|
* 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
|
| ykuroda |
0:13a5d365ba16
|
462
|
* and right \em singular \em vectors of \a A respectively.
|
| ykuroda |
0:13a5d365ba16
|
463
|
*
|
| ykuroda |
0:13a5d365ba16
|
464
|
* Singular values are always sorted in decreasing order.
|
| ykuroda |
0:13a5d365ba16
|
465
|
*
|
| ykuroda |
0:13a5d365ba16
|
466
|
* 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.
|
| ykuroda |
0:13a5d365ba16
|
467
|
*
|
| ykuroda |
0:13a5d365ba16
|
468
|
* 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
|
| ykuroda |
0:13a5d365ba16
|
469
|
* 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
|
| ykuroda |
0:13a5d365ba16
|
470
|
* 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,
|
| ykuroda |
0:13a5d365ba16
|
471
|
* 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.
|
| ykuroda |
0:13a5d365ba16
|
472
|
*
|
| ykuroda |
0:13a5d365ba16
|
473
|
* Here's an example demonstrating basic usage:
|
| ykuroda |
0:13a5d365ba16
|
474
|
* \include JacobiSVD_basic.cpp
|
| ykuroda |
0:13a5d365ba16
|
475
|
* Output: \verbinclude JacobiSVD_basic.out
|
| ykuroda |
0:13a5d365ba16
|
476
|
*
|
| ykuroda |
0:13a5d365ba16
|
477
|
* This JacobiSVD class is a two-sided Jacobi R-SVD decomposition, ensuring optimal reliability and accuracy. The downside is that it's slower than
|
| ykuroda |
0:13a5d365ba16
|
478
|
* 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
|
| ykuroda |
0:13a5d365ba16
|
479
|
* \a p is the greater dimension, meaning that it is still of the same order of complexity as the faster bidiagonalizing R-SVD algorithms.
|
| ykuroda |
0:13a5d365ba16
|
480
|
* In particular, like any R-SVD, it takes advantage of non-squareness in that its complexity is only linear in the greater dimension.
|
| ykuroda |
0:13a5d365ba16
|
481
|
*
|
| ykuroda |
0:13a5d365ba16
|
482
|
* If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to
|
| ykuroda |
0:13a5d365ba16
|
483
|
* terminate in finite (and reasonable) time.
|
| ykuroda |
0:13a5d365ba16
|
484
|
*
|
| ykuroda |
0:13a5d365ba16
|
485
|
* The possible values for QRPreconditioner are:
|
| ykuroda |
0:13a5d365ba16
|
486
|
* \li ColPivHouseholderQRPreconditioner is the default. In practice it's very safe. It uses column-pivoting QR.
|
| ykuroda |
0:13a5d365ba16
|
487
|
* \li FullPivHouseholderQRPreconditioner, is the safest and slowest. It uses full-pivoting QR.
|
| ykuroda |
0:13a5d365ba16
|
488
|
* Contrary to other QRs, it doesn't allow computing thin unitaries.
|
| ykuroda |
0:13a5d365ba16
|
489
|
* \li HouseholderQRPreconditioner is the fastest, and less safe and accurate than the pivoting variants. It uses non-pivoting QR.
|
| ykuroda |
0:13a5d365ba16
|
490
|
* This is very similar in safety and accuracy to the bidiagonalization process used by bidiagonalizing SVD algorithms (since bidiagonalization
|
| ykuroda |
0:13a5d365ba16
|
491
|
* is inherently non-pivoting). However the resulting SVD is still more reliable than bidiagonalizing SVDs because the Jacobi-based iterarive
|
| ykuroda |
0:13a5d365ba16
|
492
|
* process is more reliable than the optimized bidiagonal SVD iterations.
|
| ykuroda |
0:13a5d365ba16
|
493
|
* \li NoQRPreconditioner allows not to use a QR preconditioner at all. This is useful if you know that you will only be computing
|
| ykuroda |
0:13a5d365ba16
|
494
|
* JacobiSVD decompositions of square matrices. Non-square matrices require a QR preconditioner. Using this option will result in
|
| ykuroda |
0:13a5d365ba16
|
495
|
* faster compilation and smaller executable code. It won't significantly speed up computation, since JacobiSVD is always checking
|
| ykuroda |
0:13a5d365ba16
|
496
|
* if QR preconditioning is needed before applying it anyway.
|
| ykuroda |
0:13a5d365ba16
|
497
|
*
|
| ykuroda |
0:13a5d365ba16
|
498
|
* \sa MatrixBase::jacobiSvd()
|
| ykuroda |
0:13a5d365ba16
|
499
|
*/
|
| ykuroda |
0:13a5d365ba16
|
500
|
template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
|
| ykuroda |
0:13a5d365ba16
|
501
|
{
|
| ykuroda |
0:13a5d365ba16
|
502
|
public:
|
| ykuroda |
0:13a5d365ba16
|
503
|
|
| ykuroda |
0:13a5d365ba16
|
504
|
typedef _MatrixType MatrixType;
|
| ykuroda |
0:13a5d365ba16
|
505
|
typedef typename MatrixType::Scalar Scalar;
|
| ykuroda |
0:13a5d365ba16
|
506
|
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
|
| ykuroda |
0:13a5d365ba16
|
507
|
typedef typename MatrixType::Index Index;
|
| ykuroda |
0:13a5d365ba16
|
508
|
enum {
|
| ykuroda |
0:13a5d365ba16
|
509
|
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
| ykuroda |
0:13a5d365ba16
|
510
|
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
| ykuroda |
0:13a5d365ba16
|
511
|
DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime),
|
| ykuroda |
0:13a5d365ba16
|
512
|
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
| ykuroda |
0:13a5d365ba16
|
513
|
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
|
| ykuroda |
0:13a5d365ba16
|
514
|
MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime),
|
| ykuroda |
0:13a5d365ba16
|
515
|
MatrixOptions = MatrixType::Options
|
| ykuroda |
0:13a5d365ba16
|
516
|
};
|
| ykuroda |
0:13a5d365ba16
|
517
|
|
| ykuroda |
0:13a5d365ba16
|
518
|
typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
|
| ykuroda |
0:13a5d365ba16
|
519
|
MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
|
| ykuroda |
0:13a5d365ba16
|
520
|
MatrixUType;
|
| ykuroda |
0:13a5d365ba16
|
521
|
typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
|
| ykuroda |
0:13a5d365ba16
|
522
|
MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
|
| ykuroda |
0:13a5d365ba16
|
523
|
MatrixVType;
|
| ykuroda |
0:13a5d365ba16
|
524
|
typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
|
| ykuroda |
0:13a5d365ba16
|
525
|
typedef typename internal::plain_row_type<MatrixType>::type RowType;
|
| ykuroda |
0:13a5d365ba16
|
526
|
typedef typename internal::plain_col_type<MatrixType>::type ColType;
|
| ykuroda |
0:13a5d365ba16
|
527
|
typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
|
| ykuroda |
0:13a5d365ba16
|
528
|
MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime>
|
| ykuroda |
0:13a5d365ba16
|
529
|
WorkMatrixType;
|
| ykuroda |
0:13a5d365ba16
|
530
|
|
| ykuroda |
0:13a5d365ba16
|
531
|
/** \brief Default Constructor.
|
| ykuroda |
0:13a5d365ba16
|
532
|
*
|
| ykuroda |
0:13a5d365ba16
|
533
|
* The default constructor is useful in cases in which the user intends to
|
| ykuroda |
0:13a5d365ba16
|
534
|
* perform decompositions via JacobiSVD::compute(const MatrixType&).
|
| ykuroda |
0:13a5d365ba16
|
535
|
*/
|
| ykuroda |
0:13a5d365ba16
|
536
|
JacobiSVD()
|
| ykuroda |
0:13a5d365ba16
|
537
|
: m_isInitialized(false),
|
| ykuroda |
0:13a5d365ba16
|
538
|
m_isAllocated(false),
|
| ykuroda |
0:13a5d365ba16
|
539
|
m_usePrescribedThreshold(false),
|
| ykuroda |
0:13a5d365ba16
|
540
|
m_computationOptions(0),
|
| ykuroda |
0:13a5d365ba16
|
541
|
m_rows(-1), m_cols(-1), m_diagSize(0)
|
| ykuroda |
0:13a5d365ba16
|
542
|
{}
|
| ykuroda |
0:13a5d365ba16
|
543
|
|
| ykuroda |
0:13a5d365ba16
|
544
|
|
| ykuroda |
0:13a5d365ba16
|
545
|
/** \brief Default Constructor with memory preallocation
|
| ykuroda |
0:13a5d365ba16
|
546
|
*
|
| ykuroda |
0:13a5d365ba16
|
547
|
* Like the default constructor but with preallocation of the internal data
|
| ykuroda |
0:13a5d365ba16
|
548
|
* according to the specified problem size.
|
| ykuroda |
0:13a5d365ba16
|
549
|
* \sa JacobiSVD()
|
| ykuroda |
0:13a5d365ba16
|
550
|
*/
|
| ykuroda |
0:13a5d365ba16
|
551
|
JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0)
|
| ykuroda |
0:13a5d365ba16
|
552
|
: m_isInitialized(false),
|
| ykuroda |
0:13a5d365ba16
|
553
|
m_isAllocated(false),
|
| ykuroda |
0:13a5d365ba16
|
554
|
m_usePrescribedThreshold(false),
|
| ykuroda |
0:13a5d365ba16
|
555
|
m_computationOptions(0),
|
| ykuroda |
0:13a5d365ba16
|
556
|
m_rows(-1), m_cols(-1)
|
| ykuroda |
0:13a5d365ba16
|
557
|
{
|
| ykuroda |
0:13a5d365ba16
|
558
|
allocate(rows, cols, computationOptions);
|
| ykuroda |
0:13a5d365ba16
|
559
|
}
|
| ykuroda |
0:13a5d365ba16
|
560
|
|
| ykuroda |
0:13a5d365ba16
|
561
|
/** \brief Constructor performing the decomposition of given matrix.
|
| ykuroda |
0:13a5d365ba16
|
562
|
*
|
| ykuroda |
0:13a5d365ba16
|
563
|
* \param matrix the matrix to decompose
|
| ykuroda |
0:13a5d365ba16
|
564
|
* \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
|
| ykuroda |
0:13a5d365ba16
|
565
|
* By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
|
| ykuroda |
0:13a5d365ba16
|
566
|
* #ComputeFullV, #ComputeThinV.
|
| ykuroda |
0:13a5d365ba16
|
567
|
*
|
| ykuroda |
0:13a5d365ba16
|
568
|
* Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
|
| ykuroda |
0:13a5d365ba16
|
569
|
* available with the (non-default) FullPivHouseholderQR preconditioner.
|
| ykuroda |
0:13a5d365ba16
|
570
|
*/
|
| ykuroda |
0:13a5d365ba16
|
571
|
JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
|
| ykuroda |
0:13a5d365ba16
|
572
|
: m_isInitialized(false),
|
| ykuroda |
0:13a5d365ba16
|
573
|
m_isAllocated(false),
|
| ykuroda |
0:13a5d365ba16
|
574
|
m_usePrescribedThreshold(false),
|
| ykuroda |
0:13a5d365ba16
|
575
|
m_computationOptions(0),
|
| ykuroda |
0:13a5d365ba16
|
576
|
m_rows(-1), m_cols(-1)
|
| ykuroda |
0:13a5d365ba16
|
577
|
{
|
| ykuroda |
0:13a5d365ba16
|
578
|
compute(matrix, computationOptions);
|
| ykuroda |
0:13a5d365ba16
|
579
|
}
|
| ykuroda |
0:13a5d365ba16
|
580
|
|
| ykuroda |
0:13a5d365ba16
|
581
|
/** \brief Method performing the decomposition of given matrix using custom options.
|
| ykuroda |
0:13a5d365ba16
|
582
|
*
|
| ykuroda |
0:13a5d365ba16
|
583
|
* \param matrix the matrix to decompose
|
| ykuroda |
0:13a5d365ba16
|
584
|
* \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
|
| ykuroda |
0:13a5d365ba16
|
585
|
* By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
|
| ykuroda |
0:13a5d365ba16
|
586
|
* #ComputeFullV, #ComputeThinV.
|
| ykuroda |
0:13a5d365ba16
|
587
|
*
|
| ykuroda |
0:13a5d365ba16
|
588
|
* Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
|
| ykuroda |
0:13a5d365ba16
|
589
|
* available with the (non-default) FullPivHouseholderQR preconditioner.
|
| ykuroda |
0:13a5d365ba16
|
590
|
*/
|
| ykuroda |
0:13a5d365ba16
|
591
|
JacobiSVD& compute(const MatrixType& matrix, unsigned int computationOptions);
|
| ykuroda |
0:13a5d365ba16
|
592
|
|
| ykuroda |
0:13a5d365ba16
|
593
|
/** \brief Method performing the decomposition of given matrix using current options.
|
| ykuroda |
0:13a5d365ba16
|
594
|
*
|
| ykuroda |
0:13a5d365ba16
|
595
|
* \param matrix the matrix to decompose
|
| ykuroda |
0:13a5d365ba16
|
596
|
*
|
| ykuroda |
0:13a5d365ba16
|
597
|
* This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
|
| ykuroda |
0:13a5d365ba16
|
598
|
*/
|
| ykuroda |
0:13a5d365ba16
|
599
|
JacobiSVD& compute(const MatrixType& matrix)
|
| ykuroda |
0:13a5d365ba16
|
600
|
{
|
| ykuroda |
0:13a5d365ba16
|
601
|
return compute(matrix, m_computationOptions);
|
| ykuroda |
0:13a5d365ba16
|
602
|
}
|
| ykuroda |
0:13a5d365ba16
|
603
|
|
| ykuroda |
0:13a5d365ba16
|
604
|
/** \returns the \a U matrix.
|
| ykuroda |
0:13a5d365ba16
|
605
|
*
|
| ykuroda |
0:13a5d365ba16
|
606
|
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
|
| ykuroda |
0:13a5d365ba16
|
607
|
* the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.
|
| ykuroda |
0:13a5d365ba16
|
608
|
*
|
| ykuroda |
0:13a5d365ba16
|
609
|
* The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
|
| ykuroda |
0:13a5d365ba16
|
610
|
*
|
| ykuroda |
0:13a5d365ba16
|
611
|
* This method asserts that you asked for \a U to be computed.
|
| ykuroda |
0:13a5d365ba16
|
612
|
*/
|
| ykuroda |
0:13a5d365ba16
|
613
|
const MatrixUType& matrixU() const
|
| ykuroda |
0:13a5d365ba16
|
614
|
{
|
| ykuroda |
0:13a5d365ba16
|
615
|
eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
|
| ykuroda |
0:13a5d365ba16
|
616
|
eigen_assert(computeU() && "This JacobiSVD decomposition didn't compute U. Did you ask for it?");
|
| ykuroda |
0:13a5d365ba16
|
617
|
return m_matrixU;
|
| ykuroda |
0:13a5d365ba16
|
618
|
}
|
| ykuroda |
0:13a5d365ba16
|
619
|
|
| ykuroda |
0:13a5d365ba16
|
620
|
/** \returns the \a V matrix.
|
| ykuroda |
0:13a5d365ba16
|
621
|
*
|
| ykuroda |
0:13a5d365ba16
|
622
|
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
|
| ykuroda |
0:13a5d365ba16
|
623
|
* the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV.
|
| ykuroda |
0:13a5d365ba16
|
624
|
*
|
| ykuroda |
0:13a5d365ba16
|
625
|
* The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
|
| ykuroda |
0:13a5d365ba16
|
626
|
*
|
| ykuroda |
0:13a5d365ba16
|
627
|
* This method asserts that you asked for \a V to be computed.
|
| ykuroda |
0:13a5d365ba16
|
628
|
*/
|
| ykuroda |
0:13a5d365ba16
|
629
|
const MatrixVType& matrixV() const
|
| ykuroda |
0:13a5d365ba16
|
630
|
{
|
| ykuroda |
0:13a5d365ba16
|
631
|
eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
|
| ykuroda |
0:13a5d365ba16
|
632
|
eigen_assert(computeV() && "This JacobiSVD decomposition didn't compute V. Did you ask for it?");
|
| ykuroda |
0:13a5d365ba16
|
633
|
return m_matrixV;
|
| ykuroda |
0:13a5d365ba16
|
634
|
}
|
| ykuroda |
0:13a5d365ba16
|
635
|
|
| ykuroda |
0:13a5d365ba16
|
636
|
/** \returns the vector of singular values.
|
| ykuroda |
0:13a5d365ba16
|
637
|
*
|
| ykuroda |
0:13a5d365ba16
|
638
|
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
|
| ykuroda |
0:13a5d365ba16
|
639
|
* returned vector has size \a m. Singular values are always sorted in decreasing order.
|
| ykuroda |
0:13a5d365ba16
|
640
|
*/
|
| ykuroda |
0:13a5d365ba16
|
641
|
const SingularValuesType& singularValues() const
|
| ykuroda |
0:13a5d365ba16
|
642
|
{
|
| ykuroda |
0:13a5d365ba16
|
643
|
eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
|
| ykuroda |
0:13a5d365ba16
|
644
|
return m_singularValues;
|
| ykuroda |
0:13a5d365ba16
|
645
|
}
|
| ykuroda |
0:13a5d365ba16
|
646
|
|
| ykuroda |
0:13a5d365ba16
|
647
|
/** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
|
| ykuroda |
0:13a5d365ba16
|
648
|
inline bool computeU() const { return m_computeFullU || m_computeThinU; }
|
| ykuroda |
0:13a5d365ba16
|
649
|
/** \returns true if \a V (full or thin) is asked for in this SVD decomposition */
|
| ykuroda |
0:13a5d365ba16
|
650
|
inline bool computeV() const { return m_computeFullV || m_computeThinV; }
|
| ykuroda |
0:13a5d365ba16
|
651
|
|
| ykuroda |
0:13a5d365ba16
|
652
|
/** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
|
| ykuroda |
0:13a5d365ba16
|
653
|
*
|
| ykuroda |
0:13a5d365ba16
|
654
|
* \param b the right-hand-side of the equation to solve.
|
| ykuroda |
0:13a5d365ba16
|
655
|
*
|
| ykuroda |
0:13a5d365ba16
|
656
|
* \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.
|
| ykuroda |
0:13a5d365ba16
|
657
|
*
|
| ykuroda |
0:13a5d365ba16
|
658
|
* \note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving.
|
| ykuroda |
0:13a5d365ba16
|
659
|
* In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert A x - b \Vert \f$.
|
| ykuroda |
0:13a5d365ba16
|
660
|
*/
|
| ykuroda |
0:13a5d365ba16
|
661
|
template<typename Rhs>
|
| ykuroda |
0:13a5d365ba16
|
662
|
inline const internal::solve_retval<JacobiSVD, Rhs>
|
| ykuroda |
0:13a5d365ba16
|
663
|
solve(const MatrixBase<Rhs>& b) const
|
| ykuroda |
0:13a5d365ba16
|
664
|
{
|
| ykuroda |
0:13a5d365ba16
|
665
|
eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
|
| ykuroda |
0:13a5d365ba16
|
666
|
eigen_assert(computeU() && computeV() && "JacobiSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
|
| ykuroda |
0:13a5d365ba16
|
667
|
return internal::solve_retval<JacobiSVD, Rhs>(*this, b.derived());
|
| ykuroda |
0:13a5d365ba16
|
668
|
}
|
| ykuroda |
0:13a5d365ba16
|
669
|
|
| ykuroda |
0:13a5d365ba16
|
670
|
/** \returns the number of singular values that are not exactly 0 */
|
| ykuroda |
0:13a5d365ba16
|
671
|
Index nonzeroSingularValues() const
|
| ykuroda |
0:13a5d365ba16
|
672
|
{
|
| ykuroda |
0:13a5d365ba16
|
673
|
eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
|
| ykuroda |
0:13a5d365ba16
|
674
|
return m_nonzeroSingularValues;
|
| ykuroda |
0:13a5d365ba16
|
675
|
}
|
| ykuroda |
0:13a5d365ba16
|
676
|
|
| ykuroda |
0:13a5d365ba16
|
677
|
/** \returns the rank of the matrix of which \c *this is the SVD.
|
| ykuroda |
0:13a5d365ba16
|
678
|
*
|
| ykuroda |
0:13a5d365ba16
|
679
|
* \note This method has to determine which singular values should be considered nonzero.
|
| ykuroda |
0:13a5d365ba16
|
680
|
* For that, it uses the threshold value that you can control by calling
|
| ykuroda |
0:13a5d365ba16
|
681
|
* setThreshold(const RealScalar&).
|
| ykuroda |
0:13a5d365ba16
|
682
|
*/
|
| ykuroda |
0:13a5d365ba16
|
683
|
inline Index rank() const
|
| ykuroda |
0:13a5d365ba16
|
684
|
{
|
| ykuroda |
0:13a5d365ba16
|
685
|
using std::abs;
|
| ykuroda |
0:13a5d365ba16
|
686
|
eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
|
| ykuroda |
0:13a5d365ba16
|
687
|
if(m_singularValues.size()==0) return 0;
|
| ykuroda |
0:13a5d365ba16
|
688
|
RealScalar premultiplied_threshold = m_singularValues.coeff(0) * threshold();
|
| ykuroda |
0:13a5d365ba16
|
689
|
Index i = m_nonzeroSingularValues-1;
|
| ykuroda |
0:13a5d365ba16
|
690
|
while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
|
| ykuroda |
0:13a5d365ba16
|
691
|
return i+1;
|
| ykuroda |
0:13a5d365ba16
|
692
|
}
|
| ykuroda |
0:13a5d365ba16
|
693
|
|
| ykuroda |
0:13a5d365ba16
|
694
|
/** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
|
| ykuroda |
0:13a5d365ba16
|
695
|
* which need to determine when singular values are to be considered nonzero.
|
| ykuroda |
0:13a5d365ba16
|
696
|
* This is not used for the SVD decomposition itself.
|
| ykuroda |
0:13a5d365ba16
|
697
|
*
|
| ykuroda |
0:13a5d365ba16
|
698
|
* When it needs to get the threshold value, Eigen calls threshold().
|
| ykuroda |
0:13a5d365ba16
|
699
|
* The default is \c NumTraits<Scalar>::epsilon()
|
| ykuroda |
0:13a5d365ba16
|
700
|
*
|
| ykuroda |
0:13a5d365ba16
|
701
|
* \param threshold The new value to use as the threshold.
|
| ykuroda |
0:13a5d365ba16
|
702
|
*
|
| ykuroda |
0:13a5d365ba16
|
703
|
* A singular value will be considered nonzero if its value is strictly greater than
|
| ykuroda |
0:13a5d365ba16
|
704
|
* \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
|
| ykuroda |
0:13a5d365ba16
|
705
|
*
|
| ykuroda |
0:13a5d365ba16
|
706
|
* If you want to come back to the default behavior, call setThreshold(Default_t)
|
| ykuroda |
0:13a5d365ba16
|
707
|
*/
|
| ykuroda |
0:13a5d365ba16
|
708
|
JacobiSVD& setThreshold(const RealScalar& threshold)
|
| ykuroda |
0:13a5d365ba16
|
709
|
{
|
| ykuroda |
0:13a5d365ba16
|
710
|
m_usePrescribedThreshold = true;
|
| ykuroda |
0:13a5d365ba16
|
711
|
m_prescribedThreshold = threshold;
|
| ykuroda |
0:13a5d365ba16
|
712
|
return *this;
|
| ykuroda |
0:13a5d365ba16
|
713
|
}
|
| ykuroda |
0:13a5d365ba16
|
714
|
|
| ykuroda |
0:13a5d365ba16
|
715
|
/** Allows to come back to the default behavior, letting Eigen use its default formula for
|
| ykuroda |
0:13a5d365ba16
|
716
|
* determining the threshold.
|
| ykuroda |
0:13a5d365ba16
|
717
|
*
|
| ykuroda |
0:13a5d365ba16
|
718
|
* You should pass the special object Eigen::Default as parameter here.
|
| ykuroda |
0:13a5d365ba16
|
719
|
* \code svd.setThreshold(Eigen::Default); \endcode
|
| ykuroda |
0:13a5d365ba16
|
720
|
*
|
| ykuroda |
0:13a5d365ba16
|
721
|
* See the documentation of setThreshold(const RealScalar&).
|
| ykuroda |
0:13a5d365ba16
|
722
|
*/
|
| ykuroda |
0:13a5d365ba16
|
723
|
JacobiSVD& setThreshold(Default_t)
|
| ykuroda |
0:13a5d365ba16
|
724
|
{
|
| ykuroda |
0:13a5d365ba16
|
725
|
m_usePrescribedThreshold = false;
|
| ykuroda |
0:13a5d365ba16
|
726
|
return *this;
|
| ykuroda |
0:13a5d365ba16
|
727
|
}
|
| ykuroda |
0:13a5d365ba16
|
728
|
|
| ykuroda |
0:13a5d365ba16
|
729
|
/** Returns the threshold that will be used by certain methods such as rank().
|
| ykuroda |
0:13a5d365ba16
|
730
|
*
|
| ykuroda |
0:13a5d365ba16
|
731
|
* See the documentation of setThreshold(const RealScalar&).
|
| ykuroda |
0:13a5d365ba16
|
732
|
*/
|
| ykuroda |
0:13a5d365ba16
|
733
|
RealScalar threshold() const
|
| ykuroda |
0:13a5d365ba16
|
734
|
{
|
| ykuroda |
0:13a5d365ba16
|
735
|
eigen_assert(m_isInitialized || m_usePrescribedThreshold);
|
| ykuroda |
0:13a5d365ba16
|
736
|
return m_usePrescribedThreshold ? m_prescribedThreshold
|
| ykuroda |
0:13a5d365ba16
|
737
|
: (std::max<Index>)(1,m_diagSize)*NumTraits<Scalar>::epsilon();
|
| ykuroda |
0:13a5d365ba16
|
738
|
}
|
| ykuroda |
0:13a5d365ba16
|
739
|
|
| ykuroda |
0:13a5d365ba16
|
740
|
inline Index rows() const { return m_rows; }
|
| ykuroda |
0:13a5d365ba16
|
741
|
inline Index cols() const { return m_cols; }
|
| ykuroda |
0:13a5d365ba16
|
742
|
|
| ykuroda |
0:13a5d365ba16
|
743
|
private:
|
| ykuroda |
0:13a5d365ba16
|
744
|
void allocate(Index rows, Index cols, unsigned int computationOptions);
|
| ykuroda |
0:13a5d365ba16
|
745
|
|
| ykuroda |
0:13a5d365ba16
|
746
|
static void check_template_parameters()
|
| ykuroda |
0:13a5d365ba16
|
747
|
{
|
| ykuroda |
0:13a5d365ba16
|
748
|
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
|
| ykuroda |
0:13a5d365ba16
|
749
|
}
|
| ykuroda |
0:13a5d365ba16
|
750
|
|
| ykuroda |
0:13a5d365ba16
|
751
|
protected:
|
| ykuroda |
0:13a5d365ba16
|
752
|
MatrixUType m_matrixU;
|
| ykuroda |
0:13a5d365ba16
|
753
|
MatrixVType m_matrixV;
|
| ykuroda |
0:13a5d365ba16
|
754
|
SingularValuesType m_singularValues;
|
| ykuroda |
0:13a5d365ba16
|
755
|
WorkMatrixType m_workMatrix;
|
| ykuroda |
0:13a5d365ba16
|
756
|
bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;
|
| ykuroda |
0:13a5d365ba16
|
757
|
bool m_computeFullU, m_computeThinU;
|
| ykuroda |
0:13a5d365ba16
|
758
|
bool m_computeFullV, m_computeThinV;
|
| ykuroda |
0:13a5d365ba16
|
759
|
unsigned int m_computationOptions;
|
| ykuroda |
0:13a5d365ba16
|
760
|
Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;
|
| ykuroda |
0:13a5d365ba16
|
761
|
RealScalar m_prescribedThreshold;
|
| ykuroda |
0:13a5d365ba16
|
762
|
|
| ykuroda |
0:13a5d365ba16
|
763
|
template<typename __MatrixType, int _QRPreconditioner, bool _IsComplex>
|
| ykuroda |
0:13a5d365ba16
|
764
|
friend struct internal::svd_precondition_2x2_block_to_be_real;
|
| ykuroda |
0:13a5d365ba16
|
765
|
template<typename __MatrixType, int _QRPreconditioner, int _Case, bool _DoAnything>
|
| ykuroda |
0:13a5d365ba16
|
766
|
friend struct internal::qr_preconditioner_impl;
|
| ykuroda |
0:13a5d365ba16
|
767
|
|
| ykuroda |
0:13a5d365ba16
|
768
|
internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreColsThanRows> m_qr_precond_morecols;
|
| ykuroda |
0:13a5d365ba16
|
769
|
internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols> m_qr_precond_morerows;
|
| ykuroda |
0:13a5d365ba16
|
770
|
MatrixType m_scaledMatrix;
|
| ykuroda |
0:13a5d365ba16
|
771
|
};
|
| ykuroda |
0:13a5d365ba16
|
772
|
|
| ykuroda |
0:13a5d365ba16
|
773
|
template<typename MatrixType, int QRPreconditioner>
|
| ykuroda |
0:13a5d365ba16
|
774
|
void JacobiSVD<MatrixType, QRPreconditioner>::allocate(Index rows, Index cols, unsigned int computationOptions)
|
| ykuroda |
0:13a5d365ba16
|
775
|
{
|
| ykuroda |
0:13a5d365ba16
|
776
|
eigen_assert(rows >= 0 && cols >= 0);
|
| ykuroda |
0:13a5d365ba16
|
777
|
|
| ykuroda |
0:13a5d365ba16
|
778
|
if (m_isAllocated &&
|
| ykuroda |
0:13a5d365ba16
|
779
|
rows == m_rows &&
|
| ykuroda |
0:13a5d365ba16
|
780
|
cols == m_cols &&
|
| ykuroda |
0:13a5d365ba16
|
781
|
computationOptions == m_computationOptions)
|
| ykuroda |
0:13a5d365ba16
|
782
|
{
|
| ykuroda |
0:13a5d365ba16
|
783
|
return;
|
| ykuroda |
0:13a5d365ba16
|
784
|
}
|
| ykuroda |
0:13a5d365ba16
|
785
|
|
| ykuroda |
0:13a5d365ba16
|
786
|
m_rows = rows;
|
| ykuroda |
0:13a5d365ba16
|
787
|
m_cols = cols;
|
| ykuroda |
0:13a5d365ba16
|
788
|
m_isInitialized = false;
|
| ykuroda |
0:13a5d365ba16
|
789
|
m_isAllocated = true;
|
| ykuroda |
0:13a5d365ba16
|
790
|
m_computationOptions = computationOptions;
|
| ykuroda |
0:13a5d365ba16
|
791
|
m_computeFullU = (computationOptions & ComputeFullU) != 0;
|
| ykuroda |
0:13a5d365ba16
|
792
|
m_computeThinU = (computationOptions & ComputeThinU) != 0;
|
| ykuroda |
0:13a5d365ba16
|
793
|
m_computeFullV = (computationOptions & ComputeFullV) != 0;
|
| ykuroda |
0:13a5d365ba16
|
794
|
m_computeThinV = (computationOptions & ComputeThinV) != 0;
|
| ykuroda |
0:13a5d365ba16
|
795
|
eigen_assert(!(m_computeFullU && m_computeThinU) && "JacobiSVD: you can't ask for both full and thin U");
|
| ykuroda |
0:13a5d365ba16
|
796
|
eigen_assert(!(m_computeFullV && m_computeThinV) && "JacobiSVD: you can't ask for both full and thin V");
|
| ykuroda |
0:13a5d365ba16
|
797
|
eigen_assert(EIGEN_IMPLIES(m_computeThinU || m_computeThinV, MatrixType::ColsAtCompileTime==Dynamic) &&
|
| ykuroda |
0:13a5d365ba16
|
798
|
"JacobiSVD: thin U and V are only available when your matrix has a dynamic number of columns.");
|
| ykuroda |
0:13a5d365ba16
|
799
|
if (QRPreconditioner == FullPivHouseholderQRPreconditioner)
|
| ykuroda |
0:13a5d365ba16
|
800
|
{
|
| ykuroda |
0:13a5d365ba16
|
801
|
eigen_assert(!(m_computeThinU || m_computeThinV) &&
|
| ykuroda |
0:13a5d365ba16
|
802
|
"JacobiSVD: can't compute thin U or thin V with the FullPivHouseholderQR preconditioner. "
|
| ykuroda |
0:13a5d365ba16
|
803
|
"Use the ColPivHouseholderQR preconditioner instead.");
|
| ykuroda |
0:13a5d365ba16
|
804
|
}
|
| ykuroda |
0:13a5d365ba16
|
805
|
m_diagSize = (std::min)(m_rows, m_cols);
|
| ykuroda |
0:13a5d365ba16
|
806
|
m_singularValues.resize(m_diagSize);
|
| ykuroda |
0:13a5d365ba16
|
807
|
if(RowsAtCompileTime==Dynamic)
|
| ykuroda |
0:13a5d365ba16
|
808
|
m_matrixU.resize(m_rows, m_computeFullU ? m_rows
|
| ykuroda |
0:13a5d365ba16
|
809
|
: m_computeThinU ? m_diagSize
|
| ykuroda |
0:13a5d365ba16
|
810
|
: 0);
|
| ykuroda |
0:13a5d365ba16
|
811
|
if(ColsAtCompileTime==Dynamic)
|
| ykuroda |
0:13a5d365ba16
|
812
|
m_matrixV.resize(m_cols, m_computeFullV ? m_cols
|
| ykuroda |
0:13a5d365ba16
|
813
|
: m_computeThinV ? m_diagSize
|
| ykuroda |
0:13a5d365ba16
|
814
|
: 0);
|
| ykuroda |
0:13a5d365ba16
|
815
|
m_workMatrix.resize(m_diagSize, m_diagSize);
|
| ykuroda |
0:13a5d365ba16
|
816
|
|
| ykuroda |
0:13a5d365ba16
|
817
|
if(m_cols>m_rows) m_qr_precond_morecols.allocate(*this);
|
| ykuroda |
0:13a5d365ba16
|
818
|
if(m_rows>m_cols) m_qr_precond_morerows.allocate(*this);
|
| ykuroda |
0:13a5d365ba16
|
819
|
if(m_rows!=m_cols) m_scaledMatrix.resize(rows,cols);
|
| ykuroda |
0:13a5d365ba16
|
820
|
}
|
| ykuroda |
0:13a5d365ba16
|
821
|
|
| ykuroda |
0:13a5d365ba16
|
822
|
template<typename MatrixType, int QRPreconditioner>
|
| ykuroda |
0:13a5d365ba16
|
823
|
JacobiSVD<MatrixType, QRPreconditioner>&
|
| ykuroda |
0:13a5d365ba16
|
824
|
JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsigned int computationOptions)
|
| ykuroda |
0:13a5d365ba16
|
825
|
{
|
| ykuroda |
0:13a5d365ba16
|
826
|
check_template_parameters();
|
| ykuroda |
0:13a5d365ba16
|
827
|
|
| ykuroda |
0:13a5d365ba16
|
828
|
using std::abs;
|
| ykuroda |
0:13a5d365ba16
|
829
|
allocate(matrix.rows(), matrix.cols(), computationOptions);
|
| ykuroda |
0:13a5d365ba16
|
830
|
|
| ykuroda |
0:13a5d365ba16
|
831
|
// currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number of iterations,
|
| ykuroda |
0:13a5d365ba16
|
832
|
// only worsening the precision of U and V as we accumulate more rotations
|
| ykuroda |
0:13a5d365ba16
|
833
|
const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();
|
| ykuroda |
0:13a5d365ba16
|
834
|
|
| ykuroda |
0:13a5d365ba16
|
835
|
// limit for very small denormal numbers to be considered zero in order to avoid infinite loops (see bug 286)
|
| ykuroda |
0:13a5d365ba16
|
836
|
const RealScalar considerAsZero = RealScalar(2) * std::numeric_limits<RealScalar>::denorm_min();
|
| ykuroda |
0:13a5d365ba16
|
837
|
|
| ykuroda |
0:13a5d365ba16
|
838
|
// Scaling factor to reduce over/under-flows
|
| ykuroda |
0:13a5d365ba16
|
839
|
RealScalar scale = matrix.cwiseAbs().maxCoeff();
|
| ykuroda |
0:13a5d365ba16
|
840
|
if(scale==RealScalar(0)) scale = RealScalar(1);
|
| ykuroda |
0:13a5d365ba16
|
841
|
|
| ykuroda |
0:13a5d365ba16
|
842
|
/*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */
|
| ykuroda |
0:13a5d365ba16
|
843
|
|
| ykuroda |
0:13a5d365ba16
|
844
|
if(m_rows!=m_cols)
|
| ykuroda |
0:13a5d365ba16
|
845
|
{
|
| ykuroda |
0:13a5d365ba16
|
846
|
m_scaledMatrix = matrix / scale;
|
| ykuroda |
0:13a5d365ba16
|
847
|
m_qr_precond_morecols.run(*this, m_scaledMatrix);
|
| ykuroda |
0:13a5d365ba16
|
848
|
m_qr_precond_morerows.run(*this, m_scaledMatrix);
|
| ykuroda |
0:13a5d365ba16
|
849
|
}
|
| ykuroda |
0:13a5d365ba16
|
850
|
else
|
| ykuroda |
0:13a5d365ba16
|
851
|
{
|
| ykuroda |
0:13a5d365ba16
|
852
|
m_workMatrix = matrix.block(0,0,m_diagSize,m_diagSize) / scale;
|
| ykuroda |
0:13a5d365ba16
|
853
|
if(m_computeFullU) m_matrixU.setIdentity(m_rows,m_rows);
|
| ykuroda |
0:13a5d365ba16
|
854
|
if(m_computeThinU) m_matrixU.setIdentity(m_rows,m_diagSize);
|
| ykuroda |
0:13a5d365ba16
|
855
|
if(m_computeFullV) m_matrixV.setIdentity(m_cols,m_cols);
|
| ykuroda |
0:13a5d365ba16
|
856
|
if(m_computeThinV) m_matrixV.setIdentity(m_cols, m_diagSize);
|
| ykuroda |
0:13a5d365ba16
|
857
|
}
|
| ykuroda |
0:13a5d365ba16
|
858
|
|
| ykuroda |
0:13a5d365ba16
|
859
|
/*** step 2. The main Jacobi SVD iteration. ***/
|
| ykuroda |
0:13a5d365ba16
|
860
|
|
| ykuroda |
0:13a5d365ba16
|
861
|
bool finished = false;
|
| ykuroda |
0:13a5d365ba16
|
862
|
while(!finished)
|
| ykuroda |
0:13a5d365ba16
|
863
|
{
|
| ykuroda |
0:13a5d365ba16
|
864
|
finished = true;
|
| ykuroda |
0:13a5d365ba16
|
865
|
|
| ykuroda |
0:13a5d365ba16
|
866
|
// do a sweep: for all index pairs (p,q), perform SVD of the corresponding 2x2 sub-matrix
|
| ykuroda |
0:13a5d365ba16
|
867
|
|
| ykuroda |
0:13a5d365ba16
|
868
|
for(Index p = 1; p < m_diagSize; ++p)
|
| ykuroda |
0:13a5d365ba16
|
869
|
{
|
| ykuroda |
0:13a5d365ba16
|
870
|
for(Index q = 0; q < p; ++q)
|
| ykuroda |
0:13a5d365ba16
|
871
|
{
|
| ykuroda |
0:13a5d365ba16
|
872
|
// if this 2x2 sub-matrix is not diagonal already...
|
| ykuroda |
0:13a5d365ba16
|
873
|
// notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't
|
| ykuroda |
0:13a5d365ba16
|
874
|
// keep us iterating forever. Similarly, small denormal numbers are considered zero.
|
| ykuroda |
0:13a5d365ba16
|
875
|
using std::max;
|
| ykuroda |
0:13a5d365ba16
|
876
|
RealScalar threshold = (max)(considerAsZero, precision * (max)(abs(m_workMatrix.coeff(p,p)),
|
| ykuroda |
0:13a5d365ba16
|
877
|
abs(m_workMatrix.coeff(q,q))));
|
| ykuroda |
0:13a5d365ba16
|
878
|
// We compare both values to threshold instead of calling max to be robust to NaN (See bug 791)
|
| ykuroda |
0:13a5d365ba16
|
879
|
if(abs(m_workMatrix.coeff(p,q))>threshold || abs(m_workMatrix.coeff(q,p)) > threshold)
|
| ykuroda |
0:13a5d365ba16
|
880
|
{
|
| ykuroda |
0:13a5d365ba16
|
881
|
finished = false;
|
| ykuroda |
0:13a5d365ba16
|
882
|
|
| ykuroda |
0:13a5d365ba16
|
883
|
// perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal
|
| ykuroda |
0:13a5d365ba16
|
884
|
internal::svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner>::run(m_workMatrix, *this, p, q);
|
| ykuroda |
0:13a5d365ba16
|
885
|
JacobiRotation<RealScalar> j_left, j_right;
|
| ykuroda |
0:13a5d365ba16
|
886
|
internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right);
|
| ykuroda |
0:13a5d365ba16
|
887
|
|
| ykuroda |
0:13a5d365ba16
|
888
|
// accumulate resulting Jacobi rotations
|
| ykuroda |
0:13a5d365ba16
|
889
|
m_workMatrix.applyOnTheLeft(p,q,j_left);
|
| ykuroda |
0:13a5d365ba16
|
890
|
if(computeU()) m_matrixU.applyOnTheRight(p,q,j_left.transpose());
|
| ykuroda |
0:13a5d365ba16
|
891
|
|
| ykuroda |
0:13a5d365ba16
|
892
|
m_workMatrix.applyOnTheRight(p,q,j_right);
|
| ykuroda |
0:13a5d365ba16
|
893
|
if(computeV()) m_matrixV.applyOnTheRight(p,q,j_right);
|
| ykuroda |
0:13a5d365ba16
|
894
|
}
|
| ykuroda |
0:13a5d365ba16
|
895
|
}
|
| ykuroda |
0:13a5d365ba16
|
896
|
}
|
| ykuroda |
0:13a5d365ba16
|
897
|
}
|
| ykuroda |
0:13a5d365ba16
|
898
|
|
| ykuroda |
0:13a5d365ba16
|
899
|
/*** step 3. The work matrix is now diagonal, so ensure it's positive so its diagonal entries are the singular values ***/
|
| ykuroda |
0:13a5d365ba16
|
900
|
|
| ykuroda |
0:13a5d365ba16
|
901
|
for(Index i = 0; i < m_diagSize; ++i)
|
| ykuroda |
0:13a5d365ba16
|
902
|
{
|
| ykuroda |
0:13a5d365ba16
|
903
|
RealScalar a = abs(m_workMatrix.coeff(i,i));
|
| ykuroda |
0:13a5d365ba16
|
904
|
m_singularValues.coeffRef(i) = a;
|
| ykuroda |
0:13a5d365ba16
|
905
|
if(computeU() && (a!=RealScalar(0))) m_matrixU.col(i) *= m_workMatrix.coeff(i,i)/a;
|
| ykuroda |
0:13a5d365ba16
|
906
|
}
|
| ykuroda |
0:13a5d365ba16
|
907
|
|
| ykuroda |
0:13a5d365ba16
|
908
|
/*** step 4. Sort singular values in descending order and compute the number of nonzero singular values ***/
|
| ykuroda |
0:13a5d365ba16
|
909
|
|
| ykuroda |
0:13a5d365ba16
|
910
|
m_nonzeroSingularValues = m_diagSize;
|
| ykuroda |
0:13a5d365ba16
|
911
|
for(Index i = 0; i < m_diagSize; i++)
|
| ykuroda |
0:13a5d365ba16
|
912
|
{
|
| ykuroda |
0:13a5d365ba16
|
913
|
Index pos;
|
| ykuroda |
0:13a5d365ba16
|
914
|
RealScalar maxRemainingSingularValue = m_singularValues.tail(m_diagSize-i).maxCoeff(&pos);
|
| ykuroda |
0:13a5d365ba16
|
915
|
if(maxRemainingSingularValue == RealScalar(0))
|
| ykuroda |
0:13a5d365ba16
|
916
|
{
|
| ykuroda |
0:13a5d365ba16
|
917
|
m_nonzeroSingularValues = i;
|
| ykuroda |
0:13a5d365ba16
|
918
|
break;
|
| ykuroda |
0:13a5d365ba16
|
919
|
}
|
| ykuroda |
0:13a5d365ba16
|
920
|
if(pos)
|
| ykuroda |
0:13a5d365ba16
|
921
|
{
|
| ykuroda |
0:13a5d365ba16
|
922
|
pos += i;
|
| ykuroda |
0:13a5d365ba16
|
923
|
std::swap(m_singularValues.coeffRef(i), m_singularValues.coeffRef(pos));
|
| ykuroda |
0:13a5d365ba16
|
924
|
if(computeU()) m_matrixU.col(pos).swap(m_matrixU.col(i));
|
| ykuroda |
0:13a5d365ba16
|
925
|
if(computeV()) m_matrixV.col(pos).swap(m_matrixV.col(i));
|
| ykuroda |
0:13a5d365ba16
|
926
|
}
|
| ykuroda |
0:13a5d365ba16
|
927
|
}
|
| ykuroda |
0:13a5d365ba16
|
928
|
|
| ykuroda |
0:13a5d365ba16
|
929
|
m_singularValues *= scale;
|
| ykuroda |
0:13a5d365ba16
|
930
|
|
| ykuroda |
0:13a5d365ba16
|
931
|
m_isInitialized = true;
|
| ykuroda |
0:13a5d365ba16
|
932
|
return *this;
|
| ykuroda |
0:13a5d365ba16
|
933
|
}
|
| ykuroda |
0:13a5d365ba16
|
934
|
|
| ykuroda |
0:13a5d365ba16
|
935
|
namespace internal {
|
| ykuroda |
0:13a5d365ba16
|
936
|
template<typename _MatrixType, int QRPreconditioner, typename Rhs>
|
| ykuroda |
0:13a5d365ba16
|
937
|
struct solve_retval<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs>
|
| ykuroda |
0:13a5d365ba16
|
938
|
: solve_retval_base<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs>
|
| ykuroda |
0:13a5d365ba16
|
939
|
{
|
| ykuroda |
0:13a5d365ba16
|
940
|
typedef JacobiSVD<_MatrixType, QRPreconditioner> JacobiSVDType;
|
| ykuroda |
0:13a5d365ba16
|
941
|
EIGEN_MAKE_SOLVE_HELPERS(JacobiSVDType,Rhs)
|
| ykuroda |
0:13a5d365ba16
|
942
|
|
| ykuroda |
0:13a5d365ba16
|
943
|
template<typename Dest> void evalTo(Dest& dst) const
|
| ykuroda |
0:13a5d365ba16
|
944
|
{
|
| ykuroda |
0:13a5d365ba16
|
945
|
eigen_assert(rhs().rows() == dec().rows());
|
| ykuroda |
0:13a5d365ba16
|
946
|
|
| ykuroda |
0:13a5d365ba16
|
947
|
// A = U S V^*
|
| ykuroda |
0:13a5d365ba16
|
948
|
// So A^{-1} = V S^{-1} U^*
|
| ykuroda |
0:13a5d365ba16
|
949
|
|
| ykuroda |
0:13a5d365ba16
|
950
|
Matrix<Scalar, Dynamic, Rhs::ColsAtCompileTime, 0, _MatrixType::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime> tmp;
|
| ykuroda |
0:13a5d365ba16
|
951
|
Index rank = dec().rank();
|
| ykuroda |
0:13a5d365ba16
|
952
|
|
| ykuroda |
0:13a5d365ba16
|
953
|
tmp.noalias() = dec().matrixU().leftCols(rank).adjoint() * rhs();
|
| ykuroda |
0:13a5d365ba16
|
954
|
tmp = dec().singularValues().head(rank).asDiagonal().inverse() * tmp;
|
| ykuroda |
0:13a5d365ba16
|
955
|
dst = dec().matrixV().leftCols(rank) * tmp;
|
| ykuroda |
0:13a5d365ba16
|
956
|
}
|
| ykuroda |
0:13a5d365ba16
|
957
|
};
|
| ykuroda |
0:13a5d365ba16
|
958
|
} // end namespace internal
|
| ykuroda |
0:13a5d365ba16
|
959
|
|
| ykuroda |
0:13a5d365ba16
|
960
|
/** \svd_module
|
| ykuroda |
0:13a5d365ba16
|
961
|
*
|
| ykuroda |
0:13a5d365ba16
|
962
|
* \return the singular value decomposition of \c *this computed by two-sided
|
| ykuroda |
0:13a5d365ba16
|
963
|
* Jacobi transformations.
|
| ykuroda |
0:13a5d365ba16
|
964
|
*
|
| ykuroda |
0:13a5d365ba16
|
965
|
* \sa class JacobiSVD
|
| ykuroda |
0:13a5d365ba16
|
966
|
*/
|
| ykuroda |
0:13a5d365ba16
|
967
|
template<typename Derived>
|
| ykuroda |
0:13a5d365ba16
|
968
|
JacobiSVD<typename MatrixBase<Derived>::PlainObject>
|
| ykuroda |
0:13a5d365ba16
|
969
|
MatrixBase<Derived>::jacobiSvd(unsigned int computationOptions) const
|
| ykuroda |
0:13a5d365ba16
|
970
|
{
|
| ykuroda |
0:13a5d365ba16
|
971
|
return JacobiSVD<PlainObject>(*this, computationOptions);
|
| ykuroda |
0:13a5d365ba16
|
972
|
}
|
| ykuroda |
0:13a5d365ba16
|
973
|
|
| ykuroda |
0:13a5d365ba16
|
974
|
} // end namespace Eigen
|
| ykuroda |
0:13a5d365ba16
|
975
|
|
| ykuroda |
0:13a5d365ba16
|
976
|
#endif // EIGEN_JACOBISVD_H |