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diff --git a/third_party/eigen3/Eigen/src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h b/third_party/eigen3/Eigen/src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h deleted file mode 100644 index 07bf1ea095..0000000000 --- a/third_party/eigen3/Eigen/src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h +++ /dev/null @@ -1,227 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr> -// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk> -// -// 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_GENERALIZEDSELFADJOINTEIGENSOLVER_H -#define EIGEN_GENERALIZEDSELFADJOINTEIGENSOLVER_H - -#include "./Tridiagonalization.h" - -namespace Eigen { - -/** \eigenvalues_module \ingroup Eigenvalues_Module - * - * - * \class GeneralizedSelfAdjointEigenSolver - * - * \brief Computes eigenvalues and eigenvectors of the generalized selfadjoint eigen problem - * - * \tparam _MatrixType the type of the matrix of which we are computing the - * eigendecomposition; this is expected to be an instantiation of the Matrix - * class template. - * - * This class solves the generalized eigenvalue problem - * \f$ Av = \lambda Bv \f$. In this case, the matrix \f$ A \f$ should be - * selfadjoint and the matrix \f$ B \f$ should be positive definite. - * - * Only the \b lower \b triangular \b part of the input matrix is referenced. - * - * Call the function compute() to compute the eigenvalues and eigenvectors of - * a given matrix. Alternatively, you can use the - * GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int) - * constructor which computes the eigenvalues and eigenvectors at construction time. - * Once the eigenvalue and eigenvectors are computed, they can be retrieved with the eigenvalues() - * and eigenvectors() functions. - * - * The documentation for GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int) - * contains an example of the typical use of this class. - * - * \sa class SelfAdjointEigenSolver, class EigenSolver, class ComplexEigenSolver - */ -template<typename _MatrixType> -class GeneralizedSelfAdjointEigenSolver : public SelfAdjointEigenSolver<_MatrixType> -{ - typedef SelfAdjointEigenSolver<_MatrixType> Base; - public: - - typedef typename Base::Index Index; - typedef _MatrixType MatrixType; - - /** \brief Default constructor for fixed-size matrices. - * - * The default constructor is useful in cases in which the user intends to - * perform decompositions via compute(). This constructor - * can only be used if \p _MatrixType is a fixed-size matrix; use - * GeneralizedSelfAdjointEigenSolver(Index) for dynamic-size matrices. - */ - GeneralizedSelfAdjointEigenSolver() : Base() {} - - /** \brief Constructor, pre-allocates memory for dynamic-size matrices. - * - * \param [in] size Positive integer, size of the matrix whose - * eigenvalues and eigenvectors will be computed. - * - * This constructor is useful for dynamic-size matrices, when the user - * intends to perform decompositions via compute(). The \p size - * parameter is only used as a hint. It is not an error to give a wrong - * \p size, but it may impair performance. - * - * \sa compute() for an example - */ - GeneralizedSelfAdjointEigenSolver(Index size) - : Base(size) - {} - - /** \brief Constructor; computes generalized eigendecomposition of given matrix pencil. - * - * \param[in] matA Selfadjoint matrix in matrix pencil. - * Only the lower triangular part of the matrix is referenced. - * \param[in] matB Positive-definite matrix in matrix pencil. - * Only the lower triangular part of the matrix is referenced. - * \param[in] options A or-ed set of flags {#ComputeEigenvectors,#EigenvaluesOnly} | {#Ax_lBx,#ABx_lx,#BAx_lx}. - * Default is #ComputeEigenvectors|#Ax_lBx. - * - * This constructor calls compute(const MatrixType&, const MatrixType&, int) - * to compute the eigenvalues and (if requested) the eigenvectors of the - * generalized eigenproblem \f$ Ax = \lambda B x \f$ with \a matA the - * selfadjoint matrix \f$ A \f$ and \a matB the positive definite matrix - * \f$ B \f$. Each eigenvector \f$ x \f$ satisfies the property - * \f$ x^* B x = 1 \f$. The eigenvectors are computed if - * \a options contains ComputeEigenvectors. - * - * In addition, the two following variants can be solved via \p options: - * - \c ABx_lx: \f$ ABx = \lambda x \f$ - * - \c BAx_lx: \f$ BAx = \lambda x \f$ - * - * Example: \include SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp - * Output: \verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.out - * - * \sa compute(const MatrixType&, const MatrixType&, int) - */ - GeneralizedSelfAdjointEigenSolver(const MatrixType& matA, const MatrixType& matB, - int options = ComputeEigenvectors|Ax_lBx) - : Base(matA.cols()) - { - compute(matA, matB, options); - } - - /** \brief Computes generalized eigendecomposition of given matrix pencil. - * - * \param[in] matA Selfadjoint matrix in matrix pencil. - * Only the lower triangular part of the matrix is referenced. - * \param[in] matB Positive-definite matrix in matrix pencil. - * Only the lower triangular part of the matrix is referenced. - * \param[in] options A or-ed set of flags {#ComputeEigenvectors,#EigenvaluesOnly} | {#Ax_lBx,#ABx_lx,#BAx_lx}. - * Default is #ComputeEigenvectors|#Ax_lBx. - * - * \returns Reference to \c *this - * - * Accoring to \p options, this function computes eigenvalues and (if requested) - * the eigenvectors of one of the following three generalized eigenproblems: - * - \c Ax_lBx: \f$ Ax = \lambda B x \f$ - * - \c ABx_lx: \f$ ABx = \lambda x \f$ - * - \c BAx_lx: \f$ BAx = \lambda x \f$ - * with \a matA the selfadjoint matrix \f$ A \f$ and \a matB the positive definite - * matrix \f$ B \f$. - * In addition, each eigenvector \f$ x \f$ satisfies the property \f$ x^* B x = 1 \f$. - * - * The eigenvalues() function can be used to retrieve - * the eigenvalues. If \p options contains ComputeEigenvectors, then the - * eigenvectors are also computed and can be retrieved by calling - * eigenvectors(). - * - * The implementation uses LLT to compute the Cholesky decomposition - * \f$ B = LL^* \f$ and computes the classical eigendecomposition - * of the selfadjoint matrix \f$ L^{-1} A (L^*)^{-1} \f$ if \p options contains Ax_lBx - * and of \f$ L^{*} A L \f$ otherwise. This solves the - * generalized eigenproblem, because any solution of the generalized - * eigenproblem \f$ Ax = \lambda B x \f$ corresponds to a solution - * \f$ L^{-1} A (L^*)^{-1} (L^* x) = \lambda (L^* x) \f$ of the - * eigenproblem for \f$ L^{-1} A (L^*)^{-1} \f$. Similar statements - * can be made for the two other variants. - * - * Example: \include SelfAdjointEigenSolver_compute_MatrixType2.cpp - * Output: \verbinclude SelfAdjointEigenSolver_compute_MatrixType2.out - * - * \sa GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int) - */ - GeneralizedSelfAdjointEigenSolver& compute(const MatrixType& matA, const MatrixType& matB, - int options = ComputeEigenvectors|Ax_lBx); - - protected: - -}; - - -template<typename MatrixType> -GeneralizedSelfAdjointEigenSolver<MatrixType>& GeneralizedSelfAdjointEigenSolver<MatrixType>:: -compute(const MatrixType& matA, const MatrixType& matB, int options) -{ - eigen_assert(matA.cols()==matA.rows() && matB.rows()==matA.rows() && matB.cols()==matB.rows()); - eigen_assert((options&~(EigVecMask|GenEigMask))==0 - && (options&EigVecMask)!=EigVecMask - && ((options&GenEigMask)==0 || (options&GenEigMask)==Ax_lBx - || (options&GenEigMask)==ABx_lx || (options&GenEigMask)==BAx_lx) - && "invalid option parameter"); - - bool computeEigVecs = ((options&EigVecMask)==0) || ((options&EigVecMask)==ComputeEigenvectors); - - // Compute the cholesky decomposition of matB = L L' = U'U - LLT<MatrixType> cholB(matB); - - int type = (options&GenEigMask); - if(type==0) - type = Ax_lBx; - - if(type==Ax_lBx) - { - // compute C = inv(L) A inv(L') - MatrixType matC = matA.template selfadjointView<Lower>(); - cholB.matrixL().template solveInPlace<OnTheLeft>(matC); - cholB.matrixU().template solveInPlace<OnTheRight>(matC); - - Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly ); - - // transform back the eigen vectors: evecs = inv(U) * evecs - if(computeEigVecs) - cholB.matrixU().solveInPlace(Base::m_eivec); - } - else if(type==ABx_lx) - { - // compute C = L' A L - MatrixType matC = matA.template selfadjointView<Lower>(); - matC = matC * cholB.matrixL(); - matC = cholB.matrixU() * matC; - - Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly); - - // transform back the eigen vectors: evecs = inv(U) * evecs - if(computeEigVecs) - cholB.matrixU().solveInPlace(Base::m_eivec); - } - else if(type==BAx_lx) - { - // compute C = L' A L - MatrixType matC = matA.template selfadjointView<Lower>(); - matC = matC * cholB.matrixL(); - matC = cholB.matrixU() * matC; - - Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly); - - // transform back the eigen vectors: evecs = L * evecs - if(computeEigVecs) - Base::m_eivec = cholB.matrixL() * Base::m_eivec; - } - - return *this; -} - -} // end namespace Eigen - -#endif // EIGEN_GENERALIZEDSELFADJOINTEIGENSOLVER_H |