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-// 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 _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
-      */
-    explicit 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