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diff --git a/third_party/eigen3/Eigen/src/Eigenvalues/Tridiagonalization.h b/third_party/eigen3/Eigen/src/Eigenvalues/Tridiagonalization.h deleted file mode 100644 index 192278d685..0000000000 --- a/third_party/eigen3/Eigen/src/Eigenvalues/Tridiagonalization.h +++ /dev/null @@ -1,557 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 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_TRIDIAGONALIZATION_H -#define EIGEN_TRIDIAGONALIZATION_H - -namespace Eigen { - -namespace internal { - -template<typename MatrixType> struct TridiagonalizationMatrixTReturnType; -template<typename MatrixType> -struct traits<TridiagonalizationMatrixTReturnType<MatrixType> > -{ - typedef typename MatrixType::PlainObject ReturnType; -}; - -template<typename MatrixType, typename CoeffVectorType> -void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs); -} - -/** \eigenvalues_module \ingroup Eigenvalues_Module - * - * - * \class Tridiagonalization - * - * \brief Tridiagonal decomposition of a selfadjoint matrix - * - * \tparam _MatrixType the type of the matrix of which we are computing the - * tridiagonal decomposition; this is expected to be an instantiation of the - * Matrix class template. - * - * This class performs a tridiagonal decomposition of a selfadjoint matrix \f$ A \f$ such that: - * \f$ A = Q T Q^* \f$ where \f$ Q \f$ is unitary and \f$ T \f$ a real symmetric tridiagonal matrix. - * - * A tridiagonal matrix is a matrix which has nonzero elements only on the - * main diagonal and the first diagonal below and above it. The Hessenberg - * decomposition of a selfadjoint matrix is in fact a tridiagonal - * decomposition. This class is used in SelfAdjointEigenSolver to compute the - * eigenvalues and eigenvectors of a selfadjoint matrix. - * - * Call the function compute() to compute the tridiagonal decomposition of a - * given matrix. Alternatively, you can use the Tridiagonalization(const MatrixType&) - * constructor which computes the tridiagonal Schur decomposition at - * construction time. Once the decomposition is computed, you can use the - * matrixQ() and matrixT() functions to retrieve the matrices Q and T in the - * decomposition. - * - * The documentation of Tridiagonalization(const MatrixType&) contains an - * example of the typical use of this class. - * - * \sa class HessenbergDecomposition, class SelfAdjointEigenSolver - */ -template<typename _MatrixType> class Tridiagonalization -{ - public: - - /** \brief Synonym for the template parameter \p _MatrixType. */ - typedef _MatrixType MatrixType; - - typedef typename MatrixType::Scalar Scalar; - typedef typename NumTraits<Scalar>::Real RealScalar; - typedef typename MatrixType::Index Index; - - enum { - Size = MatrixType::RowsAtCompileTime, - SizeMinusOne = Size == Dynamic ? Dynamic : (Size > 1 ? Size - 1 : 1), - Options = MatrixType::Options, - MaxSize = MatrixType::MaxRowsAtCompileTime, - MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : (MaxSize > 1 ? MaxSize - 1 : 1) - }; - - typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType; - typedef typename internal::plain_col_type<MatrixType, RealScalar>::type DiagonalType; - typedef Matrix<RealScalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> SubDiagonalType; - typedef typename internal::remove_all<typename MatrixType::RealReturnType>::type MatrixTypeRealView; - typedef internal::TridiagonalizationMatrixTReturnType<MatrixTypeRealView> MatrixTReturnType; - - typedef typename internal::conditional<NumTraits<Scalar>::IsComplex, - typename internal::add_const_on_value_type<typename Diagonal<const MatrixType>::RealReturnType>::type, - const Diagonal<const MatrixType> - >::type DiagonalReturnType; - - typedef typename internal::conditional<NumTraits<Scalar>::IsComplex, - typename internal::add_const_on_value_type<typename Diagonal< - Block<const MatrixType,SizeMinusOne,SizeMinusOne> >::RealReturnType>::type, - const Diagonal< - Block<const MatrixType,SizeMinusOne,SizeMinusOne> > - >::type SubDiagonalReturnType; - - /** \brief Return type of matrixQ() */ - typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename CoeffVectorType::ConjugateReturnType>::type> HouseholderSequenceType; - - /** \brief Default constructor. - * - * \param [in] size Positive integer, size of the matrix whose tridiagonal - * decomposition will be computed. - * - * The default constructor is useful in cases in which 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. - */ - Tridiagonalization(Index size = Size==Dynamic ? 2 : Size) - : m_matrix(size,size), - m_hCoeffs(size > 1 ? size-1 : 1), - m_isInitialized(false) - {} - - /** \brief Constructor; computes tridiagonal decomposition of given matrix. - * - * \param[in] matrix Selfadjoint matrix whose tridiagonal decomposition - * is to be computed. - * - * This constructor calls compute() to compute the tridiagonal decomposition. - * - * Example: \include Tridiagonalization_Tridiagonalization_MatrixType.cpp - * Output: \verbinclude Tridiagonalization_Tridiagonalization_MatrixType.out - */ - Tridiagonalization(const MatrixType& matrix) - : m_matrix(matrix), - m_hCoeffs(matrix.cols() > 1 ? matrix.cols()-1 : 1), - m_isInitialized(false) - { - internal::tridiagonalization_inplace(m_matrix, m_hCoeffs); - m_isInitialized = true; - } - - /** \brief Computes tridiagonal decomposition of given matrix. - * - * \param[in] matrix Selfadjoint matrix whose tridiagonal decomposition - * is to be computed. - * \returns Reference to \c *this - * - * The tridiagonal decomposition is computed by bringing the columns of - * the matrix successively in the required form using Householder - * reflections. The cost is \f$ 4n^3/3 \f$ flops, where \f$ n \f$ denotes - * the size of the given matrix. - * - * This method reuses of the allocated data in the Tridiagonalization - * object, if the size of the matrix does not change. - * - * Example: \include Tridiagonalization_compute.cpp - * Output: \verbinclude Tridiagonalization_compute.out - */ - Tridiagonalization& compute(const MatrixType& matrix) - { - m_matrix = matrix; - m_hCoeffs.resize(matrix.rows()-1, 1); - internal::tridiagonalization_inplace(m_matrix, m_hCoeffs); - m_isInitialized = true; - return *this; - } - - /** \brief Returns the Householder coefficients. - * - * \returns a const reference to the vector of Householder coefficients - * - * \pre Either the constructor Tridiagonalization(const MatrixType&) or - * the member function compute(const MatrixType&) has been called before - * to compute the tridiagonal decomposition of a matrix. - * - * The Householder coefficients allow the reconstruction of the matrix - * \f$ Q \f$ in the tridiagonal decomposition from the packed data. - * - * Example: \include Tridiagonalization_householderCoefficients.cpp - * Output: \verbinclude Tridiagonalization_householderCoefficients.out - * - * \sa packedMatrix(), \ref Householder_Module "Householder module" - */ - inline CoeffVectorType householderCoefficients() const - { - eigen_assert(m_isInitialized && "Tridiagonalization is not initialized."); - return m_hCoeffs; - } - - /** \brief Returns the internal representation of the decomposition - * - * \returns a const reference to a matrix with the internal representation - * of the decomposition. - * - * \pre Either the constructor Tridiagonalization(const MatrixType&) or - * the member function compute(const MatrixType&) has been called before - * to compute the tridiagonal decomposition of a matrix. - * - * The returned matrix contains the following information: - * - the strict upper triangular part is equal to the input matrix A. - * - the diagonal and lower sub-diagonal represent the real tridiagonal - * symmetric matrix T. - * - the rest of the lower part contains the Householder vectors that, - * combined with Householder coefficients returned by - * householderCoefficients(), allows to reconstruct the matrix Q as - * \f$ Q = H_{N-1} \ldots H_1 H_0 \f$. - * Here, the matrices \f$ H_i \f$ are the Householder transformations - * \f$ H_i = (I - h_i v_i v_i^T) \f$ - * where \f$ h_i \f$ is the \f$ i \f$th Householder coefficient and - * \f$ v_i \f$ is the Householder vector defined by - * \f$ v_i = [ 0, \ldots, 0, 1, M(i+2,i), \ldots, M(N-1,i) ]^T \f$ - * with M the matrix returned by this function. - * - * See LAPACK for further details on this packed storage. - * - * Example: \include Tridiagonalization_packedMatrix.cpp - * Output: \verbinclude Tridiagonalization_packedMatrix.out - * - * \sa householderCoefficients() - */ - inline const MatrixType& packedMatrix() const - { - eigen_assert(m_isInitialized && "Tridiagonalization is not initialized."); - return m_matrix; - } - - /** \brief Returns the unitary matrix Q in the decomposition - * - * \returns object representing the matrix Q - * - * \pre Either the constructor Tridiagonalization(const MatrixType&) or - * the member function compute(const MatrixType&) has been called before - * to compute the tridiagonal decomposition of a matrix. - * - * This function returns a light-weight object of template class - * HouseholderSequence. You can either apply it directly to a matrix or - * you can convert it to a matrix of type #MatrixType. - * - * \sa Tridiagonalization(const MatrixType&) for an example, - * matrixT(), class HouseholderSequence - */ - HouseholderSequenceType matrixQ() const - { - eigen_assert(m_isInitialized && "Tridiagonalization is not initialized."); - return HouseholderSequenceType(m_matrix, m_hCoeffs.conjugate()) - .setLength(m_matrix.rows() - 1) - .setShift(1); - } - - /** \brief Returns an expression of the tridiagonal matrix T in the decomposition - * - * \returns expression object representing the matrix T - * - * \pre Either the constructor Tridiagonalization(const MatrixType&) or - * the member function compute(const MatrixType&) has been called before - * to compute the tridiagonal decomposition of a matrix. - * - * Currently, this function can be used to extract the matrix T from internal - * data and copy it to a dense matrix object. In most cases, it may be - * sufficient to directly use the packed matrix or the vector expressions - * returned by diagonal() and subDiagonal() instead of creating a new - * dense copy matrix with this function. - * - * \sa Tridiagonalization(const MatrixType&) for an example, - * matrixQ(), packedMatrix(), diagonal(), subDiagonal() - */ - MatrixTReturnType matrixT() const - { - eigen_assert(m_isInitialized && "Tridiagonalization is not initialized."); - return MatrixTReturnType(m_matrix.real()); - } - - /** \brief Returns the diagonal of the tridiagonal matrix T in the decomposition. - * - * \returns expression representing the diagonal of T - * - * \pre Either the constructor Tridiagonalization(const MatrixType&) or - * the member function compute(const MatrixType&) has been called before - * to compute the tridiagonal decomposition of a matrix. - * - * Example: \include Tridiagonalization_diagonal.cpp - * Output: \verbinclude Tridiagonalization_diagonal.out - * - * \sa matrixT(), subDiagonal() - */ - DiagonalReturnType diagonal() const; - - /** \brief Returns the subdiagonal of the tridiagonal matrix T in the decomposition. - * - * \returns expression representing the subdiagonal of T - * - * \pre Either the constructor Tridiagonalization(const MatrixType&) or - * the member function compute(const MatrixType&) has been called before - * to compute the tridiagonal decomposition of a matrix. - * - * \sa diagonal() for an example, matrixT() - */ - SubDiagonalReturnType subDiagonal() const; - - protected: - - MatrixType m_matrix; - CoeffVectorType m_hCoeffs; - bool m_isInitialized; -}; - -template<typename MatrixType> -typename Tridiagonalization<MatrixType>::DiagonalReturnType -Tridiagonalization<MatrixType>::diagonal() const -{ - eigen_assert(m_isInitialized && "Tridiagonalization is not initialized."); - return m_matrix.diagonal(); -} - -template<typename MatrixType> -typename Tridiagonalization<MatrixType>::SubDiagonalReturnType -Tridiagonalization<MatrixType>::subDiagonal() const -{ - eigen_assert(m_isInitialized && "Tridiagonalization is not initialized."); - Index n = m_matrix.rows(); - return Block<const MatrixType,SizeMinusOne,SizeMinusOne>(m_matrix, 1, 0, n-1,n-1).diagonal(); -} - -namespace internal { - -/** \internal - * Performs a tridiagonal decomposition of the selfadjoint matrix \a matA in-place. - * - * \param[in,out] matA On input the selfadjoint matrix. Only the \b lower triangular part is referenced. - * On output, the strict upper part is left unchanged, and the lower triangular part - * represents the T and Q matrices in packed format has detailed below. - * \param[out] hCoeffs returned Householder coefficients (see below) - * - * On output, the tridiagonal selfadjoint matrix T is stored in the diagonal - * and lower sub-diagonal of the matrix \a matA. - * The unitary matrix Q is represented in a compact way as a product of - * Householder reflectors \f$ H_i \f$ such that: - * \f$ Q = H_{N-1} \ldots H_1 H_0 \f$. - * The Householder reflectors are defined as - * \f$ H_i = (I - h_i v_i v_i^T) \f$ - * where \f$ h_i = hCoeffs[i]\f$ is the \f$ i \f$th Householder coefficient and - * \f$ v_i \f$ is the Householder vector defined by - * \f$ v_i = [ 0, \ldots, 0, 1, matA(i+2,i), \ldots, matA(N-1,i) ]^T \f$. - * - * Implemented from Golub's "Matrix Computations", algorithm 8.3.1. - * - * \sa Tridiagonalization::packedMatrix() - */ -template<typename MatrixType, typename CoeffVectorType> -void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs) -{ - using numext::conj; - typedef typename MatrixType::Index Index; - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::RealScalar RealScalar; - Index n = matA.rows(); - eigen_assert(n==matA.cols()); - eigen_assert(n==hCoeffs.size()+1 || n==1); - - for (Index i = 0; i<n-1; ++i) - { - Index remainingSize = n-i-1; - RealScalar beta; - Scalar h; - matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta); - - // Apply similarity transformation to remaining columns, - // i.e., A = H A H' where H = I - h v v' and v = matA.col(i).tail(n-i-1) - matA.col(i).coeffRef(i+1) = 1; - - hCoeffs.tail(n-i-1).noalias() = (matA.bottomRightCorner(remainingSize,remainingSize).template selfadjointView<Lower>() - * (conj(h) * matA.col(i).tail(remainingSize))); - - hCoeffs.tail(n-i-1) += (conj(h)*Scalar(-0.5)*(hCoeffs.tail(remainingSize).dot(matA.col(i).tail(remainingSize)))) * matA.col(i).tail(n-i-1); - - matA.bottomRightCorner(remainingSize, remainingSize).template selfadjointView<Lower>() - .rankUpdate(matA.col(i).tail(remainingSize), hCoeffs.tail(remainingSize), -1); - - matA.col(i).coeffRef(i+1) = beta; - hCoeffs.coeffRef(i) = h; - } -} - -// forward declaration, implementation at the end of this file -template<typename MatrixType, - int Size=MatrixType::ColsAtCompileTime, - bool IsComplex=NumTraits<typename MatrixType::Scalar>::IsComplex> -struct tridiagonalization_inplace_selector; - -/** \brief Performs a full tridiagonalization in place - * - * \param[in,out] mat On input, the selfadjoint matrix whose tridiagonal - * decomposition is to be computed. Only the lower triangular part referenced. - * The rest is left unchanged. On output, the orthogonal matrix Q - * in the decomposition if \p extractQ is true. - * \param[out] diag The diagonal of the tridiagonal matrix T in the - * decomposition. - * \param[out] subdiag The subdiagonal of the tridiagonal matrix T in - * the decomposition. - * \param[in] extractQ If true, the orthogonal matrix Q in the - * decomposition is computed and stored in \p mat. - * - * Computes the tridiagonal decomposition of the selfadjoint matrix \p mat in place - * such that \f$ mat = Q T Q^* \f$ where \f$ Q \f$ is unitary and \f$ T \f$ a real - * symmetric tridiagonal matrix. - * - * The tridiagonal matrix T is passed to the output parameters \p diag and \p subdiag. If - * \p extractQ is true, then the orthogonal matrix Q is passed to \p mat. Otherwise the lower - * part of the matrix \p mat is destroyed. - * - * The vectors \p diag and \p subdiag are not resized. The function - * assumes that they are already of the correct size. The length of the - * vector \p diag should equal the number of rows in \p mat, and the - * length of the vector \p subdiag should be one left. - * - * This implementation contains an optimized path for 3-by-3 matrices - * which is especially useful for plane fitting. - * - * \note Currently, it requires two temporary vectors to hold the intermediate - * Householder coefficients, and to reconstruct the matrix Q from the Householder - * reflectors. - * - * Example (this uses the same matrix as the example in - * Tridiagonalization::Tridiagonalization(const MatrixType&)): - * \include Tridiagonalization_decomposeInPlace.cpp - * Output: \verbinclude Tridiagonalization_decomposeInPlace.out - * - * \sa class Tridiagonalization - */ -template<typename MatrixType, typename DiagonalType, typename SubDiagonalType> -void tridiagonalization_inplace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ) -{ - eigen_assert(mat.cols()==mat.rows() && diag.size()==mat.rows() && subdiag.size()==mat.rows()-1); - tridiagonalization_inplace_selector<MatrixType>::run(mat, diag, subdiag, extractQ); -} - -/** \internal - * General full tridiagonalization - */ -template<typename MatrixType, int Size, bool IsComplex> -struct tridiagonalization_inplace_selector -{ - typedef typename Tridiagonalization<MatrixType>::CoeffVectorType CoeffVectorType; - typedef typename Tridiagonalization<MatrixType>::HouseholderSequenceType HouseholderSequenceType; - typedef typename MatrixType::Index Index; - template<typename DiagonalType, typename SubDiagonalType> - static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ) - { - CoeffVectorType hCoeffs(mat.cols()-1); - tridiagonalization_inplace(mat,hCoeffs); - diag = mat.diagonal().real(); - subdiag = mat.template diagonal<-1>().real(); - if(extractQ) - mat = HouseholderSequenceType(mat, hCoeffs.conjugate()) - .setLength(mat.rows() - 1) - .setShift(1); - } -}; - -/** \internal - * Specialization for 3x3 real matrices. - * Especially useful for plane fitting. - */ -template<typename MatrixType> -struct tridiagonalization_inplace_selector<MatrixType,3,false> -{ - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::RealScalar RealScalar; - - template<typename DiagonalType, typename SubDiagonalType> - static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ) - { - using std::sqrt; - diag[0] = mat(0,0); - RealScalar v1norm2 = numext::abs2(mat(2,0)); - if(v1norm2 == RealScalar(0)) - { - diag[1] = mat(1,1); - diag[2] = mat(2,2); - subdiag[0] = mat(1,0); - subdiag[1] = mat(2,1); - if (extractQ) - mat.setIdentity(); - } - else - { - RealScalar beta = sqrt(numext::abs2(mat(1,0)) + v1norm2); - RealScalar invBeta = RealScalar(1)/beta; - Scalar m01 = mat(1,0) * invBeta; - Scalar m02 = mat(2,0) * invBeta; - Scalar q = RealScalar(2)*m01*mat(2,1) + m02*(mat(2,2) - mat(1,1)); - diag[1] = mat(1,1) + m02*q; - diag[2] = mat(2,2) - m02*q; - subdiag[0] = beta; - subdiag[1] = mat(2,1) - m01 * q; - if (extractQ) - { - mat << 1, 0, 0, - 0, m01, m02, - 0, m02, -m01; - } - } - } -}; - -/** \internal - * Trivial specialization for 1x1 matrices - */ -template<typename MatrixType, bool IsComplex> -struct tridiagonalization_inplace_selector<MatrixType,1,IsComplex> -{ - typedef typename MatrixType::Scalar Scalar; - - template<typename DiagonalType, typename SubDiagonalType> - static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType&, bool extractQ) - { - diag(0,0) = numext::real(mat(0,0)); - if(extractQ) - mat(0,0) = Scalar(1); - } -}; - -/** \internal - * \eigenvalues_module \ingroup Eigenvalues_Module - * - * \brief Expression type for return value of Tridiagonalization::matrixT() - * - * \tparam MatrixType type of underlying dense matrix - */ -template<typename MatrixType> struct TridiagonalizationMatrixTReturnType -: public ReturnByValue<TridiagonalizationMatrixTReturnType<MatrixType> > -{ - typedef typename MatrixType::Index Index; - public: - /** \brief Constructor. - * - * \param[in] mat The underlying dense matrix - */ - TridiagonalizationMatrixTReturnType(const MatrixType& mat) : m_matrix(mat) { } - - template <typename ResultType> - inline void evalTo(ResultType& result) const - { - result.setZero(); - result.template diagonal<1>() = m_matrix.template diagonal<-1>().conjugate(); - result.diagonal() = m_matrix.diagonal(); - result.template diagonal<-1>() = m_matrix.template diagonal<-1>(); - } - - Index rows() const { return m_matrix.rows(); } - Index cols() const { return m_matrix.cols(); } - - protected: - typename MatrixType::Nested m_matrix; -}; - -} // end namespace internal - -} // end namespace Eigen - -#endif // EIGEN_TRIDIAGONALIZATION_H |