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Diffstat (limited to 'extern/Eigen2/Eigen/src/QR/HessenbergDecomposition.h')
| -rw-r--r-- | extern/Eigen2/Eigen/src/QR/HessenbergDecomposition.h | 250 |
1 files changed, 0 insertions, 250 deletions
diff --git a/extern/Eigen2/Eigen/src/QR/HessenbergDecomposition.h b/extern/Eigen2/Eigen/src/QR/HessenbergDecomposition.h deleted file mode 100644 index 6d0ff794ec2..00000000000 --- a/extern/Eigen2/Eigen/src/QR/HessenbergDecomposition.h +++ /dev/null @@ -1,250 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. Eigen itself is part of the KDE project. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> -// -// Eigen is free software; you can redistribute it and/or -// modify it under the terms of the GNU Lesser General Public -// License as published by the Free Software Foundation; either -// version 3 of the License, or (at your option) any later version. -// -// Alternatively, you can redistribute it and/or -// modify it under the terms of the GNU General Public License as -// published by the Free Software Foundation; either version 2 of -// the License, or (at your option) any later version. -// -// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY -// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS -// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the -// GNU General Public License for more details. -// -// You should have received a copy of the GNU Lesser General Public -// License and a copy of the GNU General Public License along with -// Eigen. If not, see <http://www.gnu.org/licenses/>. - -#ifndef EIGEN_HESSENBERGDECOMPOSITION_H -#define EIGEN_HESSENBERGDECOMPOSITION_H - -/** \ingroup QR_Module - * \nonstableyet - * - * \class HessenbergDecomposition - * - * \brief Reduces a squared matrix to an Hessemberg form - * - * \param MatrixType the type of the matrix of which we are computing the Hessenberg decomposition - * - * This class performs an Hessenberg decomposition of a matrix \f$ A \f$ such that: - * \f$ A = Q H Q^* \f$ where \f$ Q \f$ is unitary and \f$ H \f$ a Hessenberg matrix. - * - * \sa class Tridiagonalization, class Qr - */ -template<typename _MatrixType> class HessenbergDecomposition -{ - public: - - typedef _MatrixType MatrixType; - typedef typename MatrixType::Scalar Scalar; - typedef typename NumTraits<Scalar>::Real RealScalar; - - enum { - Size = MatrixType::RowsAtCompileTime, - SizeMinusOne = MatrixType::RowsAtCompileTime==Dynamic - ? Dynamic - : MatrixType::RowsAtCompileTime-1 - }; - - typedef Matrix<Scalar, SizeMinusOne, 1> CoeffVectorType; - typedef Matrix<RealScalar, Size, 1> DiagonalType; - typedef Matrix<RealScalar, SizeMinusOne, 1> SubDiagonalType; - - typedef typename NestByValue<DiagonalCoeffs<MatrixType> >::RealReturnType DiagonalReturnType; - - typedef typename NestByValue<DiagonalCoeffs< - NestByValue<Block<MatrixType,SizeMinusOne,SizeMinusOne> > > >::RealReturnType SubDiagonalReturnType; - - /** This constructor initializes a HessenbergDecomposition object for - * further use with HessenbergDecomposition::compute() - */ - HessenbergDecomposition(int size = Size==Dynamic ? 2 : Size) - : m_matrix(size,size), m_hCoeffs(size-1) - {} - - HessenbergDecomposition(const MatrixType& matrix) - : m_matrix(matrix), - m_hCoeffs(matrix.cols()-1) - { - _compute(m_matrix, m_hCoeffs); - } - - /** Computes or re-compute the Hessenberg decomposition for the matrix \a matrix. - * - * This method allows to re-use the allocated data. - */ - void compute(const MatrixType& matrix) - { - m_matrix = matrix; - m_hCoeffs.resize(matrix.rows()-1,1); - _compute(m_matrix, m_hCoeffs); - } - - /** \returns the householder coefficients allowing to - * reconstruct the matrix Q from the packed data. - * - * \sa packedMatrix() - */ - CoeffVectorType householderCoefficients(void) const { return m_hCoeffs; } - - /** \returns the internal result of the decomposition. - * - * The returned matrix contains the following information: - * - the upper part and lower sub-diagonal represent the Hessenberg matrix H - * - 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 follow: - * Q = H_{N-1} ... H_1 H_0 - * where the matrices H are the Householder transformation: - * H_i = (I - h_i * v_i * v_i') - * where h_i == householderCoefficients()[i] and v_i is a Householder vector: - * v_i = [ 0, ..., 0, 1, M(i+2,i), ..., M(N-1,i) ] - * - * See LAPACK for further details on this packed storage. - */ - const MatrixType& packedMatrix(void) const { return m_matrix; } - - MatrixType matrixQ(void) const; - MatrixType matrixH(void) const; - - private: - - static void _compute(MatrixType& matA, CoeffVectorType& hCoeffs); - - protected: - MatrixType m_matrix; - CoeffVectorType m_hCoeffs; -}; - -#ifndef EIGEN_HIDE_HEAVY_CODE - -/** \internal - * Performs a tridiagonal decomposition of \a matA in place. - * - * \param matA the input selfadjoint matrix - * \param hCoeffs returned Householder coefficients - * - * The result is written in the lower triangular part of \a matA. - * - * Implemented from Golub's "Matrix Computations", algorithm 8.3.1. - * - * \sa packedMatrix() - */ -template<typename MatrixType> -void HessenbergDecomposition<MatrixType>::_compute(MatrixType& matA, CoeffVectorType& hCoeffs) -{ - assert(matA.rows()==matA.cols()); - int n = matA.rows(); - for (int i = 0; i<n-2; ++i) - { - // let's consider the vector v = i-th column starting at position i+1 - - // start of the householder transformation - // squared norm of the vector v skipping the first element - RealScalar v1norm2 = matA.col(i).end(n-(i+2)).squaredNorm(); - - if (ei_isMuchSmallerThan(v1norm2,static_cast<Scalar>(1))) - { - hCoeffs.coeffRef(i) = 0.; - } - else - { - Scalar v0 = matA.col(i).coeff(i+1); - RealScalar beta = ei_sqrt(ei_abs2(v0)+v1norm2); - if (ei_real(v0)>=0.) - beta = -beta; - matA.col(i).end(n-(i+2)) *= (Scalar(1)/(v0-beta)); - matA.col(i).coeffRef(i+1) = beta; - Scalar h = (beta - v0) / beta; - // end of the householder transformation - - // Apply similarity transformation to remaining columns, - // i.e., A = H' A H where H = I - h v v' and v = matA.col(i).end(n-i-1) - matA.col(i).coeffRef(i+1) = 1; - - // first let's do A = H A - matA.corner(BottomRight,n-i-1,n-i-1) -= ((ei_conj(h) * matA.col(i).end(n-i-1)) * - (matA.col(i).end(n-i-1).adjoint() * matA.corner(BottomRight,n-i-1,n-i-1))).lazy(); - - // now let's do A = A H - matA.corner(BottomRight,n,n-i-1) -= ((matA.corner(BottomRight,n,n-i-1) * matA.col(i).end(n-i-1)) - * (h * matA.col(i).end(n-i-1).adjoint())).lazy(); - - matA.col(i).coeffRef(i+1) = beta; - hCoeffs.coeffRef(i) = h; - } - } - if (NumTraits<Scalar>::IsComplex) - { - // Householder transformation on the remaining single scalar - int i = n-2; - Scalar v0 = matA.coeff(i+1,i); - - RealScalar beta = ei_sqrt(ei_abs2(v0)); - if (ei_real(v0)>=0.) - beta = -beta; - Scalar h = (beta - v0) / beta; - hCoeffs.coeffRef(i) = h; - - // A = H* A - matA.corner(BottomRight,n-i-1,n-i) -= ei_conj(h) * matA.corner(BottomRight,n-i-1,n-i); - - // A = A H - matA.col(n-1) -= h * matA.col(n-1); - } - else - { - hCoeffs.coeffRef(n-2) = 0; - } -} - -/** reconstructs and returns the matrix Q */ -template<typename MatrixType> -typename HessenbergDecomposition<MatrixType>::MatrixType -HessenbergDecomposition<MatrixType>::matrixQ(void) const -{ - int n = m_matrix.rows(); - MatrixType matQ = MatrixType::Identity(n,n); - for (int i = n-2; i>=0; i--) - { - Scalar tmp = m_matrix.coeff(i+1,i); - m_matrix.const_cast_derived().coeffRef(i+1,i) = 1; - - matQ.corner(BottomRight,n-i-1,n-i-1) -= - ((m_hCoeffs.coeff(i) * m_matrix.col(i).end(n-i-1)) * - (m_matrix.col(i).end(n-i-1).adjoint() * matQ.corner(BottomRight,n-i-1,n-i-1)).lazy()).lazy(); - - m_matrix.const_cast_derived().coeffRef(i+1,i) = tmp; - } - return matQ; -} - -#endif // EIGEN_HIDE_HEAVY_CODE - -/** constructs and returns the matrix H. - * Note that the matrix H is equivalent to the upper part of the packed matrix - * (including the lower sub-diagonal). Therefore, it might be often sufficient - * to directly use the packed matrix instead of creating a new one. - */ -template<typename MatrixType> -typename HessenbergDecomposition<MatrixType>::MatrixType -HessenbergDecomposition<MatrixType>::matrixH(void) const -{ - // FIXME should this function (and other similar) rather take a matrix as argument - // and fill it (to avoid temporaries) - int n = m_matrix.rows(); - MatrixType matH = m_matrix; - if (n>2) - matH.corner(BottomLeft,n-2, n-2).template part<LowerTriangular>().setZero(); - return matH; -} - -#endif // EIGEN_HESSENBERGDECOMPOSITION_H |