Eigne Matrix Class Library
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Eigen Matrix Class Library for mbed.
Finally, you can use Eigen on your mbed!!!
src/Eigenvalues/MatrixBaseEigenvalues.h@0:13a5d365ba16, 2016-10-13 (annotated)
- Committer:
- ykuroda
- Date:
- Thu Oct 13 04:07:23 2016 +0000
- Revision:
- 0:13a5d365ba16
First commint, Eigne Matrix Class Library
Who changed what in which revision?
User | Revision | Line number | New contents of line |
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ykuroda | 0:13a5d365ba16 | 1 | // This file is part of Eigen, a lightweight C++ template library |
ykuroda | 0:13a5d365ba16 | 2 | // for linear algebra. |
ykuroda | 0:13a5d365ba16 | 3 | // |
ykuroda | 0:13a5d365ba16 | 4 | // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> |
ykuroda | 0:13a5d365ba16 | 5 | // Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk> |
ykuroda | 0:13a5d365ba16 | 6 | // |
ykuroda | 0:13a5d365ba16 | 7 | // This Source Code Form is subject to the terms of the Mozilla |
ykuroda | 0:13a5d365ba16 | 8 | // Public License v. 2.0. If a copy of the MPL was not distributed |
ykuroda | 0:13a5d365ba16 | 9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
ykuroda | 0:13a5d365ba16 | 10 | |
ykuroda | 0:13a5d365ba16 | 11 | #ifndef EIGEN_MATRIXBASEEIGENVALUES_H |
ykuroda | 0:13a5d365ba16 | 12 | #define EIGEN_MATRIXBASEEIGENVALUES_H |
ykuroda | 0:13a5d365ba16 | 13 | |
ykuroda | 0:13a5d365ba16 | 14 | namespace Eigen { |
ykuroda | 0:13a5d365ba16 | 15 | |
ykuroda | 0:13a5d365ba16 | 16 | namespace internal { |
ykuroda | 0:13a5d365ba16 | 17 | |
ykuroda | 0:13a5d365ba16 | 18 | template<typename Derived, bool IsComplex> |
ykuroda | 0:13a5d365ba16 | 19 | struct eigenvalues_selector |
ykuroda | 0:13a5d365ba16 | 20 | { |
ykuroda | 0:13a5d365ba16 | 21 | // this is the implementation for the case IsComplex = true |
ykuroda | 0:13a5d365ba16 | 22 | static inline typename MatrixBase<Derived>::EigenvaluesReturnType const |
ykuroda | 0:13a5d365ba16 | 23 | run(const MatrixBase<Derived>& m) |
ykuroda | 0:13a5d365ba16 | 24 | { |
ykuroda | 0:13a5d365ba16 | 25 | typedef typename Derived::PlainObject PlainObject; |
ykuroda | 0:13a5d365ba16 | 26 | PlainObject m_eval(m); |
ykuroda | 0:13a5d365ba16 | 27 | return ComplexEigenSolver<PlainObject>(m_eval, false).eigenvalues(); |
ykuroda | 0:13a5d365ba16 | 28 | } |
ykuroda | 0:13a5d365ba16 | 29 | }; |
ykuroda | 0:13a5d365ba16 | 30 | |
ykuroda | 0:13a5d365ba16 | 31 | template<typename Derived> |
ykuroda | 0:13a5d365ba16 | 32 | struct eigenvalues_selector<Derived, false> |
ykuroda | 0:13a5d365ba16 | 33 | { |
ykuroda | 0:13a5d365ba16 | 34 | static inline typename MatrixBase<Derived>::EigenvaluesReturnType const |
ykuroda | 0:13a5d365ba16 | 35 | run(const MatrixBase<Derived>& m) |
ykuroda | 0:13a5d365ba16 | 36 | { |
ykuroda | 0:13a5d365ba16 | 37 | typedef typename Derived::PlainObject PlainObject; |
ykuroda | 0:13a5d365ba16 | 38 | PlainObject m_eval(m); |
ykuroda | 0:13a5d365ba16 | 39 | return EigenSolver<PlainObject>(m_eval, false).eigenvalues(); |
ykuroda | 0:13a5d365ba16 | 40 | } |
ykuroda | 0:13a5d365ba16 | 41 | }; |
ykuroda | 0:13a5d365ba16 | 42 | |
ykuroda | 0:13a5d365ba16 | 43 | } // end namespace internal |
ykuroda | 0:13a5d365ba16 | 44 | |
ykuroda | 0:13a5d365ba16 | 45 | /** \brief Computes the eigenvalues of a matrix |
ykuroda | 0:13a5d365ba16 | 46 | * \returns Column vector containing the eigenvalues. |
ykuroda | 0:13a5d365ba16 | 47 | * |
ykuroda | 0:13a5d365ba16 | 48 | * \eigenvalues_module |
ykuroda | 0:13a5d365ba16 | 49 | * This function computes the eigenvalues with the help of the EigenSolver |
ykuroda | 0:13a5d365ba16 | 50 | * class (for real matrices) or the ComplexEigenSolver class (for complex |
ykuroda | 0:13a5d365ba16 | 51 | * matrices). |
ykuroda | 0:13a5d365ba16 | 52 | * |
ykuroda | 0:13a5d365ba16 | 53 | * The eigenvalues are repeated according to their algebraic multiplicity, |
ykuroda | 0:13a5d365ba16 | 54 | * so there are as many eigenvalues as rows in the matrix. |
ykuroda | 0:13a5d365ba16 | 55 | * |
ykuroda | 0:13a5d365ba16 | 56 | * The SelfAdjointView class provides a better algorithm for selfadjoint |
ykuroda | 0:13a5d365ba16 | 57 | * matrices. |
ykuroda | 0:13a5d365ba16 | 58 | * |
ykuroda | 0:13a5d365ba16 | 59 | * Example: \include MatrixBase_eigenvalues.cpp |
ykuroda | 0:13a5d365ba16 | 60 | * Output: \verbinclude MatrixBase_eigenvalues.out |
ykuroda | 0:13a5d365ba16 | 61 | * |
ykuroda | 0:13a5d365ba16 | 62 | * \sa EigenSolver::eigenvalues(), ComplexEigenSolver::eigenvalues(), |
ykuroda | 0:13a5d365ba16 | 63 | * SelfAdjointView::eigenvalues() |
ykuroda | 0:13a5d365ba16 | 64 | */ |
ykuroda | 0:13a5d365ba16 | 65 | template<typename Derived> |
ykuroda | 0:13a5d365ba16 | 66 | inline typename MatrixBase<Derived>::EigenvaluesReturnType |
ykuroda | 0:13a5d365ba16 | 67 | MatrixBase<Derived>::eigenvalues() const |
ykuroda | 0:13a5d365ba16 | 68 | { |
ykuroda | 0:13a5d365ba16 | 69 | typedef typename internal::traits<Derived>::Scalar Scalar; |
ykuroda | 0:13a5d365ba16 | 70 | return internal::eigenvalues_selector<Derived, NumTraits<Scalar>::IsComplex>::run(derived()); |
ykuroda | 0:13a5d365ba16 | 71 | } |
ykuroda | 0:13a5d365ba16 | 72 | |
ykuroda | 0:13a5d365ba16 | 73 | /** \brief Computes the eigenvalues of a matrix |
ykuroda | 0:13a5d365ba16 | 74 | * \returns Column vector containing the eigenvalues. |
ykuroda | 0:13a5d365ba16 | 75 | * |
ykuroda | 0:13a5d365ba16 | 76 | * \eigenvalues_module |
ykuroda | 0:13a5d365ba16 | 77 | * This function computes the eigenvalues with the help of the |
ykuroda | 0:13a5d365ba16 | 78 | * SelfAdjointEigenSolver class. The eigenvalues are repeated according to |
ykuroda | 0:13a5d365ba16 | 79 | * their algebraic multiplicity, so there are as many eigenvalues as rows in |
ykuroda | 0:13a5d365ba16 | 80 | * the matrix. |
ykuroda | 0:13a5d365ba16 | 81 | * |
ykuroda | 0:13a5d365ba16 | 82 | * Example: \include SelfAdjointView_eigenvalues.cpp |
ykuroda | 0:13a5d365ba16 | 83 | * Output: \verbinclude SelfAdjointView_eigenvalues.out |
ykuroda | 0:13a5d365ba16 | 84 | * |
ykuroda | 0:13a5d365ba16 | 85 | * \sa SelfAdjointEigenSolver::eigenvalues(), MatrixBase::eigenvalues() |
ykuroda | 0:13a5d365ba16 | 86 | */ |
ykuroda | 0:13a5d365ba16 | 87 | template<typename MatrixType, unsigned int UpLo> |
ykuroda | 0:13a5d365ba16 | 88 | inline typename SelfAdjointView<MatrixType, UpLo>::EigenvaluesReturnType |
ykuroda | 0:13a5d365ba16 | 89 | SelfAdjointView<MatrixType, UpLo>::eigenvalues() const |
ykuroda | 0:13a5d365ba16 | 90 | { |
ykuroda | 0:13a5d365ba16 | 91 | typedef typename SelfAdjointView<MatrixType, UpLo>::PlainObject PlainObject; |
ykuroda | 0:13a5d365ba16 | 92 | PlainObject thisAsMatrix(*this); |
ykuroda | 0:13a5d365ba16 | 93 | return SelfAdjointEigenSolver<PlainObject>(thisAsMatrix, false).eigenvalues(); |
ykuroda | 0:13a5d365ba16 | 94 | } |
ykuroda | 0:13a5d365ba16 | 95 | |
ykuroda | 0:13a5d365ba16 | 96 | |
ykuroda | 0:13a5d365ba16 | 97 | |
ykuroda | 0:13a5d365ba16 | 98 | /** \brief Computes the L2 operator norm |
ykuroda | 0:13a5d365ba16 | 99 | * \returns Operator norm of the matrix. |
ykuroda | 0:13a5d365ba16 | 100 | * |
ykuroda | 0:13a5d365ba16 | 101 | * \eigenvalues_module |
ykuroda | 0:13a5d365ba16 | 102 | * This function computes the L2 operator norm of a matrix, which is also |
ykuroda | 0:13a5d365ba16 | 103 | * known as the spectral norm. The norm of a matrix \f$ A \f$ is defined to be |
ykuroda | 0:13a5d365ba16 | 104 | * \f[ \|A\|_2 = \max_x \frac{\|Ax\|_2}{\|x\|_2} \f] |
ykuroda | 0:13a5d365ba16 | 105 | * where the maximum is over all vectors and the norm on the right is the |
ykuroda | 0:13a5d365ba16 | 106 | * Euclidean vector norm. The norm equals the largest singular value, which is |
ykuroda | 0:13a5d365ba16 | 107 | * the square root of the largest eigenvalue of the positive semi-definite |
ykuroda | 0:13a5d365ba16 | 108 | * matrix \f$ A^*A \f$. |
ykuroda | 0:13a5d365ba16 | 109 | * |
ykuroda | 0:13a5d365ba16 | 110 | * The current implementation uses the eigenvalues of \f$ A^*A \f$, as computed |
ykuroda | 0:13a5d365ba16 | 111 | * by SelfAdjointView::eigenvalues(), to compute the operator norm of a |
ykuroda | 0:13a5d365ba16 | 112 | * matrix. The SelfAdjointView class provides a better algorithm for |
ykuroda | 0:13a5d365ba16 | 113 | * selfadjoint matrices. |
ykuroda | 0:13a5d365ba16 | 114 | * |
ykuroda | 0:13a5d365ba16 | 115 | * Example: \include MatrixBase_operatorNorm.cpp |
ykuroda | 0:13a5d365ba16 | 116 | * Output: \verbinclude MatrixBase_operatorNorm.out |
ykuroda | 0:13a5d365ba16 | 117 | * |
ykuroda | 0:13a5d365ba16 | 118 | * \sa SelfAdjointView::eigenvalues(), SelfAdjointView::operatorNorm() |
ykuroda | 0:13a5d365ba16 | 119 | */ |
ykuroda | 0:13a5d365ba16 | 120 | template<typename Derived> |
ykuroda | 0:13a5d365ba16 | 121 | inline typename MatrixBase<Derived>::RealScalar |
ykuroda | 0:13a5d365ba16 | 122 | MatrixBase<Derived>::operatorNorm() const |
ykuroda | 0:13a5d365ba16 | 123 | { |
ykuroda | 0:13a5d365ba16 | 124 | using std::sqrt; |
ykuroda | 0:13a5d365ba16 | 125 | typename Derived::PlainObject m_eval(derived()); |
ykuroda | 0:13a5d365ba16 | 126 | // FIXME if it is really guaranteed that the eigenvalues are already sorted, |
ykuroda | 0:13a5d365ba16 | 127 | // then we don't need to compute a maxCoeff() here, comparing the 1st and last ones is enough. |
ykuroda | 0:13a5d365ba16 | 128 | return sqrt((m_eval*m_eval.adjoint()) |
ykuroda | 0:13a5d365ba16 | 129 | .eval() |
ykuroda | 0:13a5d365ba16 | 130 | .template selfadjointView<Lower>() |
ykuroda | 0:13a5d365ba16 | 131 | .eigenvalues() |
ykuroda | 0:13a5d365ba16 | 132 | .maxCoeff() |
ykuroda | 0:13a5d365ba16 | 133 | ); |
ykuroda | 0:13a5d365ba16 | 134 | } |
ykuroda | 0:13a5d365ba16 | 135 | |
ykuroda | 0:13a5d365ba16 | 136 | /** \brief Computes the L2 operator norm |
ykuroda | 0:13a5d365ba16 | 137 | * \returns Operator norm of the matrix. |
ykuroda | 0:13a5d365ba16 | 138 | * |
ykuroda | 0:13a5d365ba16 | 139 | * \eigenvalues_module |
ykuroda | 0:13a5d365ba16 | 140 | * This function computes the L2 operator norm of a self-adjoint matrix. For a |
ykuroda | 0:13a5d365ba16 | 141 | * self-adjoint matrix, the operator norm is the largest eigenvalue. |
ykuroda | 0:13a5d365ba16 | 142 | * |
ykuroda | 0:13a5d365ba16 | 143 | * The current implementation uses the eigenvalues of the matrix, as computed |
ykuroda | 0:13a5d365ba16 | 144 | * by eigenvalues(), to compute the operator norm of the matrix. |
ykuroda | 0:13a5d365ba16 | 145 | * |
ykuroda | 0:13a5d365ba16 | 146 | * Example: \include SelfAdjointView_operatorNorm.cpp |
ykuroda | 0:13a5d365ba16 | 147 | * Output: \verbinclude SelfAdjointView_operatorNorm.out |
ykuroda | 0:13a5d365ba16 | 148 | * |
ykuroda | 0:13a5d365ba16 | 149 | * \sa eigenvalues(), MatrixBase::operatorNorm() |
ykuroda | 0:13a5d365ba16 | 150 | */ |
ykuroda | 0:13a5d365ba16 | 151 | template<typename MatrixType, unsigned int UpLo> |
ykuroda | 0:13a5d365ba16 | 152 | inline typename SelfAdjointView<MatrixType, UpLo>::RealScalar |
ykuroda | 0:13a5d365ba16 | 153 | SelfAdjointView<MatrixType, UpLo>::operatorNorm() const |
ykuroda | 0:13a5d365ba16 | 154 | { |
ykuroda | 0:13a5d365ba16 | 155 | return eigenvalues().cwiseAbs().maxCoeff(); |
ykuroda | 0:13a5d365ba16 | 156 | } |
ykuroda | 0:13a5d365ba16 | 157 | |
ykuroda | 0:13a5d365ba16 | 158 | } // end namespace Eigen |
ykuroda | 0:13a5d365ba16 | 159 | |
ykuroda | 0:13a5d365ba16 | 160 | #endif |