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Diffstat (limited to 'eigen/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h')
-rw-r--r-- | eigen/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h | 160 |
1 files changed, 160 insertions, 0 deletions
diff --git a/eigen/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h b/eigen/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h new file mode 100644 index 0000000..4fec8af --- /dev/null +++ b/eigen/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h @@ -0,0 +1,160 @@ +// 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_MATRIXBASEEIGENVALUES_H +#define EIGEN_MATRIXBASEEIGENVALUES_H + +namespace Eigen { + +namespace internal { + +template<typename Derived, bool IsComplex> +struct eigenvalues_selector +{ + // this is the implementation for the case IsComplex = true + static inline typename MatrixBase<Derived>::EigenvaluesReturnType const + run(const MatrixBase<Derived>& m) + { + typedef typename Derived::PlainObject PlainObject; + PlainObject m_eval(m); + return ComplexEigenSolver<PlainObject>(m_eval, false).eigenvalues(); + } +}; + +template<typename Derived> +struct eigenvalues_selector<Derived, false> +{ + static inline typename MatrixBase<Derived>::EigenvaluesReturnType const + run(const MatrixBase<Derived>& m) + { + typedef typename Derived::PlainObject PlainObject; + PlainObject m_eval(m); + return EigenSolver<PlainObject>(m_eval, false).eigenvalues(); + } +}; + +} // end namespace internal + +/** \brief Computes the eigenvalues of a matrix + * \returns Column vector containing the eigenvalues. + * + * \eigenvalues_module + * This function computes the eigenvalues with the help of the EigenSolver + * class (for real matrices) or the ComplexEigenSolver class (for complex + * matrices). + * + * The eigenvalues are repeated according to their algebraic multiplicity, + * so there are as many eigenvalues as rows in the matrix. + * + * The SelfAdjointView class provides a better algorithm for selfadjoint + * matrices. + * + * Example: \include MatrixBase_eigenvalues.cpp + * Output: \verbinclude MatrixBase_eigenvalues.out + * + * \sa EigenSolver::eigenvalues(), ComplexEigenSolver::eigenvalues(), + * SelfAdjointView::eigenvalues() + */ +template<typename Derived> +inline typename MatrixBase<Derived>::EigenvaluesReturnType +MatrixBase<Derived>::eigenvalues() const +{ + typedef typename internal::traits<Derived>::Scalar Scalar; + return internal::eigenvalues_selector<Derived, NumTraits<Scalar>::IsComplex>::run(derived()); +} + +/** \brief Computes the eigenvalues of a matrix + * \returns Column vector containing the eigenvalues. + * + * \eigenvalues_module + * This function computes the eigenvalues with the help of the + * SelfAdjointEigenSolver class. The eigenvalues are repeated according to + * their algebraic multiplicity, so there are as many eigenvalues as rows in + * the matrix. + * + * Example: \include SelfAdjointView_eigenvalues.cpp + * Output: \verbinclude SelfAdjointView_eigenvalues.out + * + * \sa SelfAdjointEigenSolver::eigenvalues(), MatrixBase::eigenvalues() + */ +template<typename MatrixType, unsigned int UpLo> +inline typename SelfAdjointView<MatrixType, UpLo>::EigenvaluesReturnType +SelfAdjointView<MatrixType, UpLo>::eigenvalues() const +{ + typedef typename SelfAdjointView<MatrixType, UpLo>::PlainObject PlainObject; + PlainObject thisAsMatrix(*this); + return SelfAdjointEigenSolver<PlainObject>(thisAsMatrix, false).eigenvalues(); +} + + + +/** \brief Computes the L2 operator norm + * \returns Operator norm of the matrix. + * + * \eigenvalues_module + * This function computes the L2 operator norm of a matrix, which is also + * known as the spectral norm. The norm of a matrix \f$ A \f$ is defined to be + * \f[ \|A\|_2 = \max_x \frac{\|Ax\|_2}{\|x\|_2} \f] + * where the maximum is over all vectors and the norm on the right is the + * Euclidean vector norm. The norm equals the largest singular value, which is + * the square root of the largest eigenvalue of the positive semi-definite + * matrix \f$ A^*A \f$. + * + * The current implementation uses the eigenvalues of \f$ A^*A \f$, as computed + * by SelfAdjointView::eigenvalues(), to compute the operator norm of a + * matrix. The SelfAdjointView class provides a better algorithm for + * selfadjoint matrices. + * + * Example: \include MatrixBase_operatorNorm.cpp + * Output: \verbinclude MatrixBase_operatorNorm.out + * + * \sa SelfAdjointView::eigenvalues(), SelfAdjointView::operatorNorm() + */ +template<typename Derived> +inline typename MatrixBase<Derived>::RealScalar +MatrixBase<Derived>::operatorNorm() const +{ + using std::sqrt; + typename Derived::PlainObject m_eval(derived()); + // FIXME if it is really guaranteed that the eigenvalues are already sorted, + // then we don't need to compute a maxCoeff() here, comparing the 1st and last ones is enough. + return sqrt((m_eval*m_eval.adjoint()) + .eval() + .template selfadjointView<Lower>() + .eigenvalues() + .maxCoeff() + ); +} + +/** \brief Computes the L2 operator norm + * \returns Operator norm of the matrix. + * + * \eigenvalues_module + * This function computes the L2 operator norm of a self-adjoint matrix. For a + * self-adjoint matrix, the operator norm is the largest eigenvalue. + * + * The current implementation uses the eigenvalues of the matrix, as computed + * by eigenvalues(), to compute the operator norm of the matrix. + * + * Example: \include SelfAdjointView_operatorNorm.cpp + * Output: \verbinclude SelfAdjointView_operatorNorm.out + * + * \sa eigenvalues(), MatrixBase::operatorNorm() + */ +template<typename MatrixType, unsigned int UpLo> +inline typename SelfAdjointView<MatrixType, UpLo>::RealScalar +SelfAdjointView<MatrixType, UpLo>::operatorNorm() const +{ + return eigenvalues().cwiseAbs().maxCoeff(); +} + +} // end namespace Eigen + +#endif |