blob: c8df26083ff3ea537abaf3e9de1c7b34c5780225 [file] [log] [blame]
 // This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2008 Gael Guennebaud // Copyright (C) 2010 Jitse Niesen // // 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 #include "./InternalHeaderCheck.h" namespace Eigen { namespace internal { template struct eigenvalues_selector { // this is the implementation for the case IsComplex = true static inline typename MatrixBase::EigenvaluesReturnType const run(const MatrixBase& m) { typedef typename Derived::PlainObject PlainObject; PlainObject m_eval(m); return ComplexEigenSolver(m_eval, false).eigenvalues(); } }; template struct eigenvalues_selector { static inline typename MatrixBase::EigenvaluesReturnType const run(const MatrixBase& m) { typedef typename Derived::PlainObject PlainObject; PlainObject m_eval(m); return EigenSolver(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 inline typename MatrixBase::EigenvaluesReturnType MatrixBase::eigenvalues() const { return internal::eigenvalues_selector::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 EIGEN_DEVICE_FUNC inline typename SelfAdjointView::EigenvaluesReturnType SelfAdjointView::eigenvalues() const { PlainObject thisAsMatrix(*this); return SelfAdjointEigenSolver(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 inline typename MatrixBase::RealScalar MatrixBase::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() .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 EIGEN_DEVICE_FUNC inline typename SelfAdjointView::RealScalar SelfAdjointView::operatorNorm() const { return eigenvalues().cwiseAbs().maxCoeff(); } } // end namespace Eigen #endif