123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158 |
- // 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
- {
- 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
- {
- 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
|