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-// 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