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 Sourcecode: eigen3 version 3.0.0-23.0.1-13.0.2-23.0.3-13.0.4-13.0.5-13.1.0~alpha1-1

# MatrixBaseEigenvalues.h

// 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>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.

#ifndef EIGEN_MATRIXBASEEIGENVALUES_H
#define EIGEN_MATRIXBASEEIGENVALUES_H

namespace internal {

template<typename Derived, bool IsComplex>
00032 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>
00045 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(),
*/
template<typename Derived>
inline typename MatrixBase<Derived>::EigenvaluesReturnType
00080 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
00102 SelfAdjointView<MatrixType, UpLo>::eigenvalues() const
{
typedef typename SelfAdjointView<MatrixType, UpLo>::PlainObject PlainObject;
PlainObject thisAsMatrix(*this);
}

/** \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
*
* Example: \include MatrixBase_operatorNorm.cpp
* Output: \verbinclude MatrixBase_operatorNorm.out
*
*/
template<typename Derived>
inline typename MatrixBase<Derived>::RealScalar
00135 MatrixBase<Derived>::operatorNorm() const
{
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.
.eval()
.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
00165 SelfAdjointView<MatrixType, UpLo>::operatorNorm() const
{
return eigenvalues().cwiseAbs().maxCoeff();
}

#endif


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