fmatrixev.hh File Reference

Eigenvalue computations for the FieldMatrix class. More...

#include <iostream>
#include <cmath>
#include <cassert>
#include <dune/common/exceptions.hh>
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>

Go to the source code of this file.

Namespaces
namespace	Dune
	Dune namespace.

Functions
template<typename K >
static void	Dune::FMatrixHelp::eigenValues (const FieldMatrix< K, 1, 1 > &matrix, FieldVector< K, 1 > &eigenvalues)
	calculates the eigenvalues of a symmetric field matrix More...
template<typename K >
static void	Dune::FMatrixHelp::eigenValues (const FieldMatrix< K, 2, 2 > &matrix, FieldVector< K, 2 > &eigenvalues)
	calculates the eigenvalues of a symmetric field matrix More...
template<typename K >
static void	Dune::FMatrixHelp::eigenValues (const FieldMatrix< K, 3, 3 > &matrix, FieldVector< K, 3 > &eigenvalues)
	Calculates the eigenvalues of a symmetric 3x3 field matrix. More...
template<int dim, typename K >
static void	Dune::FMatrixHelp::eigenValues (const FieldMatrix< K, dim, dim > &matrix, FieldVector< K, dim > &eigenvalues)
	calculates the eigenvalues of a symmetric field matrix More...
template<int dim, typename K , class C >
static void	Dune::FMatrixHelp::eigenValuesNonSym (const FieldMatrix< K, dim, dim > &matrix, FieldVector< C, dim > &eigenValues)
	calculates the eigenvalues of a symmetric field matrix More...

Detailed Description

Eigenvalue computations for the FieldMatrix class.

Function Documentation

eigenValues() [1/4]

template<typename K >

static void Dune::FMatrixHelp::eigenValues ( const FieldMatrix< K, 1, 1 > &  matrix, FieldVector< K, 1 > &  eigenvalues  )

static

calculates the eigenvalues of a symmetric field matrix

Parameters

[in]	matrix	matrix eigenvalues are calculated for
[out]	eigenvalues	FieldVector that contains eigenvalues in ascending order

References Dune::FMatrixHelp::eigenValues().

Referenced by Dune::FMatrixHelp::eigenValues().

eigenValues() [2/4]

template<typename K >

static void Dune::FMatrixHelp::eigenValues ( const FieldMatrix< K, 2, 2 > &  matrix, FieldVector< K, 2 > &  eigenvalues  )

static

calculates the eigenvalues of a symmetric field matrix

Parameters

[in]	matrix	matrix eigenvalues are calculated for
[out]	eigenvalues	FieldVector that contains eigenvalues in ascending order

References Dune::FMatrixHelp::eigenValues().

eigenValues() [3/4]

template<typename K >

static void Dune::FMatrixHelp::eigenValues ( const FieldMatrix< K, 3, 3 > &  matrix, FieldVector< K, 3 > &  eigenvalues  )

static

Calculates the eigenvalues of a symmetric 3x3 field matrix.

Parameters

[in]	matrix	matrix eigenvalues are calculated for
[out]	eigenvalues	Eigenvalues in ascending order

Note

If the input matrix is not symmetric the behavior of this method is undefined.

This implementation was adapted from the pseudo-code (Python?) implementation found on http://en.wikipedia.org/wiki/Eigenvalue_algorithm (retrieved late August 2014). Wikipedia claims to have taken it from Smith, Oliver K. (April 1961), Eigenvalues of a symmetric 3 × 3 matrix., Communications of the ACM 4 (4): 168, doi:10.1145/355578.366316

References Dune::DenseMatrix< MAT >::determinant(), and Dune::FMatrixHelp::eigenValues().

eigenValues() [4/4]

template<int dim, typename K >

static void Dune::FMatrixHelp::eigenValues ( const FieldMatrix< K, dim, dim > &  matrix, FieldVector< K, dim > &  eigenvalues  )

static

calculates the eigenvalues of a symmetric field matrix

Parameters

[in]	matrix	matrix eigenvalues are calculated for
[out]	eigenvalues	FieldVector that contains eigenvalues in ascending order

Note

LAPACK::dsyev is used to calculate the eigenvalues

References Dune::FMatrixHelp::eigenValues().

eigenValuesNonSym()

template<int dim, typename K , class C >

static void Dune::FMatrixHelp::eigenValuesNonSym ( const FieldMatrix< K, dim, dim > &  matrix, FieldVector< C, dim > &  eigenValues  )

static

calculates the eigenvalues of a symmetric field matrix

Parameters

[in]	matrix	matrix eigenvalues are calculated for
[out]	eigenValues	FieldVector that contains eigenvalues in ascending order

Note

LAPACK::dgeev is used to calculate the eigen values

References Dune::FMatrixHelp::eigenValuesNonSym().

Referenced by Dune::FMatrixHelp::eigenValuesNonSym().