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>
#include <dune/common/math.hh>

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::eigenValuesVectorsLapack (const FieldMatrix< K, dim, dim > &matrix, FieldVector< K, dim > &eigenValues, FieldMatrix< K, dim, dim > &eigenVectors, const char &jobz)
	calculates the eigenvalues and/or eigenvectors of a symmetric 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 >
static void	Dune::FMatrixHelp::eigenValuesVectors (const FieldMatrix< K, dim, dim > &matrix, FieldVector< K, dim > &eigenValues, FieldMatrix< K, dim, dim > &eigenVectors)
	calculates the eigenvalues and eigenvectors 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 non-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(), and Dune::FMatrixHelp::eigenValuesVectors().

◆ 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_THROW, and 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(), Dune::FMatrixHelp::eigenValues(), and Dune::StandardMathematicalConstants< Field >::pi().

◆ 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(), and Dune::FMatrixHelp::eigenValuesVectorsLapack().

◆ 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 non-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().

◆ eigenValuesVectors()

template<int dim, typename K >

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

static

calculates the eigenvalues and eigenvectors of a symmetric field matrix

Parameters

[in]	matrix	matrix eigenvalues are calculated for
[out]	eigenValues	FieldVector that contains eigenvalues in ascending order
[out]	eigenVectors	FieldMatrix that contains the eigenvectors

Note: LAPACK::dsyev is used to calculate the eigenvalues and eigenvectors

References Dune::FMatrixHelp::eigenValues(), Dune::FMatrixHelp::eigenValuesVectors(), and Dune::FMatrixHelp::eigenValuesVectorsLapack().

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

◆ eigenValuesVectorsLapack()

template<int dim, typename K >

static void Dune::FMatrixHelp::eigenValuesVectorsLapack	(	const FieldMatrix< K, dim, dim > &	matrix,
		FieldVector< K, dim > &	eigenValues,
		FieldMatrix< K, dim, dim > &	eigenVectors,
		const char &	jobz
	)

static

calculates the eigenvalues and/or eigenvectors of a symmetric field matrix

Parameters

[in]	matrix	matrix eigenvalues are calculated for
[out]	eigenValues	FieldVector that contains eigenvalues in ascending order
[out]	eigenVectors	FieldMatrix that contains the eigenvectors
[in]	jobz	jobz=n (only eigenvalues), jobz=v (eigenvalues and eigenvetors)