Dune::FMatrixHelp Namespace Reference

Functions
template<typename K>
static K	invertMatrix (const FieldMatrix< K, 1, 1 > &matrix, FieldMatrix< K, 1, 1 > &inverse)
	invert scalar without changing the original matrix
template<typename K>
static K	invertMatrix_retTransposed (const FieldMatrix< K, 1, 1 > &matrix, FieldMatrix< K, 1, 1 > &inverse)
	invert scalar without changing the original matrix
template<typename K>
static K	invertMatrix (const FieldMatrix< K, 2, 2 > &matrix, FieldMatrix< K, 2, 2 > &inverse)
	invert 2x2 Matrix without changing the original matrix
template<typename K>
static K	invertMatrix_retTransposed (const FieldMatrix< K, 2, 2 > &matrix, FieldMatrix< K, 2, 2 > &inverse)
template<typename K>
static K	invertMatrix (const FieldMatrix< K, 3, 3 > &matrix, FieldMatrix< K, 3, 3 > &inverse)
	invert 3x3 Matrix without changing the original matrix
template<typename K>
static K	invertMatrix_retTransposed (const FieldMatrix< K, 3, 3 > &matrix, FieldMatrix< K, 3, 3 > &inverse)
	invert 3x3 Matrix without changing the original matrix
template<class K, int m, int n, int p>
static void	multMatrix (const FieldMatrix< K, m, n > &A, const FieldMatrix< K, n, p > &B, FieldMatrix< K, m, p > &ret)
	calculates ret = A * B
template<typename K, int rows, int cols>
static void	multTransposedMatrix (const FieldMatrix< K, rows, cols > &matrix, FieldMatrix< K, cols, cols > &ret)
	calculates ret= A_t*A
template<typename K, int rows, int cols>
static void	multAssignTransposed (const FieldMatrix< K, rows, cols > &matrix, const FieldVector< K, rows > &x, FieldVector< K, cols > &ret)
	calculates ret = matrix^T * x
template<typename K, int rows, int cols>
static FieldVector< K, rows >	mult (const FieldMatrix< K, rows, cols > &matrix, const FieldVector< K, cols > &x)
	calculates ret = matrix * x
template<typename K, int rows, int cols>
static FieldVector< K, cols >	multTransposed (const FieldMatrix< K, rows, cols > &matrix, const FieldVector< K, rows > &x)
	calculates ret = matrix^T * x
template<int dim, typename K>
static void	eigenValues (const FieldMatrix< K, dim, dim > &matrix, FieldVector< K, dim > &eigenValues)
	calculates the eigenvalues of a symmetric field matrix
template<int dim, typename K>
static void	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
template<int dim, typename K>
static void	eigenValuesLapack (const FieldMatrix< K, dim, dim > &matrix, FieldVector< K, dim > &eigenValues)
	calculates the eigenvalues of a symmetric field matrix
template<int dim, typename K>
static void	eigenValuesVectorsLapack (const FieldMatrix< K, dim, dim > &matrix, FieldVector< K, dim > &eigenValues, FieldMatrix< K, dim, dim > &eigenVectors)
	calculates the eigenvalues and -vectors of a symmetric field matrix
template<int dim, typename K, class C>
static void	eigenValuesNonSym (const FieldMatrix< K, dim, dim > &matrix, FieldVector< C, dim > &eigenValues)
	calculates the eigenvalues of a non-symmetric field matrix
template<typename MAT, typename V1, typename V2>
static void	multAssign (const DenseMatrix< MAT > &matrix, const DenseVector< V1 > &x, DenseVector< V2 > &ret)
	calculates ret = matrix * x

Function Documentation

eigenValues()

template<int dim, typename K>

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

specializations for dim=1,2,3 exist, for dim>3 LAPACK::dsyev is used

eigenValuesLapack()

template<int dim, typename K>

void Dune::FMatrixHelp::eigenValuesLapack ( 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

eigenValuesNonSym()

template<int dim, typename K, class C>

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 eigenvalues

eigenValuesVectors()

template<int dim, typename K>

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

specializations for dim=1,2,3 exist, for dim>3 LAPACK::dsyev is used

eigenValuesVectorsLapack()

template<int dim, typename K>

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

static

calculates the eigenvalues and -vectors 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 -vectors

invertMatrix() [1/3]

template<typename K>

K Dune::FMatrixHelp::invertMatrix ( const FieldMatrix< K, 1, 1 > & matrix, FieldMatrix< K, 1, 1 > & inverse )

inlinestatic

invert scalar without changing the original matrix

invertMatrix() [2/3]

template<typename K>

K Dune::FMatrixHelp::invertMatrix ( const FieldMatrix< K, 2, 2 > & matrix, FieldMatrix< K, 2, 2 > & inverse )

inlinestatic

invert 2x2 Matrix without changing the original matrix

invertMatrix() [3/3]

template<typename K>

K Dune::FMatrixHelp::invertMatrix ( const FieldMatrix< K, 3, 3 > & matrix, FieldMatrix< K, 3, 3 > & inverse )

inlinestatic

invert 3x3 Matrix without changing the original matrix

invertMatrix_retTransposed() [1/3]

template<typename K>

K Dune::FMatrixHelp::invertMatrix_retTransposed ( const FieldMatrix< K, 1, 1 > & matrix, FieldMatrix< K, 1, 1 > & inverse )

inlinestatic

invert scalar without changing the original matrix

invertMatrix_retTransposed() [2/3]

template<typename K>

K Dune::FMatrixHelp::invertMatrix_retTransposed ( const FieldMatrix< K, 2, 2 > & matrix, FieldMatrix< K, 2, 2 > & inverse )

inlinestatic

invert 2x2 Matrix without changing the original matrix return transposed matrix

invertMatrix_retTransposed() [3/3]

template<typename K>

K Dune::FMatrixHelp::invertMatrix_retTransposed ( const FieldMatrix< K, 3, 3 > & matrix, FieldMatrix< K, 3, 3 > & inverse )

inlinestatic

invert 3x3 Matrix without changing the original matrix

mult()

template<typename K, int rows, int cols>

FieldVector< K, rows > Dune::FMatrixHelp::mult ( const FieldMatrix< K, rows, cols > & matrix, const FieldVector< K, cols > & x )

inlinestatic

calculates ret = matrix * x

multAssign()

template<typename MAT, typename V1, typename V2>

void Dune::DenseMatrixHelp::multAssign ( const DenseMatrix< MAT > & matrix, const DenseVector< V1 > & x, DenseVector< V2 > & ret )

inlinestatic

calculates ret = matrix * x

multAssignTransposed()

template<typename K, int rows, int cols>

void Dune::FMatrixHelp::multAssignTransposed ( const FieldMatrix< K, rows, cols > & matrix, const FieldVector< K, rows > & x, FieldVector< K, cols > & ret )

inlinestatic

calculates ret = matrix^T * x

multMatrix()

template<class K, int m, int n, int p>

void Dune::FMatrixHelp::multMatrix ( const FieldMatrix< K, m, n > & A, const FieldMatrix< K, n, p > & B, FieldMatrix< K, m, p > & ret )

inlinestatic

calculates ret = A * B

multTransposed()

template<typename K, int rows, int cols>

FieldVector< K, cols > Dune::FMatrixHelp::multTransposed ( const FieldMatrix< K, rows, cols > & matrix, const FieldVector< K, rows > & x )

inlinestatic

calculates ret = matrix^T * x

multTransposedMatrix()

template<typename K, int rows, int cols>

void Dune::FMatrixHelp::multTransposedMatrix ( const FieldMatrix< K, rows, cols > & matrix, FieldMatrix< K, cols, cols > & ret )

inlinestatic

calculates ret= A_t*A