dune-geometry 3.0-git
Public Types | Static Public Member Functions | List of all members
Dune::GenericGeometry::MatrixHelper< Traits > Struct Template Reference

#include <dune/geometry/genericgeometry/matrixhelper.hh>

Public Types

typedef Traits::ctype FieldType
 

Static Public Member Functions

static FieldType abs (const FieldType &x)
 
template<int m, int n>
static void Ax (const typename Traits ::template Matrix< m, n > ::type &A, const typename Traits ::template Vector< n > ::type &x, typename Traits ::template Vector< m > ::type &ret)
 
template<int m, int n>
static void ATx (const typename Traits ::template Matrix< m, n > ::type &A, const typename Traits ::template Vector< m > ::type &x, typename Traits ::template Vector< n > ::type &ret)
 
template<int m, int n, int p>
static void AB (const typename Traits ::template Matrix< m, n > ::type &A, const typename Traits ::template Matrix< n, p > ::type &B, typename Traits ::template Matrix< m, p > ::type &ret)
 
template<int m, int n, int p>
static void ATBT (const typename Traits ::template Matrix< m, n > ::type &A, const typename Traits ::template Matrix< p, m > ::type &B, typename Traits ::template Matrix< n, p > ::type &ret)
 
template<int m, int n>
static void ATA_L (const typename Traits ::template Matrix< m, n > ::type &A, typename Traits ::template Matrix< n, n > ::type &ret)
 
template<int m, int n>
static void ATA (const typename Traits ::template Matrix< m, n > ::type &A, typename Traits ::template Matrix< n, n > ::type &ret)
 
template<int m, int n>
static void AAT_L (const typename Traits ::template Matrix< m, n > ::type &A, typename Traits ::template Matrix< m, m > ::type &ret)
 
template<int m, int n>
static void AAT (const typename Traits ::template Matrix< m, n > ::type &A, typename Traits ::template Matrix< m, m > ::type &ret)
 
template<int n>
static void Lx (const typename Traits ::template Matrix< n, n > ::type &L, const typename Traits ::template Vector< n > ::type &x, typename Traits ::template Vector< n > ::type &ret)
 
template<int n>
static void LTx (const typename Traits ::template Matrix< n, n > ::type &L, const typename Traits ::template Vector< n > ::type &x, typename Traits ::template Vector< n > ::type &ret)
 
template<int n>
static void LTL (const typename Traits ::template Matrix< n, n > ::type &L, typename Traits ::template Matrix< n, n > ::type &ret)
 
template<int n>
static void LLT (const typename Traits ::template Matrix< n, n > ::type &L, typename Traits ::template Matrix< n, n > ::type &ret)
 
template<int n>
static void cholesky_L (const typename Traits ::template Matrix< n, n > ::type &A, typename Traits ::template Matrix< n, n > ::type &ret)
 
template<int n>
static FieldType detL (const typename Traits ::template Matrix< n, n > ::type &L)
 
template<int n>
static FieldType invL (typename Traits ::template Matrix< n, n > ::type &L)
 
template<int n>
static void invLx (typename Traits ::template Matrix< n, n > ::type &L, typename Traits ::template Vector< n > ::type &x)
 
template<int n>
static void invLTx (typename Traits ::template Matrix< n, n > ::type &L, typename Traits ::template Vector< n > ::type &x)
 
template<int n>
static FieldType spdDetA (const typename Traits ::template Matrix< n, n > ::type &A)
 
template<int n>
static FieldType spdInvA (typename Traits ::template Matrix< n, n > ::type &A)
 
template<int n>
static void spdInvAx (typename Traits ::template Matrix< n, n > ::type &A, typename Traits ::template Vector< n > ::type &x)
 
template<int m, int n>
static FieldType detATA (const typename Traits ::template Matrix< m, n > ::type &A)
 
template<int m, int n>
static FieldType sqrtDetAAT (const typename Traits::template Matrix< m, n >::type &A)
 Compute the square root of the determinant of A times A transposed.
 
template<int m, int n>
static FieldType leftInvA (const typename Traits ::template Matrix< m, n > ::type &A, typename Traits ::template Matrix< n, m > ::type &ret)
 
template<int m, int n>
static void leftInvAx (const typename Traits ::template Matrix< m, n > ::type &A, const typename Traits ::template Vector< m > ::type &x, typename Traits ::template Vector< n > ::type &y)
 
template<int m, int n>
static FieldType rightInvA (const typename Traits ::template Matrix< m, n > ::type &A, typename Traits ::template Matrix< n, m > ::type &ret)
 Compute right pseudo-inverse of matrix A.
 
template<int m, int n>
static void xTRightInvA (const typename Traits ::template Matrix< m, n > ::type &A, const typename Traits ::template Vector< n > ::type &x, typename Traits ::template Vector< m > ::type &y)
 

Member Typedef Documentation

◆ FieldType

template<class Traits >
typedef Traits::ctype Dune::GenericGeometry::MatrixHelper< Traits >::FieldType

Member Function Documentation

◆ AAT()

template<class Traits >
template<int m, int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::AAT ( const typename Traits ::template Matrix< m, n > ::type &  A,
typename Traits ::template Matrix< m, m > ::type &  ret 
)
inlinestatic

◆ AAT_L()

template<class Traits >
template<int m, int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::AAT_L ( const typename Traits ::template Matrix< m, n > ::type &  A,
typename Traits ::template Matrix< m, m > ::type &  ret 
)
inlinestatic

◆ AB()

template<class Traits >
template<int m, int n, int p>
static void Dune::GenericGeometry::MatrixHelper< Traits >::AB ( const typename Traits ::template Matrix< m, n > ::type &  A,
const typename Traits ::template Matrix< n, p > ::type &  B,
typename Traits ::template Matrix< m, p > ::type &  ret 
)
inlinestatic

◆ abs()

template<class Traits >
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::abs ( const FieldType x)
inlinestatic

◆ ATA()

template<class Traits >
template<int m, int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::ATA ( const typename Traits ::template Matrix< m, n > ::type &  A,
typename Traits ::template Matrix< n, n > ::type &  ret 
)
inlinestatic

◆ ATA_L()

template<class Traits >
template<int m, int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::ATA_L ( const typename Traits ::template Matrix< m, n > ::type &  A,
typename Traits ::template Matrix< n, n > ::type &  ret 
)
inlinestatic

◆ ATBT()

template<class Traits >
template<int m, int n, int p>
static void Dune::GenericGeometry::MatrixHelper< Traits >::ATBT ( const typename Traits ::template Matrix< m, n > ::type &  A,
const typename Traits ::template Matrix< p, m > ::type &  B,
typename Traits ::template Matrix< n, p > ::type &  ret 
)
inlinestatic

◆ ATx()

template<class Traits >
template<int m, int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::ATx ( const typename Traits ::template Matrix< m, n > ::type &  A,
const typename Traits ::template Vector< m > ::type &  x,
typename Traits ::template Vector< n > ::type &  ret 
)
inlinestatic

◆ Ax()

template<class Traits >
template<int m, int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::Ax ( const typename Traits ::template Matrix< m, n > ::type &  A,
const typename Traits ::template Vector< n > ::type &  x,
typename Traits ::template Vector< m > ::type &  ret 
)
inlinestatic

◆ cholesky_L()

template<class Traits >
template<int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::cholesky_L ( const typename Traits ::template Matrix< n, n > ::type &  A,
typename Traits ::template Matrix< n, n > ::type &  ret 
)
inlinestatic

◆ detATA()

template<class Traits >
template<int m, int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::detATA ( const typename Traits ::template Matrix< m, n > ::type &  A)
inlinestatic

◆ detL()

template<class Traits >
template<int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::detL ( const typename Traits ::template Matrix< n, n > ::type &  L)
inlinestatic

◆ invL()

template<class Traits >
template<int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::invL ( typename Traits ::template Matrix< n, n > ::type &  L)
inlinestatic

◆ invLTx()

template<class Traits >
template<int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::invLTx ( typename Traits ::template Matrix< n, n > ::type &  L,
typename Traits ::template Vector< n > ::type &  x 
)
inlinestatic

◆ invLx()

template<class Traits >
template<int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::invLx ( typename Traits ::template Matrix< n, n > ::type &  L,
typename Traits ::template Vector< n > ::type &  x 
)
inlinestatic

◆ leftInvA()

template<class Traits >
template<int m, int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::leftInvA ( const typename Traits ::template Matrix< m, n > ::type &  A,
typename Traits ::template Matrix< n, m > ::type &  ret 
)
inlinestatic

◆ leftInvAx()

template<class Traits >
template<int m, int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::leftInvAx ( const typename Traits ::template Matrix< m, n > ::type &  A,
const typename Traits ::template Vector< m > ::type &  x,
typename Traits ::template Vector< n > ::type &  y 
)
inlinestatic

◆ LLT()

template<class Traits >
template<int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::LLT ( const typename Traits ::template Matrix< n, n > ::type &  L,
typename Traits ::template Matrix< n, n > ::type &  ret 
)
inlinestatic

◆ LTL()

template<class Traits >
template<int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::LTL ( const typename Traits ::template Matrix< n, n > ::type &  L,
typename Traits ::template Matrix< n, n > ::type &  ret 
)
inlinestatic

◆ LTx()

template<class Traits >
template<int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::LTx ( const typename Traits ::template Matrix< n, n > ::type &  L,
const typename Traits ::template Vector< n > ::type &  x,
typename Traits ::template Vector< n > ::type &  ret 
)
inlinestatic

◆ Lx()

template<class Traits >
template<int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::Lx ( const typename Traits ::template Matrix< n, n > ::type &  L,
const typename Traits ::template Vector< n > ::type &  x,
typename Traits ::template Vector< n > ::type &  ret 
)
inlinestatic

◆ rightInvA()

template<class Traits >
template<int m, int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::rightInvA ( const typename Traits ::template Matrix< m, n > ::type &  A,
typename Traits ::template Matrix< n, m > ::type &  ret 
)
inlinestatic

Compute right pseudo-inverse of matrix A.

◆ spdDetA()

template<class Traits >
template<int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::spdDetA ( const typename Traits ::template Matrix< n, n > ::type &  A)
inlinestatic

◆ spdInvA()

template<class Traits >
template<int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::spdInvA ( typename Traits ::template Matrix< n, n > ::type &  A)
inlinestatic

◆ spdInvAx()

template<class Traits >
template<int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::spdInvAx ( typename Traits ::template Matrix< n, n > ::type &  A,
typename Traits ::template Vector< n > ::type &  x 
)
inlinestatic

◆ sqrtDetAAT()

template<class Traits >
template<int m, int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::sqrtDetAAT ( const typename Traits::template Matrix< m, n >::type &  A)
inlinestatic

Compute the square root of the determinant of A times A transposed.

This is the volume element for an embedded submanifold and needed to implement the method integrationElement().

◆ xTRightInvA()

template<class Traits >
template<int m, int n>
static void Dune::GenericGeometry::MatrixHelper< Traits >::xTRightInvA ( const typename Traits ::template Matrix< m, n > ::type &  A,
const typename Traits ::template Vector< n > ::type &  x,
typename Traits ::template Vector< m > ::type &  y 
)
inlinestatic

The documentation for this struct was generated from the following file: