dune-geometry  2.2.0
Public Types | Static Public Member Functions
Dune::GenericGeometry::MatrixHelper< Traits > Struct Template Reference

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

List of all members.

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)
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)

template<class Traits>
struct Dune::GenericGeometry::MatrixHelper< Traits >


Member Typedef Documentation

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

Member Function Documentation

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 
) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
template<class Traits >
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::abs ( const FieldType x) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
template<class Traits >
template<int m, int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::detATA ( const typename Traits::template Matrix< m, n >::type &  A) [inline, static]
template<class Traits >
template<int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::detL ( const typename Traits::template Matrix< n, n >::type &  L) [inline, static]
template<class Traits >
template<int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::invL ( typename Traits::template Matrix< n, n >::type &  L) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
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 
) [inline, static]
template<class Traits >
template<int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::spdDetA ( const typename Traits::template Matrix< n, n >::type &  A) [inline, static]
template<class Traits >
template<int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::spdInvA ( typename Traits::template Matrix< n, n >::type &  A) [inline, static]
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 
) [inline, static]
template<class Traits >
template<int m, int n>
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::sqrtDetAAT ( const typename Traits::template Matrix< m, n >::type &  A) [inline, static]

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().

References Dune::GenericGeometry::MatrixHelper< Traits >::abs().

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 
) [inline, static]

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