dune-geometry
2.2.0
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#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) |
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) |
typedef Traits::ctype Dune::GenericGeometry::MatrixHelper< Traits >::FieldType |
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] |
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] |
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] |
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::abs | ( | const FieldType & | x | ) | [inline, static] |
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] |
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] |
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] |
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] |
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] |
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] |
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::detATA | ( | const typename Traits::template Matrix< m, n >::type & | A | ) | [inline, static] |
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::detL | ( | const typename Traits::template Matrix< n, n >::type & | L | ) | [inline, static] |
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::invL | ( | typename Traits::template Matrix< n, n >::type & | L | ) | [inline, static] |
static void Dune::GenericGeometry::MatrixHelper< Traits >::invLTx | ( | typename Traits::template Matrix< n, n >::type & | L, |
typename Traits::template Vector< n >::type & | x | ||
) | [inline, static] |
static void Dune::GenericGeometry::MatrixHelper< Traits >::invLx | ( | typename Traits::template Matrix< n, n >::type & | L, |
typename Traits::template Vector< n >::type & | x | ||
) | [inline, static] |
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] |
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] |
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] |
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] |
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] |
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] |
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] |
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::spdDetA | ( | const typename Traits::template Matrix< n, n >::type & | A | ) | [inline, static] |
static FieldType Dune::GenericGeometry::MatrixHelper< Traits >::spdInvA | ( | typename Traits::template Matrix< n, n >::type & | A | ) | [inline, static] |
static void Dune::GenericGeometry::MatrixHelper< Traits >::spdInvAx | ( | typename Traits::template Matrix< n, n >::type & | A, |
typename Traits::template Vector< n >::type & | x | ||
) | [inline, static] |
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().
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] |