Mathematical support

Description

Collaboration diagram for Mathematical support:

Namespaces
	chrono::fea::ChRotUtils
	Utility functions for rotations in 3D and their derivatives.

Classes
class	chrono::fea::ChGaussIntegrationRule
	Class for the management of the Gauss Quadrature in 1D, 2D or 3D space. More...
class	chrono::fea::ChGaussPoint
	Class for a Gauss point, that has a position (1D-3D) and a weight. More...
class	chrono::fea::ChMatrixCorotation
	Perform a corotation (warping) of a K matrix by pre- or post- multiplying it with a C matrix that has 3x3 rotation matrices R as diagonal blocks, so that C*K means: More...
class	chrono::fea::PolarDecomposition
	Polar decomposition of a general 3x3 matrix. More...
class	chrono::fea::ChPolarDecomposition< Real >
	Perform a polar decomposition of a 3x3 P matrix in order to retrieve the orthogonal Q and the symmetric S form, as P=Q*S. More...

Functions
template<int N>
bool	chrono::fea::LU_factor (ChMatrixNM< double, N, N > &A, ChMatrixNM< int, N, 1 > &INDX, bool &pivoting)
	In-place LU factorization. More...
template<int N>
void	chrono::fea::LU_solve (const ChMatrixNM< double, N, N > &A, const ChMatrixNM< int, N, 1 > &INDX, ChMatrixNM< double, N, 1 > &B)
	LU linear system solution (back substitution) More...

Function Documentation

LU_factor()

template<int N>

bool chrono::fea::LU_factor	(	ChMatrixNM< double, N, N > &	A,
		ChMatrixNM< int, N, 1 > &	INDX,
		bool &	pivoting
	)

In-place LU factorization.

Return false if the matrix is (close to) singular

Parameters

[in,out]	A	matrix to be factorized
[out]	INDX	vector of pivots
[out]	pivoting	true if pivoting was required; false otherwise

LU_solve()

template<int N>

void chrono::fea::LU_solve	(	const ChMatrixNM< double, N, N > &	A,
		const ChMatrixNM< int, N, 1 > &	INDX,
		ChMatrixNM< double, N, 1 > &	B
	)

LU linear system solution (back substitution)

Parameters

[in]	A	LU factorized matrix
[out]	INDX	vector of pivots
[in,out]	B	on entry, the RHS; on return, the solution vector