#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/matrix_expression.hpp>
#include "petsc.h"
#include "petscblaslapack.h"
#include "Exception.hpp"
#include "MathsCustomFunctions.hpp"

Include dependency graph for UblasCustomFunctions.hpp:

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Functions
template<class T >
T	Determinant (const boost::numeric::ublas::c_matrix< T, 1, 1 > &rM)
template<class T >
T	Determinant (const boost::numeric::ublas::c_matrix< T, 2, 2 > &rM)
template<class T >
T	Determinant (const boost::numeric::ublas::c_matrix< T, 3, 3 > &rM)
template<class T >
T	Determinant (const boost::numeric::ublas::c_matrix< T, 3, 2 > &rM)
template<class T >
T	Determinant (const boost::numeric::ublas::c_matrix< T, 3, 1 > &rM)
template<class T >
T	Determinant (const boost::numeric::ublas::c_matrix< T, 2, 1 > &rM)
template<class T >
T	Determinant (const boost::numeric::ublas::c_matrix< T, 3, 0 > &rM)
template<class T >
T	Determinant (const boost::numeric::ublas::c_matrix< T, 2, 0 > &rM)
template<class T >
T	Determinant (const boost::numeric::ublas::c_matrix< T, 1, 0 > &rM)
template<class T >
T	SubDeterminant (const boost::numeric::ublas::c_matrix< T, 1, 1 > &rM, const unsigned missrow, const unsigned misscol)
template<class T >
T	SubDeterminant (const boost::numeric::ublas::c_matrix< T, 2, 2 > &rM, const unsigned missrow, const unsigned misscol)
template<class T >
T	SubDeterminant (const boost::numeric::ublas::c_matrix< T, 3, 3 > &rM, const unsigned missrow, const unsigned misscol)
template<class T >
T	SubDeterminant (const boost::numeric::ublas::c_matrix< T, 3, 2 > &rM, const unsigned missrow, const unsigned misscol)
template<class T >
T	SubDeterminant (const boost::numeric::ublas::c_matrix< T, 3, 1 > &rM, const unsigned missrow, const unsigned misscol)
template<class T >
T	SubDeterminant (const boost::numeric::ublas::c_matrix< T, 2, 1 > &rM, const unsigned missrow, const unsigned misscol)
template<class T >
T	SubDeterminant (const boost::numeric::ublas::c_matrix< T, 3, 0 > &rM, const unsigned missrow, const unsigned misscol)
template<class T >
T	SubDeterminant (const boost::numeric::ublas::c_matrix< T, 2, 0 > &rM, const unsigned missrow, const unsigned misscol)
template<class T >
T	SubDeterminant (const boost::numeric::ublas::c_matrix< T, 1, 0 > &rM, const unsigned missrow, const unsigned misscol)
template<class T >
boost::numeric::ublas::c_matrix < T, 1, 1 >	Inverse (const boost::numeric::ublas::c_matrix< T, 1, 1 > &rM)
template<class T >
boost::numeric::ublas::c_matrix < T, 2, 2 >	Inverse (const boost::numeric::ublas::c_matrix< T, 2, 2 > &rM)
template<class T >
boost::numeric::ublas::c_matrix < T, 3, 3 >	Inverse (const boost::numeric::ublas::c_matrix< T, 3, 3 > &rM)
template<class T >
boost::numeric::ublas::c_matrix < T, 2, 3 >	Inverse (const boost::numeric::ublas::c_matrix< T, 3, 2 > &rM)
template<class T >
boost::numeric::ublas::c_matrix < T, 1, 2 >	Inverse (const boost::numeric::ublas::c_matrix< T, 2, 1 > &rM)
template<class T >
boost::numeric::ublas::c_matrix < T, 1, 3 >	Inverse (const boost::numeric::ublas::c_matrix< T, 3, 1 > &rM)
template<class T >
T	Trace (const c_matrix< T, 1, 1 > &rM)
template<class T >
T	Trace (const c_matrix< T, 2, 2 > &rM)
template<class T >
T	Trace (const c_matrix< T, 3, 3 > &rM)
template<class T >
T	Trace (const c_matrix< T, 4, 4 > &rM)
template<class T >
T	SecondInvariant (const c_matrix< T, 3, 3 > &rM)
template<class T >
T	SecondInvariant (const c_matrix< T, 2, 2 > &rM)
c_vector< double, 3 >	CalculateEigenvectorForSmallestNonzeroEigenvalue (c_matrix< double, 3, 3 > &rA)
template<class T >
c_vector< T, 3 >	VectorProduct (const c_vector< T, 3 > &rA, const c_vector< T, 3 > &rB)
c_vector< double, 1 >	Create_c_vector (double x)
c_vector< double, 2 >	Create_c_vector (double x, double y)
c_vector< double, 3 >	Create_c_vector (double x, double y, double z)

Detailed Description

A collection of useful functions extending the functionality of the Boost Ublas library.

Definition in file UblasCustomFunctions.hpp.

Function Documentation

c_vector<double,3> CalculateEigenvectorForSmallestNonzeroEigenvalue ( c_matrix< double, 3, 3 > & rA )

Use LAPACK functionality to find the eigenvector corresponding real eigenvalue which is smallest in magnitude. Caveat: if there are zero eigenvalues they are ignored. It's the smallest magnitude non-zero real eigenvalue which is used.

Parameters:

rA	3x3 matrix is question

Returns:: 3-vector corresponding to right-eigenvector in question

Definition at line 62 of file UblasCustomFunctions.cpp.

c_vector<double, 1> Create_c_vector ( double x )

Convenience function for quickly creating test vectors (1D).

Parameters:

x	entry in vector

Returns:: vector=(x)

Definition at line 38 of file UblasCustomFunctions.cpp.

c_vector<double, 2> Create_c_vector	(	double	x,
		double	y
	)

Convenience function for quickly creating test vectors (2D).

Parameters:

x	entry in vector
y	entry in vector

Returns:: vector=(x,y)

Definition at line 45 of file UblasCustomFunctions.cpp.

c_vector<double, 3> Create_c_vector	(	double	x,
		double	y,
		double	z
	)

Convenience function for quickly creating test vectors (3D).

Parameters:

x	entry in vector
y	entry in vector
z	entry in vector

Returns:: vector=(x,y,z)

Definition at line 53 of file UblasCustomFunctions.cpp.

template<class T >

T Determinant ( const boost::numeric::ublas::c_matrix< T, 3, 2 > & rM )

3x2 (Generalized determinant). Calculate the generalized determinant of a 3x2 matrix. The generalized determinant is given by det(T) = sqrt(det(T'T));

Parameters:

rM	The matrix of which to find the generalized determinant.

Definition at line 120 of file UblasCustomFunctions.hpp.

References Determinant().

template<class T >

T Determinant ( const boost::numeric::ublas::c_matrix< T, 2, 0 > & rM )

2x0 (Generalized determinant) - not implement, but needed by some compilers.

Parameters:

rM	The matrix of which to find the generalized determinant.

Definition at line 172 of file UblasCustomFunctions.hpp.

References NEVER_REACHED.

template<class T >

T Determinant ( const boost::numeric::ublas::c_matrix< T, 2, 2 > & rM )

2x2 Determinant. Get the determinant of a ublas matrix.

Parameters:

rM	The matrix of which to find the determinant.

Definition at line 87 of file UblasCustomFunctions.hpp.

template<class T >

T Determinant ( const boost::numeric::ublas::c_matrix< T, 1, 0 > & rM )

1x0 (Generalized determinant) - not implement, but needed by some compilers.

Parameters:

rM	The matrix of which to find the generalized determinant.

Definition at line 183 of file UblasCustomFunctions.hpp.

References NEVER_REACHED.

template<class T >

T Determinant ( const boost::numeric::ublas::c_matrix< T, 3, 1 > & rM )

3x1 (Generalized determinant). Calculate the generalized determinant of a 3x1 matrix. The generalized determinant is given by det(T) = sqrt(det(T'T));

Parameters:

rM	The matrix of which to find the generalized determinant.

Definition at line 135 of file UblasCustomFunctions.hpp.

template<class T >

T Determinant ( const boost::numeric::ublas::c_matrix< T, 1, 1 > & rM )

1x1 Determinant. Get the determinant of a ublas matrix.

Parameters:

rM	The matrix of which to find the determinant.

Definition at line 73 of file UblasCustomFunctions.hpp.

Referenced by AbstractCardiacMechanicsSolver< ELASTICITY_SOLVER, DIM >::AddActiveStressAndStressDerivative(), AbstractNonlinearElasticitySolver< DIM >::AssembleOnBoundaryElementForPressureOnDeformedBc(), IncompressibleNonlinearElasticitySolver< DIM >::AssembleOnElement(), AbstractTetrahedralElement< ELEMENT_DIM, SPACE_DIM >::CalculateJacobian(), AbstractMaterialLaw< DIM >::ComputeCauchyStress(), CompressibleExponentialLaw< DIM >::ComputeStressAndStressDerivative(), AbstractIsotropicCompressibleMaterialLaw< DIM >::ComputeStressAndStressDerivative(), Determinant(), Inverse(), and SecondInvariant().

template<class T >

T Determinant ( const boost::numeric::ublas::c_matrix< T, 2, 1 > & rM )

2x1 (Generalized determinant). Calculate the generalized determinant of a 2x1 matrix. The generalized determinant is given by det(T) = sqrt(det(T'T));

Parameters:

rM	The matrix of which to find the generalized determinant.

Definition at line 149 of file UblasCustomFunctions.hpp.

template<class T >

T Determinant ( const boost::numeric::ublas::c_matrix< T, 3, 3 > & rM )

3x3 Determinant. Get the determinant of a ublas matrix.

Parameters:

rM	The matrix of which to find the determinant.

Definition at line 101 of file UblasCustomFunctions.hpp.

template<class T >

T Determinant ( const boost::numeric::ublas::c_matrix< T, 3, 0 > & rM )

3x0 (Generalized determinant) - not implement, but needed by some compilers.

Parameters:

rM	The matrix of which to find the generalized determinant.

Definition at line 161 of file UblasCustomFunctions.hpp.

References NEVER_REACHED.

template<class T >

boost::numeric::ublas::c_matrix<T, 1, 2> Inverse ( const boost::numeric::ublas::c_matrix< T, 2, 1 > & rM )

2x1 pseudo-inverse of a matrix. The pseudo-inverse is given by pinv(T) = (T'T)^(-1)*T'.

Parameters:

rM	The matrix of which to find the inverse.

Returns:: The inverse

Definition at line 491 of file UblasCustomFunctions.hpp.

References Determinant().

template<class T >

boost::numeric::ublas::c_matrix<T, 1, 1> Inverse ( const boost::numeric::ublas::c_matrix< T, 1, 1 > & rM )

1x1 Inverse. Get the inverse of a ublas matrix.

Parameters:

rM	The matrix of which to find the inverse.

Returns:: The inverse

Definition at line 378 of file UblasCustomFunctions.hpp.

References Determinant().

Referenced by AbstractCardiacMechanicsSolver< ELASTICITY_SOLVER, DIM >::AddActiveStressAndStressDerivative(), AbstractNonlinearElasticitySolver< DIM >::AssembleOnBoundaryElementForPressureOnDeformedBc(), IncompressibleNonlinearElasticitySolver< DIM >::AssembleOnElement(), CompressibleNonlinearElasticitySolver< DIM >::AssembleOnElement(), AbstractTetrahedralElement< ELEMENT_DIM, SPACE_DIM >::CalculateInverseJacobian(), AbstractMaterialLaw< DIM >::Compute1stPiolaKirchoffStress(), AbstractMaterialLaw< DIM >::Compute2ndPiolaKirchoffStress(), AbstractMaterialLaw< DIM >::ComputeCauchyStress(), and CardiacElectroMechanicsProblem< DIM, ELEC_PROB_DIM >::rGetModifiedConductivityTensor().

template<class T >

boost::numeric::ublas::c_matrix<T, 2, 2> Inverse ( const boost::numeric::ublas::c_matrix< T, 2, 2 > & rM )

2x2 Inverse. Get the inverse of a ublas matrix.

Parameters:

rM	The matrix of which to find the inverse.

Returns:: The inverse

Definition at line 397 of file UblasCustomFunctions.hpp.

References Determinant().

template<class T >

boost::numeric::ublas::c_matrix<T, 3, 3> Inverse ( const boost::numeric::ublas::c_matrix< T, 3, 3 > & rM )

3x3 Inverse. Get the inverse of a ublas matrix.

Parameters:

rM	The matrix of which to find the inverse.

Returns:: The inverse

Definition at line 420 of file UblasCustomFunctions.hpp.

References Determinant().

template<class T >

boost::numeric::ublas::c_matrix<T, 2, 3> Inverse ( const boost::numeric::ublas::c_matrix< T, 3, 2 > & rM )

2x3 pseudo-inverse of a matrix. The pseudo-inverse is given by pinv(T) = (T'T)^(-1)*T'.

Parameters:

rM	The matrix of which to find the inverse.

Returns:: The inverse

Definition at line 451 of file UblasCustomFunctions.hpp.

template<class T >

boost::numeric::ublas::c_matrix<T, 1, 3> Inverse ( const boost::numeric::ublas::c_matrix< T, 3, 1 > & rM )

3x1 pseudo-inverse of a matrix. The pseudo-inverse is given by pinv(T) = (T'T)^(-1)*T'.

Parameters:

rM	The matrix of which to find the inverse.

Returns:: The inverse

Definition at line 512 of file UblasCustomFunctions.hpp.

References Determinant().

template<class T >

T SecondInvariant ( const c_matrix< T, 2, 2 > & rM )

2x2 second invariant. Second invariant of a 2d matrix, i.e. the determinant. This function is mainly here just so that the same code can be used in 2d and 3d.

Parameters:

rM	The matrix

Definition at line 601 of file UblasCustomFunctions.hpp.

References Determinant().

template<class T >

T SecondInvariant ( const c_matrix< T, 3, 3 > & rM )

3x3 second invariant.

Note:: Implementation only correct for a SYMMETRIC matrix though. It is up to the user to check the input matrix is symmetric.

Parameters:

rM	The matrix

Definition at line 587 of file UblasCustomFunctions.hpp.

Referenced by AbstractIsotropicIncompressibleMaterialLaw< DIM >::ComputeStressAndStressDerivative(), and AbstractIsotropicCompressibleMaterialLaw< DIM >::ComputeStressAndStressDerivative().

template<class T >

T SubDeterminant	(	const boost::numeric::ublas::c_matrix< T, 3, 0 > &	rM,
		const unsigned	missrow,
		const unsigned	misscol
	)

SubDeterminant 3x0 - Not implemented, but needed by some compilers for recursive template calls. Determinant of a submatrix after removing a particular row and column.

Parameters:

rM	The matrix of which to find the subdeterminant.
missrow	The index to the row to remove
misscol	The index to the column to remove

Definition at line 334 of file UblasCustomFunctions.hpp.

References NEVER_REACHED.

template<class T >

T SubDeterminant	(	const boost::numeric::ublas::c_matrix< T, 2, 1 > &	rM,
		const unsigned	missrow,
		const unsigned	misscol
	)

SubDeterminant 2x1. Determinant of a submatrix after removing a particular row and column.

Parameters:

rM	The matrix of which to find the subdeterminant.
missrow	The index to the row to remove
misscol	The index to the column to remove

Definition at line 310 of file UblasCustomFunctions.hpp.

template<class T >

T SubDeterminant	(	const boost::numeric::ublas::c_matrix< T, 2, 0 > &	rM,
		const unsigned	missrow,
		const unsigned	misscol
	)

SubDeterminant 2x0 - Not implemented, but needed by some compilers for recursive template calls. Determinant of a submatrix after removing a particular row and column.

Parameters:

rM	The matrix of which to find the subdeterminant.
missrow	The index to the row to remove
misscol	The index to the column to remove

Definition at line 348 of file UblasCustomFunctions.hpp.

References NEVER_REACHED.

template<class T >

T SubDeterminant	(	const boost::numeric::ublas::c_matrix< T, 1, 0 > &	rM,
		const unsigned	missrow,
		const unsigned	misscol
	)

SubDeterminant 1x0 - Not implemented, but needed by some compilers for recursive template calls. Determinant of a submatrix after removing a particular row and column.

Parameters:

rM	The matrix of which to find the subdeterminant.
missrow	The index to the row to remove
misscol	The index to the column to remove

Definition at line 362 of file UblasCustomFunctions.hpp.

References NEVER_REACHED.

template<class T >

T SubDeterminant	(	const boost::numeric::ublas::c_matrix< T, 3, 1 > &	rM,
		const unsigned	missrow,
		const unsigned	misscol
	)

SubDeterminant 3x1. Determinant of a submatrix after removing a particular row and column.

Parameters:

rM	The matrix of which to find the subdeterminant.
missrow	The index to the row to remove
misscol	The index to the column to remove

Definition at line 287 of file UblasCustomFunctions.hpp.

template<class T >

T SubDeterminant	(	const boost::numeric::ublas::c_matrix< T, 1, 1 > &	rM,
		const unsigned	missrow,
		const unsigned	misscol
	)

1x1 SubDeterminant. Return the determinant of a submatrix after removing a particular row and column For a 1x1 matrix this should always remove the only row and column (0,0).

Parameters:

rM	The matrix of which to find the subdeterminant.
missrow	The index to the row to remove
misscol	The index to the column to remove

Definition at line 200 of file UblasCustomFunctions.hpp.

Referenced by AbstractTetrahedralElement< ELEMENT_DIM, SPACE_DIM >::CalculateWeightedDirection().

template<class T >

T SubDeterminant	(	const boost::numeric::ublas::c_matrix< T, 2, 2 > &	rM,
		const unsigned	missrow,
		const unsigned	misscol
	)

2x2 SubDeterminant. Return the determinant of a submatrix after removing a particular row and column.

Parameters:

rM	The matrix of which to find the subdeterminant.
missrow	The index to the row to remove
misscol	The index to the column to remove

Definition at line 218 of file UblasCustomFunctions.hpp.

template<class T >

T SubDeterminant	(	const boost::numeric::ublas::c_matrix< T, 3, 3 > &	rM,
		const unsigned	missrow,
		const unsigned	misscol
	)

SubDeterminant 3x3. Determinant of a submatrix after removing a particular row and column.

Parameters:

rM	The matrix of which to find the subdeterminant.
missrow	The index to the row to remove
misscol	The index to the column to remove

Definition at line 239 of file UblasCustomFunctions.hpp.

template<class T >

T SubDeterminant	(	const boost::numeric::ublas::c_matrix< T, 3, 2 > &	rM,
		const unsigned	missrow,
		const unsigned	misscol
	)

SubDeterminant 3x2. Determinant of a submatrix after removing a particular row and column.

Parameters:

rM	The matrix of which to find the subdeterminant.
missrow	The index to the row to remove
misscol	The index to the column to remove

Definition at line 264 of file UblasCustomFunctions.hpp.

template<class T >

T Trace ( const c_matrix< T, 1, 1 > & rM )

1x1 matrix trace (sum of diagonal elements).

Parameters:

rM	The matrix of which to find the trace.

Returns:: The trace

Definition at line 535 of file UblasCustomFunctions.hpp.

Referenced by AbstractIsotropicIncompressibleMaterialLaw< DIM >::ComputeStressAndStressDerivative(), and AbstractIsotropicCompressibleMaterialLaw< DIM >::ComputeStressAndStressDerivative().

template<class T >

T Trace ( const c_matrix< T, 3, 3 > & rM )

3x3 matrix trace (sum of diagonal elements).

Parameters:

rM	The matrix of which to find the trace.

Returns:: The trace

Definition at line 559 of file UblasCustomFunctions.hpp.

template<class T >

T Trace ( const c_matrix< T, 2, 2 > & rM )

2x2 matrix trace (sum of diagonal elements).

Parameters:

rM	The matrix of which to find the trace.

Returns:: The trace

Definition at line 547 of file UblasCustomFunctions.hpp.

template<class T >

T Trace ( const c_matrix< T, 4, 4 > & rM )

4x4 matrix trace (sum of diagonal elements).

Parameters:

rM	The matrix of which to find the trace.

Returns:: The trace

Definition at line 571 of file UblasCustomFunctions.hpp.

template<class T >

c_vector<T, 3> VectorProduct	(	const c_vector< T, 3 > &	rA,
		const c_vector< T, 3 > &	rB
	)

This is a cross-product aka vector-product, only implemented for 3-vectors.

Parameters:

rA	first vector
rB	second vector

Returns:: rA x rB

Definition at line 627 of file UblasCustomFunctions.hpp.

Referenced by StreeterFibreGenerator< SPACE_DIM >::GenerateOrthotropicFibreOrientation().