A namespace containing the different wrapper functions. More...

Classes
struct	LAPACKexception
	Exception to be thrown if LAPACK's solve fails. More...

Typedefs
template<unsigned int hyEdge_dim, unsigned int space_dim, typename TPCC::boundaries bndT = TPCC::boundaries::both, typename index_t = unsigned int>
using	tpcc_t = TPCC::Lexicographic< space_dim, hyEdge_dim, bndT, index_t, unsigned int, unsigned int >
	Type of a tensor product chain complex. More...

template<unsigned int hyEdge_dim, unsigned int space_dim>
using	tpcc_elem_t = TPCC::Element< space_dim, hyEdge_dim, unsigned int, unsigned int >
	Type of an element of a tensor product chain complex. More...

Functions
template<unsigned int system_size, unsigned int n_rhs_cols = 1, typename lapack_float_t >
std::array< lapack_float_t, system_size *n_rhs_cols >	lapack_solve (std::array< lapack_float_t, system_size system_size > &dense_mat, std::array< lapack_float_t, system_size n_rhs_cols > &rhs)
	Solve local system of equations. More...

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >
lapack_float_t	lapack_det (std::array< lapack_float_t, n_rows *n_cols > &dense_mat)
	Determinant of a rectangular system. More...

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >
std::array< lapack_float_t, n_rows *n_rows >	lapack_qr_decomp_q (std::array< lapack_float_t, n_rows *n_cols > &dense_mat)
	Matrix Q of QR decomposition. More...

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >
std::array< lapack_float_t, n_rows *n_cols > &	lapack_qr_decomp_r (std::array< lapack_float_t, n_rows *n_cols > &dense_mat)
	Matrix R of QR decomposition. More...

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >
void	lapack_qr_decomp (std::array< lapack_float_t, n_rows n_cols > &dense_mat, std::array< lapack_float_t, n_rows n_rows > &mat_q)
	Matrices Q and R of QR decomposition. More...

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >
void	lapack_qr_decomp (std::array< lapack_float_t, n_rows n_cols > &dense_mat, std::array< lapack_float_t, n_rows n_rows > &mat_q, std::array< lapack_float_t, n_cols *n_cols > &mat_r)
	Matrices Q and R of QR decomposition. More...

void	lapack_solve (int system_size, int n_rhs_cols, double mat_a, double rhs_b)
	Solve local system of equations with `double` floating point numbers — DO NOT USE. More...

void	lapack_solve (int system_size, int n_rhs_cols, float mat_a, float rhs_b)
	Solve local system of equations with `float` floating point numbers — DO NOT USE. More...

void	lapack_qr (int n_rows, int n_cols, double mat_a, double tau)
	QR decomposition in `double` floating point arithmetic — DO NOT USE. More...

void	lapack_qr (int n_rows, int n_cols, float mat_a, float tau)
	QR decomposition in `float` floating point arithmetic — DO NOT USE. More...

template<unsigned int n_rows, unsigned int n_cols, unsigned int rank, typename lapack_float_t >
std::array< lapack_float_t, n_rows *n_rows >	get_q_from_lapack_qr_result (const std::array< lapack_float_t, n_rows *n_cols > &dense_mat, const std::array< lapack_float_t, rank > &tau)
	Matrix Q of QR decomposition — DO NOT USE. More...

template<unsigned int n_rows, unsigned int n_cols, unsigned int rank, typename lapack_float_t >
void	get_q_from_lapack_qr_result (const std::array< lapack_float_t, n_rows n_cols > &dense_mat, const std::array< lapack_float_t, rank > &tau, std::array< lapack_float_t, n_rows n_rows > &mat_q)
	Matrix Q of QR decomposition — DO NOT USE. More...

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >
std::array< lapack_float_t, n_rows *n_cols > &	get_r_from_lapack_qr_result (std::array< lapack_float_t, n_rows *n_cols > &dense_mat)
	Matrix R of QR decomposition — DO NOT USE. More...

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >
void	get_r_from_lapack_qr_result (const std::array< lapack_float_t, n_rows n_cols > &lapack_mat, std::array< lapack_float_t, n_cols n_cols > &mat_r)
	Matrix R of QR decomposition — DO NOT USE. More...

unsigned int	binomial (unsigned int n, unsigned int k)
	Binomial coefficient of unsigned integers. More...

template<unsigned int hyEdge_dim, unsigned int space_dim, typename TPCC::boundaries bndT = TPCC::boundaries::both, typename index_t = unsigned int>
tpcc_t< hyEdge_dim, space_dim, bndT, index_t >	create_tpcc (const SmallVec< space_dim, index_t > &vec)
	Create a tensor product chain complex. More...

template<typename TPCC::boundaries bndT>
auto	tpcc_faces (const auto &elements)
	Create a tensor product chain complex associated to the facets. More...

template<typename index_t = unsigned int>
index_t	n_elements (const auto &tpcc)
	Return the element of given index the TPCC. More...

auto	get_element (const auto &tpcc, const auto index)
	Return the element of given index the TPCC. More...

template<typename index_t = unsigned int>
index_t	get_index (const auto &tpcc, const auto &elem)
	Return index of given element within TPCC. More...

template<typename index_t = unsigned int>
index_t	get_index_in_slice (const auto &tpcc, const auto &elem)
	Return index of given element within TPCC. More...

auto	get_face (const auto &elem, const unsigned int index)
	Return i-th element facet. More...

unsigned int	elem_orientation (const auto &elem)
	Determine the orientation of an element. More...

unsigned int	exterior_direction (const auto &elem, const unsigned int index)
	Return the index-th orthonormal direction to element. More...

unsigned int	exterior_coordinate (const auto &elem, const unsigned int index)
	Return coordinate value with respect to index-th orthonormal direction on element. More...

unsigned int	interior_coordinate (const auto &elem, const unsigned int index)
	Return coordinate value with respect to index-th orthonormal direction of element. More...

Detailed Description

A namespace containing the different wrapper functions.

Authors: Guido Kanschat, Heidelberg University, 2019–2020.; Andreas Rupp, Heidelberg University, 2019–2020.

Typedef Documentation

◆ tpcc_elem_t

template<unsigned int hyEdge_dim, unsigned int space_dim>

using Wrapper::tpcc_elem_t = typedef TPCC::Element<space_dim, hyEdge_dim, unsigned int, unsigned int>

Type of an element of a tensor product chain complex.

◆ tpcc_t

template<unsigned int hyEdge_dim, unsigned int space_dim, typename TPCC::boundaries bndT = TPCC::boundaries::both, typename index_t = unsigned int>

using Wrapper::tpcc_t = typedef TPCC::Lexicographic<space_dim, hyEdge_dim, bndT, index_t, unsigned int, unsigned int>

Type of a tensor product chain complex.

Function Documentation

◆ binomial()

unsigned int Wrapper::binomial	(	unsigned int	n,
		unsigned int	k
	)

Binomial coefficient of unsigned integers.

◆ create_tpcc()

template<unsigned int hyEdge_dim, unsigned int space_dim, typename TPCC::boundaries bndT = TPCC::boundaries::both, typename index_t = unsigned int>

tpcc_t<hyEdge_dim, space_dim, bndT, index_t> Wrapper::create_tpcc ( const SmallVec< space_dim, index_t > & vec )

Create a tensor product chain complex.

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◆ elem_orientation()

unsigned int Wrapper::elem_orientation ( const auto & elem )

Determine the orientation of an element.

◆ exterior_coordinate()

unsigned int Wrapper::exterior_coordinate	(	const auto &	elem,
		const unsigned int	index
	)

Return coordinate value with respect to index-th orthonormal direction on element.

◆ exterior_direction()

unsigned int Wrapper::exterior_direction	(	const auto &	elem,
		const unsigned int	index
	)

Return the index-th orthonormal direction to element.

◆ get_element()

auto Wrapper::get_element	(	const auto &	tpcc,
		const auto	index
	)

Return the element of given index the TPCC.

◆ get_face()

auto Wrapper::get_face	(	const auto &	elem,
		const unsigned int	index
	)

Return i-th element facet.

◆ get_index()

template<typename index_t = unsigned int>

index_t Wrapper::get_index	(	const auto &	tpcc,
		const auto &	elem
	)

Return index of given element within TPCC.

◆ get_index_in_slice()

template<typename index_t = unsigned int>

index_t Wrapper::get_index_in_slice	(	const auto &	tpcc,
		const auto &	elem
	)

Return index of given element within TPCC.

◆ get_q_from_lapack_qr_result() [1/2]

template<unsigned int n_rows, unsigned int n_cols, unsigned int rank, typename lapack_float_t >

std::array<lapack_float_t, n_rows * n_rows> Wrapper::get_q_from_lapack_qr_result	(	const std::array< lapack_float_t, n_rows *n_cols > &	dense_mat,
		const std::array< lapack_float_t, rank > &	tau
	)

inline

Matrix Q of QR decomposition — DO NOT USE.

Return matrix Q of the Householder QR decomposition of the matrix. The matrix is supposed to contain the Householder QR decomposition which is encoded in the style of LAPACK. The function returns matrix Q in standard encoding.

Template Parameters

n_rows	Number of rows of the matrix whose determinant should be calculated.
n_cols	Number of columns of the matrix whose determinant should be calculated.
float_t	Floating type which this function should be executed with. Only `float` and `double` are supported.

Parameters

dense_mat	Array comprising the QR decomposed matrix.
tau	Auxiliary data from LAPACK to encode matrix Q.

Return values

mat_q Matrix Q of Householder QR decomposition.

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◆ get_q_from_lapack_qr_result() [2/2]

template<unsigned int n_rows, unsigned int n_cols, unsigned int rank, typename lapack_float_t >

void Wrapper::get_q_from_lapack_qr_result	(	const std::array< lapack_float_t, n_rows *n_cols > &	dense_mat,
		const std::array< lapack_float_t, rank > &	tau,
		std::array< lapack_float_t, n_rows *n_rows > &	mat_q
	)

inline

Matrix Q of QR decomposition — DO NOT USE.

Return matrix Q of the Householder QR decomposition of the matrix. The matrix is supposed to contain the Householder QR decomposition which is encoded in the style of LAPACK. The function returns matrix Q in standard encoding.

Template Parameters

n_rows	Number of rows of the matrix whose determinant should be calculated.
n_cols	Number of columns of the matrix whose determinant should be calculated.
float_t	Floating type which this function should be executed with. Only `float` and `double` are supported.

Parameters

dense_mat	Array comprising the QR decomposed matrix.
tau	Auxiliary data from LAPACK to encode matrix Q.
mat_q	Matrix to be filled with entries of the return value.

Return values

mat_q Matrix Q of Householder QR decomposition.

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◆ get_r_from_lapack_qr_result() [1/2]

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >

void Wrapper::get_r_from_lapack_qr_result	(	const std::array< lapack_float_t, n_rows *n_cols > &	lapack_mat,
		std::array< lapack_float_t, n_cols *n_cols > &	mat_r
	)

inline

Matrix R of QR decomposition — DO NOT USE.

Return matrix R of the Householder QR decomposition of the matrix. The matrix is supposed to contain the Householder QR decomposition which is encoded in the style of LAPACK. The function returns matrix R in standard encoding, but with dimensions n_cols times n_cols.

Template Parameters

n_rows	Number of rows of the matrix whose determinant should be calculated.
n_cols	Number of columns of the matrix whose determinant should be calculated.
float_t	Floating type which this function should be executed with. Only `float` and `double` are supported.

Parameters

lapack_mat	Array comprising the QR decomposed matrix.
mat_r	Matrix to be filled with the entries of the return value.

Return values

mat_r Matrix R of Householder QR decomposition.

◆ get_r_from_lapack_qr_result() [2/2]

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >

std::array<lapack_float_t, n_rows * n_cols>& Wrapper::get_r_from_lapack_qr_result ( std::array< lapack_float_t, n_rows *n_cols > & dense_mat )

inline

Matrix R of QR decomposition — DO NOT USE.

Return matrix R of the Householder QR decomposition of the matrix. The matrix is supposed to contain the Householder QR decomposition which is encoded in the style of LAPACK. The function returns matrix R in standard encoding.

The function also manipulates the input matrix to be R.

Template Parameters

n_rows	Number of rows of the matrix whose determinant should be calculated.
n_cols	Number of columns of the matrix whose determinant should be calculated.
float_t	Floating type which this function should be executed with. Only `float` and `double` are supported.

Parameters

dense_mat Array comprising the QR decomposed matrix.

Return values

mat_r Matrix R of Householder QR decomposition.

◆ interior_coordinate()

unsigned int Wrapper::interior_coordinate	(	const auto &	elem,
		const unsigned int	index
	)

Return coordinate value with respect to index-th orthonormal direction of element.

◆ lapack_det()

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >

lapack_float_t Wrapper::lapack_det ( std::array< lapack_float_t, n_rows *n_cols > & dense_mat )

Determinant of a rectangular system.

Calculate the generalized determinant of a rectangular matrix. If the matrix is square, this is the standard determinant. The determinant is determined by doing a QR decomposition based on Householder transformations. Thus det(Q) = +1, if the number of rows if even and det(Q) = -1, if the number of rows is odd. This number is multiplied by the diagonal entries of R.

The matrix is destroyed using this function. Its entries might be used to generate matrices Q and R of the QR descomposition.

Template Parameters

n_rows	Number of rows of the matrix whose determinant should be calculated.
n_cols	Number of columns of the matrix whose determinant should be calculated.
float_t	Floating type which this function should be executed with. Only `float` and `double` are supported.

Parameters

dense_mat Array comprising the matrix describing the linear system of equations.

Return values

determinant Generalized determinant of the matrix.

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◆ lapack_qr() [1/2]

void Wrapper::lapack_qr	(	int	n_rows,
		int	n_cols,
		double *	mat_a,
		double *	tau
	)

inline

QR decomposition in double floating point arithmetic — DO NOT USE.

Perform QR decomposition of a given matrix using Householder transformations. The matrices Q and R are stored according to the LAPACK function in an encoded way in matrix mat_a and vector tau.

Parameters

n_rows	Number of rows of matrix.
n_cols	Number of columns of matrix.
mat_a	Matrix that is to be decomposed.
tau	Space for return value, i.e. vector with auxiliary darta.

Return values

mat_a	Encoded QR decomposition of the matrix.
tau	Auxiliary parameters needed to reconstruct matrix Q.

◆ lapack_qr() [2/2]

void Wrapper::lapack_qr	(	int	n_rows,
		int	n_cols,
		float *	mat_a,
		float *	tau
	)

inline

QR decomposition in float floating point arithmetic — DO NOT USE.

Perform QR decomposition of a given matrix using Householder transformations. The matrices Q and R are stored according to the LAPACK function in an encoded way in matrix mat_a and vector tau.

Parameters

n_rows	Number of rows of matrix.
n_cols	Number of columns of matrix.
mat_a	Matrix that is to be decomposed.
tau	Space for return value, i.e. vector with auxiliary darta.

Return values

mat_a	Encoded QR decomposition of the matrix.
tau	Auxiliary parameters needed to reconstruct matrix Q.

◆ lapack_qr_decomp() [1/2]

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >

void Wrapper::lapack_qr_decomp	(	std::array< lapack_float_t, n_rows *n_cols > &	dense_mat,
		std::array< lapack_float_t, n_rows *n_rows > &	mat_q
	)

Matrices Q and R of QR decomposition.

Return matriices Q and R of the Householder QR decomposition of the matrix.

Template Parameters

n_rows	Number of rows of the matrix whose determinant should be calculated.
n_cols	Number of columns of the matrix whose determinant should be calculated.
float_t	Floating type which this function should be executed with. Only `float` and `double` are supported.

Parameters

dense_mat	Array comprising the matrix describing the linear system of equations.
mat_q	Reference to empy matrix to be filled.

Return values

dense_mat	Matrix R of Householder QR decomposition.
mat_q	Matrix Q of Householder QR decomposition.

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◆ lapack_qr_decomp() [2/2]

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >

void Wrapper::lapack_qr_decomp	(	std::array< lapack_float_t, n_rows *n_cols > &	dense_mat,
		std::array< lapack_float_t, n_rows *n_rows > &	mat_q,
		std::array< lapack_float_t, n_cols *n_cols > &	mat_r
	)

Matrices Q and R of QR decomposition.

Return matriices Q and R of the Householder QR decomposition of the matrix.

Template Parameters

n_rows	Number of rows of the matrix whose determinant should be calculated.
n_cols	Number of columns of the matrix whose determinant should be calculated.
float_t	Floating type which this function should be executed with. Only `float` and `double` are supported.

Parameters

dense_mat	Array comprising the matrix describing the linear system of equations.
mat_q	Reference to empy matrix to be filled.
mat_r	Reference to empy matrix to be filled.

Return values

dense_mat	Matrix R of Householder QR decomposition.
mat_q	Matrix Q of Householder QR decomposition.
mat_r	Square system of size n_cols that contains respective part of R.

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◆ lapack_qr_decomp_q()

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >

std::array< lapack_float_t, n_rows *n_rows > Wrapper::lapack_qr_decomp_q ( std::array< lapack_float_t, n_rows *n_cols > & dense_mat )

Matrix Q of QR decomposition.

Return matrix Q of the Householder QR decomposition of the matrix. The matrix is destroyed using this function. Its entries might be used to generate matrices Q and R of the QR descomposition.

Template Parameters

n_rows	Number of rows of the matrix whose determinant should be calculated.
n_cols	Number of columns of the matrix whose determinant should be calculated.
float_t	Floating type which this function should be executed with. Only `float` and `double` are supported.

Parameters

dense_mat Array comprising the matrix describing the linear system of equations.

Return values

mat_q Matrix Q of Householder QR decomposition.

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◆ lapack_qr_decomp_r()

template<unsigned int n_rows, unsigned int n_cols, typename lapack_float_t >

std::array< lapack_float_t, n_rows *n_cols > & Wrapper::lapack_qr_decomp_r ( std::array< lapack_float_t, n_rows *n_cols > & dense_mat )

Matrix R of QR decomposition.

Return matrix R of the Householder QR decomposition of the matrix. The matrix is destroyed using this function. Its entries are the same as the ones of R of the QR descomposition.

Template Parameters

n_rows	Number of rows of the matrix whose determinant should be calculated.
n_cols	Number of columns of the matrix whose determinant should be calculated.
float_t	Floating type which this function should be executed with. Only `float` and `double` are supported.

Parameters

dense_mat Array comprising the matrix describing the linear system of equations.

Return values

dense_mat	Matrix R of Householder QR decomposition.
mat_r	Matrix R of Householder QR decomposition.

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◆ lapack_solve() [1/3]

void Wrapper::lapack_solve	(	int	system_size,
		int	n_rhs_cols,
		double *	mat_a,
		double *	rhs_b
	)

inline

Solve local system of equations with double floating point numbers — DO NOT USE.

Solve linear (dense) system of equations $Ax=b$, where $A$ is an $n \times n$ square matrix, which enters as a pointer to double, $n$ is provided via system_size, and the double pointer rhs_b is both, input (i.e., $b$) and output (i.e., $x$) of the function.

Independent of const expressions of functions using lapack_solve one should not use mat_a after calling this function. The input that has been within rhs_b will have been replaced by the solution of the system of equations.

Parameters

system_size	Size of the system of equations.
n_rhs_cols	Number of right-hand sides the system is solved for.
mat_a	Pointer to the matrix describing the linear system of equations.
rhs_b	Pointer to the right-hand side of the system.

Return values

rhs_b Pointer to the solution of the system of equations.

◆ lapack_solve() [2/3]

void Wrapper::lapack_solve	(	int	system_size,
		int	n_rhs_cols,
		float *	mat_a,
		float *	rhs_b
	)

inline

Solve local system of equations with float floating point numbers — DO NOT USE.

Solve linear (dense) system of equations $Ax=b$, where $A$ is an $n \times n$ square matrix, which enters as a pointer to float, $n$ is provided via system_size, and the float pointer rhs_b is both, input (i.e., $b$) and output (i.e., $x$) of the function.

Independent of const expressions of functions using lapack_solve one should not use mat_a after calling this function. The input that has been within rhs_b will have been replaced by the solution of the system of equations.

Parameters

system_size	Size of the system of equations.
n_rhs_cols	Number of right-hand sides the system is solved for.
mat_a	Pointer to the matrix describing the linear system of equations.
rhs_b	Pointer to the right-hand side of the system.

Return values

rhs_b Pointer to the solution of the system of equations.

◆ lapack_solve() [3/3]

template<unsigned int system_size, unsigned int n_rhs_cols = 1, typename lapack_float_t >

std::array< lapack_float_t, system_size *n_rhs_cols > Wrapper::lapack_solve	(	std::array< lapack_float_t, system_size *system_size > &	dense_mat,
		std::array< lapack_float_t, system_size *n_rhs_cols > &	rhs
	)

Solve local system of equations.

Solve linear (dense) system of equations $Ax=b$, where $A$ is an $n \times n$ square matrix, which enters as a std::array of double, $n$ is provided via system_size, and the std::array of double rhs_b is both, input (i.e., $b$) and output (i.e., $x$) of the function.

Independent of const expressions of functions using lapack_solve one should not use mat_a after calling this function. The input that has been within rhs_b will have been replaced by the solution of the system of equations.

Template Parameters

system_size	Size of the system of equations.
n_rhs_cols	Number of columns of the right hand side matrix. Defaults to 1.
float_t	Floating type which this function should be executed with. Only `float` and `double` are supported.

Parameters

dense_mat	Array comprising the matrix describing the linear system of equations.
rhs	Array comprising the right-hand side of the system.

Return values

rhs_b Array comprising the solution of the system of equations.

◆ n_elements()

template<typename index_t = unsigned int>

index_t Wrapper::n_elements ( const auto & tpcc )

Return the element of given index the TPCC.

◆ tpcc_faces()

template<typename TPCC::boundaries bndT>

auto Wrapper::tpcc_faces ( const auto & elements )

Create a tensor product chain complex associated to the facets.

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ tpcc_elem_t

◆ tpcc_t

Function Documentation

◆ binomial()

◆ create_tpcc()

◆ elem_orientation()

◆ exterior_coordinate()

◆ exterior_direction()

◆ get_element()

◆ get_face()

◆ get_index()

◆ get_index_in_slice()

◆ get_q_from_lapack_qr_result() [1/2]

◆ get_q_from_lapack_qr_result() [2/2]

◆ get_r_from_lapack_qr_result() [1/2]

◆ get_r_from_lapack_qr_result() [2/2]

◆ interior_coordinate()

◆ lapack_det()

◆ lapack_qr() [1/2]

◆ lapack_qr() [2/2]

◆ lapack_qr_decomp() [1/2]

◆ lapack_qr_decomp() [2/2]

◆ lapack_qr_decomp_q()

◆ lapack_qr_decomp_r()

◆ lapack_solve() [1/3]

◆ lapack_solve() [2/3]

◆ lapack_solve() [3/3]

◆ n_elements()

◆ tpcc_faces()