basix::math Namespace Reference

Functions
template<typename U , typename V >
std::pair< std::vector< typename U::value_type >, std::array< std::size_t, 2 > >	outer (const U &u, const V &v)
	Compute the outer product of vectors u and v. More...
template<typename U , typename V >
std::array< typename U::value_type, 3 >	cross (const U &u, const V &v)
std::pair< std::vector< double >, std::vector< double > >	eigh (const std::span< const double > &A, std::size_t n)
std::vector< double >	solve (const std::experimental::mdspan< const double, std::experimental::dextents< std::size_t, 2 >> &A, const std::experimental::mdspan< const double, std::experimental::dextents< std::size_t, 2 >> &B)
bool	is_singular (const std::experimental::mdspan< const double, std::experimental::dextents< std::size_t, 2 >> &A)
std::vector< std::size_t >	transpose_lu (std::pair< std::vector< double >, std::array< std::size_t, 2 >> &A)
template<typename U , typename V , typename W >
void	dot (const U &A, const V &B, W &&C)
std::vector< double >	eye (std::size_t n)

Detailed Description

Mathematical functions

Note

The functions in this namespace are designed to be called multiple times at runtime, so their performance is critical.

Function Documentation

cross()

template<typename U , typename V >

std::array<typename U::value_type, 3> basix::math::cross	(	const U &	u,
		const V &	v
	)

Compute the cross product u x v

Parameters

u	The first vector. It must has size 3.
v	The second vector. It must has size 3.

Returns

The cross product u x v. The type will be the same as u.

dot()

template<typename U , typename V , typename W >

void basix::math::dot	(	const U &	A,
		const V &	B,
		W &&	C
	)

Compute C = A * B

Parameters

[in]	A	Input matrix
[in]	B	Input matrix
[out]	C	Output matrix. Must be sized correctly before calling this function.

eigh()

std::pair< std::vector< double >, std::vector< double > > basix::math::eigh	(	const std::span< const double > &	A,
		std::size_t	n
	)

Compute the eigenvalues and eigenvectors of a square Hermitian matrix A

Parameters

[in]	A	Input matrix, row-major storage
[in]	n	Number of rows

Returns

Eigenvalues (0) and eigenvectors (1). The eigenvector array uses column-major storage, which each column being an eigenvector.

Precondition

The matrix A must be symmetric

eye()

std::vector< double > basix::math::eye

(

std::size_t

n

)

Build an identity matrix

Parameters

[in]

n

The number of rows/columns

Returns

Identity matrix using row-major storage

is_singular()

bool basix::math::is_singular

(

const std::experimental::mdspan< const double, std::experimental::dextents< std::size_t, 2 >> &

A

)

Check if A is a singular matrix

Parameters

[in]

A

The matrix

Returns

A bool indicating if the matrix is singular

outer()

template<typename U , typename V >

std::pair<std::vector<typename U::value_type>, std::array<std::size_t, 2> > basix::math::outer	(	const U &	u,
		const V &	v
	)

Compute the outer product of vectors u and v.

Parameters

u	The first vector
v	The second vector

Returns

The outer product. The type will be the same as u.

solve()

std::vector< double > basix::math::solve	(	const std::experimental::mdspan< const double, std::experimental::dextents< std::size_t, 2 >> &	A,
		const std::experimental::mdspan< const double, std::experimental::dextents< std::size_t, 2 >> &	B
	)

Solve A X = B

Parameters

[in]	A	The matrix
[in]	B	Right-hand side matrix/vector

Returns

A^{-1} B

transpose_lu()

std::vector< std::size_t > basix::math::transpose_lu

(

std::pair< std::vector< double >, std::array< std::size_t, 2 >> &

A

)

Compute the LU decomposition of the transpose of a square matrix A

Parameters

[in,out]

A

The matrix

Returns

The LU permutation, in prepared format (see basix::precompute::prepare_permutation)