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)
template<std::floating_point T>
std::pair< std::vector< T >, std::vector< T > >	eigh (std::span< const T > A, std::size_t n)
template<std::floating_point T>
std::vector< T >	solve (MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< const T, MDSPAN_IMPL_STANDARD_NAMESPACE::dextents< std::size_t, 2 >> A, MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< const T, MDSPAN_IMPL_STANDARD_NAMESPACE::dextents< std::size_t, 2 >> B)
template<std::floating_point T>
bool	is_singular (MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< const T, MDSPAN_IMPL_STANDARD_NAMESPACE::dextents< std::size_t, 2 >> A)
template<std::floating_point T>
std::vector< std::size_t >	transpose_lu (std::pair< std::vector< T >, std::array< std::size_t, 2 >> &A)
template<typename U , typename V , typename W >
void	dot (const U &A, const V &B, W &&C)
template<std::floating_point T>
std::vector< T >	eye (std::size_t n)
template<std::floating_point T>
void	orthogonalise (MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< T, MDSPAN_IMPL_STANDARD_NAMESPACE::dextents< std::size_t, 2 >> wcoeffs, std::size_t start=0)

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()

template<std::floating_point T>

std::pair<std::vector<T>, std::vector<T> > basix::math::eigh	(	std::span< const T >	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()

template<std::floating_point T>

std::vector<T> 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()

template<std::floating_point T>

bool basix::math::is_singular

(

MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< const T, MDSPAN_IMPL_STANDARD_NAMESPACE::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

orthogonalise()

template<std::floating_point T>

void basix::math::orthogonalise	(	MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< T, MDSPAN_IMPL_STANDARD_NAMESPACE::dextents< std::size_t, 2 >>	wcoeffs,
		std::size_t	start = 0
	)

Orthogonalise the rows of a matrix (in place)

Parameters

[in]	wcoeffs	The matrix
[in]	start	The row to start from. The rows before this should already be orthogonal

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()

template<std::floating_point T>

std::vector<T> basix::math::solve	(	MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< const T, MDSPAN_IMPL_STANDARD_NAMESPACE::dextents< std::size_t, 2 >>	A,
		MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< const T, MDSPAN_IMPL_STANDARD_NAMESPACE::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()

template<std::floating_point T>

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

(

std::pair< std::vector< T >, 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)