basix::math Namespace Reference

Mathematical functions. More...

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)
	Solve A X = B. More...
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)
	Check if A is a singular matrix,. More...
template<std::floating_point T>
std::vector< std::size_t >	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. More...
template<typename U , typename V , typename W >
void	dot (const U &A, const V &B, W &&C)
	Compute C = A * B. More...
template<std::floating_point T>
std::vector< T >	eye (std::size_t n)
	Build an identity matrix. More...
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)
	Orthogonalise the rows of a matrix (in place). More...

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

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.

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.

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

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

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

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 precompute::prepare_permutation)

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.

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

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.