basix::math Namespace Reference

Mathematical functions. More...

Functions
template<typename U , typename V >
xt::xtensor< typename U::value_type, 2 >	outer (const U &u, const V &v)
template<typename U , typename V >
xt::xtensor_fixed< typename U::value_type, xt::xshape< 3 > >	cross (const U &u, const V &v)
template<typename U , typename V >
xt::xtensor< typename U::value_type, 2 >	dot (const U &A, const V &B)
std::pair< xt::xtensor< double, 1 >, xt::xtensor< double, 2, xt::layout_type::column_major > >	eigh (const xt::xtensor< double, 2 > &A)
xt::xarray< double, xt::layout_type::column_major >	solve (const xt::xtensor< double, 2 > &A, const xt::xarray< double > &B)
bool	is_singular (const xt::xtensor< double, 2 > &A)

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 >

xt::xtensor_fixed<typename U::value_type, xt::xshape<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 >

xt::xtensor<typename U::value_type, 2> basix::math::dot	(	const U &	A,
		const V &	B
	)

Compute C = A * B

Parameters

[in]	A	Input matrix
[in]	B	Input matrix return A * B

eigh()

std::pair< xt::xtensor< double, 1 >, xt::xtensor< double, 2, xt::layout_type::column_major > > basix::math::eigh

(

const xt::xtensor< double, 2 > &

A

)

Compute the eigenvalues and eigenvectors of a square Hermitian matrix A

Parameters

[in]

A

Input matrix

Returns

Eigenvalues and eigenvectors

is_singular()

bool basix::math::is_singular

(

const xt::xtensor< double, 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 >

xt::xtensor<typename U::value_type, 2> basix::math::outer	(	const U &	u,
		const V &	v
	)

Compute the outer product of vectors u and v

Parameters

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

Returns

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

solve()

xt::xarray< double, xt::layout_type::column_major > basix::math::solve	(	const xt::xtensor< double, 2 > &	A,
		const xt::xarray< double > &	B
	)

Solve A X = B

Parameters

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

Returns

A^{-1} B