Basix 0.5.0

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Functions
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
uThe first vector. It must has size 3.
vThe 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]AInput matrix
[in]BInput matrix
[out]COutput 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]AInput matrix, row-major storage
[in]nNumber 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]nThe 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]AThe 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
uThe first vector
vThe 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]AThe matrix
[in]BRight-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]AThe matrix
Returns
The LU permutation, in prepared format (see basix::precompute::prepare_permutation)