dolfinx::la Namespace Reference

Linear algebra interface. More...

Namespaces
namespace	petsc
	PETSc linear algebra functions.

Classes
class	MatrixCSR
	Distributed sparse matrix. More...
class	SLEPcEigenSolver
	This class provides an eigenvalue solver for PETSc matrices. It is a wrapper for the SLEPc eigenvalue solver. More...
class	SparsityPattern
class	Vector

Concepts
concept	MatSet
	Matrix accumulate/set concept for functions that can be used in assemblers to accumulate or set values in a matrix.

Enumerations
enum class	BlockMode : int { compact = 0 , expanded = 1 }
	Modes for representing block structured matrices. More...
enum class	Norm { l1 , l2 , linf , frobenius }
	Norm types.

Functions
template<class V >
auto	inner_product (const V &a, const V &b)
template<class V >
auto	squared_norm (const V &a)
template<class V >
auto	norm (const V &x, Norm type=Norm::l2)
template<class V >
void	orthonormalize (std::vector< std::reference_wrapper< V > > basis)
template<class V >
bool	is_orthonormal (std::vector< std::reference_wrapper< const V > > basis, dolfinx::scalar_value_type_t< typename V::value_type > eps=std::numeric_limits< dolfinx::scalar_value_type_t< typename V::value_type > >::epsilon())
	Test if basis is orthonormal.

Detailed Description

Linear algebra interface.

Interface to linear algebra data structures and solvers.

Enumeration Type Documentation

BlockMode

enum class BlockMode : int

strong

Modes for representing block structured matrices.

Enumerator
expanded	Each entry in the sparsity pattern of the matrix refers to a block of data of size (bs[0], bs[1]).

Function Documentation

inner_product()

template<class V >

auto inner_product	(	const V &	a,
		const V &	b )

Compute the inner product of two vectors. The two vectors must have the same parallel layout

Note

Collective MPI operation

Parameters

a	A vector
b	A vector

Returns

Returns a^{H} b (a^{T} b if a and b are real)

is_orthonormal()

template<class V >

bool is_orthonormal	(	std::vector< std::reference_wrapper< const V > >	basis,
		dolfinx::scalar_value_type_t< typename V::value_type >	eps = std::numeric_limits< dolfinx::scalar_value_type_t<typename V::value_type>>::epsilon() )

Test if basis is orthonormal.

Returns true if ||x_i - x_j|| - delta_{ij} < eps fro all i, j, and otherwise false.

Parameters

[in]	basis	Set of vectors to check.
[in]	eps	Tolerance.

Returns

True is basis is orthonormal, otherwise false.

norm()

template<class V >

auto norm	(	const V &	x,
		Norm	type = Norm::l2 )

Compute the norm of the vector

Note

Collective MPI operation

Parameters

x	A vector
type	Norm type

orthonormalize()

template<class V >

void orthonormalize

(

std::vector< std::reference_wrapper< V > >

basis

)

Orthonormalize a set of vectors

Parameters

[in,out]

basis

The set of vectors to orthonormalise. The vectors must have identical parallel layouts. The vectors are modified in-place.

Template Parameters

V	dolfinx::la::Vector

squared_norm()

template<class V >

auto squared_norm

(

const V &

a

)

Compute the squared L2 norm of vector

Note

Collective MPI operation