dolfinx::la Namespace Reference

Linear algebra interface. More...

Classes
class	MatrixCSR
	Distributed sparse matrix using compressed sparse row storage. More...
class	SparsityPattern
class	Vector
	A vector that can be distributed across processes. More...

Concepts
concept	MatSet
	Matrix accumulate/set concept for functions that can be used in assemblers to accumulate or set values in a matrix.
concept	VectorPackKernel
	la::Vector scatter pack/unpack function concept.
concept	GetPtrConcept
	Access to pointer function concept.

Enumerations
enum class	BlockMode : int { compact = 0 , expanded = 1 }
	Modes for representing block structured matrices. More...
enum class	Norm : std::int8_t { l1 , l2 , linf , frobenius }
	Norm types.

Functions
template<class V>
auto	inner_product (const V &a, const V &b)
	Compute the inner product of two vectors.
template<class V>
auto	squared_norm (const V &a)
	Compute the squared L2 norm of vector.
template<class V>
auto	norm (const V &x, Norm type=Norm::l2)
	Compute the norm of the vector.
template<class V>
void	orthonormalize (std::vector< std::reference_wrapper< V > > basis)
	Orthonormalize a set of vectors.
template<class V>
bool	is_orthonormal (std::vector< std::reference_wrapper< const V > > basis, dolfinx::scalar_value_t< typename V::value_type > eps=std::numeric_limits< dolfinx::scalar_value_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.

Computes a^{H} b (a^{T} b if a and b are real). The two vectors must have the same parallel layout.

Note

Collective MPI operation

Parameters

a	Vector a.
b	Vector b.

Returns

Inner product between a and b.

is_orthonormal()

template<class V>

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

Test if basis is orthonormal.

Returns true if ||x_i - x_j|| - delta_{ij} < eps for 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	Vector to compute the norm of.
type	Norm type.

orthonormalize()

template<class V>

void orthonormalize

(

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

basis

)

Orthonormalize a set of vectors.

Template Parameters

V	dolfinx::la::Vector

Parameters

[in,out]

basis

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

squared_norm()

template<class V>

auto squared_norm

(

const V &

a

)

Compute the squared L2 norm of vector.

Note

Collective MPI operation.