dolfinx::la Namespace Reference

Linear algebra interface. More...

Namespaces
namespace	petsc
	PETSc linear algebra functions.

Classes
class	MatrixCSR
	Distributed sparse matrix using compressed sparse row storage. 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	SuperLUDistStructs
	Forward declare structs to avoid exposing SuperLU_DIST headers. More...
struct	SuperMatrixDeleter
class	SuperLUDistMatrix
	SuperLU_DIST matrix interface. More...
struct	GridInfoDeleter
struct	ScalePermStructDeleter
struct	LUStructDeleter
struct	SolveStructDeleter
class	SuperLUDistSolver
	SuperLU_DIST linear solver interface. More...
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.

Typedefs
template<typename T>
using	map_t = impl::map<T>
	Map scalar type to SuperLU_DIST 'typed' structs.

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.