dolfinx::la Namespace Reference

Linear algebra interface. More...

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
	This class provides a sparsity pattern data structure that can be used to initialize sparse matrices. After assembly, column indices are always sorted in increasing order. Ghost entries are kept after assembly. More...
class	Vector
	Distributed vector. More...

Enumerations
enum class	Norm { l1 , l2 , linf , frobenius }
	Norm types.

Functions
template<typename T , class Allocator >
T	inner_product (const Vector< T, Allocator > &a, const Vector< T, Allocator > &b)
	Compute the inner product of two vectors. The two vectors must have the same parallel layout. More...
template<typename T , class Allocator >
auto	squared_norm (const Vector< T, Allocator > &a)
	Compute the squared L2 norm of vector. More...
template<typename T , class Allocator >
auto	norm (const Vector< T, Allocator > &a, Norm type=Norm::l2)
	Compute the norm of the vector. More...
template<typename T , typename U >
void	orthonormalize (const std::span< Vector< T, U >> &basis, double tol=1.0e-10)
	Orthonormalize a set of vectors. More...
template<typename T , typename U >
bool	is_orthonormal (const std::span< const Vector< T, U >> &basis, double tol=1.0e-10)
	Test if basis is orthonormal. More...

Detailed Description

Linear algebra interface.

Interface to linear algebra data structures and solvers

Function Documentation

inner_product()

T dolfinx::la::inner_product	(	const Vector< T, Allocator > &	a,
		const Vector< T, Allocator > &	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()

bool dolfinx::la::is_orthonormal	(	const std::span< const Vector< T, U >> &	basis,
		double	tol = 1.0e-10
	)

Test if basis is orthonormal.

Parameters

[in]	basis	The set of vectors to check
[in]	tol	The tolerance used to test for orthonormality

Returns

True is basis is orthonormal, otherwise false

norm()

auto dolfinx::la::norm	(	const Vector< T, Allocator > &	a,
		Norm	type = Norm::l2
	)

Compute the norm of the vector.

Note

Collective MPI operation

Parameters

a	A vector
type	Norm type (supported types are \(L^2\) and \(L^\infty\))

orthonormalize()

void dolfinx::la::orthonormalize	(	const std::span< Vector< T, U >> &	basis,
		double	tol = 1.0e-10
	)

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.
[in]	tol	The tolerance used to detect a linear dependency

squared_norm()

auto dolfinx::la::squared_norm

(

const Vector< T, Allocator > &

a

)

Compute the squared L2 norm of vector.

Note

Collective MPI operation