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 = std::allocator<T>>
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 , typename U >
void	orthonormalize (const xtl::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 xtl::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

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 xtl::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

orthonormalize()

void dolfinx::la::orthonormalize	(	const xtl::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