This class defines a basis for vector spaces, typically used for expressing nullspaces of singular operators and 'near nullspaces' used in smoothed aggregation algebraic multigrid. More...

#include <VectorSpaceBasis.h>

Public Member Functions
	VectorSpaceBasis (const std::vector< std::shared_ptr< PETScVector >> &basis)
	Constructor.

	VectorSpaceBasis (const VectorSpaceBasis &basis)=delete
	Delete copy constructor.

	VectorSpaceBasis (VectorSpaceBasis &&basis)=default
	Move constructor.

	~VectorSpaceBasis ()=default
	Destructor.

void	orthonormalize (double tol=1.0e-10)
	Apply the Gram-Schmidt process to orthonormalize the basis. Throws an error if a (near) linear dependency is detected. Error is thrown if <x_i, x_i> < tol.

bool	is_orthonormal (double tol=1.0e-10) const
	Test if basis is orthonormal.

bool	is_orthogonal (double tol=1.0e-10) const
	Test if basis is orthogonal.

bool	in_nullspace (const Mat A, double tol=1.0e-10) const
	Test if basis is in null space of A.

void	orthogonalize (PETScVector &x) const
	Orthogonalize x with respect to basis.

int	dim () const
	Number of vectors in the basis.

std::shared_ptr< const PETScVector >	operator[] (int i) const
	Get a particular basis vector.

Detailed Description

This class defines a basis for vector spaces, typically used for expressing nullspaces of singular operators and 'near nullspaces' used in smoothed aggregation algebraic multigrid.

The documentation for this class was generated from the following files:

/__w/dolfinx/dolfinx/cpp/dolfinx/la/VectorSpaceBasis.h
/__w/dolfinx/dolfinx/cpp/dolfinx/la/VectorSpaceBasis.cpp

Public Member Functions

Detailed Description