Linear algebra interface. More...

Namespaces
namespace	impl
	Fetch the rows of B that correspond to the ghost columns of A.
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
struct	GridInfoDeleter
struct	ScalePermStructDeleter
struct	LUStructDeleter
struct	SolveStructDeleter
class	SuperLUDistSolver
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<typename T, int BS = -1>
dolfinx::la::MatrixCSR< T >	matmul (const dolfinx::la::MatrixCSR< T > &A, const dolfinx::la::MatrixCSR< T > &B)
	Compute C = A*B as a distributed MatrixCSR.
template<typename T, int BS0 = -1, int BS1 = -1>
dolfinx::la::MatrixCSR< T >	transpose (const dolfinx::la::MatrixCSR< T > &A)
	Compute the distributed transpose of a MatrixCSR.
template<dolfinx::scalar T>
void	set_diagonal (MatSet< T > auto &&set_fn, const common::LocalIndexRange auto &rows, T diagonal=T(1))
	Set a value on the diagonal of a matrix for specified rows.
template<dolfinx::scalar T>
void	set_diagonal (MatSet< T > auto &&set_fn, const common::LocalIndexRange auto &rows, std::span< const T > diagonals)
	Set values on the diagonal of a matrix for specified rows, with a value per row.
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.

◆ matmul()

template<typename T, int BS = -1>

dolfinx::la::MatrixCSR< T > matmul	(	const dolfinx::la::MatrixCSR< T > &	A,
		const dolfinx::la::MatrixCSR< T > &	B )

Compute C = A*B as a distributed MatrixCSR.

Both A and B must have square block size {BS, BS}. Passing the compile-time block size as the template argument enables compile-time loop unrolling in the inner GEMM.

Template Parameters

T	Scalar type.
BS	Square block size, or -1 for runtime dispatch (non-optimised). When >= 1, A and B must have block_size() == {BS, BS}.

Parameters

A	Left matrix.
B	Right matrix.

Returns: The product C = A*B as a MatrixCSR with row distribution matching A and column distribution determined by B. The row IndexMap of C has no ghosts, and the column IndexMap of C will generally be a larger superset of the column IndexMap of B.

◆ 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.

◆ set_diagonal() [1/2]

template<dolfinx::scalar T>

void set_diagonal	(	MatSet< T > auto &&	set_fn,
		const common::LocalIndexRange auto &	rows,
		std::span< const T >	diagonals )

Set values on the diagonal of a matrix for specified rows, with a value per row.

See the single-value set_diagonal for usage.

Parameters

[in]	set_fn	The function for setting values to a matrix.
[in]	rows	Row blocks, in local indices, whose diagonal to set. May have static or dynamic extent.
[in]	diagonals	Diagonal values, with diagonals[i] the value for rows[i]. Must have the same length as rows.

◆ set_diagonal() [2/2]

template<dolfinx::scalar T>

void set_diagonal	(	MatSet< T > auto &&	set_fn,
		const common::LocalIndexRange auto &	rows,
		T	diagonal = T(1) )

Set a value on the diagonal of a matrix for specified rows.

This function is typically called after assembly. The assembly function zeroes Dirichlet rows and columns. For block matrices, this function should normally be called only on the diagonal blocks, i.e. blocks for which the test and trial spaces are the same.

Note: set_fn decides whether the value replaces the existing entry or is added to it. A row repeated in rows is passed to set_fn once per occurrence, which an adding set_fn accumulates.

Parameters

[in]	set_fn	The function for setting values to a matrix.
[in]	rows	Row blocks, in local indices, whose diagonal to set. May have static or dynamic extent.
[in]	diagonal	Value for the diagonal of each row in rows.

◆ squared_norm()

template<class V>

auto squared_norm ( const V & a )

Compute the squared L2 norm of vector.

Note: Collective MPI operation.

◆ transpose()

template<typename T, int BS0 = -1, int BS1 = -1>

dolfinx::la::MatrixCSR< T > transpose ( const dolfinx::la::MatrixCSR< T > & A )

Compute the distributed transpose of a MatrixCSR.

Given A with row map R (n_row owned rows) and column map C (n_col owned columns plus any ghost columns from remote ranks), returns Aᵀ with: row map = ghost-free column map of A (n_col owned rows, no ghosts) col map = row map of A extended with any ghost row indices that appear as nonzeros contributed by remote ranks.

Communication strategy:

Exchange per-neighbour entry counts (MPI_Neighbor_alltoall).
Build displacements and pack send buffers.
Post non-blocking data exchange (three MPI_Ineighbor_alltoallv in flight simultaneously: row global indices, column global indices, and values).
While data exchange is in flight, compute the local (diagonal-block) part of the transpose via local_transpose.
Wait for data, merge received entries, finalise sparsity and construct the MatrixCSR.

Parameters

A	Input matrix.

Template Parameters

T	Scalar type
BS0	Row block size of A, or -1 for unoptimized.
BS1	Col block size of A, or -1 for unoptimized.

Returns: Aᵀ as a distributed MatrixCSR.

Namespaces

Classes

Concepts

Typedefs

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ BlockMode

Function Documentation

◆ inner_product()

◆ is_orthonormal()

◆ matmul()

◆ norm()

◆ orthonormalize()

◆ set_diagonal() [1/2]

◆ set_diagonal() [2/2]

◆ squared_norm()

◆ transpose()