Class to represent a structured matrix. This is the abstract base class for several types of structured matrices. More...

#include <StructuredMatrix.hpp>

Inheritance diagram for strumpack::structured::StructuredMatrix< scalar_t >:

[legend]

Public Member Functions
virtual	~StructuredMatrix ()=default

virtual std::size_t	rows () const =0

virtual std::size_t	cols () const =0

virtual std::size_t	memory () const =0

virtual std::size_t	nonzeros () const =0

virtual std::size_t	rank () const =0

virtual std::size_t	local_rows () const

virtual std::size_t	begin_row () const

virtual std::size_t	end_row () const

virtual const std::vector< int > &	dist () const

virtual const std::vector< int > &	rdist () const

virtual const std::vector< int > &	cdist () const

virtual void	mult (Trans op, const DenseMatrix< scalar_t > &x, DenseMatrix< scalar_t > &y) const

void	mult (Trans op, int m, const scalar_t x, int ldx, scalar_t y, int ldy) const

virtual void	mult (Trans op, const DistributedMatrix< scalar_t > &x, DistributedMatrix< scalar_t > &y) const

virtual void	factor ()

virtual void	solve (DenseMatrix< scalar_t > &b) const

virtual void	solve (int nrhs, scalar_t *b, int ldb) const

virtual void	solve (DistributedMatrix< scalar_t > &b) const

virtual void	shift (scalar_t s)

Detailed Description

template<typename scalar_t>
class strumpack::structured::StructuredMatrix< scalar_t >

Class to represent a structured matrix. This is the abstract base class for several types of structured matrices.

Template Parameters

scalar_t Can be float, double, std::complex<float> or std::complex<double>. Some formats do not support all precisions, see the table below.

For construction, use one of:

structured::construct_from_dense (DENSE)
structured::construct_from_elements (ELEM)
structured::construct_matrix_free (MF)
structured::construct_partially_matrix_free (PMF)
nearest neighbors (NN)

However, not all formats support all construction methods, matrix operations, or precisions (s: float, d: double, c: std::complex<float>, z: std::complex<double>):

	parallel?		construct from ..					operation				precision
	seq	MPI	DENSE	ELEM	MF	PMF	NN	mult	factor	solve	shift	s	d	c	z
BLR	X	X	X	X				X	X	X	?	X	X	X	X
HSS	X	X	X			X	X	X	X	X	X	X	X	X	X
HODLR		X	X	X	X		X	X	X	X	?		X		X
HODBF		X	X	X	X		X	X	X	X	?		X		X
BUTTERFLY		X	X	X	X		X	X					X		X
LR		X	X	X	X		X	X					X		X
LOSSY	X		X									X	X	X	X
LOSSLESS	X		X									X	X	X	X

See also: HSS::HSSMatrix, BLR::BLRMatrix, HODLR::HODLRMatrix, HODLR::ButterflyMatrix, ...

Constructor & Destructor Documentation

◆ ~StructuredMatrix()

template<typename scalar_t >

virtual strumpack::structured::StructuredMatrix< scalar_t >::~StructuredMatrix ( )

virtualdefault

Virtual destructor.

Member Function Documentation

◆ begin_row()

template<typename scalar_t >

virtual std::size_t strumpack::structured::StructuredMatrix< scalar_t >::begin_row ( ) const

inlinevirtual

For a distributed matrix, which uses a block row distribution, this gives the first rows stored on this process.

Returns: first rows, should be dist()[p] for rank p

Reimplemented in strumpack::HODLR::HODLRMatrix< scalar_t >, and strumpack::HODLR::ButterflyMatrix< scalar_t >.

◆ cdist()

template<typename scalar_t >

virtual const std::vector<int>& strumpack::structured::StructuredMatrix< scalar_t >::cdist ( ) const

inlinevirtual

For a distributed rectangular matrix, return the 1D block columns distribution.

Returns: vector with P+1 elements, process with rank p will own columns [cdist()[p],cdist()[p+1])

Reimplemented in strumpack::HODLR::ButterflyMatrix< scalar_t >.

◆ cols()

template<typename scalar_t >

virtual std::size_t strumpack::structured::StructuredMatrix< scalar_t >::cols ( ) const

pure virtual

Get number of columns in this matrix

Implemented in strumpack::HSS::HSSMatrixBase< scalar_t >, strumpack::HODLR::HODLRMatrix< scalar_t >, strumpack::HODLR::ButterflyMatrix< scalar_t >, strumpack::BLR::BLRMatrixMPI< scalar_t >, and strumpack::BLR::BLRMatrix< scalar_t >.

◆ dist()

template<typename scalar_t >

virtual const std::vector<int>& strumpack::structured::StructuredMatrix< scalar_t >::dist ( ) const

inlinevirtual

For a distributed matrix, return the 1D block row distribution over processes. This is for square matrices, for rectagular use rdist for the rows and cdist for the columns.

Returns: vector with P+1 elements, process with rank p will own rows [dist()[p],dist()[p+1])

Reimplemented in strumpack::HODLR::HODLRMatrix< scalar_t >.

◆ end_row()

template<typename scalar_t >

virtual std::size_t strumpack::structured::StructuredMatrix< scalar_t >::end_row ( ) const

inlinevirtual

For a distributed matrix, which uses a block row distribution, this gives the final row (+1) stored on this process.

Returns: last row + 1, should be dist()[p+1] for rank p

Reimplemented in strumpack::HODLR::HODLRMatrix< scalar_t >, and strumpack::HODLR::ButterflyMatrix< scalar_t >.

◆ factor()

template<typename scalar_t >

virtual void strumpack::structured::StructuredMatrix< scalar_t >::factor ( )

virtual

Compute a factorization (or the inverse) of this matrix, to be used later for solving linear systems. The actual type of factorization depends on the StructuredMatrix::Type of this matrix.

Reimplemented in strumpack::HSS::HSSMatrixMPI< scalar_t >, strumpack::HSS::HSSMatrix< scalar_t >, and strumpack::HODLR::HODLRMatrix< scalar_t >.

◆ local_rows()

template<typename scalar_t >

virtual std::size_t strumpack::structured::StructuredMatrix< scalar_t >::local_rows ( ) const

inlinevirtual

For a distributed matrix, which uses a block row distribution, this gives the number of rows stored on this process.

Returns: local rows, should be dist()[p+1]-dist()[p] for rank p

Reimplemented in strumpack::HODLR::HODLRMatrix< scalar_t >, and strumpack::HODLR::ButterflyMatrix< scalar_t >.

◆ memory()

template<typename scalar_t >

virtual std::size_t strumpack::structured::StructuredMatrix< scalar_t >::memory ( ) const

pure virtual

Return the total amount of memory used by this matrix, in bytes.

Returns: Memory usage in bytes.

See also: nonzeros

Implemented in strumpack::HSS::HSSMatrixMPI< scalar_t >, strumpack::HSS::HSSMatrix< scalar_t >, strumpack::HODLR::HODLRMatrix< scalar_t >, strumpack::HODLR::ButterflyMatrix< scalar_t >, strumpack::BLR::BLRMatrixMPI< scalar_t >, and strumpack::BLR::BLRMatrix< scalar_t >.

◆ mult() [1/3]

template<typename scalar_t >

virtual void strumpack::structured::StructuredMatrix< scalar_t >::mult	(	Trans	op,
		const DenseMatrix< scalar_t > &	x,
		DenseMatrix< scalar_t > &	y
	)		const

virtual

Multiply the StructuredMatrix (A) with a dense matrix: y = op(A)*x.

Parameters

op	take transpose/conjugate or not
x	matrix, x.rows() == op(A).cols()
y	matrix, y.cols() == x.cols(), y.rows() == A.rows()

Reimplemented in strumpack::HSS::HSSMatrix< scalar_t >, strumpack::HODLR::HODLRMatrix< scalar_t >, strumpack::HODLR::ButterflyMatrix< scalar_t >, and strumpack::BLR::BLRMatrix< scalar_t >.

◆ mult() [2/3]

template<typename scalar_t >

virtual void strumpack::structured::StructuredMatrix< scalar_t >::mult	(	Trans	op,
		const DistributedMatrix< scalar_t > &	x,
		DistributedMatrix< scalar_t > &	y
	)		const

virtual

Multiply the StructuredMatrix (A) with a dense matrix: y = op(A)*x. x and y are 2d block cyclic.

Parameters

op	take transpose/conjugate or not
x	matrix, x.rows() == op(A).cols()
y	matrix, y.cols() == x.cols(), y.rows() == A.rows()

Reimplemented in strumpack::HSS::HSSMatrixMPI< scalar_t >, strumpack::HODLR::HODLRMatrix< scalar_t >, and strumpack::HODLR::ButterflyMatrix< scalar_t >.

◆ mult() [3/3]

template<typename scalar_t >

void strumpack::structured::StructuredMatrix< scalar_t >::mult	(	Trans	op,
		int	m,
		const scalar_t *	x,
		int	ldx,
		scalar_t *	y,
		int	ldy
	)		const

Multiply the StructuredMatrix (A) with a dense matrix: y = op(A)*x.

Parameters

op	take transpose/conjugate or not
m	columns in x and y
x	matrix, x should have rows == op(A).cols()
ldx	leading dimension of x
y	matrix, y should have cols == x.cols(), and rows == A.rows()
ldy	leading dimension of y

◆ nonzeros()

template<typename scalar_t >

virtual std::size_t strumpack::structured::StructuredMatrix< scalar_t >::nonzeros ( ) const

pure virtual

Return the total number of nonzeros stored by this matrix.

Returns: Nonzeros in the matrix representation.

See also: memory

Implemented in strumpack::HSS::HSSMatrixMPI< scalar_t >, strumpack::HSS::HSSMatrix< scalar_t >, strumpack::HODLR::HODLRMatrix< scalar_t >, strumpack::HODLR::ButterflyMatrix< scalar_t >, strumpack::BLR::BLRMatrixMPI< scalar_t >, and strumpack::BLR::BLRMatrix< scalar_t >.

◆ rank()

template<typename scalar_t >

virtual std::size_t strumpack::structured::StructuredMatrix< scalar_t >::rank ( ) const

pure virtual

Return the maximum rank of this matrix over all low-rank compressed blocks.

Returns: Maximum rank.

Implemented in strumpack::HSS::HSSMatrixMPI< scalar_t >, strumpack::HSS::HSSMatrix< scalar_t >, strumpack::HODLR::HODLRMatrix< scalar_t >, strumpack::HODLR::ButterflyMatrix< scalar_t >, strumpack::BLR::BLRMatrixMPI< scalar_t >, and strumpack::BLR::BLRMatrix< scalar_t >.

◆ rdist()

template<typename scalar_t >

virtual const std::vector<int>& strumpack::structured::StructuredMatrix< scalar_t >::rdist ( ) const

inlinevirtual

For a distributed rectangular matrix, return the 1D block row distribution.

Returns: vector with P+1 elements, process with rank p will own rows [cdist()[p],cdist()[p+1])

Reimplemented in strumpack::HODLR::ButterflyMatrix< scalar_t >.

◆ rows()

template<typename scalar_t >

virtual std::size_t strumpack::structured::StructuredMatrix< scalar_t >::rows ( ) const

pure virtual

Get number of rows in this matrix

Implemented in strumpack::HSS::HSSMatrixBase< scalar_t >, strumpack::HODLR::HODLRMatrix< scalar_t >, strumpack::HODLR::ButterflyMatrix< scalar_t >, strumpack::BLR::BLRMatrixMPI< scalar_t >, and strumpack::BLR::BLRMatrix< scalar_t >.

◆ shift()

template<typename scalar_t >

virtual void strumpack::structured::StructuredMatrix< scalar_t >::shift ( scalar_t s )

virtual

Apply a shift to the diagonal of this matrix. Ie, this += s*I, with I the identity matrix. If this is called after calling factor, then the factors are not updated. To solve a linear system with the shifted matrix, you need to call factor again.

Parameters

s	Shift to be applied to the diagonal.

Reimplemented in strumpack::HSS::HSSMatrixBase< scalar_t >, strumpack::HSS::HSSMatrixMPI< scalar_t >, and strumpack::HSS::HSSMatrix< scalar_t >.

◆ solve() [1/3]

template<typename scalar_t >

virtual void strumpack::structured::StructuredMatrix< scalar_t >::solve ( DenseMatrix< scalar_t > & b ) const

virtual

Solve a linear system A*x=b, with this StructuredMatrix (A). This solve is done in-place.

Parameters

b	right-hand side, b.rows() == A.cols(), will be overwritten with the solution x.

Reimplemented in strumpack::HSS::HSSMatrix< scalar_t >, and strumpack::HODLR::HODLRMatrix< scalar_t >.

◆ solve() [2/3]

template<typename scalar_t >

virtual void strumpack::structured::StructuredMatrix< scalar_t >::solve ( DistributedMatrix< scalar_t > & b ) const

virtual

Solve a linear system A*x=b, with this StructuredMatrix (A). This solve is done in-place.

Parameters

b	right-hand side, b.rows() == A.cols(), will be overwritten with the solution x.

Reimplemented in strumpack::HSS::HSSMatrixMPI< scalar_t >, and strumpack::HODLR::HODLRMatrix< scalar_t >.

◆ solve() [3/3]

template<typename scalar_t >

virtual void strumpack::structured::StructuredMatrix< scalar_t >::solve	(	int	nrhs,
		scalar_t *	b,
		int	ldb
	)		const

inlinevirtual

Solve a linear system A*x=b, with this StructuredMatrix (A). This solve is done in-place.

Parameters

nrhs	number of right-hand sides
b	right-hand side, should have this->cols() rows, will be overwritten with the solution x.
ldb	leading dimension of b

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

/home/pieterg/LBL/STRUMPACK/src/structured/StructuredMatrix.hpp

Public Member Functions

Detailed Description

template<typename scalar_t> class strumpack::structured::StructuredMatrix< scalar_t >

Constructor & Destructor Documentation

◆ ~StructuredMatrix()

Member Function Documentation

◆ begin_row()

◆ cdist()

◆ cols()

◆ dist()

◆ end_row()

◆ factor()

◆ local_rows()

◆ memory()

◆ mult() [1/3]

◆ mult() [2/3]

◆ mult() [3/3]

◆ nonzeros()

◆ rank()

◆ rdist()

◆ rows()

◆ shift()

◆ solve() [1/3]

◆ solve() [2/3]

◆ solve() [3/3]

template<typename scalar_t>
class strumpack::structured::StructuredMatrix< scalar_t >