#include <stdio.h>
#include "cs_base.h"
#include "cs_cdo.h"
#include "cs_cdo_toolbox.h"
#include "cs_param.h"

Include dependency graph for cs_sla.h:

Data Structures
struct	cs_sla_matrix_info_t

struct	cs_sla_matrix_t

struct	cs_sla_sumup_t

Macros
#define	CS_SLA_MATRIX_SYM (1 << 0) /* 1: symmetric */

#define	CS_SLA_MATRIX_SORTED (1 << 1) /* 2: sorted */

#define	CS_SLA_MATRIX_SHARED (1 << 2) /* 4: share pattern */

Enumerations
enum	cs_sla_matrix_type_t { CS_SLA_MAT_NONE, CS_SLA_MAT_DEC, CS_SLA_MAT_CSR, CS_SLA_MAT_MSR, CS_SLA_MAT_N_TYPES }

Functions
void	cs_sla_bwrite (const char name, const cs_sla_matrix_t m, const double rhs, const double sol)
	Write in binary format a matrix in CSR format, its righ hand side and the solution. More...

void	cs_sla_bread (const char name, cs_sla_matrix_t p_mat, double p_rhs[], double *p_sol[])
	Read from a binary file a matrix in CSR format, its righ hand side and the solution. Matrix must have a stride equal to 1. More...

void	cs_sla_matrix_msr2csr (cs_sla_matrix_t *a)
	Change matrix representation from MSR to CSR. More...

void	cs_sla_matrix_csr2msr (cs_sla_matrix_t *a)
	Change matrix representation from CSR to MSR. More...

void	cs_sla_matrix_share2own (cs_sla_matrix_t *a)
	Allocate its own pattern if shared. More...

cs_sla_matrix_t *	cs_sla_matrix_pack (cs_lnum_t n_final_rows, cs_lnum_t n_final_cols, const cs_sla_matrix_t init, const cs_lnum_t row_z2i_ids, const cs_lnum_t *col_i2z_ids, bool keep_sym)
	Build a new matrix resulting from the extraction of some listed rows and columns. The output is a new matrix packed (or zipped) w.r.t the initial matrix. More...

void	cs_sla_matrix_diag_idx (cs_sla_matrix_t *m)
	Build diagonal index. More...

void	cs_sla_matrix_get_diag (const cs_sla_matrix_t m, double p_diag[])
	Get the diagonal entries of a given matrix. More...

void	cs_sla_matrix_sort (cs_sla_matrix_t *m)
	Sort each row by increasing colomn number. More...

cs_sla_matrix_t *	cs_sla_block2mat (cs_sla_matrix_t A, const cs_sla_matrix_t B, const cs_sla_matrix_t C, const cs_sla_matrix_t D, bool sym)

void	cs_sla_matvec (const cs_sla_matrix_t m, const double v[], double inout[], bool reset)

void	cs_sla_amxby (double alpha, const cs_sla_matrix_t m, const double x[], double beta, const double y[], double inout[])

void	cs_sla_matvec_block2 (const cs_sla_matrix_t A, const cs_sla_matrix_t B, const cs_sla_matrix_t C, const cs_sla_matrix_t D, const double X[], const double Y[], double F[], double G[], bool reset)
	Matrix block 2x2 multiply by a vector. More...

cs_sla_matrix_t *	cs_sla_matrix_add (double alpha, const cs_sla_matrix_t a, double beta, const cs_sla_matrix_t b)
	Add two sparse matrices a and b. c = alphaa + betab. More...

cs_sla_matrix_t *	cs_sla_matrix_multiply (const cs_sla_matrix_t a, const cs_sla_matrix_t b)
	Main subroutine to multiply two sparse matrices a and b. c= a*b. More...

cs_sla_matrix_t *	cs_sla_matrix_combine (double alpha, const cs_sla_matrix_t a, double beta, const cs_sla_matrix_t bt, const cs_sla_matrix_t *b)
	Specific matrix multiplication. Compute Bt * beta * B + alpha * A alpha and beta are scalar. More...

cs_sla_matrix_t *	cs_sla_multiply_AtDA (const cs_sla_matrix_t At, const double D[], const cs_sla_matrix_t A, int *w)
	Compute the product C = At * Diag * A. More...

int	cs_sla_get_mat_spectral_radius (const cs_sla_matrix_t matrix, int iter_max, double epsilon, double lambda)

double	cs_sla_get_matrix_norm (const cs_sla_matrix_t *m)

cs_sla_matrix_t *	cs_sla_matrix_create (int n_rows, int n_cols, int stride, cs_sla_matrix_type_t type, bool sym)
	Create a cs_sla_matrix_t structure. More...

cs_sla_matrix_t *	cs_sla_matrix_create_from_pattern (const cs_sla_matrix_t *ref, cs_sla_matrix_type_t type, int stride)
	Create a cs_sla_matrix_t structure from an existing one. More...

cs_sla_matrix_t *	cs_sla_matrix_copy (const cs_sla_matrix_t *a, bool shared)
	Create a new matrix structure from the copy of an existing one. More...

cs_sla_matrix_t *	cs_sla_matrix_transpose (const cs_sla_matrix_t *mat)
	Transpose a cs_sla_matrix_t structure. More...

cs_sla_matrix_t *	cs_sla_matrix_free (cs_sla_matrix_t *m)
	Free a cs_sla_matrix_t structure. More...

void	cs_sla_matrix_clean (cs_sla_matrix_t *m, double eps)
	Remove entries in a cs_sla_matrix_t structure below a given threshold. \|a(i,j)\| < eps * max\|a(i,j)\|. More...

size_t	cs_sla_matrix_get_nnz (const cs_sla_matrix_t *m)
	Retrieve the number of non-zeros (nnz) elements in a matrix. More...

cs_sla_matrix_info_t	cs_sla_matrix_analyse (const cs_sla_matrix_t *m)
	Compute general information related to a cs_sla_matrix_t structure. More...

void	cs_sla_matrix_resume (const char name, FILE f, const cs_sla_matrix_t *m)
	Synthesis of a cs_sla_matrix_t structure. More...

void	cs_sla_matrix_dump (const char name, FILE f, const cs_sla_matrix_t *m)
	Dump a cs_sla_matrix_t structure. More...

void	cs_sla_system_dump (const char name, FILE f, const cs_sla_matrix_t m, const double rhs)
	Dump a cs_sla_matrix_t structure and its related right-hand side. More...

void	cs_sla_assemble_msr (const cs_toolbox_locmat_t loc, cs_sla_matrix_t ass)
	Assemble a MSR matrix from local contributions –> We assume that the local matrices are symmetric –> We assume that the assembled matrix has its columns sorted. More...

Macro Definition Documentation

#define CS_SLA_MATRIX_SHARED (1 << 2) /* 4: share pattern */

#define CS_SLA_MATRIX_SORTED (1 << 1) /* 2: sorted */

#define CS_SLA_MATRIX_SYM (1 << 0) /* 1: symmetric */

Enumeration Type Documentation

enum cs_sla_matrix_type_t

Enumerator
CS_SLA_MAT_NONE
CS_SLA_MAT_DEC
CS_SLA_MAT_CSR
CS_SLA_MAT_MSR
CS_SLA_MAT_N_TYPES

Function Documentation

void cs_sla_amxby	(	double	alpha,
		const cs_sla_matrix_t *	m,
		const double	x[],
		double	beta,
		const double	y[],
		double *	inout[]
	)

void cs_sla_assemble_msr	(	const cs_toolbox_locmat_t *	loc,
		cs_sla_matrix_t *	ass
	)

Assemble a MSR matrix from local contributions –> We assume that the local matrices are symmetric –> We assume that the assembled matrix has its columns sorted.

Parameters

[in]	loc	pointer to a local matrix
[in,out]	ass	pointer to a cs_sla_matrix_t struct. collecting data

cs_sla_matrix_t* cs_sla_block2mat	(	cs_sla_matrix_t *	A,
		const cs_sla_matrix_t *	B,
		const cs_sla_matrix_t *	C,
		const cs_sla_matrix_t *	D,
		bool	sym
	)

void cs_sla_bread	(	const char *	name,
		cs_sla_matrix_t **	p_mat,
		double *	p_rhs[],
		double *	p_sol[]
	)

Read from a binary file a matrix in CSR format, its righ hand side and the solution. Matrix must have a stride equal to 1.

Parameters

[in]	name	name of the output file
[in,out]	p_mat	system to solve
[in,out]	p_rhs	right hand side
[in,out]	p_sol	solution

void cs_sla_bwrite	(	const char *	name,
		const cs_sla_matrix_t *	m,
		const double *	rhs,
		const double *	sol
	)

Write in binary format a matrix in CSR format, its righ hand side and the solution.

Parameters

[in]	name	name of the output file
[in]	A	system to solve
[in]	rhs	right hand side
[in]	x	solution

int cs_sla_get_mat_spectral_radius	(	const cs_sla_matrix_t *	matrix,
		int	iter_max,
		double	epsilon,
		double *	lambda
	)

double cs_sla_get_matrix_norm ( const cs_sla_matrix_t * m )

cs_sla_matrix_t* cs_sla_matrix_add	(	double	alpha,
		const cs_sla_matrix_t *	a,
		double	beta,
		const cs_sla_matrix_t *	b
	)

Add two sparse matrices a and b. c = alpha*a + beta*b.

Parameters

[in]	alpha	first coef.
[in]	a	first matrix to add
[in]	beta	second coef.
[in]	b	second matrix to add

Returns: a pointer to the resulting matrix

cs_sla_matrix_info_t cs_sla_matrix_analyse ( const cs_sla_matrix_t * m )

Compute general information related to a cs_sla_matrix_t structure.

Parameters

[in] m matrix to analyse

void cs_sla_matrix_clean	(	cs_sla_matrix_t *	m,
		double	eps
	)

Remove entries in a cs_sla_matrix_t structure below a given threshold. |a(i,j)| < eps * max|a(i,j)|.

Parameters

[in,out]	mat	matrix to clean
[in]	eps	value of the threshold

Remove entries in a cs_sla_matrix_t structure below a given threshold. |a(i,j)| < eps * max|a(i,j)|.

Parameters

[in,out]	mat	matrix to clean
[in]	eps	value of the threshold

cs_sla_matrix_t* cs_sla_matrix_combine	(	double	alpha,
		const cs_sla_matrix_t *	a,
		double	beta,
		const cs_sla_matrix_t *	bt,
		const cs_sla_matrix_t *	b
	)

Specific matrix multiplication. Compute Bt * beta * B + alpha * A alpha and beta are scalar.

Parameters

[in]	alpha	real coefficient
[in]	a	square sym. matrix
[in]	beta	real coefficient
[in]	b	matrix (CSR or DEC)
[in]	bt	adjoint matrix of b

Returns: the matrix corresponding to this operation

Parameters

[in]	alpha	real coefficient
[in]	a	square sym. matrix
[in]	beta	real coefficient
[in]	b	matrix (CSR or DEC)
[in]	bt	adjoint matrix of b

Returns: the matrix corresponding to this operation in MSR storage

cs_sla_matrix_t* cs_sla_matrix_copy	(	const cs_sla_matrix_t *	a,
		bool	shared
	)

Create a new matrix structure from the copy of an existing one.

Parameters

[in]	a	matrix to copy
[in]	shared	true: only pointer are copied other allocated

Returns: the matrix corresponding to this operation

cs_sla_matrix_t* cs_sla_matrix_create	(	int	n_rows,
		int	n_cols,
		int	stride,
		cs_sla_matrix_type_t	type,
		bool	sym
	)

Create a cs_sla_matrix_t structure.

Parameters

[in]	n_rows	number of rows
[in]	n_cols	number of columns
[in]	stride	number of values related to each entry
[in]	type	kind of matrix
[in]	sym	true or false

Returns: a pointer to new allocated matrix structure

cs_sla_matrix_t* cs_sla_matrix_create_from_pattern	(	const cs_sla_matrix_t *	ref,
		cs_sla_matrix_type_t	type,
		int	stride
	)

Create a cs_sla_matrix_t structure from an existing one.

Parameters

[in]	ref	pointer to a reference matrix with the same pattern
[in]	type	type of the matrix to create
[in]	stride	number of values associated to each entry

Returns: a pointer to new allocated matrix structure

Parameters

[in]	ref	pointer to a reference matrix with the same pattern
[in]	type	type of the matrix to create
[in]	stride	true or false

Returns: a pointer to new allocated matrix structure

void cs_sla_matrix_csr2msr ( cs_sla_matrix_t * a )

Change matrix representation from CSR to MSR.

Parameters

[in,out] a matrix to transform

void cs_sla_matrix_diag_idx ( cs_sla_matrix_t * m )

Build diagonal index.

Parameters

[in,out] m matrix to work with

void cs_sla_matrix_dump	(	const char *	name,
		FILE *	f,
		const cs_sla_matrix_t *	m
	)

Dump a cs_sla_matrix_t structure.

Parameters

[in]	name	either name of the file if f is NULL or description
[in]	f	pointer to a FILE struct.
[in]	m	matrix to dump
[in]	name	either name of the file if f is NULL or description
[in]	f	pointer to a FILE struct.
[in]	m	matrix to dump
[in]	dump_level	level of information displayed

cs_sla_matrix_t* cs_sla_matrix_free ( cs_sla_matrix_t * m )

Free a cs_sla_matrix_t structure.

Parameters

[in] m matrix to free

Returns: a NULL pointer

void cs_sla_matrix_get_diag	(	const cs_sla_matrix_t *	m,
		double *	p_diag[]
	)

Get the diagonal entries of a given matrix.

Parameters

[in]	m	matrix to work with
[in,out]	p_diag	pointer to diag array to define (allocated if NULL)

size_t cs_sla_matrix_get_nnz ( const cs_sla_matrix_t * m )

Retrieve the number of non-zeros (nnz) elements in a matrix.

Parameters

[in] mat matrix

Returns: the number of nnz

void cs_sla_matrix_msr2csr ( cs_sla_matrix_t * a )

Change matrix representation from MSR to CSR.

Parameters

[in,out] a matrix to transform

cs_sla_matrix_t* cs_sla_matrix_multiply	(	const cs_sla_matrix_t *	a,
		const cs_sla_matrix_t *	b
	)

Main subroutine to multiply two sparse matrices a and b. c= a*b.

Parameters

[in]	a	first matrix to multiply
[in]	b	second matrix to multiply

Returns: a pointer to the resulting matrix

cs_sla_matrix_t* cs_sla_matrix_pack	(	cs_lnum_t	n_final_rows,
		cs_lnum_t	n_final_cols,
		const cs_sla_matrix_t *	init,
		const cs_lnum_t *	row_z2i_ids,
		const cs_lnum_t *	col_i2z_ids,
		bool	keep_sym
	)

Build a new matrix resulting from the extraction of some listed rows and columns. The output is a new matrix packed (or zipped) w.r.t the initial matrix.

Parameters

[in]	n_final_rows	number of rows to extract
[in]	n_final_cols	number of columns to extract
[in]	init	init matrix to work with
[in]	row_z2i_ids	zipped -> initial ids for rows
[in]	col_i2z_ids	initial-> zipped ids for columns (-1 ==> remove)
[in]	keep_sym	true or false

Returns: a pointer to the new (packed) matrix structure

void cs_sla_matrix_resume	(	const char *	name,
		FILE *	f,
		const cs_sla_matrix_t *	m
	)

Synthesis of a cs_sla_matrix_t structure.

Parameters

[in]	name	either name of the file if f is NULL or description
[in]	f	pointer to a FILE struct.
[in]	m	matrix to dump

void cs_sla_matrix_share2own ( cs_sla_matrix_t * a )

Allocate its own pattern if shared.

Parameters

[in,out] a matrix to transform

void cs_sla_matrix_sort ( cs_sla_matrix_t * m )

Sort each row by increasing colomn number.

Parameters

[in] mat matrix to sort

cs_sla_matrix_t* cs_sla_matrix_transpose ( const cs_sla_matrix_t * a )

Transpose a cs_sla_matrix_t structure.

Parameters

[in] mat matrix to transpose

Returns: a pointer to new allocated matrix which is transposed to mat

void cs_sla_matvec	(	const cs_sla_matrix_t *	m,
		const double	v[],
		double *	inout[],
		bool	reset
	)

void cs_sla_matvec_block2	(	const cs_sla_matrix_t *	A,
		const cs_sla_matrix_t *	B,
		const cs_sla_matrix_t *	C,
		const cs_sla_matrix_t *	D,
		const double	X[],
		const double	Y[],
		double *	F[],
		double *	G[],
		bool	reset
	)

Matrix block 2x2 multiply by a vector.

| A B | |X| = |F|= |AX + BY| | C D | |Y| |G| |CX + DY|

Parameters

[in]	A	pointer to a cs_sla_matrix_t block (1,1)
[in]	B	pointer to a cs_sla_matrix_t block (1,2)
[in]	C	pointer to a cs_sla_matrix_t block (2,1)
[in]	D	pointer to a cs_sla_matrix_t block (2,2)
[in]	X	upper vector
[in]	Y	lower vector
[in,out]	F	upper result
[in,out]	G	lower result
[in]	reset	reset before computation (true/false)

cs_sla_matrix_t* cs_sla_multiply_AtDA	(	const cs_sla_matrix_t *	At,
		const double	D[],
		const cs_sla_matrix_t *	A,
		int *	w
	)

Compute the product C = At * Diag * A.

Parameters

[in]	At	pointer to a cs_sla_matrix_t struct. (DEC type)
[in]	D	array standing for a diagonal operator
[in]	A	pointer to a cs_sla_matrix_t struct. (DEC type)
[in,out]	w	work buffer

Returns: a pointer to a new cs_sla_matrix_t

void cs_sla_system_dump	(	const char *	name,
		FILE *	f,
		const cs_sla_matrix_t *	m,
		const double *	rhs
	)

Dump a cs_sla_matrix_t structure and its related right-hand side.

Parameters

[in]	name	either name of the file if f is NULL or description
[in]	f	pointer to a FILE struct.
[in]	m	matrix to dump
[in]	rhs	right-hand side to dump

Data Structures

Macros

Enumerations

Functions

Macro Definition Documentation

Enumeration Type Documentation

Function Documentation