solvers_direct.c File Reference

#include <math.h>
#include <unistd.h>
#include <stdio.h>
#include <string.h>
#include <grass/gis.h>
#include <grass/gmath.h>
#include <grass/glocale.h>

Include dependency graph for solvers_direct.c:

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Macros
#define	TINY   1.0e-20
#define	COMP_PIVOT   100

Functions
int	G_math_solver_gauss (double **A, double *x, double *b, int rows)
	The gauss elimination solver for quardatic matrices. More...
int	G_math_solver_lu (double **A, double *x, double *b, int rows)
	The LU solver for quardatic matrices. More...
int	G_math_solver_cholesky (double **A, double *x, double *b, int bandwidth, int rows)
	The choleksy decomposition solver for quardatic, symmetric positive definite matrices. More...
void	G_math_gauss_elimination (double **A, double *b, int rows)
	Gauss elimination. More...
void	G_math_lu_decomposition (double **A, double *b UNUSED, int rows)
	lu decomposition More...
int	G_math_cholesky_decomposition (double **A, int rows, int bandwidth)
	cholesky decomposition for symmetric, positive definite matrices with bandwidth optimization More...
void	G_math_backward_substitution (double **A, double *x, double *b, int rows)
	backward substitution More...
void	G_math_forward_substitution (double **A, double *x, double *b, int rows)
	forward substitution More...

Macro Definition Documentation

COMP_PIVOT

#define COMP_PIVOT   100

Definition at line 27 of file solvers_direct.c.

TINY

#define TINY   1.0e-20

Definition at line 26 of file solvers_direct.c.

Function Documentation

G_math_backward_substitution()

void G_math_backward_substitution	(	double **	A,
		double *	x,
		double *	b,
		int	rows
	)

backward substitution

Parameters

A	double **
x	double *
b	double *
rows	int

Returns

void

Definition at line 286 of file solvers_direct.c.

G_math_cholesky_decomposition()

int G_math_cholesky_decomposition	(	double **	A,
		int	rows,
		int	bandwidth
	)

cholesky decomposition for symmetric, positive definite matrices with bandwidth optimization

The provided matrix will be overwritten with the lower and upper triangle matrix A = LL^T

Parameters

A	double **
rows	int
bandwidth	int – the bandwidth of the matrix (0 > bandwidth <= cols)

Returns

void

Definition at line 217 of file solvers_direct.c.

G_math_forward_substitution()

void G_math_forward_substitution	(	double **	A,
		double *	x,
		double *	b,
		int	rows
	)

forward substitution

Parameters

A	double **
x	double *
b	double *
rows	int

Returns

void

Definition at line 310 of file solvers_direct.c.

G_math_gauss_elimination()

void G_math_gauss_elimination	(	double **	A,
		double *	b,
		int	rows
	)

Gauss elimination.

To run this solver efficiently, no pivoting is supported. The matrix will be overwritten with the decomposite form

Parameters

A	double **
b	double *
rows	int

Returns

void

Definition at line 153 of file solvers_direct.c.

G_math_lu_decomposition()

void G_math_lu_decomposition	(	double **	A,
		double *b	UNUSED,
		int	rows
	)

lu decomposition

To run this solver efficiently, no pivoting is supported. The matrix will be overwritten with the decomposite form

Parameters

A	double **
b	double * – this vector is needed if its part of the linear equation system, otherwise set it to NULL
rows	int

Returns

void

Definition at line 186 of file solvers_direct.c.

G_math_solver_cholesky()

int G_math_solver_cholesky	(	double **	A,
		double *	x,
		double *	b,
		int	bandwidth,
		int	rows
	)

The choleksy decomposition solver for quardatic, symmetric positive definite matrices.

This solver does not support sparse matrices The matrix A will be overwritten. The result is written to the vector x

Parameters

A	double **
x	double *
b	double *
bandwidth	int – the bandwidth of the band matrix, if unsure set to rows
rows	int

Returns

int – 1 success

Definition at line 124 of file solvers_direct.c.

G_math_solver_gauss()

int G_math_solver_gauss	(	double **	A,
		double *	x,
		double *	b,
		int	rows
	)

The gauss elimination solver for quardatic matrices.

This solver does not support sparse matrices The matrix A will be overwritten. The result is written to the vector x

Parameters

A	double **
x	double *
b	double *
rows	int

Returns

int – 1 success

Definition at line 42 of file solvers_direct.c.

G_math_solver_lu()

int G_math_solver_lu	(	double **	A,
		double *	x,
		double *	b,
		int	rows
	)

The LU solver for quardatic matrices.

This solver does not support sparse matrices The matrix A will be overwritten. The result is written to the vector x in the G_math_les structure

Parameters

A	double **
x	double *
b	double *
rows	int

Returns

int – 1 success

Definition at line 66 of file solvers_direct.c.