krylov.h File Reference

Header file for Krylov subspace methods. More...

#include "mkl.h"
#include "ucfd_types.h"
#include "config.h"

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Macros
#define	eps   2.22e-16

Functions
ucfd_status_t	serial_gmres (sparse_matrix_t op, ucfd_precon_type_t precon_type, int bn, int block, int m, int *iter, double tol, int *row_ptr, int *col_ind, int *diag_ind, double *precon_nnz_data, double *x, double *b, double *H, double *V, double *g, double *y, double *w, double *r)
	Serial GMRES routine. More...
ucfd_status_t	step_gmres (sparse_matrix_t op, ucfd_precon_solve psolve, const struct matrix_descr descr, int bn, int m, int *flag, int *row_ptr, int *col_ind, int *diag_ind, double *precon_nnz_data, double *x, double *b, double *H, double *V, double *g, double *y, double *w, double *r)
	Single GMRES iteration routine. More...
ucfd_status_t	serial_bicgstab (sparse_matrix_t op, ucfd_precon_type_t precon_type, int bn, int *iter, double tol, int *row_ptr, int *col_ind, int *diag_ind, double *precon_nnz_data, double *x, double *b, double *r, double *p, double *v, double *s, double *t)
	Serial BiCGstab routine. More...

Detailed Description

Header file for Krylov subspace methods.

Definition in file krylov.h.

Macro Definition Documentation

eps

#define eps   2.22e-16

Definition at line 12 of file krylov.h.

Function Documentation

serial_bicgstab()

ucfd_status_t serial_bicgstab	(	sparse_matrix_t	op,
		ucfd_precon_type_t	precon_type,
		int	bn,
		int *	iter,
		double	tol,
		int *	row_ptr,
		int *	col_ind,
		int *	diag_ind,
		double *	precon_nnz_data,
		double *	x,
		double *	b,
		double *	r,
		double *	p,
		double *	v,
		double *	s,
		double *	t
	)

Serial BiCGstab routine.

Parameters

op	Intel MKL sparse matrix handler (System matrix)
precon_type	Preconditioner type
bn	Number of element cells (= Number of block rows)
block	Block size of BSR matrix (= Size of blocks)
iter	Maximum iteration number
tol	Tolerence of convergence
row_ptr	Row-directional index pointer array of the matrix
col_ind	Column index array of the matrix
diag_ind	Diagonal matrix index array based on row_ptr
precon_nnz_data	Non-zero value array of the preconditioner matrix
x	Solution array
b	Right-hand-side array
r	Residual array
p

Overall process of BiCGstab routine. Outer iteration ends when solution is converged or reached in maximum iteration number. UCFD_STATUS_CONVERGED is returned when L-2 norm of the residual vector becomes smaller than tol, and UCFD_STATUS_NOT_CONVERGED is returned when maximum iteration finished.

Definition at line 286 of file krylov.c.

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serial_gmres()

ucfd_status_t serial_gmres	(	sparse_matrix_t	op,
		ucfd_precon_type_t	precon_type,
		int	bn,
		int	block,
		int	m,
		int *	iter,
		double	tol,
		int *	row_ptr,
		int *	col_ind,
		int *	diag_ind,
		double *	precon_nnz_data,
		double *	x,
		double *	b,
		double *	H,
		double *	V,
		double *	g,
		double *	y,
		double *	w,
		double *	r
	)

Serial GMRES routine.

Parameters

op	Intel MKL sparse matrix handler (System matrix)
precon_type	Preconditioner type
bn	Number of element cells (= Number of block rows)
block	Block size of BSR matrix (= Size of blocks)
m	Restart number
iter	Maximum iteration number
tol	Tolerence of convergence
row_ptr	Row-directional index pointer array of the matrix
col_ind	Column index array of the matrix
diag_ind	Diagonal matrix index array based on row_ptr
precon_nnz_data	Non-zero value array of the preconditioner matrix
x	Solution array
b	Right-hand-side array
H	Upper Hessenberg matrix
V	Orthogonal matrix
g	Givens rotation prameters
y	Least squares array for argmin(||beta - Hy||)
w	Arnoldi iteration array
r	Residual array

Overall process of GMRES routine. Outer iteration ends when solution is converged or reached in maximum iteration number. UCFD_STATUS_CONVERGED is returned when L-2 norm of the residual vector becomes smaller than tol, and UCFD_STATUS_NOT_CONVERGED is returned when maximum iteration finished.

Definition at line 46 of file krylov.c.

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step_gmres()

ucfd_status_t step_gmres	(	sparse_matrix_t	op,
		ucfd_precon_solve	psolve,
		const struct matrix_descr	descr,
		int	bn,
		int	m,
		int *	flag,
		int *	row_ptr,
		int *	col_ind,
		int *	diag_ind,
		double *	precon_nnz_data,
		double *	x,
		double *	b,
		double *	H,
		double *	V,
		double *	g,
		double *	y,
		double *	w,
		double *	r
	)

Single GMRES iteration routine.

Parameters

op	Intel MKL sparse matrix handler (System matrix)
precon_type	Preconditioner type
bn	Number of element cells (= Number of block rows)
block	Block size of BSR matrix (= Size of blocks)
m	Restart number
row_ptr	Row-directional index pointer array of the matrix
col_ind	Column index array of the matrix
diag_ind	Diagonal matrix index array based on row_ptr
precon_nnz_data	Non-zero value array of the preconditioner matrix
x	Solution array
b	Right-hand-side array
H	Upper Hessenberg matrix
V	Orthogonal matrix
g	Givens rotation prameters
y	Least squares array for argmin(||beta - Hy||)
w	Arnoldi iteration array
r	Residual array

Single iteration of GMRES.

Note

Residual array r must be initialized, r := b - A @ x.

Definition at line 185 of file krylov.c.