psgsequb.c File Reference

Computes row and column scalings, restricting the scale factors to be power-of-radix. More...

#include <math.h>
#include "superlu_sdefs.h"

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Functions
void	psgsequb (SuperMatrix *A, float *r, float *c, float *rowcnd, float *colcnd, float *amax, int_t *info, gridinfo_t *grid)

Detailed Description

Computes row and column scalings, restricting the scale factors to be power-of-radix.

Copyright (c) 2003, The Regents of the University of California, through Lawrence Berkeley National Laboratory (subject to receipt of any required approvals from U.S. Dept. of Energy)

All rights reserved.

The source code is distributed under BSD license, see the file License.txt at the top-level directory.

File name: psgsequb.c History: similar to LAPACK routine SGEEQUB

Function Documentation

psgsequb()

void psgsequb	(	SuperMatrix *	A,
		float *	r,
		float *	c,
		float *	rowcnd,
		float *	colcnd,
		float *	amax,
		int_t *	info,
		gridinfo_t *	grid
	)

    Purpose
    =======

    PSGSEQUB computes row and column scalings intended to equilibrate an
    M-by-N sparse matrix A and reduce its condition number. R returns the row
    scale factors and C the column scale factors, chosen to try to make
    the largest element in each row and column of the matrix B with
    elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.

    R(i) and C(j) are restricted to be a power-of-radix between 
    SMLNUM = smallest safe number and BIGNUM = largest safe number.
    Use of these scaling factors is not guaranteed to reduce the 
    condition number of A but works well in practice.

    This routine differs from PSGSEQU by restricting the scaling factors                       
    to a power-of-radix.  Barring over- and underflow, scaling by                           
    these factors introduces no additional rounding errors.  However,
    the scaled entries' magnitudes are no longer approximately 1 but lie                            
    between sqrt(radix) and 1/sqrt(radix).

    See supermatrix.h for the definition of 'SuperMatrix' structure.

    Arguments
    =========

    A       (input) SuperMatrix*
            The matrix of dimension (A->nrow, A->ncol) whose equilibration
            factors are to be computed. The type of A can be:
            Stype = SLU_NR_loc; Dtype = SLU_S; Mtype = SLU_GE.

    R       (output) float*, size A->nrow
            If INFO = 0 or INFO > M, R contains the row scale factors
            for A.

    C       (output) float*, size A->ncol
            If INFO = 0,  C contains the column scale factors for A.

    ROWCND  (output) float*
            If INFO = 0 or INFO > M, ROWCND contains the ratio of the
            smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
            AMAX is neither too large nor too small, it is not worth
            scaling by R.

    COLCND  (output) float*
            If INFO = 0, COLCND contains the ratio of the smallest
            C(i) to the largest C(i).  If COLCND >= 0.1, it is not
            worth scaling by C.

    AMAX    (output) float*
            Absolute value of largest matrix element.  If AMAX is very
            close to overflow or very close to underflow, the matrix
            should be scaled.

    INFO    (output) int*
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            > 0:  if INFO = i,  and i is
                  <= M:  the i-th row of A is exactly zero
                  >  M:  the (i-M)-th column of A is exactly zero

    GRID    (input) gridinof_t*
            The 2D process mesh.
    =====================================================================

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