sgbequ

NAME

sgbequ - compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number

SYNOPSIS

  SUBROUTINE SGBEQU( M, N, NSUB, NSUPER, A, LDA, ROWSC, COLSC, ROWCN, 
 *      COLCN, AMAX, INFO)
  INTEGER M, N, NSUB, NSUPER, LDA, INFO
  REAL ROWCN, COLCN, AMAX
  REAL A(LDA,*), ROWSC(*), COLSC(*)
 
  SUBROUTINE SGBEQU_64( M, N, NSUB, NSUPER, A, LDA, ROWSC, COLSC, 
 *      ROWCN, COLCN, AMAX, INFO)
  INTEGER*8 M, N, NSUB, NSUPER, LDA, INFO
  REAL ROWCN, COLCN, AMAX
  REAL A(LDA,*), ROWSC(*), COLSC(*)

F95 INTERFACE

  SUBROUTINE GBEQU( [M], [N], NSUB, NSUPER, A, [LDA], ROWSC, COLSC, 
 *       ROWCN, COLCN, AMAX, [INFO])
  INTEGER :: M, N, NSUB, NSUPER, LDA, INFO
  REAL :: ROWCN, COLCN, AMAX
  REAL, DIMENSION(:) :: ROWSC, COLSC
  REAL, DIMENSION(:,:) :: A
 
  SUBROUTINE GBEQU_64( [M], [N], NSUB, NSUPER, A, [LDA], ROWSC, COLSC, 
 *       ROWCN, COLCN, AMAX, [INFO])
  INTEGER(8) :: M, N, NSUB, NSUPER, LDA, INFO
  REAL :: ROWCN, COLCN, AMAX
  REAL, DIMENSION(:) :: ROWSC, COLSC
  REAL, DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

void sgbequ(int m, int n, int nsub, int nsuper, float *a, int lda, float *rowsc, float *colsc, float *rowcn, float *colcn, float *amax, int *info);

void sgbequ_64(long m, long n, long nsub, long nsuper, float *a, long lda, float *rowsc, float *colsc, float *rowcn, float *colcn, float *amax, long *info);

PURPOSE

sgbequ computes row and column scalings intended to equilibrate an M-by-N band 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 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.

ARGUMENTS

* M (input): The number of rows of the matrix A. M >= 0.
* N (input): The number of columns of the matrix A. N >= 0.
* NSUB (input): The number of subdiagonals within the band of A. NSUB >= 0.
* NSUPER (input): The number of superdiagonals within the band of A. NSUPER >= 0.
* A (input): The band matrix A, stored in rows 1 to NSUB+NSUPER+1. The j-th column of A is stored in the j-th column of the array A as follows: A(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
* LDA (input): The leading dimension of the array A. LDA >= NSUB+NSUPER+1.
* ROWSC (output): If INFO = 0, or INFO > M, ROWSC contains the row scale factors for A.
* COLSC (output): If INFO = 0, COLSC contains the column scale factors for A.
* ROWCN (output): If INFO = 0 or INFO > M, ROWCN contains the ratio of the smallest ROWSC(i) to the largest ROWSC(i). If ROWCN >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by ROWSC.
* COLCN (output): If INFO = 0, COLCN contains the ratio of the smallest COLSC(i) to the largest COLSC(i). If COLCN >= 0.1, it is not worth scaling by COLSC.
* AMAX (output): 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)