• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

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

SYNOPSIS

  SUBROUTINE ZGBEQU( M, N, NSUB, NSUPER, A, LDA, ROWSC, COLSC, ROWCN, 
 *      COLCN, AMAX, INFO)
  DOUBLE COMPLEX A(LDA,*)
  INTEGER M, N, NSUB, NSUPER, LDA, INFO
  DOUBLE PRECISION ROWCN, COLCN, AMAX
  DOUBLE PRECISION ROWSC(*), COLSC(*)

  SUBROUTINE ZGBEQU_64( M, N, NSUB, NSUPER, A, LDA, ROWSC, COLSC, 
 *      ROWCN, COLCN, AMAX, INFO)
  DOUBLE COMPLEX A(LDA,*)
  INTEGER*8 M, N, NSUB, NSUPER, LDA, INFO
  DOUBLE PRECISION ROWCN, COLCN, AMAX
  DOUBLE PRECISION ROWSC(*), COLSC(*)

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

void zgbequ(int m, int n, int nsub, int nsuper, doublecomplex *a, int lda, double *rowsc, double *colsc, double *rowcn, double *colcn, double *amax, int *info);

void zgbequ_64(long m, long n, long nsub, long nsuper, doublecomplex *a, long lda, double *rowsc, double *colsc, double *rowcn, double *colcn, double *amax, long *info);

PURPOSE

zgbequ 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)
  

   = 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