dgbequ(3P) Sun Performance Library dgbequ(3P)NAMEdgbequ - compute row and column scalings intended to equilibrate an M-
by-N band matrix A and reduce its condition number
SYNOPSIS
SUBROUTINE DGBEQU(M, N, KL, KU, A, LDA, R, C, ROWCND,
COLCND, AMAX, INFO)
INTEGER M, N, KL, KU, LDA, INFO
DOUBLE PRECISION ROWCND, COLCND, AMAX
DOUBLE PRECISION A(LDA,*), R(*), C(*)
SUBROUTINE DGBEQU_64(M, N, KL, KU, A, LDA, R, C, ROWCND,
COLCND, AMAX, INFO)
INTEGER*8 M, N, KL, KU, LDA, INFO
DOUBLE PRECISION ROWCND, COLCND, AMAX
DOUBLE PRECISION A(LDA,*), R(*), C(*)
F95 INTERFACE
SUBROUTINE GBEQU([M], [N], KL, KU, A, [LDA], R, C,
ROWCND, COLCND, AMAX, [INFO])
INTEGER :: M, N, KL, KU, LDA, INFO
REAL(8) :: ROWCND, COLCND, AMAX
REAL(8), DIMENSION(:) :: R, C
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE GBEQU_64([M], [N], KL, KU, A, [LDA], R, C,
ROWCND, COLCND, AMAX, [INFO])
INTEGER(8) :: M, N, KL, KU, LDA, INFO
REAL(8) :: ROWCND, COLCND, AMAX
REAL(8), DIMENSION(:) :: R, C
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dgbequ(int m, int n, int kl, int ku, double *a, int lda, double
*r, double *c, double *rowcnd, double *colcnd, double *amax,
int *info);
void dgbequ_64(long m, long n, long kl, long ku, double *a, long lda,
double *r, double *c, double *rowcnd, double *colcnd, double
*amax, long *info);
PURPOSEdgbequ 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 num‐
ber 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.
KL (input)
The number of subdiagonals within the band of A. KL >= 0.
KU (input)
The number of superdiagonals within the band of A. KU >= 0.
A (input) The band matrix A, stored in rows 1 to KL+KU+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 >= KL+KU+1.
R (output)
If INFO = 0, or INFO > M, R contains the row scale factors
for A.
C (output)
If INFO = 0, C contains the column scale factors for A.
ROWCND (output)
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)
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 scal‐
ing by C.
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
6 Mar 2009 dgbequ(3P)
