Contents
zgbequ - compute row and column scalings intended to equili-
brate an M-by-N band matrix A and reduce its condition
number
SUBROUTINE ZGBEQU(M, N, KL, KU, A, LDA, R, C, ROWCN,
COLCN, AMAX, INFO)
DOUBLE COMPLEX A(LDA,*)
INTEGER M, N, KL, KU, LDA, INFO
DOUBLE PRECISION ROWCN, COLCN, AMAX
DOUBLE PRECISION R(*), C(*)
SUBROUTINE ZGBEQU_64(M, N, KL, KU, A, LDA, R, C, ROWCN,
COLCN, AMAX, INFO)
DOUBLE COMPLEX A(LDA,*)
INTEGER*8 M, N, KL, KU, LDA, INFO
DOUBLE PRECISION ROWCN, COLCN, AMAX
DOUBLE PRECISION R(*), C(*)
F95 INTERFACE
SUBROUTINE GBEQU([M], [N], KL, KU, A, [LDA], R, C,
ROWCN, COLCN, AMAX, [INFO])
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: M, N, KL, KU, LDA, INFO
REAL(8) :: ROWCN, COLCN, AMAX
REAL(8), DIMENSION(:) :: R, C
SUBROUTINE GBEQU_64([M], [N], KL, KU, A, [LDA], R, C,
ROWCN, COLCN, AMAX, [INFO])
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: M, N, KL, KU, LDA, INFO
REAL(8) :: ROWCN, COLCN, AMAX
REAL(8), DIMENSION(:) :: R, C
C INTERFACE
#include <sunperf.h>
void zgbequ(int m, int n, int kl, int ku, doublecomplex *a,
int lda, double *r, double *c, double *rowcn, dou-
ble *colcn, double *amax, int *info);
void zgbequ_64(long m, long n, long kl, long ku, doublecom-
plex *a, long lda, double *r, double *c, double
*rowcn, double *colcn, double *amax, long *info);
zgbequ computes row and column scalings intended to equili-
brate 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.
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.
ROWCN (output)
If INFO = 0 or INFO > M, ROWCN contains the ratio
of the smallest R(i) to the largest R(i). If
ROWCN >= 0.1 and AMAX is neither too large nor too
small, it is not worth scaling by R.
COLCN (output)
If INFO = 0, COLCN contains the ratio of the smal-
lest C(i) to the largest C(i). If COLCN >= 0.1,
it is not worth scaling by C.
AMAX (output)
Absolute value of largest matrix element. If AMAX
is very close to overflow or very close to under-
flow, the matrix should be scaled.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal 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