Contents
sgbequ - compute row and column scalings intended to equili-
brate an M-by-N band matrix A and reduce its condition
number
SUBROUTINE SGBEQU(M, N, KL, KU, A, LDA, R, C, ROWCN,
COLCN, AMAX, INFO)
INTEGER M, N, KL, KU, LDA, INFO
REAL ROWCN, COLCN, AMAX
REAL A(LDA,*), R(*), C(*)
SUBROUTINE SGBEQU_64(M, N, KL, KU, A, LDA, R, C, ROWCN,
COLCN, AMAX, INFO)
INTEGER*8 M, N, KL, KU, LDA, INFO
REAL ROWCN, COLCN, AMAX
REAL A(LDA,*), R(*), C(*)
F95 INTERFACE
SUBROUTINE GBEQU([M], [N], KL, KU, A, [LDA], R, C,
ROWCN, COLCN, AMAX, [INFO])
INTEGER :: M, N, KL, KU, LDA, INFO
REAL :: ROWCN, COLCN, AMAX
REAL, DIMENSION(:) :: R, C
REAL, DIMENSION(:,:) :: A
SUBROUTINE GBEQU_64([M], [N], KL, KU, A, [LDA], R, C,
ROWCN, COLCN, AMAX, [INFO])
INTEGER(8) :: M, N, KL, KU, LDA, INFO
REAL :: ROWCN, COLCN, AMAX
REAL, DIMENSION(:) :: R, C
REAL, DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void sgbequ(int m, int n, int kl, int ku, float *a, int lda,
float *r, float *c, float *rowcn, float *colcn,
float *amax, int *info);
void sgbequ_64(long m, long n, long kl, long ku, float *a,
long lda, float *r, float *c, float *rowcn, float
*colcn, float *amax, long *info);
sgbequ 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