Contents
cgbequ - compute row and column scalings intended to equili-
brate an M-by-N band matrix A and reduce its condition
number
SUBROUTINE CGBEQU(M, N, KL, KU, A, LDA, R, C, ROWCND,
COLCND, AMAX, INFO)
COMPLEX A(LDA,*)
INTEGER M, N, KL, KU, LDA, INFO
REAL ROWCND, COLCND, AMAX
REAL R(*), C(*)
SUBROUTINE CGBEQU_64(M, N, KL, KU, A, LDA, R, C,
ROWCND, COLCND, AMAX, INFO)
COMPLEX A(LDA,*)
INTEGER*8 M, N, KL, KU, LDA, INFO
REAL ROWCND, COLCND, AMAX
REAL R(*), C(*)
F95 INTERFACE
SUBROUTINE GBEQU([M], [N], KL, KU, A, [LDA], R, C,
ROWCND, COLCND, AMAX, [INFO])
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: M, N, KL, KU, LDA, INFO
REAL :: ROWCND, COLCND, AMAX
REAL, DIMENSION(:) :: R, C
SUBROUTINE GBEQU_64([M], [N], KL, KU, A, [LDA], R, C,
ROWCND, COLCND, AMAX, [INFO])
COMPLEX, DIMENSION(:,:) :: A
INTEGER(8) :: M, N, KL, KU, LDA, INFO
REAL :: ROWCND, COLCND, AMAX
REAL, DIMENSION(:) :: R, C
C INTERFACE
#include <sunperf.h>
void cgbequ(int m, int n, int kl, int ku, complex *a, int
lda, float *r, float *c, float *rowcnd, float
*colcnd, float *amax, int *info);
void cgbequ_64(long m, long n, long kl, long ku, complex *a,
long lda, float *r, float *c, float *rowcnd, float
*colcnd, float *amax, long *info);
cgbequ 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.
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 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