Contents
sgeequ - compute row and column scalings intended to equili-
brate an M-by-N matrix A and reduce its condition number
SUBROUTINE SGEEQU(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
INFO)
INTEGER M, N, LDA, INFO
REAL ROWCND, COLCND, AMAX
REAL A(LDA,*), R(*), C(*)
SUBROUTINE SGEEQU_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
INFO)
INTEGER*8 M, N, LDA, INFO
REAL ROWCND, COLCND, AMAX
REAL A(LDA,*), R(*), C(*)
F95 INTERFACE
SUBROUTINE GEEQU([M], [N], A, [LDA], R, C, ROWCND, COLCND,
AMAX, [INFO])
INTEGER :: M, N, LDA, INFO
REAL :: ROWCND, COLCND, AMAX
REAL, DIMENSION(:) :: R, C
REAL, DIMENSION(:,:) :: A
SUBROUTINE GEEQU_64([M], [N], A, [LDA], R, C, ROWCND, COLCND,
AMAX, [INFO])
INTEGER(8) :: M, N, LDA, INFO
REAL :: ROWCND, COLCND, AMAX
REAL, DIMENSION(:) :: R, C
REAL, DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void sgeequ(int m, int n, float *a, int lda, float *r, float
*c, float *rowcnd, float *colcnd, float *amax, int
*info);
void sgeequ_64(long m, long n, float *a, long lda, float *r,
float *c, float *rowcnd, float *colcnd, float
*amax, long *info);
sgeequ computes row and column scalings intended to equili-
brate an M-by-N matrix A and reduce its condition number. R
returns the row scale factors and C the column scale fac-
tors, 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.
A (input) The M-by-N matrix whose equilibration factors are
to be computed.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,M).
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