sgeequ - compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number
SUBROUTINE SGEEQU( M, N, A, LDA, ROWSC, COLSC, ROWCN, COLCN, AMAX, * INFO) INTEGER M, N, LDA, INFO REAL ROWCN, COLCN, AMAX REAL A(LDA,*), ROWSC(*), COLSC(*)
SUBROUTINE SGEEQU_64( M, N, A, LDA, ROWSC, COLSC, ROWCN, COLCN, * AMAX, INFO) INTEGER*8 M, N, LDA, INFO REAL ROWCN, COLCN, AMAX REAL A(LDA,*), ROWSC(*), COLSC(*)
SUBROUTINE GEEQU( [M], [N], A, [LDA], ROWSC, COLSC, ROWCN, COLCN, * AMAX, [INFO]) INTEGER :: M, N, LDA, INFO REAL :: ROWCN, COLCN, AMAX REAL, DIMENSION(:) :: ROWSC, COLSC REAL, DIMENSION(:,:) :: A
SUBROUTINE GEEQU_64( [M], [N], A, [LDA], ROWSC, COLSC, ROWCN, COLCN, * AMAX, [INFO]) INTEGER(8) :: M, N, LDA, INFO REAL :: ROWCN, COLCN, AMAX REAL, DIMENSION(:) :: ROWSC, COLSC REAL, DIMENSION(:,:) :: A
#include <sunperf.h>
void sgeequ(int m, int n, float *a, int lda, float *rowsc, float *colsc, float *rowcn, float *colcn, float *amax, int *info);
void sgeequ_64(long m, long n, float *a, long lda, float *rowsc, float *colsc, float *rowcn, float *colcn, float *amax, long *info);
sgeequ computes row and column scalings intended to equilibrate an
M-by-N 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.
ROWSC(i)
to the largest ROWSC(i). If ROWCN > = 0.1 and
AMAX is neither too large nor too small, it is not worth
scaling by ROWSC.
COLSC(i)
to the largest COLSC(i). If COLCN > = 0.1, it is not
worth scaling by COLSC.
= 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