dgbequ - compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number
SUBROUTINE DGBEQU( M, N, NSUB, NSUPER, A, LDA, ROWSC, COLSC, ROWCN, * COLCN, AMAX, INFO) INTEGER M, N, NSUB, NSUPER, LDA, INFO DOUBLE PRECISION ROWCN, COLCN, AMAX DOUBLE PRECISION A(LDA,*), ROWSC(*), COLSC(*)
SUBROUTINE DGBEQU_64( M, N, NSUB, NSUPER, A, LDA, ROWSC, COLSC, * ROWCN, COLCN, AMAX, INFO) INTEGER*8 M, N, NSUB, NSUPER, LDA, INFO DOUBLE PRECISION ROWCN, COLCN, AMAX DOUBLE PRECISION A(LDA,*), ROWSC(*), COLSC(*)
SUBROUTINE GBEQU( [M], [N], NSUB, NSUPER, A, [LDA], ROWSC, COLSC, * ROWCN, COLCN, AMAX, [INFO]) INTEGER :: M, N, NSUB, NSUPER, LDA, INFO REAL(8) :: ROWCN, COLCN, AMAX REAL(8), DIMENSION(:) :: ROWSC, COLSC REAL(8), DIMENSION(:,:) :: A
SUBROUTINE GBEQU_64( [M], [N], NSUB, NSUPER, A, [LDA], ROWSC, COLSC, * ROWCN, COLCN, AMAX, [INFO]) INTEGER(8) :: M, N, NSUB, NSUPER, LDA, INFO REAL(8) :: ROWCN, COLCN, AMAX REAL(8), DIMENSION(:) :: ROWSC, COLSC REAL(8), DIMENSION(:,:) :: A
#include <sunperf.h>
void dgbequ(int m, int n, int nsub, int nsuper, double *a, int lda, double *rowsc, double *colsc, double *rowcn, double *colcn, double *amax, int *info);
void dgbequ_64(long m, long n, long nsub, long nsuper, double *a, long lda, double *rowsc, double *colsc, double *rowcn, double *colcn, double *amax, long *info);
dgbequ computes row and column scalings intended to equilibrate 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.
A(ku+1+i-j,j)
= A(i,j)
for max(1,j-ku)
< =i < =min(m,j+kl).
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