cgbequ
cgbequ - compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number
SUBROUTINE CGBEQU( M, N, NSUB, NSUPER, A, LDA, ROWSC, COLSC, ROWCND,
* COLCND, AMAX, INFO)
COMPLEX A(LDA,*)
INTEGER M, N, NSUB, NSUPER, LDA, INFO
REAL ROWCND, COLCND, AMAX
REAL ROWSC(*), COLSC(*)
SUBROUTINE CGBEQU_64( M, N, NSUB, NSUPER, A, LDA, ROWSC, COLSC,
* ROWCND, COLCND, AMAX, INFO)
COMPLEX A(LDA,*)
INTEGER*8 M, N, NSUB, NSUPER, LDA, INFO
REAL ROWCND, COLCND, AMAX
REAL ROWSC(*), COLSC(*)
SUBROUTINE GBEQU( [M], [N], NSUB, NSUPER, A, [LDA], ROWSC, COLSC,
* ROWCND, COLCND, AMAX, [INFO])
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: M, N, NSUB, NSUPER, LDA, INFO
REAL :: ROWCND, COLCND, AMAX
REAL, DIMENSION(:) :: ROWSC, COLSC
SUBROUTINE GBEQU_64( [M], [N], NSUB, NSUPER, A, [LDA], ROWSC, COLSC,
* ROWCND, COLCND, AMAX, [INFO])
COMPLEX, DIMENSION(:,:) :: A
INTEGER(8) :: M, N, NSUB, NSUPER, LDA, INFO
REAL :: ROWCND, COLCND, AMAX
REAL, DIMENSION(:) :: ROWSC, COLSC
#include <sunperf.h>
void cgbequ(int m, int n, int nsub, int nsuper, complex *a, int lda, float *rowsc, float *colsc, float *rowcnd, float *colcnd, float *amax, int *info);
void cgbequ_64(long m, long n, long nsub, long nsuper, complex *a, long lda, float *rowsc, float *colsc, float *rowcnd, float *colcnd, float *amax, long *info);
cgbequ 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.
-
* M (input)
-
The number of rows of the matrix A. M >= 0.
-
* N (input)
-
The number of columns of the matrix A. N >= 0.
-
* NSUB (input)
-
The number of subdiagonals within the band of A. NSUB >= 0.
-
* NSUPER (input)
-
The number of superdiagonals within the band of A. NSUPER >= 0.
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* A (input)
-
The band matrix A, stored in rows 1 to NSUB+NSUPER+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 >= NSUB+NSUPER+1.
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* ROWSC (output)
-
If INFO = 0, or INFO > M, ROWSC contains the row scale factors
for A.
-
* COLSC (output)
-
If INFO = 0, COLSC contains the column scale factors for A.
-
* ROWCND (output)
-
If INFO = 0 or INFO > M, ROWCND contains the ratio of the
smallest ROWSC(i) to the largest ROWSC(i). If ROWCND >= 0.1 and
AMAX is neither too large nor too small, it is not worth
scaling by ROWSC.
-
* COLCND (output)
-
If INFO = 0, COLCND contains the ratio of the smallest
COLSC(i) to the largest COLSC(i). If COLCND >= 0.1, it is not
worth scaling by COLSC.
-
* AMAX (output)
-
Absolute value of largest matrix element. If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.
-
* INFO (output)
-