dgbequ
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.
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* M (input)
-
The number of rows of the matrix A. M >= 0.
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* N (input)
-
The number of columns of the matrix A. N >= 0.
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* NSUB (input)
-
The number of subdiagonals within the band of A. NSUB >= 0.
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* 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).
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* 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.
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* COLSC (output)
-
If INFO = 0, COLSC contains the column scale factors for A.
-
* ROWCN (output)
-
If INFO = 0 or INFO > M, ROWCN contains the ratio of the
smallest 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.
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* COLCN (output)
-
If INFO = 0, COLCN contains the ratio of the smallest
COLSC(i) to the largest COLSC(i). If COLCN >= 0.1, it is not
worth scaling by COLSC.
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* 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)
-