zgbequb - by-N matrix A and reduce its condition number
SUBROUTINE ZGBEQUB(M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO) INTEGER INFO, KL, KU, LDAB, M, N DOUBLE PRECISION AMAX, COLCND, ROWCND DOUBLE PRECISION C(*), R(*) DOUBLE COMPLEX AB(LDAB,*) SUBROUTINE ZGBEQUB_64(M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO) INTEGER*8 INFO, KL, KU, LDAB, M, N DOUBLE PRECISION AMAX, COLCND, ROWCND DOUBLE PRECISION C(*), R(*) DOUBLE COMPLEX AB(LDAB,*) F95 INTERFACE SUBROUTINE GBEQUB(M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO) INTEGER :: M, N, KL, KU, LDAB, INFO REAL(8), DIMENSION(:) :: R, C COMPLEX(8), DIMENSION(:,:) :: AB REAL(8) :: ROWCND, COLCND, AMAX SUBROUTINE GBEQUB_64(M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO) INTEGER(8) :: M, N, KL, KU, LDAB, INFO REAL(8), DIMENSION(:) :: R, C COMPLEX(8), DIMENSION(:,:) :: AB REAL(8) :: ROWCND, COLCND, AMAX C INTERFACE #include <sunperf.h> void zgbequb (int m, int n, int kl, int ku, doublecomplex *ab, int ldab, double *r, double *c, double *rowcnd, double *colcnd, double *amax, int *info); void zgbequb_64 (long m, long n, long kl, long ku, doublecomplex *ab, long ldab, double *r, double *c, double *rowcnd, double *col- cnd, double *amax, long *info);
Oracle Solaris Studio Performance Library zgbequb(3P)
NAME
zgbequb - compute row and column scalings intended to equilibrate an M-
by-N matrix A and reduce its condition number
SYNOPSIS
SUBROUTINE ZGBEQUB(M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX,
INFO)
INTEGER INFO, KL, KU, LDAB, M, N
DOUBLE PRECISION AMAX, COLCND, ROWCND
DOUBLE PRECISION C(*), R(*)
DOUBLE COMPLEX AB(LDAB,*)
SUBROUTINE ZGBEQUB_64(M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
AMAX, INFO)
INTEGER*8 INFO, KL, KU, LDAB, M, N
DOUBLE PRECISION AMAX, COLCND, ROWCND
DOUBLE PRECISION C(*), R(*)
DOUBLE COMPLEX AB(LDAB,*)
F95 INTERFACE
SUBROUTINE GBEQUB(M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX,
INFO)
INTEGER :: M, N, KL, KU, LDAB, INFO
REAL(8), DIMENSION(:) :: R, C
COMPLEX(8), DIMENSION(:,:) :: AB
REAL(8) :: ROWCND, COLCND, AMAX
SUBROUTINE GBEQUB_64(M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
AMAX, INFO)
INTEGER(8) :: M, N, KL, KU, LDAB, INFO
REAL(8), DIMENSION(:) :: R, C
COMPLEX(8), DIMENSION(:,:) :: AB
REAL(8) :: ROWCND, COLCND, AMAX
C INTERFACE
#include <sunperf.h>
void zgbequb (int m, int n, int kl, int ku, doublecomplex *ab, int
ldab, double *r, double *c, double *rowcnd, double *colcnd,
double *amax, int *info);
void zgbequb_64 (long m, long n, long kl, long ku, doublecomplex *ab,
long ldab, double *r, double *c, double *rowcnd, double *col-
cnd, double *amax, long *info);
PURPOSE
zgbequb 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 an absolute value of at most the radix.
R(i) and C(j) are restricted to be a power of the radix 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.
This routine differs from ZGEEQU by restricting the scaling factors to
a power of the radix. Baring over- and underflow, scaling by these
factors introduces no additional rounding errors. However, the scaled
entries' magnitured are no longer approximately 1 but lie between
sqrt(radix) and 1/sqrt(radix).
ARGUMENTS
M (input)
M is INTEGER
The number of rows of the matrix A. M >= 0.
N (input)
N is INTEGER
The number of columns of the matrix A. N >= 0.
KL (input)
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU (input)
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
AB (input)
AB is DOUBLE PRECISION array, dimension (LDAB,N)
On entry, the matrix A in band storage, in rows
1 to KL+KU+1. The j-th column of A is stored in the j-th
column of the array AB as follows:
AB(KU+1+i-j,j) = A(i,j)
for max(1,j-KU)<=i<=min(N,j+kl).
LDAB (input)
LDAB is INTEGER
The leading dimension of the array A.
LDAB >= max(1,M).
R (output)
R is DOUBLE PRECISION array, dimension (M).
If INFO = 0 or INFO > M, R contains the row scale factors for
A.
C (output)
C is DOUBLE PRECISION array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
ROWCND (output)
ROWCND is DOUBLE PRECISION
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)
COLCND is DOUBLE PRECISION
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)
AMAX is DOUBLE PRECISION
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)
INFO is INTEGER
= 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.
7 Nov 2015 zgbequb(3P)