Go to main content
Oracle Developer Studio 12.5 Man Pages

Exit Print View

Updated: June 2017
 
 

dgbequb (3p)

Name

dgbequb - by-N matrix A and reduce its condition number

Synopsis

SUBROUTINE DGBEQUB(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 AB(LDAB,*), C(*), R(*)


SUBROUTINE  DGBEQUB_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 AB(LDAB,*), C(*), R(*)


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(:,:) :: AB

REAL(8), DIMENSION(:) :: R, C

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(:,:) :: AB

REAL(8), DIMENSION(:) :: R, C

REAL(8) :: ROWCND, COLCND, AMAX


C INTERFACE
#include <sunperf.h>

void dgbequb (int m, int n, int kl, int ku, double *ab, int ldab,  dou-
ble  *r,  double  *c,  double *rowcnd, double *colcnd, double
*amax, int *info);


void dgbequb_64 (long m, long n, long kl, long  ku,  double  *ab,  long
ldab,  double  *r, double *c, double *rowcnd, double *colcnd,
double *amax, long *info);

Description

Oracle Solaris Studio Performance Library                          dgbequb(3P)



NAME
       dgbequb - compute row and column scalings intended to equilibrate an M-
       by-N matrix A and reduce its condition number


SYNOPSIS
       SUBROUTINE DGBEQUB(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 AB(LDAB,*), C(*), R(*)


       SUBROUTINE  DGBEQUB_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 AB(LDAB,*), C(*), R(*)


   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(:,:) :: AB

       REAL(8), DIMENSION(:) :: R, C

       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(:,:) :: AB

       REAL(8), DIMENSION(:) :: R, C

       REAL(8) :: ROWCND, COLCND, AMAX


   C INTERFACE
       #include <sunperf.h>

       void dgbequb (int m, int n, int kl, int ku, double *ab, int ldab,  dou-
                 ble  *r,  double  *c,  double *rowcnd, double *colcnd, double
                 *amax, int *info);


       void dgbequb_64 (long m, long n, long kl, long  ku,  double  *ab,  long
                 ldab,  double  *r, double *c, double *rowcnd, double *colcnd,
                 double *amax, long *info);


PURPOSE
       dgbequb 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 DGEEQU 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                       dgbequb(3P)