spbequ (3p)

Name

spbequ - metric positive definite band matrix A and reduce its condition number (with respect to the two-norm)

Synopsis

SUBROUTINE SPBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO)

CHARACTER*1 UPLO
INTEGER N, KD, LDA, INFO
REAL SCOND, AMAX
REAL A(LDA,*), SCALE(*)

SUBROUTINE SPBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX,
INFO)

CHARACTER*1 UPLO
INTEGER*8 N, KD, LDA, INFO
REAL SCOND, AMAX
REAL A(LDA,*), SCALE(*)




F95 INTERFACE
SUBROUTINE PBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX,
INFO)

CHARACTER(LEN=1) :: UPLO
INTEGER :: N, KD, LDA, INFO
REAL :: SCOND, AMAX
REAL, DIMENSION(:) :: SCALE
REAL, DIMENSION(:,:) :: A

SUBROUTINE PBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX,
INFO)

CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, KD, LDA, INFO
REAL :: SCOND, AMAX
REAL, DIMENSION(:) :: SCALE
REAL, DIMENSION(:,:) :: A




C INTERFACE
#include <sunperf.h>

void  spbequ(char uplo, int n, int kd, float *a, int lda, float *scale,
float *scond, float *amax, int *info);

void spbequ_64(char uplo, long n, long kd, float *a,  long  lda,  float
*scale, float *scond, float *amax, long *info);

Description

Oracle Solaris Studio Performance Library                           spbequ(3P)



NAME
       spbequ - compute row and column scalings intended to equilibrate a sym-
       metric positive definite band matrix A and reduce its condition  number
       (with respect to the two-norm)


SYNOPSIS
       SUBROUTINE SPBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO)

       CHARACTER*1 UPLO
       INTEGER N, KD, LDA, INFO
       REAL SCOND, AMAX
       REAL A(LDA,*), SCALE(*)

       SUBROUTINE SPBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX,
             INFO)

       CHARACTER*1 UPLO
       INTEGER*8 N, KD, LDA, INFO
       REAL SCOND, AMAX
       REAL A(LDA,*), SCALE(*)




   F95 INTERFACE
       SUBROUTINE PBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX,
              INFO)

       CHARACTER(LEN=1) :: UPLO
       INTEGER :: N, KD, LDA, INFO
       REAL :: SCOND, AMAX
       REAL, DIMENSION(:) :: SCALE
       REAL, DIMENSION(:,:) :: A

       SUBROUTINE PBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX,
              INFO)

       CHARACTER(LEN=1) :: UPLO
       INTEGER(8) :: N, KD, LDA, INFO
       REAL :: SCOND, AMAX
       REAL, DIMENSION(:) :: SCALE
       REAL, DIMENSION(:,:) :: A




   C INTERFACE
       #include <sunperf.h>

       void  spbequ(char uplo, int n, int kd, float *a, int lda, float *scale,
                 float *scond, float *amax, int *info);

       void spbequ_64(char uplo, long n, long kd, float *a,  long  lda,  float
                 *scale, float *scond, float *amax, long *info);



PURPOSE
       spbequ  computes row and column scalings intended to equilibrate a sym-
       metric positive definite band matrix A and reduce its condition  number
       (with  respect  to the two-norm).  S contains the scale factors, S(i) =
       1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j)
       = S(i)*A(i,j)*S(j) has ones on the diagonal.  This choice of S puts the
       condition number of B within a factor N of the smallest possible condi-
       tion number over all possible diagonal scalings.


ARGUMENTS
       UPLO (input)
                 = 'U':  Upper triangular of A is stored;
                 = 'L':  Lower triangular of A is stored.


       N (input) The order of the matrix A.  N >= 0.


       KD (input)
                 The  number  of superdiagonals of the matrix A if UPLO = 'U',
                 or the number of subdiagonals if UPLO = 'L'.  KD >= 0.


       A (input) The upper or lower triangle of the symmetric band  matrix  A,
                 stored  in the first KD+1 rows of the array.  The j-th column
                 of A is stored in the j-th column of the array A as  follows:
                 if  UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
                 if UPLO = 'L', A(1+i-j,j)    = A(i,j) for  j<=i<=min(n,j+kd).


       LDA (input)
                 The leading dimension of the array A.  LDA >= KD+1.


       SCALE (output)
                 If INFO = 0, SCALE contains the scale factors for A.


       SCOND (output)
                 If  INFO  =  0,  SCALE  contains  the  ratio  of the smallest
                 SCALE(i) to the largest SCALE(i).  If SCOND >= 0.1  and  AMAX
                 is  neither  too large nor too small, it is not worth scaling
                 by SCALE.


       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)
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value.
                 > 0:  if INFO = i, the i-th diagonal element is  nonpositive.




                                  7 Nov 2015                        spbequ(3P)