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sppequ (3)
  • >> sppequ (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         sppequ - compute row and column scalings intended to equili-
         brate  a  symmetric  positive  definite  matrix  A in packed
         storage and reduce its condition number (with respect to the
         two-norm)
    
    SYNOPSIS
         SUBROUTINE SPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
    
         CHARACTER UPLO
    
         INTEGER INFO, N
    
         REAL AMAX, SCOND
    
         REAL AP( * ), S( * )
    
    
    
         #include <sunperf.h>
    
         void sppequ(char uplo, int n, float *sap,  float  *s,  float
                   *scond, float *amax, int *info) ;
    
    PURPOSE
         SPPEQU computes row and column scalings intended to  equili-
         brate  a  symmetric  positive  definite  matrix  A in packed
         storage 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 condition number over all
         possible diagonal scalings.
    
    
    ARGUMENTS
         UPLO      (input) CHARACTER*1
                   = 'U':  Upper triangle of A is stored;
                   = 'L':  Lower triangle of A is stored.
    
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         AP        (input) REAL array, dimension (N*(N+1)/2)
                   The upper  or  lower  triangle  of  the  symmetric
                   matrix  A,  packed  columnwise  in a linear array.
                   The j-th column of A is stored in the array AP  as
                   follows:   if  UPLO  =  'U',  AP(i  + (j-1)*j/2) =
                   A(i,j) for 1<=i<=j; if UPLO  =  'L',  AP(i  +  (j-
                   1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    
         S         (output) REAL array, dimension (N)
                   If INFO = 0, S contains the scale factors for A.
    
         SCOND     (output) REAL
                   If INFO = 0, S contains the ratio of the  smallest
                   S(i)  to  the  largest  S(i).  If SCOND >= 0.1 and
                   AMAX is neither too large nor too small, it is not
                   worth scaling by S.
    
         AMAX      (output) REAL
                   Absolute value of largest matrix element.  If AMAX
                   is  very close to overflow or very close to under-
                   flow, the matrix should be scaled.
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value
                   > 0:  if INFO = i, the i-th  diagonal  element  is
                   nonpositive.
    
    
    
    


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