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spoequ (3)
  • >> spoequ (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         spoequ - compute row and column scalings intended to equili-
         brate  a symmetric positive definite matrix A and reduce its
         condition number (with respect to the two-norm)
    
    SYNOPSIS
         SUBROUTINE SPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
    
         INTEGER INFO, LDA, N
    
         REAL AMAX, SCOND
    
         REAL A( LDA, * ), S( * )
    
    
    
         #include <sunperf.h>
    
         void spoequ(int n, float  *sa,  int  lda,  float  *s,  float
                   *scond, float *amax, int *info) ;
    
    PURPOSE
         SPOEQU computes row and column scalings intended to  equili-
         brate  a symmetric positive definite 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  con-
         dition number over all possible diagonal scalings.
    
    
    ARGUMENTS
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         A         (input) REAL array, dimension (LDA,N)
                   The  N-by-N  symmetric  positive  definite  matrix
                   whose  scaling  factors  are to be computed.  Only
                   the diagonal elements of A are referenced.
    
         LDA       (input) INTEGER
                   The leading dimension of  the  array  A.   LDA  >=
                   max(1,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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