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spbequ (3)
  • >> spbequ (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         spbequ - compute row and column scalings intended to equili-
         brate a symmetric positive definite band matrix A and reduce
         its condition number (with respect to the two-norm)
    
    SYNOPSIS
         SUBROUTINE SPBEQU( UPLO, N, KD, AB, LDAB,  S,  SCOND,  AMAX,
                   INFO )
    
         CHARACTER UPLO
    
         INTEGER INFO, KD, LDAB, N
    
         REAL AMAX, SCOND
    
         REAL AB( LDAB, * ), S( * )
    
    
    
         #include <sunperf.h>
    
         void spbequ(char uplo, int n, int kd, float *sab, int  ldab,
                   float *s, float *scond, float *amax, int *info) ;
    
    PURPOSE
         SPBEQU computes row and column scalings intended to  equili-
         brate a symmetric positive definite band matrix A and reduce
         its condition number (with respect to the two-norm).  S con-
         tains  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 diago-
         nal scalings.
    
    
    ARGUMENTS
         UPLO      (input) CHARACTER*1
                   = 'U':  Upper triangular of A is stored;
                   = 'L':  Lower triangular of A is stored.
    
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         KD        (input) INTEGER
                   The number of superdiagonals of the  matrix  A  if
                   UPLO  = 'U', or the number of subdiagonals if UPLO
                   = 'L'.  KD >= 0.
    
         AB        (input) REAL array, dimension (LDAB,N)
                   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 AB as follows:  if UPLO = 'U',
                   AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;  if
                   UPLO   =   'L',   AB(1+i-j,j)      =   A(i,j)  for
                   j<=i<=min(n,j+kd).
    
         LDAB      (input) INTEGER
                   The leading dimension of the  array  A.   LDAB  >=
                   KD+1.
    
         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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