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cpbstf (3)
  • >> cpbstf (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         cpbstf - compute a split Cholesky factorization of a complex
         Hermitian positive definite band matrix A
    
    SYNOPSIS
         SUBROUTINE CPBSTF( UPLO, N, KD, AB, LDAB, INFO )
    
         CHARACTER UPLO
    
         INTEGER INFO, KD, LDAB, N
    
         COMPLEX AB( LDAB, * )
    
    
    
         #include <sunperf.h>
    
         void cpbstf(char uplo, int n,  int  kd,  complex  *cab,  int
                   ldab, int *info) ;
    
    PURPOSE
         CPBSTF computes a split Cholesky factorization of a  complex
         Hermitian positive definite band matrix A.
    
         This routine is designed to  be  used  in  conjunction  with
         CHBGST.
    
         The factorization has the form  A = S**H*S   where  S  is  a
         band  matrix  of  the  same bandwidth as A and the following
         structure:
    
           S = ( U    )
               ( M  L )
    
         where U is upper triangular of order m = (n+kd)/2, and L  is
         lower triangular of order n-m.
    
    
    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.
    
         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/output) COMPLEX array, dimension (LDAB,N)
                   On entry, the upper or lower triangle of the  Her-
                   mitian  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).
    
                   On exit, if INFO = 0, the factor S from the  split
                   Cholesky  factorization  A  =  S**H*S. See Further
                   Details.   LDAB     (input)  INTEGER  The  leading
                   dimension of the array AB.  LDAB >= KD+1.
    
         INFO      (output) INTEGER
                   = 0: successful exit
                   < 0: if INFO = -i, the i-th argument had an  ille-
                   gal value
                   > 0: if INFO = i, the factorization could  not  be
                   completed,  because the updated element a(i,i) was
                   negative; the matrix A is not positive definite.
    
    FURTHER DETAILS
         The band storage scheme  is  illustrated  by  the  following
         example, when N = 7, KD = 2:
    
         S = ( s11  s12  s13                     )
             (      s22  s23  s24                )
             (           s33  s34                )
             (                s44                )
             (           s53  s54  s55           )
             (                s64  s65  s66      )
             (                     s75  s76  s77 )
    
         If UPLO = 'U', the array AB holds:
    
         on entry:                          on exit:
    
          *    *   a13  a24  a35  a46  a57   *    *   s13  s24  s53' s64' s75'
          *   a12  a23  a34  a45  a56  a67   *   s12  s23  s34  s54' s65' s76'
         a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55  s66  s77
    
         If UPLO = 'L', the array AB holds:
    
         on entry:                          on exit:
    
         a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55  s66  s77
         a21  a32  a43  a54  a65  a76   *   s12' s23' s34' s54  s65  s76   *
         a31  a42  a53  a64  a64   *    *   s13' s24' s53  s64  s75   *    *
    
         Array elements  marked  *  are  not  used  by  the  routine;  s12'  denotes
         conjg(s12); the diagonal elements of S are real.
    
    
    
    


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