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NAME
     zpbstf - compute a split Cholesky factorization of a complex
     Hermitian positive definite band matrix A

SYNOPSIS
     SUBROUTINE ZPBSTF( UPLO, N, KD, AB, LDAB, INFO )

     CHARACTER UPLO

     INTEGER INFO, KD, LDAB, N

     COMPLEX*16 AB( LDAB, * )



     #include <sunperf.h>

     void zpbstf(char uplo, int n, int  kd,  doublecomplex  *zab,
               int ldab, int *info) ;

PURPOSE
     ZPBSTF computes a split Cholesky factorization of a  complex
     Hermitian positive definite band matrix A.

     This routine is designed to  be  used  in  conjunction  with
     ZHBGST.

     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*16    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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