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zpptrf

 NAME
      ZPPTRF - compute the Cholesky factorization of a complex
      Hermitian positive definite matrix stored in packed format

 SYNOPSIS
      SUBROUTINE ZPPTRF( UPLO, N, AP, INFO )

          CHARACTER      UPLO

          INTEGER        INFO, N

          COMPLEX*16     AP( * )

 PURPOSE
      ZPPTRF computes the Cholesky factorization of a complex Her-
      mitian positive definite matrix stored in packed format.

      The factorization has the form
         A = U**H * U,  if UPLO = 'U', or
         A = L  * L**H,  if UPLO = 'L',
      where U is an upper triangular matrix and L is lower tri-
      angular.

 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/output) COMPLEX*16 array, dimension (N*(N+1)/2)
              On entry, the upper or lower triangle of the Hermi-
              tian 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.  See below for further details.

              On exit, if INFO = 0, the triangular factor U or L
              from the Cholesky factorization A = U**H*U or A =
              L*L**H, in the same storage format as A.

      INFO    (output) INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal
              value
              > 0:  if INFO = i, the leading minor of order i is
              not positive definite, and the factorization could
              not be completed.

 FURTHER DETAILS
      The packed storage scheme is illustrated by the following
      example when N = 4, UPLO = 'U':

      Two-dimensional storage of the Hermitian matrix A:

         a11 a12 a13 a14
             a22 a23 a24
                 a33 a34     (aij = conjg(aji))
                     a44

      Packed storage of the upper triangle of A:

      AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]