dpptrf(3F)

NAME
     DPPTRF - compute the Cholesky factorization of a real symmetric positive
     definite matrix A stored in packed format

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

         CHARACTER      UPLO

         INTEGER        INFO, N

         DOUBLE         PRECISION AP( * )

PURPOSE
     DPPTRF computes the Cholesky factorization of a real symmetric positive
     definite matrix A stored in packed format.

     The factorization has the form
        A = U**T * U,  if UPLO = 'U', or
        A = L  * L**T,  if UPLO = 'L',
     where U is an upper triangular matrix and L is lower triangular.


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) DOUBLE PRECISION array, dimension (N*(N+1)/2)
             On entry, the upper or lower triangle of the symmetric 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**T*U or A = L*L**T, 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 symmetric matrix A:

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

     Packed storage of the upper triangle of A:

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