SPPTRF(l)		LAPACK routine (version	1.1)		    SPPTRF(l)

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

SYNOPSIS

  SUBROUTINE SPPTRF( UPLO, N, AP, INFO )

      CHARACTER	     UPLO

      INTEGER	     INFO, N

      REAL	     AP( * )

PURPOSE
  SPPTRF 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) REAL 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 Chole-
	  sky 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 ]