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LAPACK version 3.0
spptrf(3)

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

SYNTAX
  SUBROUTINE SPPTRF( UPLO, N, AP, INFO )

      CHARACTER	     UPLO

      INTEGER	     INFO, N

      REAL	     AP( * )

DESCRIPTION
  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
	  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 ]