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RedHat 9 (Linux i386) - man page for spptrf (redhat section l)

SPPTRF(l)					)					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 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 ]

LAPACK version 3.0			   15 June 2000 				SPPTRF(l)


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