
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 jth column of A is stored in the array AP as follows: if
UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
(j1)*(2nj)/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 ith 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':
Twodimensional 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) 
