spptrf(3)

NAME

SUBROUTINE SPPTRF( UPLO, N, AP, INFO )
    CHARACTER      UPLO
    INTEGER        INFO, N
    REAL           AP( * )

SPPTRF computes the Cholesky factorization of a real sym
metric 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 tri
angular.

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 sym; metric 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 de; tails.; 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 ille; gal value
> 0: if INFO = i, the leading minor of order i is; not positive definite, and the factorization could not be com; pleted.

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