spptrf (l)  Linux Manuals
spptrf: computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format
NAME
SPPTRF  computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed formatSYNOPSIS
 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 formA
A
where U is an upper triangular matrix and L is lower triangular.
ARGUMENTS
 UPLO (input) CHARACTER*1

= aqUaq: Upper triangle of A is stored;
= aqLaq: 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 = aqUaq, AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = aqLaq, 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 = aqUaq:Twodimensional storage of the symmetric matrix A:
a11 a12 a13 a14
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]