Spptrf.f -
subroutine spptrf (UPLO, N, AP, INFO)
SPPTRF
SPPTRF
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.
Parameters:
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. N >= 0.
AP
AP is 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
INFO is 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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
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 ]
Definition at line 120 of file spptrf.f.
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