ZPPTRF - compute the Cholesky factorization of a complex
Hermitian positive definite matrix A stored in packed for
mat
SYNOPSIS
SUBROUTINE ZPPTRF( UPLO, N, AP, INFO )
CHARACTER UPLO
INTEGER INFO, N
COMPLEX*16 AP( * )
PURPOSE
ZPPTRF computes the Cholesky factorization of a complex
Hermitian positive definite matrix A stored in packed for
mat. The factorization has the form
A = U**H * U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower tri
angular.
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) COMPLEX*16 array, dimension
(N*(N+1)/2)
On entry, the upper or lower triangle of the Her
mitian 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**H*U or A =
L*L**H, 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 completed.
The packed storage scheme is illustrated by the following
example when N = 4, UPLO = 'U':
Two-dimensional storage of the Hermitian matrix A:
a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = conjg(aji))
a44
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
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