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# zpptrf

```
NAME
ZPPTRF - compute the Cholesky factorization of a complex
Hermitian positive definite matrix stored in packed format

SYNOPSIS
SUBROUTINE ZPPTRF( UPLO, N, AP, INFO )

CHARACTER      UPLO

INTEGER        INFO, N

COMPLEX*16     AP( * )

PURPOSE
ZPPTRF computes the Cholesky factorization of a complex Her-
mitian positive definite matrix stored in packed format.

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 Hermi-
tian 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 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':

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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