---
name: "zpptrf"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/zpptrf/3lapack"
---

# zpptrf(3lapack)

computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format

## NAME

ZPPTRF - computes the Cholesky factorization of a complex Hermitian positive definite matrix A 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 Hermitian positive definite matrix A 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 triangular.

## 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 Hermitian 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 = \[ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 \]