# zpptrf.f - Man Page

SRC/zpptrf.f

## Synopsis

### Functions/Subroutines

subroutine **zpptrf** (uplo, n, ap, info)**ZPPTRF**

## Function/Subroutine Documentation

### subroutine zpptrf (character uplo, integer n, complex*16, dimension( * ) ap, integer info)

**ZPPTRF**

**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.

**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 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*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading principal minor of order i is not positive, and the factorization could not be completed.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**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 ]

Definition at line **118** of file **zpptrf.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zpptrf(3) is an alias of zpptrf.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK