cpptrf(3)

NAME

CPPTRF - compute the Cholesky factorization of a complex

Hermitian positive definite matrix A stored in packed format

SYNOPSIS

SUBROUTINE CPPTRF( UPLO, N, AP, INFO )
    CHARACTER      UPLO
    INTEGER        INFO, N
    COMPLEX        AP( * )

PURPOSE

CPPTRF 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 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 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 de

tails.

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 com

pleted.

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 ]

LAPACK version 3.0 15 June 2000

CPPTRF(3)