CPPTRF(l) — LAPACK routine (version 2.0)

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 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 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 ]