.TH CPPTRF 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME CPPTRF - the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format .SH SYNOPSIS .TP 19 SUBROUTINE CPPTRF( UPLO, N, AP, INFO ) .TP 19 .ti +4 CHARACTER UPLO .TP 19 .ti +4 INTEGER INFO, N .TP 19 .ti +4 COMPLEX AP( * ) .SH PURPOSE CPPTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format. The factorization has the form .br A = U**H * U, if UPLO = \(aqU\(aq, or .br A = L * L**H, if UPLO = \(aqL\(aq, .br where U is an upper triangular matrix and L is lower triangular. .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 = \(aqU\(aq: Upper triangle of A is stored; .br = \(aqL\(aq: Lower triangle of A is stored. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 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 = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = \(aqL\(aq, 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. .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed. .SH FURTHER DETAILS The packed storage scheme is illustrated by the following example when N = 4, UPLO = \(aqU\(aq: .br Two-dimensional storage of the Hermitian matrix A: .br a11 a12 a13 a14 .br a22 a23 a24 .br a33 a34 (aij = conjg(aji)) .br a44 .br Packed storage of the upper triangle of A: .br AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]