CPPTRF - Online Linux Manual PageSection : 1
Updated : November 2008
Source : LAPACK routine (version 3.2)
Note : LAPACK routine (version 3.2)

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

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

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PURPOSECPPTRF 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.

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ARGUMENTSUPLO (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.

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FURTHER DETAILSThe 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 ] 0

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