CPPTRF(3)      LAPACK routine of NEC Numeric Library Collection      CPPTRF(3)



NAME
       CPPTRF

SYNOPSIS
       SUBROUTINE CPPTRF (UPLO, N, AP, INFO)



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)
                     UPLO is CHARACTER*1
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N         (input)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           AP        (input/output)
                     AP is 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)
                     INFO is 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 ]



LAPACK routine                  31 October 2017                      CPPTRF(3)