ZPOTRF2 computes the Cholesky factorization of a real symmetric


 positive definite matrix A using the recursive algorithm.


 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.


 This is the recursive version of the algorithm. It divides


 the matrix into four submatrices:


        [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2


    A = [ -----|----- ]  with n1 = n/2


        [  A21 | A22  ]       n2 = n-n1


 The subroutine calls itself to factor A11. Update and scale A21


 or A12, update A22 then call itself to factor A22.

UPLO

          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER


          The order of the matrix A.  N >= 0.

A

          A is COMPLEX*16 array, dimension (LDA,N)


          On entry, the symmetric matrix A.  If UPLO = 'U', the leading


          N-by-N upper triangular part of A contains the upper


          triangular part of the matrix A, and the strictly lower


          triangular part of A is not referenced.  If UPLO = 'L', the


          leading N-by-N lower triangular part of A contains the lower


          triangular part of the matrix A, and the strictly upper


          triangular part of A is not referenced.


          On exit, if INFO = 0, the factor U or L from the Cholesky


          factorization A = U**H*U or A = L*L**H.

LDA

          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,N).

INFO

          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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016