*> \brief \b ZPOTRF2
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       RECURSIVE SUBROUTINE ZPOTRF2( UPLO, N, A, LDA, INFO )
* 
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, N
*       ..
*       .. Array Arguments ..
*       COMPLEX*16         A( LDA, * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> 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.
*> 
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  Upper triangle of A is stored;
*>          = 'L':  Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          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.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2015
*
*> \ingroup complex16POcomputational
*
*  =====================================================================
      RECURSIVE SUBROUTINE ZPOTRF2( UPLO, N, A, LDA, INFO )
*
*  -- LAPACK computational routine (version 3.6.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2015
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, N
*     ..
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
      COMPLEX*16         CONE
      PARAMETER          ( CONE = (1.0D+0, 0.0D+0) )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER            
      INTEGER            N1, N2, IINFO
      DOUBLE PRECISION   AJJ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME, DISNAN
      EXTERNAL           LSAME, DISNAN
*     ..
*     .. External Subroutines ..
      EXTERNAL           ZHERK, ZTRSM, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, DBLE, SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters
*
      INFO = 0
      UPPER = LSAME( UPLO, 'U' )
      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -4
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'ZPOTRF2', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     N=1 case
*
      IF( N.EQ.1 ) THEN
*
*        Test for non-positive-definiteness
*
         AJJ = DBLE( A( 1, 1 ) )
         IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
            INFO = 1
            RETURN
         END IF
*
*        Factor
*
         A( 1, 1 ) = SQRT( AJJ )
*
*     Use recursive code
*
      ELSE
         N1 = N/2
         N2 = N-N1
*
*        Factor A11
*
         CALL ZPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO )
         IF ( IINFO.NE.0 ) THEN
            INFO = IINFO
            RETURN
         END IF    
*
*        Compute the Cholesky factorization A = U**H*U
*
         IF( UPPER ) THEN
*
*           Update and scale A12
*
            CALL ZTRSM( 'L', 'U', 'C', 'N', N1, N2, CONE,
     $                  A( 1, 1 ), LDA, A( 1, N1+1 ), LDA )
*
*           Update and factor A22
*          
            CALL ZHERK( UPLO, 'C', N2, N1, -ONE, A( 1, N1+1 ), LDA,
     $                  ONE, A( N1+1, N1+1 ), LDA )
            CALL ZPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
            IF ( IINFO.NE.0 ) THEN
               INFO = IINFO + N1
               RETURN
            END IF
*
*        Compute the Cholesky factorization A = L*L**H
*
         ELSE
*
*           Update and scale A21
*
            CALL ZTRSM( 'R', 'L', 'C', 'N', N2, N1, CONE,
     $                  A( 1, 1 ), LDA, A( N1+1, 1 ), LDA )
*
*           Update and factor A22
*
            CALL ZHERK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA,
     $                  ONE, A( N1+1, N1+1 ), LDA )
            CALL ZPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO )
            IF ( IINFO.NE.0 ) THEN
               INFO = IINFO + N1
               RETURN
            END IF
         END IF
      END IF
      RETURN
*
*     End of ZPOTRF2
*
      END
