*> \brief \b DPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
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*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
* 
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DPOTF2 computes the Cholesky factorization of a real symmetric
*> positive definite matrix A.
*>
*> The factorization has the form
*>    A = U**T * U ,  if UPLO = 'U', or
*>    A = L  * L**T,  if UPLO = 'L',
*> where U is an upper triangular matrix and L is lower triangular.
*>
*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the upper or lower triangular part of the
*>          symmetric matrix A is stored.
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is DOUBLE PRECISION 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**T *U  or A = L*L**T.
*> \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 = -k, the k-th argument had an illegal value
*>          > 0: if INFO = k, the leading minor of order k 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 September 2012
*
*> \ingroup doublePOcomputational
*
*  =====================================================================
      SUBROUTINE GAL_DPOTF2(UPLO,N,A,LDA,INFO)
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTERUPLO
      INTEGER INFO,LDA,N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION A(LDA,*)
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION ONE,ZERO
      PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
*     ..
*     .. Local Scalars ..
      LOGICAL UPPER
      INTEGER J
      DOUBLE PRECISION AJJ
*     ..
*     .. External Functions ..
      LOGICAL GAL_LSAME,GAL_DISNAN
      DOUBLE PRECISION GAL_DDOT
      EXTERNAL GAL_LSAME,GAL_DDOT,GAL_DISNAN
*     ..
*     .. External Subroutines ..
      EXTERNAL GAL_DGEMV,GAL_DSCAL,GAL_XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC MAX,SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO=0
      UPPER=GAL_LSAME(UPLO,'U')
      IF(.NOT.UPPER.AND..NOT.GAL_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 GAL_XERBLA('GAL_DPOTF2',-INFO)
      RETURN
      END IF
*
*     Quick return if possible
*
      IF(N.EQ.0)
     $RETURN
*
      IF(UPPER)THEN
*
*        Compute the Cholesky factorization A = U**T *U.
*
      DO 10J=1,N
*
*           Compute U(J,J) and test for non-positive-definiteness.
*
      AJJ=A(J,J)-GAL_DDOT(J-1,A(1,J),1,A(1,J),1)
      IF(AJJ.LE.ZERO.OR.GAL_DISNAN(AJJ))THEN
      A(J,J)=AJJ
      GO TO 30
      END IF
      AJJ=SQRT(AJJ)
      A(J,J)=AJJ
*
*           Compute elements J+1:N of row J.
*
      IF(J.LT.N)THEN
      CALL GAL_DGEMV('TRANSPOSE',J-1,N-J,-ONE,A(1,J+1),
     $LDA,A(1,J),1,ONE,A(J,J+1),LDA)
      CALL GAL_DSCAL(N-J,ONE/AJJ,A(J,J+1),LDA)
      END IF
   10 CONTINUE
      ELSE 
*
*        Compute the Cholesky factorization A = L*L**T.
*
      DO 20J=1,N
*
*           Compute L(J,J) and test for non-positive-definiteness.
*
      AJJ=A(J,J)-GAL_DDOT(J-1,A(J,1),LDA,A(J,1),
     $LDA)
      IF(AJJ.LE.ZERO.OR.GAL_DISNAN(AJJ))THEN
      A(J,J)=AJJ
      GO TO 30
      END IF
      AJJ=SQRT(AJJ)
      A(J,J)=AJJ
*
*           Compute elements J+1:N of column J.
*
      IF(J.LT.N)THEN
      CALL GAL_DGEMV('NOTRANSPOSE',N-J,J-1,-ONE,A(J+1,1),
     $LDA,A(J,1),LDA,ONE,A(J+1,J),1)
      CALL GAL_DSCAL(N-J,ONE/AJJ,A(J+1,J),1)
      END IF
   20 CONTINUE
      END IF
      GO TO 40
*
   30 CONTINUE
      INFO=J
*
   40 CONTINUE
      RETURN
*
*     End of DPOTF2
*
      END 
