SUBROUTINE DPOTF2F( UPLO, N, A, LDA, INFO )

*

*  -- LAPACK routine (version 3.0) --

*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,

*     Courant Institute, Argonne National Lab, and Rice University

*     February 29, 1992

*

*     .. Scalar Arguments ..

      CHARACTER          UPLO

      INTEGER            INFO, LDA, N

*     ..

*     .. Array Arguments ..

      DOUBLE PRECISION   A( LDA, * )

*     ..

*

*  Purpose

*  =======

*

*  DPOTF2 computes the Cholesky factorization of a real symmetric

*  positive definite matrix A.

*

*  The factorization has the form

*     A = U' * U ,  if UPLO = 'U', or

*     A = L  * L',  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.

*

*  Arguments

*  =========

*

*  UPLO    (input) CHARACTER*1

*          Specifies whether the upper or lower triangular part of the

*          symmetric matrix A is stored.

*          = 'U':  Upper triangular

*          = 'L':  Lower triangular

*

*  N       (input) INTEGER

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

*

*  A       (input/output) 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'*U  or A = L*L'.

*

*  LDA     (input) INTEGER

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

*

*  INFO    (output) 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.

*

*  =====================================================================

*

*     .. 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            LSAME

      DOUBLE PRECISION   DDOT

      EXTERNAL           LSAME, DDOT

*     ..

*     .. External Subroutines ..

      EXTERNAL           DGEMV, DSCAL, XERBLA

*     ..

*     .. Intrinsic Functions ..

      INTRINSIC          MAX, 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( 'DPOTF2', -INFO )

         RETURN

      END IF

*

*     Quick return if possible

*

      IF( N.EQ.0 )

     $   RETURN

*

      IF( UPPER ) THEN

*

*        Compute the Cholesky factorization A = U'*U.

*

         DO 10 J = 1, N

*

*           Compute U(J,J) and test for non-positive-definiteness.

*

            AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )

            IF( AJJ.LE.ZERO ) 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 DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),

     $                     LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )

               CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )

            END IF

   10    CONTINUE

      ELSE

*

*        Compute the Cholesky factorization A = L*L'.

*

         DO 20 J = 1, N

*

*           Compute L(J,J) and test for non-positive-definiteness.

*

            AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),

     $            LDA )

            IF( AJJ.LE.ZERO ) 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 DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),

     $                     LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )

               CALL 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