SUBROUTINE DPOTRFF( 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

*     March 31, 1993

*

*     .. Scalar Arguments ..

      CHARACTER          UPLO

      INTEGER            INFO, LDA, N

*     ..

*     .. Array Arguments ..

      DOUBLE PRECISION   A( LDA, * )

*     ..

*

*  Purpose

*  =======

*

*  DPOTRF 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 block version of the algorithm, calling Level 3 BLAS.

*

*  Arguments

*  =========

*

*  UPLO    (input) CHARACTER*1

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

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

*

*  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**T*U or A = L*L**T.

*

*  LDA     (input) INTEGER

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

*

*  INFO    (output) 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.

*

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

*

*     .. Parameters ..

      DOUBLE PRECISION   ONE

      PARAMETER          ( ONE = 1.0D+0 )

*     ..

*     .. Local Scalars ..

      LOGICAL            UPPER

      INTEGER            J, JB, NB

*     ..

*     .. External Functions ..

      LOGICAL            LSAME

      EXTERNAL           LSAME

*     ..

*     .. External Subroutines ..

      EXTERNAL           DGEMM, DPOTF2, DSYRK, DTRSM, XERBLA

*     ..

*     .. Intrinsic Functions ..

      INTRINSIC          MAX, MIN

*     ..

*     .. 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( 'DPOTRF', -INFO )

         RETURN

      END IF

*

*     Quick return if possible

*

      IF( N.EQ.0 )

     $   RETURN

*

*     Determine the block size for this environment.

*

      NB = 224

      IF( NB.LE.1 .OR. NB.GE.N ) THEN

*

*        Use unblocked code.

*

         CALL DPOTF2( UPLO, N, A, LDA, INFO )

      ELSE

*

*        Use blocked code.

*

         IF( UPPER ) THEN

*

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

*

            DO 10 J = 1, N, NB

*

*              Update and factorize the current diagonal block and test

*              for non-positive-definiteness.

*

               JB = MIN( NB, N-J+1 )

               CALL DSYRK( 'Upper', 'Transpose', JB, J-1, -ONE,

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

               CALL DPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )

               IF( INFO.NE.0 )

     $            GO TO 30

               IF( J+JB.LE.N ) THEN

*

*                 Compute the current block row.

*

                  CALL DGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1,

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

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

                  CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit',

     $                        JB, N-J-JB+1, ONE, A( J, J ), LDA,

     $                        A( J, J+JB ), LDA )

               END IF

   10       CONTINUE

*

         ELSE

*

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

*

            DO 20 J = 1, N, NB

*

*              Update and factorize the current diagonal block and test

*              for non-positive-definiteness.

*

               JB = MIN( NB, N-J+1 )

               CALL DSYRK( 'Lower', 'No transpose', JB, J-1, -ONE,

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

               CALL DPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )

               IF( INFO.NE.0 )

     $            GO TO 30

               IF( J+JB.LE.N ) THEN

*

*                 Compute the current block column.

*

                  CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,

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

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

                  CALL DTRSM( 'Right', 'Lower', 'Transpose', 'Non-unit',

     $                        N-J-JB+1, JB, ONE, A( J, J ), LDA,

     $                        A( J+JB, J ), LDA )

               END IF

   20       CONTINUE

         END IF

      END IF

      GO TO 40

*

   30 CONTINUE

      INFO = INFO + J - 1

*

   40 CONTINUE

      RETURN

*

*     End of DPOTRF

*

      END