```      SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO )
*
*  -- LAPACK routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. 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
INTEGER            ILAENV
EXTERNAL           LSAME, ILAENV
*     ..
*     .. 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 = ILAENV( 1, 'DPOTRF', UPLO, N, -1, -1, -1 )
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

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