```      SUBROUTINE DPOTF2( 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
*  =======
*
*  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

```