          SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
         $                   WORK, INFO )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, LDU, LDVT, N, SMLSIZ, SQRE
    *     ..
    *     .. Array Arguments ..
          INTEGER            IWORK( * )
          DOUBLE PRECISION   D( * ), E( * ), U( LDU, * ), VT( LDVT, * ),
         $                   WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  Using a divide and conquer approach, DLASD0 computes the singular
    *  value decomposition (SVD) of a real upper bidiagonal N-by-M
    *  matrix B with diagonal D and offdiagonal E, where M = N + SQRE.
    *  The algorithm computes orthogonal matrices U and VT such that
    *  B = U * S * VT. The singular values S are overwritten on D.
    *
    *  A related subroutine, DLASDA, computes only the singular values,
    *  and optionally, the singular vectors in compact form.
    *
    *  Arguments
    *  =========
    *
    *  N      (input) INTEGER
    *         On entry, the row dimension of the upper bidiagonal matrix.
    *         This is also the dimension of the main diagonal array D.
    *
    *  SQRE   (input) INTEGER
    *         Specifies the column dimension of the bidiagonal matrix.
    *         = 0: The bidiagonal matrix has column dimension M = N;
    *         = 1: The bidiagonal matrix has column dimension M = N+1;
    *
    *  D      (input/output) DOUBLE PRECISION array, dimension (N)
    *         On entry D contains the main diagonal of the bidiagonal
    *         matrix.
    *         On exit D, if INFO = 0, contains its singular values.
    *
    *  E      (input) DOUBLE PRECISION array, dimension (M-1)
    *         Contains the subdiagonal entries of the bidiagonal matrix.
    *         On exit, E has been destroyed.
    *
    *  U      (output) DOUBLE PRECISION array, dimension at least (LDQ, N)
    *         On exit, U contains the left singular vectors.
    *
    *  LDU    (input) INTEGER
    *         On entry, leading dimension of U.
    *
    *  VT     (output) DOUBLE PRECISION array, dimension at least (LDVT, M)
    *         On exit, VT' contains the right singular vectors.
    *
    *  LDVT   (input) INTEGER
    *         On entry, leading dimension of VT.
    *
    *  SMLSIZ (input) INTEGER
    *         On entry, maximum size of the subproblems at the
    *         bottom of the computation tree.
    *
    *  IWORK  (workspace) INTEGER work array.
    *         Dimension must be at least (8 * N)
    *
    *  WORK   (workspace) DOUBLE PRECISION work array.
    *         Dimension must be at least (3 * M**2 + 2 * M)
    *
    *  INFO   (output) INTEGER
    *          = 0:  successful exit.
    *          < 0:  if INFO = -i, the i-th argument had an illegal value.
    *          > 0:  if INFO = 1, an singular value did not converge
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *     Ming Gu and Huan Ren, Computer Science Division, University of
    *     California at Berkeley, USA
    *
    *  =====================================================================
    *
    *     .. Local Scalars ..
          INTEGER            I, I1, IC, IDXQ, IDXQC, IM1, INODE, ITEMP, IWK,
         $                   J, LF, LL, LVL, M, NCC, ND, NDB1, NDIML, NDIMR,
         $                   NL, NLF, NLP1, NLVL, NR, NRF, NRP1, SQREI
          DOUBLE PRECISION   ALPHA, BETA
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DLASD1, DLASDQ, DLASDT, XERBLA
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
    *
          IF( N.LT.0 ) THEN
             INFO = -1
          ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN
             INFO = -2
          END IF
    *
          M = N + SQRE
    *
          IF( LDU.LT.N ) THEN
             INFO = -6
          ELSE IF( LDVT.LT.M ) THEN
             INFO = -8
          ELSE IF( SMLSIZ.LT.3 ) THEN
             INFO = -9
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DLASD0', -INFO )
             RETURN
          END IF
    *
    *     If the input matrix is too small, call DLASDQ to find the SVD.
    *
          IF( N.LE.SMLSIZ ) THEN
             CALL DLASDQ( 'U', SQRE, N, M, N, 0, D, E, VT, LDVT, U, LDU, U,
         $                LDU, WORK, INFO )
             RETURN
          END IF
    *
    *     Set up the computation tree.
    *
          INODE = 1
          NDIML = INODE + N
          NDIMR = NDIML + N
          IDXQ = NDIMR + N
          IWK = IDXQ + N
          CALL DLASDT( N, NLVL, ND, IWORK( INODE ), IWORK( NDIML ),
         $             IWORK( NDIMR ), SMLSIZ )
    *
    *     For the nodes on bottom level of the tree, solve
    *     their subproblems by DLASDQ.
    *
          NDB1 = ( ND+1 ) / 2
          NCC = 0
          DO 30 I = NDB1, ND
    *
    *     IC : center row of each node
    *     NL : number of rows of left  subproblem
    *     NR : number of rows of right subproblem
    *     NLF: starting row of the left   subproblem
    *     NRF: starting row of the right  subproblem
    *
             I1 = I - 1
             IC = IWORK( INODE+I1 )
             NL = IWORK( NDIML+I1 )
             NLP1 = NL + 1
             NR = IWORK( NDIMR+I1 )
             NRP1 = NR + 1
             NLF = IC - NL
             NRF = IC + 1
             SQREI = 1
             CALL DLASDQ( 'U', SQREI, NL, NLP1, NL, NCC, D( NLF ), E( NLF ),
         $                VT( NLF, NLF ), LDVT, U( NLF, NLF ), LDU,
         $                U( NLF, NLF ), LDU, WORK, INFO )
             IF( INFO.NE.0 ) THEN
                RETURN
             END IF
             ITEMP = IDXQ + NLF - 2
             DO 10 J = 1, NL
                IWORK( ITEMP+J ) = J
       10    CONTINUE
             IF( I.EQ.ND ) THEN
                SQREI = SQRE
             ELSE
                SQREI = 1
             END IF
             NRP1 = NR + SQREI
             CALL DLASDQ( 'U', SQREI, NR, NRP1, NR, NCC, D( NRF ), E( NRF ),
         $                VT( NRF, NRF ), LDVT, U( NRF, NRF ), LDU,
         $                U( NRF, NRF ), LDU, WORK, INFO )
             IF( INFO.NE.0 ) THEN
                RETURN
             END IF
             ITEMP = IDXQ + IC
             DO 20 J = 1, NR
                IWORK( ITEMP+J-1 ) = J
       20    CONTINUE
       30 CONTINUE
    *
    *     Now conquer each subproblem bottom-up.
    *
          DO 50 LVL = NLVL, 1, -1
    *
    *        Find the first node LF and last node LL on the
    *        current level LVL.
    *
             IF( LVL.EQ.1 ) THEN
                LF = 1
                LL = 1
             ELSE
                LF = 2**( LVL-1 )
                LL = 2*LF - 1
             END IF
             DO 40 I = LF, LL
                IM1 = I - 1
                IC = IWORK( INODE+IM1 )
                NL = IWORK( NDIML+IM1 )
                NR = IWORK( NDIMR+IM1 )
                NLF = IC - NL
                IF( ( SQRE.EQ.0 ) .AND. ( I.EQ.LL ) ) THEN
                   SQREI = SQRE
                ELSE
                   SQREI = 1
                END IF
                IDXQC = IDXQ + NLF - 1
                ALPHA = D( IC )
                BETA = E( IC )
                CALL DLASD1( NL, NR, SQREI, D( NLF ), ALPHA, BETA,
         $                   U( NLF, NLF ), LDU, VT( NLF, NLF ), LDVT,
         $                   IWORK( IDXQC ), IWORK( IWK ), WORK, INFO )
                IF( INFO.NE.0 ) THEN
                   RETURN
                END IF
       40    CONTINUE
       50 CONTINUE
    *
          RETURN
    *
    *     End of DLASD0
    *
          END