          SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT,
         $                   WORK, LWORK, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBU, JOBVT
          INTEGER            INFO, LDA, LDU, LDVT, LWORK, M, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   A( LDA, * ), S( * ), U( LDU, * ),
         $                   VT( LDVT, * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DGESVD computes the singular value decomposition (SVD) of a real
    *  M-by-N matrix A, optionally computing the left and/or right singular
    *  vectors. The SVD is written
    *
    *       A = U * SIGMA * transpose(V)
    *
    *  where SIGMA is an M-by-N matrix which is zero except for its
    *  min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
    *  V is an N-by-N orthogonal matrix.  The diagonal elements of SIGMA
    *  are the singular values of A; they are real and non-negative, and
    *  are returned in descending order.  The first min(m,n) columns of
    *  U and V are the left and right singular vectors of A.
    *
    *  Note that the routine returns V**T, not V.
    *
    *  Arguments
    *  =========
    *
    *  JOBU    (input) CHARACTER*1
    *          Specifies options for computing all or part of the matrix U:
    *          = 'A':  all M columns of U are returned in array U:
    *          = 'S':  the first min(m,n) columns of U (the left singular
    *                  vectors) are returned in the array U;
    *          = 'O':  the first min(m,n) columns of U (the left singular
    *                  vectors) are overwritten on the array A;
    *          = 'N':  no columns of U (no left singular vectors) are
    *                  computed.
    *
    *  JOBVT   (input) CHARACTER*1
    *          Specifies options for computing all or part of the matrix
    *          V**T:
    *          = 'A':  all N rows of V**T are returned in the array VT;
    *          = 'S':  the first min(m,n) rows of V**T (the right singular
    *                  vectors) are returned in the array VT;
    *          = 'O':  the first min(m,n) rows of V**T (the right singular
    *                  vectors) are overwritten on the array A;
    *          = 'N':  no rows of V**T (no right singular vectors) are
    *                  computed.
    *
    *          JOBVT and JOBU cannot both be 'O'.
    *
    *  M       (input) INTEGER
    *          The number of rows of the input matrix A.  M >= 0.
    *
    *  N       (input) INTEGER
    *          The number of columns of the input matrix A.  N >= 0.
    *
    *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
    *          On entry, the M-by-N matrix A.
    *          On exit,
    *          if JOBU = 'O',  A is overwritten with the first min(m,n)
    *                          columns of U (the left singular vectors,
    *                          stored columnwise);
    *          if JOBVT = 'O', A is overwritten with the first min(m,n)
    *                          rows of V**T (the right singular vectors,
    *                          stored rowwise);
    *          if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A
    *                          are destroyed.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,M).
    *
    *  S       (output) DOUBLE PRECISION array, dimension (min(M,N))
    *          The singular values of A, sorted so that S(i) >= S(i+1).
    *
    *  U       (output) DOUBLE PRECISION array, dimension (LDU,UCOL)
    *          (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'.
    *          If JOBU = 'A', U contains the M-by-M orthogonal matrix U;
    *          if JOBU = 'S', U contains the first min(m,n) columns of U
    *          (the left singular vectors, stored columnwise);
    *          if JOBU = 'N' or 'O', U is not referenced.
    *
    *  LDU     (input) INTEGER
    *          The leading dimension of the array U.  LDU >= 1; if
    *          JOBU = 'S' or 'A', LDU >= M.
    *
    *  VT      (output) DOUBLE PRECISION array, dimension (LDVT,N)
    *          If JOBVT = 'A', VT contains the N-by-N orthogonal matrix
    *          V**T;
    *          if JOBVT = 'S', VT contains the first min(m,n) rows of
    *          V**T (the right singular vectors, stored rowwise);
    *          if JOBVT = 'N' or 'O', VT is not referenced.
    *
    *  LDVT    (input) INTEGER
    *          The leading dimension of the array VT.  LDVT >= 1; if
    *          JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).
    *
    *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK;
    *          if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged
    *          superdiagonal elements of an upper bidiagonal matrix B
    *          whose diagonal is in S (not necessarily sorted). B
    *          satisfies A = U * B * VT, so it has the same singular values
    *          as A, and singular vectors related by U and VT.
    *
    *  LWORK   (input) INTEGER
    *          The dimension of the array WORK.
    *          LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)).
    *          For good performance, LWORK should generally be larger.
    *
    *          If LWORK = -1, then a workspace query is assumed; the routine
    *          only calculates the optimal size of the WORK array, returns
    *          this value as the first entry of the WORK array, and no error
    *          message related to LWORK is issued by XERBLA.
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit.
    *          < 0:  if INFO = -i, the i-th argument had an illegal value.
    *          > 0:  if DBDSQR did not converge, INFO specifies how many
    *                superdiagonals of an intermediate bidiagonal form B
    *                did not converge to zero. See the description of WORK
    *                above for details.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ZERO, ONE
          PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            LQUERY, WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS,
         $                   WNTVA, WNTVAS, WNTVN, WNTVO, WNTVS
          INTEGER            BDSPAC, BLK, CHUNK, I, IE, IERR, IR, ISCL,
         $                   ITAU, ITAUP, ITAUQ, IU, IWORK, LDWRKR, LDWRKU,
         $                   MAXWRK, MINMN, MINWRK, MNTHR, NCU, NCVT, NRU,
         $                   NRVT, WRKBL
          DOUBLE PRECISION   ANRM, BIGNUM, EPS, SMLNUM
    *     ..
    *     .. Local Arrays ..
          DOUBLE PRECISION   DUM( 1 )
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DBDSQR, DGEBRD, DGELQF, DGEMM, DGEQRF, DLACPY,
         $                   DLASCL, DLASET, DORGBR, DORGLQ, DORGQR, DORMBR,
         $                   XERBLA
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          DOUBLE PRECISION   DLAMCH, DLANGE
          EXTERNAL           LSAME, ILAENV, DLAMCH, DLANGE
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN, SQRT
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input arguments
    *
          INFO = 0
          MINMN = MIN( M, N )
          WNTUA = LSAME( JOBU, 'A' )
          WNTUS = LSAME( JOBU, 'S' )
          WNTUAS = WNTUA .OR. WNTUS
          WNTUO = LSAME( JOBU, 'O' )
          WNTUN = LSAME( JOBU, 'N' )
          WNTVA = LSAME( JOBVT, 'A' )
          WNTVS = LSAME( JOBVT, 'S' )
          WNTVAS = WNTVA .OR. WNTVS
          WNTVO = LSAME( JOBVT, 'O' )
          WNTVN = LSAME( JOBVT, 'N' )
          LQUERY = ( LWORK.EQ.-1 )
    *
          IF( .NOT.( WNTUA .OR. WNTUS .OR. WNTUO .OR. WNTUN ) ) THEN
             INFO = -1
          ELSE IF( .NOT.( WNTVA .OR. WNTVS .OR. WNTVO .OR. WNTVN ) .OR.
         $         ( WNTVO .AND. WNTUO ) ) THEN
             INFO = -2
          ELSE IF( M.LT.0 ) THEN
             INFO = -3
          ELSE IF( N.LT.0 ) THEN
             INFO = -4
          ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
             INFO = -6
          ELSE IF( LDU.LT.1 .OR. ( WNTUAS .AND. LDU.LT.M ) ) THEN
             INFO = -9
          ELSE IF( LDVT.LT.1 .OR. ( WNTVA .AND. LDVT.LT.N ) .OR.
         $         ( WNTVS .AND. LDVT.LT.MINMN ) ) THEN
             INFO = -11
          END IF
    *
    *     Compute workspace
    *      (Note: Comments in the code beginning "Workspace:" describe the
    *       minimal amount of workspace needed at that point in the code,
    *       as well as the preferred amount for good performance.
    *       NB refers to the optimal block size for the immediately
    *       following subroutine, as returned by ILAENV.)
    *
          IF( INFO.EQ.0 ) THEN
             MINWRK = 1
             MAXWRK = 1
             IF( M.GE.N .AND. MINMN.GT.0 ) THEN
    *
    *           Compute space needed for DBDSQR
    *
                MNTHR = ILAENV( 6, 'DGESVD', JOBU // JOBVT, M, N, 0, 0 )
                BDSPAC = 5*N
                IF( M.GE.MNTHR ) THEN
                   IF( WNTUN ) THEN
    *
    *                 Path 1 (M much larger than N, JOBU='N')
    *
                      MAXWRK = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1,
         $                     -1 )
                      MAXWRK = MAX( MAXWRK, 3*N+2*N*
         $                     ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
                      IF( WNTVO .OR. WNTVAS )
         $               MAXWRK = MAX( MAXWRK, 3*N+( N-1 )*
         $                        ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) )
                      MAXWRK = MAX( MAXWRK, BDSPAC )
                      MINWRK = MAX( 4*N, BDSPAC )
                   ELSE IF( WNTUO .AND. WNTVN ) THEN
    *
    *                 Path 2 (M much larger than N, JOBU='O', JOBVT='N')
    *
                      WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M,
         $                    N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+2*N*
         $                    ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+N*
         $                    ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = MAX( N*N+WRKBL, N*N+M*N+N )
                      MINWRK = MAX( 3*N+M, BDSPAC )
                   ELSE IF( WNTUO .AND. WNTVAS ) THEN
    *
    *                 Path 3 (M much larger than N, JOBU='O', JOBVT='S' or
    *                 'A')
    *
                      WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M,
         $                    N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+2*N*
         $                    ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+N*
         $                    ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+( N-1 )*
         $                    ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = MAX( N*N+WRKBL, N*N+M*N+N )
                      MINWRK = MAX( 3*N+M, BDSPAC )
                   ELSE IF( WNTUS .AND. WNTVN ) THEN
    *
    *                 Path 4 (M much larger than N, JOBU='S', JOBVT='N')
    *
                      WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M,
         $                    N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+2*N*
         $                    ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+N*
         $                    ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = N*N + WRKBL
                      MINWRK = MAX( 3*N+M, BDSPAC )
                   ELSE IF( WNTUS .AND. WNTVO ) THEN
    *
    *                 Path 5 (M much larger than N, JOBU='S', JOBVT='O')
    *
                      WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M,
         $                    N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+2*N*
         $                    ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+N*
         $                    ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+( N-1 )*
         $                    ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = 2*N*N + WRKBL
                      MINWRK = MAX( 3*N+M, BDSPAC )
                   ELSE IF( WNTUS .AND. WNTVAS ) THEN
    *
    *                 Path 6 (M much larger than N, JOBU='S', JOBVT='S' or
    *                 'A')
    *
                      WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'DORGQR', ' ', M,
         $                    N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+2*N*
         $                    ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+N*
         $                    ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+( N-1 )*
         $                    ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = N*N + WRKBL
                      MINWRK = MAX( 3*N+M, BDSPAC )
                   ELSE IF( WNTUA .AND. WNTVN ) THEN
    *
    *                 Path 7 (M much larger than N, JOBU='A', JOBVT='N')
    *
                      WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'DORGQR', ' ', M,
         $                    M, N, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+2*N*
         $                    ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+N*
         $                    ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = N*N + WRKBL
                      MINWRK = MAX( 3*N+M, BDSPAC )
                   ELSE IF( WNTUA .AND. WNTVO ) THEN
    *
    *                 Path 8 (M much larger than N, JOBU='A', JOBVT='O')
    *
                      WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'DORGQR', ' ', M,
         $                    M, N, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+2*N*
         $                    ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+N*
         $                    ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+( N-1 )*
         $                    ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = 2*N*N + WRKBL
                      MINWRK = MAX( 3*N+M, BDSPAC )
                   ELSE IF( WNTUA .AND. WNTVAS ) THEN
    *
    *                 Path 9 (M much larger than N, JOBU='A', JOBVT='S' or
    *                 'A')
    *
                      WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'DORGQR', ' ', M,
         $                    M, N, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+2*N*
         $                    ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+N*
         $                    ILAENV( 1, 'DORGBR', 'Q', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 3*N+( N-1 )*
         $                    ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = N*N + WRKBL
                      MINWRK = MAX( 3*N+M, BDSPAC )
                   END IF
                ELSE
    *
    *              Path 10 (M at least N, but not much larger)
    *
                   MAXWRK = 3*N + ( M+N )*ILAENV( 1, 'DGEBRD', ' ', M, N,
         $                  -1, -1 )
                   IF( WNTUS .OR. WNTUO )
         $            MAXWRK = MAX( MAXWRK, 3*N+N*
         $                     ILAENV( 1, 'DORGBR', 'Q', M, N, N, -1 ) )
                   IF( WNTUA )
         $            MAXWRK = MAX( MAXWRK, 3*N+M*
         $                     ILAENV( 1, 'DORGBR', 'Q', M, M, N, -1 ) )
                   IF( .NOT.WNTVN )
         $            MAXWRK = MAX( MAXWRK, 3*N+( N-1 )*
         $                     ILAENV( 1, 'DORGBR', 'P', N, N, N, -1 ) )
                   MAXWRK = MAX( MAXWRK, BDSPAC )
                   MINWRK = MAX( 3*N+M, BDSPAC )
                END IF
             ELSE IF( MINMN.GT.0 ) THEN
    *
    *           Compute space needed for DBDSQR
    *
                MNTHR = ILAENV( 6, 'DGESVD', JOBU // JOBVT, M, N, 0, 0 )
                BDSPAC = 5*M
                IF( N.GE.MNTHR ) THEN
                   IF( WNTVN ) THEN
    *
    *                 Path 1t(N much larger than M, JOBVT='N')
    *
                      MAXWRK = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1,
         $                     -1 )
                      MAXWRK = MAX( MAXWRK, 3*M+2*M*
         $                     ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
                      IF( WNTUO .OR. WNTUAS )
         $               MAXWRK = MAX( MAXWRK, 3*M+M*
         $                        ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
                      MAXWRK = MAX( MAXWRK, BDSPAC )
                      MINWRK = MAX( 4*M, BDSPAC )
                   ELSE IF( WNTVO .AND. WNTUN ) THEN
    *
    *                 Path 2t(N much larger than M, JOBU='N', JOBVT='O')
    *
                      WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M,
         $                    N, M, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+2*M*
         $                    ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+( M-1 )*
         $                    ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = MAX( M*M+WRKBL, M*M+M*N+M )
                      MINWRK = MAX( 3*M+N, BDSPAC )
                   ELSE IF( WNTVO .AND. WNTUAS ) THEN
    *
    *                 Path 3t(N much larger than M, JOBU='S' or 'A',
    *                 JOBVT='O')
    *
                      WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M,
         $                    N, M, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+2*M*
         $                    ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+( M-1 )*
         $                    ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+M*
         $                    ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = MAX( M*M+WRKBL, M*M+M*N+M )
                      MINWRK = MAX( 3*M+N, BDSPAC )
                   ELSE IF( WNTVS .AND. WNTUN ) THEN
    *
    *                 Path 4t(N much larger than M, JOBU='N', JOBVT='S')
    *
                      WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M,
         $                    N, M, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+2*M*
         $                    ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+( M-1 )*
         $                    ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = M*M + WRKBL
                      MINWRK = MAX( 3*M+N, BDSPAC )
                   ELSE IF( WNTVS .AND. WNTUO ) THEN
    *
    *                 Path 5t(N much larger than M, JOBU='O', JOBVT='S')
    *
                      WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M,
         $                    N, M, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+2*M*
         $                    ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+( M-1 )*
         $                    ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+M*
         $                    ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = 2*M*M + WRKBL
                      MINWRK = MAX( 3*M+N, BDSPAC )
                   ELSE IF( WNTVS .AND. WNTUAS ) THEN
    *
    *                 Path 6t(N much larger than M, JOBU='S' or 'A',
    *                 JOBVT='S')
    *
                      WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'DORGLQ', ' ', M,
         $                    N, M, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+2*M*
         $                    ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+( M-1 )*
         $                    ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+M*
         $                    ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = M*M + WRKBL
                      MINWRK = MAX( 3*M+N, BDSPAC )
                   ELSE IF( WNTVA .AND. WNTUN ) THEN
    *
    *                 Path 7t(N much larger than M, JOBU='N', JOBVT='A')
    *
                      WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'DORGLQ', ' ', N,
         $                    N, M, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+2*M*
         $                    ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+( M-1 )*
         $                    ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = M*M + WRKBL
                      MINWRK = MAX( 3*M+N, BDSPAC )
                   ELSE IF( WNTVA .AND. WNTUO ) THEN
    *
    *                 Path 8t(N much larger than M, JOBU='O', JOBVT='A')
    *
                      WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'DORGLQ', ' ', N,
         $                    N, M, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+2*M*
         $                    ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+( M-1 )*
         $                    ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+M*
         $                    ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = 2*M*M + WRKBL
                      MINWRK = MAX( 3*M+N, BDSPAC )
                   ELSE IF( WNTVA .AND. WNTUAS ) THEN
    *
    *                 Path 9t(N much larger than M, JOBU='S' or 'A',
    *                 JOBVT='A')
    *
                      WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'DORGLQ', ' ', N,
         $                    N, M, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+2*M*
         $                    ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+( M-1 )*
         $                    ILAENV( 1, 'DORGBR', 'P', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, 3*M+M*
         $                    ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, BDSPAC )
                      MAXWRK = M*M + WRKBL
                      MINWRK = MAX( 3*M+N, BDSPAC )
                   END IF
                ELSE
    *
    *              Path 10t(N greater than M, but not much larger)
    *
                   MAXWRK = 3*M + ( M+N )*ILAENV( 1, 'DGEBRD', ' ', M, N,
         $                  -1, -1 )
                   IF( WNTVS .OR. WNTVO )
         $            MAXWRK = MAX( MAXWRK, 3*M+M*
         $                     ILAENV( 1, 'DORGBR', 'P', M, N, M, -1 ) )
                   IF( WNTVA )
         $            MAXWRK = MAX( MAXWRK, 3*M+N*
         $                     ILAENV( 1, 'DORGBR', 'P', N, N, M, -1 ) )
                   IF( .NOT.WNTUN )
         $            MAXWRK = MAX( MAXWRK, 3*M+( M-1 )*
         $                     ILAENV( 1, 'DORGBR', 'Q', M, M, M, -1 ) )
                   MAXWRK = MAX( MAXWRK, BDSPAC )
                   MINWRK = MAX( 3*M+N, BDSPAC )
                END IF
             END IF
             MAXWRK = MAX( MAXWRK, MINWRK )
             WORK( 1 ) = MAXWRK
    *
             IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
                INFO = -13
             END IF
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DGESVD', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( M.EQ.0 .OR. N.EQ.0 ) THEN
             RETURN
          END IF
    *
    *     Get machine constants
    *
          EPS = DLAMCH( 'P' )
          SMLNUM = SQRT( DLAMCH( 'S' ) ) / EPS
          BIGNUM = ONE / SMLNUM
    *
    *     Scale A if max element outside range [SMLNUM,BIGNUM]
    *
          ANRM = DLANGE( 'M', M, N, A, LDA, DUM )
          ISCL = 0
          IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
             ISCL = 1
             CALL DLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, IERR )
          ELSE IF( ANRM.GT.BIGNUM ) THEN
             ISCL = 1
             CALL DLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, IERR )
          END IF
    *
          IF( M.GE.N ) THEN
    *
    *        A has at least as many rows as columns. If A has sufficiently
    *        more rows than columns, first reduce using the QR
    *        decomposition (if sufficient workspace available)
    *
             IF( M.GE.MNTHR ) THEN
    *
                IF( WNTUN ) THEN
    *
    *              Path 1 (M much larger than N, JOBU='N')
    *              No left singular vectors to be computed
    *
                   ITAU = 1
                   IWORK = ITAU + N
    *
    *              Compute A=Q*R
    *              (Workspace: need 2*N, prefer N+N*NB)
    *
                   CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ),
         $                      LWORK-IWORK+1, IERR )
    *
    *              Zero out below R
    *
                   CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ), LDA )
                   IE = 1
                   ITAUQ = IE + N
                   ITAUP = ITAUQ + N
                   IWORK = ITAUP + N
    *
    *              Bidiagonalize R in A
    *              (Workspace: need 4*N, prefer 3*N+2*N*NB)
    *
                   CALL DGEBRD( N, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
         $                      WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
         $                      IERR )
                   NCVT = 0
                   IF( WNTVO .OR. WNTVAS ) THEN
    *
    *                 If right singular vectors desired, generate P'.
    *                 (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
    *
                      CALL DORGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      NCVT = N
                   END IF
                   IWORK = IE + N
    *
    *              Perform bidiagonal QR iteration, computing right
    *              singular vectors of A in A if desired
    *              (Workspace: need BDSPAC)
    *
                   CALL DBDSQR( 'U', N, NCVT, 0, 0, S, WORK( IE ), A, LDA,
         $                      DUM, 1, DUM, 1, WORK( IWORK ), INFO )
    *
    *              If right singular vectors desired in VT, copy them there
    *
                   IF( WNTVAS )
         $            CALL DLACPY( 'F', N, N, A, LDA, VT, LDVT )
    *
                ELSE IF( WNTUO .AND. WNTVN ) THEN
    *
    *              Path 2 (M much larger than N, JOBU='O', JOBVT='N')
    *              N left singular vectors to be overwritten on A and
    *              no right singular vectors to be computed
    *
                   IF( LWORK.GE.N*N+MAX( 4*N, BDSPAC ) ) THEN
    *
    *                 Sufficient workspace for a fast algorithm
    *
                      IR = 1
                      IF( LWORK.GE.MAX( WRKBL, LDA*N+N )+LDA*N ) THEN
    *
    *                    WORK(IU) is LDA by N, WORK(IR) is LDA by N
    *
                         LDWRKU = LDA
                         LDWRKR = LDA
                      ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N+N )+N*N ) THEN
    *
    *                    WORK(IU) is LDA by N, WORK(IR) is N by N
    *
                         LDWRKU = LDA
                         LDWRKR = N
                      ELSE
    *
    *                    WORK(IU) is LDWRKU by N, WORK(IR) is N by N
    *
                         LDWRKU = ( LWORK-N*N-N ) / N
                         LDWRKR = N
                      END IF
                      ITAU = IR + LDWRKR*N
                      IWORK = ITAU + N
    *
    *                 Compute A=Q*R
    *                 (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
    *
                      CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                 Copy R to WORK(IR) and zero out below it
    *
                      CALL DLACPY( 'U', N, N, A, LDA, WORK( IR ), LDWRKR )
                      CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, WORK( IR+1 ),
         $                         LDWRKR )
    *
    *                 Generate Q in A
    *                 (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
    *
                      CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      IE = ITAU
                      ITAUQ = IE + N
                      ITAUP = ITAUQ + N
                      IWORK = ITAUP + N
    *
    *                 Bidiagonalize R in WORK(IR)
    *                 (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB)
    *
                      CALL DGEBRD( N, N, WORK( IR ), LDWRKR, S, WORK( IE ),
         $                         WORK( ITAUQ ), WORK( ITAUP ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                 Generate left vectors bidiagonalizing R
    *                 (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB)
    *
                      CALL DORGBR( 'Q', N, N, N, WORK( IR ), LDWRKR,
         $                         WORK( ITAUQ ), WORK( IWORK ),
         $                         LWORK-IWORK+1, IERR )
                      IWORK = IE + N
    *
    *                 Perform bidiagonal QR iteration, computing left
    *                 singular vectors of R in WORK(IR)
    *                 (Workspace: need N*N+BDSPAC)
    *
                      CALL DBDSQR( 'U', N, 0, N, 0, S, WORK( IE ), DUM, 1,
         $                         WORK( IR ), LDWRKR, DUM, 1,
         $                         WORK( IWORK ), INFO )
                      IU = IE + N
    *
    *                 Multiply Q in A by left singular vectors of R in
    *                 WORK(IR), storing result in WORK(IU) and copying to A
    *                 (Workspace: need N*N+2*N, prefer N*N+M*N+N)
    *
                      DO 10 I = 1, M, LDWRKU
                         CHUNK = MIN( M-I+1, LDWRKU )
                         CALL DGEMM( 'N', 'N', CHUNK, N, N, ONE, A( I, 1 ),
         $                           LDA, WORK( IR ), LDWRKR, ZERO,
         $                           WORK( IU ), LDWRKU )
                         CALL DLACPY( 'F', CHUNK, N, WORK( IU ), LDWRKU,
         $                            A( I, 1 ), LDA )
       10             CONTINUE
    *
                   ELSE
    *
    *                 Insufficient workspace for a fast algorithm
    *
                      IE = 1
                      ITAUQ = IE + N
                      ITAUP = ITAUQ + N
                      IWORK = ITAUP + N
    *
    *                 Bidiagonalize A
    *                 (Workspace: need 3*N+M, prefer 3*N+(M+N)*NB)
    *
                      CALL DGEBRD( M, N, A, LDA, S, WORK( IE ),
         $                         WORK( ITAUQ ), WORK( ITAUP ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                 Generate left vectors bidiagonalizing A
    *                 (Workspace: need 4*N, prefer 3*N+N*NB)
    *
                      CALL DORGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      IWORK = IE + N
    *
    *                 Perform bidiagonal QR iteration, computing left
    *                 singular vectors of A in A
    *                 (Workspace: need BDSPAC)
    *
                      CALL DBDSQR( 'U', N, 0, M, 0, S, WORK( IE ), DUM, 1,
         $                         A, LDA, DUM, 1, WORK( IWORK ), INFO )
    *
                   END IF
    *
                ELSE IF( WNTUO .AND. WNTVAS ) THEN
    *
    *              Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A')
    *              N left singular vectors to be overwritten on A and
    *              N right singular vectors to be computed in VT
    *
                   IF( LWORK.GE.N*N+MAX( 4*N, BDSPAC ) ) THEN
    *
    *                 Sufficient workspace for a fast algorithm
    *
                      IR = 1
                      IF( LWORK.GE.MAX( WRKBL, LDA*N+N )+LDA*N ) THEN
    *
    *                    WORK(IU) is LDA by N and WORK(IR) is LDA by N
    *
                         LDWRKU = LDA
                         LDWRKR = LDA
                      ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N+N )+N*N ) THEN
    *
    *                    WORK(IU) is LDA by N and WORK(IR) is N by N
    *
                         LDWRKU = LDA
                         LDWRKR = N
                      ELSE
    *
    *                    WORK(IU) is LDWRKU by N and WORK(IR) is N by N
    *
                         LDWRKU = ( LWORK-N*N-N ) / N
                         LDWRKR = N
                      END IF
                      ITAU = IR + LDWRKR*N
                      IWORK = ITAU + N
    *
    *                 Compute A=Q*R
    *                 (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
    *
                      CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                 Copy R to VT, zeroing out below it
    *
                      CALL DLACPY( 'U', N, N, A, LDA, VT, LDVT )
                      IF( N.GT.1 )
         $               CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
         $                            VT( 2, 1 ), LDVT )
    *
    *                 Generate Q in A
    *                 (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
    *
                      CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      IE = ITAU
                      ITAUQ = IE + N
                      ITAUP = ITAUQ + N
                      IWORK = ITAUP + N
    *
    *                 Bidiagonalize R in VT, copying result to WORK(IR)
    *                 (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB)
    *
                      CALL DGEBRD( N, N, VT, LDVT, S, WORK( IE ),
         $                         WORK( ITAUQ ), WORK( ITAUP ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      CALL DLACPY( 'L', N, N, VT, LDVT, WORK( IR ), LDWRKR )
    *
    *                 Generate left vectors bidiagonalizing R in WORK(IR)
    *                 (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB)
    *
                      CALL DORGBR( 'Q', N, N, N, WORK( IR ), LDWRKR,
         $                         WORK( ITAUQ ), WORK( IWORK ),
         $                         LWORK-IWORK+1, IERR )
    *
    *                 Generate right vectors bidiagonalizing R in VT
    *                 (Workspace: need N*N+4*N-1, prefer N*N+3*N+(N-1)*NB)
    *
                      CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      IWORK = IE + N
    *
    *                 Perform bidiagonal QR iteration, computing left
    *                 singular vectors of R in WORK(IR) and computing right
    *                 singular vectors of R in VT
    *                 (Workspace: need N*N+BDSPAC)
    *
                      CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ), VT, LDVT,
         $                         WORK( IR ), LDWRKR, DUM, 1,
         $                         WORK( IWORK ), INFO )
                      IU = IE + N
    *
    *                 Multiply Q in A by left singular vectors of R in
    *                 WORK(IR), storing result in WORK(IU) and copying to A
    *                 (Workspace: need N*N+2*N, prefer N*N+M*N+N)
    *
                      DO 20 I = 1, M, LDWRKU
                         CHUNK = MIN( M-I+1, LDWRKU )
                         CALL DGEMM( 'N', 'N', CHUNK, N, N, ONE, A( I, 1 ),
         $                           LDA, WORK( IR ), LDWRKR, ZERO,
         $                           WORK( IU ), LDWRKU )
                         CALL DLACPY( 'F', CHUNK, N, WORK( IU ), LDWRKU,
         $                            A( I, 1 ), LDA )
       20             CONTINUE
    *
                   ELSE
    *
    *                 Insufficient workspace for a fast algorithm
    *
                      ITAU = 1
                      IWORK = ITAU + N
    *
    *                 Compute A=Q*R
    *                 (Workspace: need 2*N, prefer N+N*NB)
    *
                      CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                 Copy R to VT, zeroing out below it
    *
                      CALL DLACPY( 'U', N, N, A, LDA, VT, LDVT )
                      IF( N.GT.1 )
         $               CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
         $                            VT( 2, 1 ), LDVT )
    *
    *                 Generate Q in A
    *                 (Workspace: need 2*N, prefer N+N*NB)
    *
                      CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      IE = ITAU
                      ITAUQ = IE + N
                      ITAUP = ITAUQ + N
                      IWORK = ITAUP + N
    *
    *                 Bidiagonalize R in VT
    *                 (Workspace: need 4*N, prefer 3*N+2*N*NB)
    *
                      CALL DGEBRD( N, N, VT, LDVT, S, WORK( IE ),
         $                         WORK( ITAUQ ), WORK( ITAUP ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                 Multiply Q in A by left vectors bidiagonalizing R
    *                 (Workspace: need 3*N+M, prefer 3*N+M*NB)
    *
                      CALL DORMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT,
         $                         WORK( ITAUQ ), A, LDA, WORK( IWORK ),
         $                         LWORK-IWORK+1, IERR )
    *
    *                 Generate right vectors bidiagonalizing R in VT
    *                 (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
    *
                      CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      IWORK = IE + N
    *
    *                 Perform bidiagonal QR iteration, computing left
    *                 singular vectors of A in A and computing right
    *                 singular vectors of A in VT
    *                 (Workspace: need BDSPAC)
    *
                      CALL DBDSQR( 'U', N, N, M, 0, S, WORK( IE ), VT, LDVT,
         $                         A, LDA, DUM, 1, WORK( IWORK ), INFO )
    *
                   END IF
    *
                ELSE IF( WNTUS ) THEN
    *
                   IF( WNTVN ) THEN
    *
    *                 Path 4 (M much larger than N, JOBU='S', JOBVT='N')
    *                 N left singular vectors to be computed in U and
    *                 no right singular vectors to be computed
    *
                      IF( LWORK.GE.N*N+MAX( 4*N, BDSPAC ) ) THEN
    *
    *                    Sufficient workspace for a fast algorithm
    *
                         IR = 1
                         IF( LWORK.GE.WRKBL+LDA*N ) THEN
    *
    *                       WORK(IR) is LDA by N
    *
                            LDWRKR = LDA
                         ELSE
    *
    *                       WORK(IR) is N by N
    *
                            LDWRKR = N
                         END IF
                         ITAU = IR + LDWRKR*N
                         IWORK = ITAU + N
    *
    *                    Compute A=Q*R
    *                    (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
    *
                         CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy R to WORK(IR), zeroing out below it
    *
                         CALL DLACPY( 'U', N, N, A, LDA, WORK( IR ),
         $                            LDWRKR )
                         CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
         $                            WORK( IR+1 ), LDWRKR )
    *
    *                    Generate Q in A
    *                    (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
    *
                         CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + N
                         ITAUP = ITAUQ + N
                         IWORK = ITAUP + N
    *
    *                    Bidiagonalize R in WORK(IR)
    *                    (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB)
    *
                         CALL DGEBRD( N, N, WORK( IR ), LDWRKR, S,
         $                            WORK( IE ), WORK( ITAUQ ),
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate left vectors bidiagonalizing R in WORK(IR)
    *                    (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB)
    *
                         CALL DORGBR( 'Q', N, N, N, WORK( IR ), LDWRKR,
         $                            WORK( ITAUQ ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         IWORK = IE + N
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of R in WORK(IR)
    *                    (Workspace: need N*N+BDSPAC)
    *
                         CALL DBDSQR( 'U', N, 0, N, 0, S, WORK( IE ), DUM,
         $                            1, WORK( IR ), LDWRKR, DUM, 1,
         $                            WORK( IWORK ), INFO )
    *
    *                    Multiply Q in A by left singular vectors of R in
    *                    WORK(IR), storing result in U
    *                    (Workspace: need N*N)
    *
                         CALL DGEMM( 'N', 'N', M, N, N, ONE, A, LDA,
         $                           WORK( IR ), LDWRKR, ZERO, U, LDU )
    *
                      ELSE
    *
    *                    Insufficient workspace for a fast algorithm
    *
                         ITAU = 1
                         IWORK = ITAU + N
    *
    *                    Compute A=Q*R, copying result to U
    *                    (Workspace: need 2*N, prefer N+N*NB)
    *
                         CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
    *
    *                    Generate Q in U
    *                    (Workspace: need 2*N, prefer N+N*NB)
    *
                         CALL DORGQR( M, N, N, U, LDU, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + N
                         ITAUP = ITAUQ + N
                         IWORK = ITAUP + N
    *
    *                    Zero out below R in A
    *
                         CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ),
         $                            LDA )
    *
    *                    Bidiagonalize R in A
    *                    (Workspace: need 4*N, prefer 3*N+2*N*NB)
    *
                         CALL DGEBRD( N, N, A, LDA, S, WORK( IE ),
         $                            WORK( ITAUQ ), WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Multiply Q in U by left vectors bidiagonalizing R
    *                    (Workspace: need 3*N+M, prefer 3*N+M*NB)
    *
                         CALL DORMBR( 'Q', 'R', 'N', M, N, N, A, LDA,
         $                            WORK( ITAUQ ), U, LDU, WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         IWORK = IE + N
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of A in U
    *                    (Workspace: need BDSPAC)
    *
                         CALL DBDSQR( 'U', N, 0, M, 0, S, WORK( IE ), DUM,
         $                            1, U, LDU, DUM, 1, WORK( IWORK ),
         $                            INFO )
    *
                      END IF
    *
                   ELSE IF( WNTVO ) THEN
    *
    *                 Path 5 (M much larger than N, JOBU='S', JOBVT='O')
    *                 N left singular vectors to be computed in U and
    *                 N right singular vectors to be overwritten on A
    *
                      IF( LWORK.GE.2*N*N+MAX( 4*N, BDSPAC ) ) THEN
    *
    *                    Sufficient workspace for a fast algorithm
    *
                         IU = 1
                         IF( LWORK.GE.WRKBL+2*LDA*N ) THEN
    *
    *                       WORK(IU) is LDA by N and WORK(IR) is LDA by N
    *
                            LDWRKU = LDA
                            IR = IU + LDWRKU*N
                            LDWRKR = LDA
                         ELSE IF( LWORK.GE.WRKBL+( LDA+N )*N ) THEN
    *
    *                       WORK(IU) is LDA by N and WORK(IR) is N by N
    *
                            LDWRKU = LDA
                            IR = IU + LDWRKU*N
                            LDWRKR = N
                         ELSE
    *
    *                       WORK(IU) is N by N and WORK(IR) is N by N
    *
                            LDWRKU = N
                            IR = IU + LDWRKU*N
                            LDWRKR = N
                         END IF
                         ITAU = IR + LDWRKR*N
                         IWORK = ITAU + N
    *
    *                    Compute A=Q*R
    *                    (Workspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB)
    *
                         CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy R to WORK(IU), zeroing out below it
    *
                         CALL DLACPY( 'U', N, N, A, LDA, WORK( IU ),
         $                            LDWRKU )
                         CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
         $                            WORK( IU+1 ), LDWRKU )
    *
    *                    Generate Q in A
    *                    (Workspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB)
    *
                         CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + N
                         ITAUP = ITAUQ + N
                         IWORK = ITAUP + N
    *
    *                    Bidiagonalize R in WORK(IU), copying result to
    *                    WORK(IR)
    *                    (Workspace: need 2*N*N+4*N,
    *                                prefer 2*N*N+3*N+2*N*NB)
    *
                         CALL DGEBRD( N, N, WORK( IU ), LDWRKU, S,
         $                            WORK( IE ), WORK( ITAUQ ),
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'U', N, N, WORK( IU ), LDWRKU,
         $                            WORK( IR ), LDWRKR )
    *
    *                    Generate left bidiagonalizing vectors in WORK(IU)
    *                    (Workspace: need 2*N*N+4*N, prefer 2*N*N+3*N+N*NB)
    *
                         CALL DORGBR( 'Q', N, N, N, WORK( IU ), LDWRKU,
         $                            WORK( ITAUQ ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate right bidiagonalizing vectors in WORK(IR)
    *                    (Workspace: need 2*N*N+4*N-1,
    *                                prefer 2*N*N+3*N+(N-1)*NB)
    *
                         CALL DORGBR( 'P', N, N, N, WORK( IR ), LDWRKR,
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         IWORK = IE + N
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of R in WORK(IU) and computing
    *                    right singular vectors of R in WORK(IR)
    *                    (Workspace: need 2*N*N+BDSPAC)
    *
                         CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ),
         $                            WORK( IR ), LDWRKR, WORK( IU ),
         $                            LDWRKU, DUM, 1, WORK( IWORK ), INFO )
    *
    *                    Multiply Q in A by left singular vectors of R in
    *                    WORK(IU), storing result in U
    *                    (Workspace: need N*N)
    *
                         CALL DGEMM( 'N', 'N', M, N, N, ONE, A, LDA,
         $                           WORK( IU ), LDWRKU, ZERO, U, LDU )
    *
    *                    Copy right singular vectors of R to A
    *                    (Workspace: need N*N)
    *
                         CALL DLACPY( 'F', N, N, WORK( IR ), LDWRKR, A,
         $                            LDA )
    *
                      ELSE
    *
    *                    Insufficient workspace for a fast algorithm
    *
                         ITAU = 1
                         IWORK = ITAU + N
    *
    *                    Compute A=Q*R, copying result to U
    *                    (Workspace: need 2*N, prefer N+N*NB)
    *
                         CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
    *
    *                    Generate Q in U
    *                    (Workspace: need 2*N, prefer N+N*NB)
    *
                         CALL DORGQR( M, N, N, U, LDU, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + N
                         ITAUP = ITAUQ + N
                         IWORK = ITAUP + N
    *
    *                    Zero out below R in A
    *
                         CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ),
         $                            LDA )
    *
    *                    Bidiagonalize R in A
    *                    (Workspace: need 4*N, prefer 3*N+2*N*NB)
    *
                         CALL DGEBRD( N, N, A, LDA, S, WORK( IE ),
         $                            WORK( ITAUQ ), WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Multiply Q in U by left vectors bidiagonalizing R
    *                    (Workspace: need 3*N+M, prefer 3*N+M*NB)
    *
                         CALL DORMBR( 'Q', 'R', 'N', M, N, N, A, LDA,
         $                            WORK( ITAUQ ), U, LDU, WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate right vectors bidiagonalizing R in A
    *                    (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
    *
                         CALL DORGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + N
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of A in U and computing right
    *                    singular vectors of A in A
    *                    (Workspace: need BDSPAC)
    *
                         CALL DBDSQR( 'U', N, N, M, 0, S, WORK( IE ), A,
         $                            LDA, U, LDU, DUM, 1, WORK( IWORK ),
         $                            INFO )
    *
                      END IF
    *
                   ELSE IF( WNTVAS ) THEN
    *
    *                 Path 6 (M much larger than N, JOBU='S', JOBVT='S'
    *                         or 'A')
    *                 N left singular vectors to be computed in U and
    *                 N right singular vectors to be computed in VT
    *
                      IF( LWORK.GE.N*N+MAX( 4*N, BDSPAC ) ) THEN
    *
    *                    Sufficient workspace for a fast algorithm
    *
                         IU = 1
                         IF( LWORK.GE.WRKBL+LDA*N ) THEN
    *
    *                       WORK(IU) is LDA by N
    *
                            LDWRKU = LDA
                         ELSE
    *
    *                       WORK(IU) is N by N
    *
                            LDWRKU = N
                         END IF
                         ITAU = IU + LDWRKU*N
                         IWORK = ITAU + N
    *
    *                    Compute A=Q*R
    *                    (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
    *
                         CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy R to WORK(IU), zeroing out below it
    *
                         CALL DLACPY( 'U', N, N, A, LDA, WORK( IU ),
         $                            LDWRKU )
                         CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
         $                            WORK( IU+1 ), LDWRKU )
    *
    *                    Generate Q in A
    *                    (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
    *
                         CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + N
                         ITAUP = ITAUQ + N
                         IWORK = ITAUP + N
    *
    *                    Bidiagonalize R in WORK(IU), copying result to VT
    *                    (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB)
    *
                         CALL DGEBRD( N, N, WORK( IU ), LDWRKU, S,
         $                            WORK( IE ), WORK( ITAUQ ),
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'U', N, N, WORK( IU ), LDWRKU, VT,
         $                            LDVT )
    *
    *                    Generate left bidiagonalizing vectors in WORK(IU)
    *                    (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB)
    *
                         CALL DORGBR( 'Q', N, N, N, WORK( IU ), LDWRKU,
         $                            WORK( ITAUQ ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate right bidiagonalizing vectors in VT
    *                    (Workspace: need N*N+4*N-1,
    *                                prefer N*N+3*N+(N-1)*NB)
    *
                         CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + N
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of R in WORK(IU) and computing
    *                    right singular vectors of R in VT
    *                    (Workspace: need N*N+BDSPAC)
    *
                         CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ), VT,
         $                            LDVT, WORK( IU ), LDWRKU, DUM, 1,
         $                            WORK( IWORK ), INFO )
    *
    *                    Multiply Q in A by left singular vectors of R in
    *                    WORK(IU), storing result in U
    *                    (Workspace: need N*N)
    *
                         CALL DGEMM( 'N', 'N', M, N, N, ONE, A, LDA,
         $                           WORK( IU ), LDWRKU, ZERO, U, LDU )
    *
                      ELSE
    *
    *                    Insufficient workspace for a fast algorithm
    *
                         ITAU = 1
                         IWORK = ITAU + N
    *
    *                    Compute A=Q*R, copying result to U
    *                    (Workspace: need 2*N, prefer N+N*NB)
    *
                         CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
    *
    *                    Generate Q in U
    *                    (Workspace: need 2*N, prefer N+N*NB)
    *
                         CALL DORGQR( M, N, N, U, LDU, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy R to VT, zeroing out below it
    *
                         CALL DLACPY( 'U', N, N, A, LDA, VT, LDVT )
                         IF( N.GT.1 )
         $                  CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
         $                               VT( 2, 1 ), LDVT )
                         IE = ITAU
                         ITAUQ = IE + N
                         ITAUP = ITAUQ + N
                         IWORK = ITAUP + N
    *
    *                    Bidiagonalize R in VT
    *                    (Workspace: need 4*N, prefer 3*N+2*N*NB)
    *
                         CALL DGEBRD( N, N, VT, LDVT, S, WORK( IE ),
         $                            WORK( ITAUQ ), WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Multiply Q in U by left bidiagonalizing vectors
    *                    in VT
    *                    (Workspace: need 3*N+M, prefer 3*N+M*NB)
    *
                         CALL DORMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT,
         $                            WORK( ITAUQ ), U, LDU, WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate right bidiagonalizing vectors in VT
    *                    (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
    *
                         CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + N
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of A in U and computing right
    *                    singular vectors of A in VT
    *                    (Workspace: need BDSPAC)
    *
                         CALL DBDSQR( 'U', N, N, M, 0, S, WORK( IE ), VT,
         $                            LDVT, U, LDU, DUM, 1, WORK( IWORK ),
         $                            INFO )
    *
                      END IF
    *
                   END IF
    *
                ELSE IF( WNTUA ) THEN
    *
                   IF( WNTVN ) THEN
    *
    *                 Path 7 (M much larger than N, JOBU='A', JOBVT='N')
    *                 M left singular vectors to be computed in U and
    *                 no right singular vectors to be computed
    *
                      IF( LWORK.GE.N*N+MAX( N+M, 4*N, BDSPAC ) ) THEN
    *
    *                    Sufficient workspace for a fast algorithm
    *
                         IR = 1
                         IF( LWORK.GE.WRKBL+LDA*N ) THEN
    *
    *                       WORK(IR) is LDA by N
    *
                            LDWRKR = LDA
                         ELSE
    *
    *                       WORK(IR) is N by N
    *
                            LDWRKR = N
                         END IF
                         ITAU = IR + LDWRKR*N
                         IWORK = ITAU + N
    *
    *                    Compute A=Q*R, copying result to U
    *                    (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
    *
                         CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
    *
    *                    Copy R to WORK(IR), zeroing out below it
    *
                         CALL DLACPY( 'U', N, N, A, LDA, WORK( IR ),
         $                            LDWRKR )
                         CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
         $                            WORK( IR+1 ), LDWRKR )
    *
    *                    Generate Q in U
    *                    (Workspace: need N*N+N+M, prefer N*N+N+M*NB)
    *
                         CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + N
                         ITAUP = ITAUQ + N
                         IWORK = ITAUP + N
    *
    *                    Bidiagonalize R in WORK(IR)
    *                    (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB)
    *
                         CALL DGEBRD( N, N, WORK( IR ), LDWRKR, S,
         $                            WORK( IE ), WORK( ITAUQ ),
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate left bidiagonalizing vectors in WORK(IR)
    *                    (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB)
    *
                         CALL DORGBR( 'Q', N, N, N, WORK( IR ), LDWRKR,
         $                            WORK( ITAUQ ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         IWORK = IE + N
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of R in WORK(IR)
    *                    (Workspace: need N*N+BDSPAC)
    *
                         CALL DBDSQR( 'U', N, 0, N, 0, S, WORK( IE ), DUM,
         $                            1, WORK( IR ), LDWRKR, DUM, 1,
         $                            WORK( IWORK ), INFO )
    *
    *                    Multiply Q in U by left singular vectors of R in
    *                    WORK(IR), storing result in A
    *                    (Workspace: need N*N)
    *
                         CALL DGEMM( 'N', 'N', M, N, N, ONE, U, LDU,
         $                           WORK( IR ), LDWRKR, ZERO, A, LDA )
    *
    *                    Copy left singular vectors of A from A to U
    *
                         CALL DLACPY( 'F', M, N, A, LDA, U, LDU )
    *
                      ELSE
    *
    *                    Insufficient workspace for a fast algorithm
    *
                         ITAU = 1
                         IWORK = ITAU + N
    *
    *                    Compute A=Q*R, copying result to U
    *                    (Workspace: need 2*N, prefer N+N*NB)
    *
                         CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
    *
    *                    Generate Q in U
    *                    (Workspace: need N+M, prefer N+M*NB)
    *
                         CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + N
                         ITAUP = ITAUQ + N
                         IWORK = ITAUP + N
    *
    *                    Zero out below R in A
    *
                         CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ),
         $                            LDA )
    *
    *                    Bidiagonalize R in A
    *                    (Workspace: need 4*N, prefer 3*N+2*N*NB)
    *
                         CALL DGEBRD( N, N, A, LDA, S, WORK( IE ),
         $                            WORK( ITAUQ ), WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Multiply Q in U by left bidiagonalizing vectors
    *                    in A
    *                    (Workspace: need 3*N+M, prefer 3*N+M*NB)
    *
                         CALL DORMBR( 'Q', 'R', 'N', M, N, N, A, LDA,
         $                            WORK( ITAUQ ), U, LDU, WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         IWORK = IE + N
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of A in U
    *                    (Workspace: need BDSPAC)
    *
                         CALL DBDSQR( 'U', N, 0, M, 0, S, WORK( IE ), DUM,
         $                            1, U, LDU, DUM, 1, WORK( IWORK ),
         $                            INFO )
    *
                      END IF
    *
                   ELSE IF( WNTVO ) THEN
    *
    *                 Path 8 (M much larger than N, JOBU='A', JOBVT='O')
    *                 M left singular vectors to be computed in U and
    *                 N right singular vectors to be overwritten on A
    *
                      IF( LWORK.GE.2*N*N+MAX( N+M, 4*N, BDSPAC ) ) THEN
    *
    *                    Sufficient workspace for a fast algorithm
    *
                         IU = 1
                         IF( LWORK.GE.WRKBL+2*LDA*N ) THEN
    *
    *                       WORK(IU) is LDA by N and WORK(IR) is LDA by N
    *
                            LDWRKU = LDA
                            IR = IU + LDWRKU*N
                            LDWRKR = LDA
                         ELSE IF( LWORK.GE.WRKBL+( LDA+N )*N ) THEN
    *
    *                       WORK(IU) is LDA by N and WORK(IR) is N by N
    *
                            LDWRKU = LDA
                            IR = IU + LDWRKU*N
                            LDWRKR = N
                         ELSE
    *
    *                       WORK(IU) is N by N and WORK(IR) is N by N
    *
                            LDWRKU = N
                            IR = IU + LDWRKU*N
                            LDWRKR = N
                         END IF
                         ITAU = IR + LDWRKR*N
                         IWORK = ITAU + N
    *
    *                    Compute A=Q*R, copying result to U
    *                    (Workspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB)
    *
                         CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
    *
    *                    Generate Q in U
    *                    (Workspace: need 2*N*N+N+M, prefer 2*N*N+N+M*NB)
    *
                         CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy R to WORK(IU), zeroing out below it
    *
                         CALL DLACPY( 'U', N, N, A, LDA, WORK( IU ),
         $                            LDWRKU )
                         CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
         $                            WORK( IU+1 ), LDWRKU )
                         IE = ITAU
                         ITAUQ = IE + N
                         ITAUP = ITAUQ + N
                         IWORK = ITAUP + N
    *
    *                    Bidiagonalize R in WORK(IU), copying result to
    *                    WORK(IR)
    *                    (Workspace: need 2*N*N+4*N,
    *                                prefer 2*N*N+3*N+2*N*NB)
    *
                         CALL DGEBRD( N, N, WORK( IU ), LDWRKU, S,
         $                            WORK( IE ), WORK( ITAUQ ),
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'U', N, N, WORK( IU ), LDWRKU,
         $                            WORK( IR ), LDWRKR )
    *
    *                    Generate left bidiagonalizing vectors in WORK(IU)
    *                    (Workspace: need 2*N*N+4*N, prefer 2*N*N+3*N+N*NB)
    *
                         CALL DORGBR( 'Q', N, N, N, WORK( IU ), LDWRKU,
         $                            WORK( ITAUQ ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate right bidiagonalizing vectors in WORK(IR)
    *                    (Workspace: need 2*N*N+4*N-1,
    *                                prefer 2*N*N+3*N+(N-1)*NB)
    *
                         CALL DORGBR( 'P', N, N, N, WORK( IR ), LDWRKR,
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         IWORK = IE + N
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of R in WORK(IU) and computing
    *                    right singular vectors of R in WORK(IR)
    *                    (Workspace: need 2*N*N+BDSPAC)
    *
                         CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ),
         $                            WORK( IR ), LDWRKR, WORK( IU ),
         $                            LDWRKU, DUM, 1, WORK( IWORK ), INFO )
    *
    *                    Multiply Q in U by left singular vectors of R in
    *                    WORK(IU), storing result in A
    *                    (Workspace: need N*N)
    *
                         CALL DGEMM( 'N', 'N', M, N, N, ONE, U, LDU,
         $                           WORK( IU ), LDWRKU, ZERO, A, LDA )
    *
    *                    Copy left singular vectors of A from A to U
    *
                         CALL DLACPY( 'F', M, N, A, LDA, U, LDU )
    *
    *                    Copy right singular vectors of R from WORK(IR) to A
    *
                         CALL DLACPY( 'F', N, N, WORK( IR ), LDWRKR, A,
         $                            LDA )
    *
                      ELSE
    *
    *                    Insufficient workspace for a fast algorithm
    *
                         ITAU = 1
                         IWORK = ITAU + N
    *
    *                    Compute A=Q*R, copying result to U
    *                    (Workspace: need 2*N, prefer N+N*NB)
    *
                         CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
    *
    *                    Generate Q in U
    *                    (Workspace: need N+M, prefer N+M*NB)
    *
                         CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + N
                         ITAUP = ITAUQ + N
                         IWORK = ITAUP + N
    *
    *                    Zero out below R in A
    *
                         CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ),
         $                            LDA )
    *
    *                    Bidiagonalize R in A
    *                    (Workspace: need 4*N, prefer 3*N+2*N*NB)
    *
                         CALL DGEBRD( N, N, A, LDA, S, WORK( IE ),
         $                            WORK( ITAUQ ), WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Multiply Q in U by left bidiagonalizing vectors
    *                    in A
    *                    (Workspace: need 3*N+M, prefer 3*N+M*NB)
    *
                         CALL DORMBR( 'Q', 'R', 'N', M, N, N, A, LDA,
         $                            WORK( ITAUQ ), U, LDU, WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate right bidiagonalizing vectors in A
    *                    (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
    *
                         CALL DORGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + N
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of A in U and computing right
    *                    singular vectors of A in A
    *                    (Workspace: need BDSPAC)
    *
                         CALL DBDSQR( 'U', N, N, M, 0, S, WORK( IE ), A,
         $                            LDA, U, LDU, DUM, 1, WORK( IWORK ),
         $                            INFO )
    *
                      END IF
    *
                   ELSE IF( WNTVAS ) THEN
    *
    *                 Path 9 (M much larger than N, JOBU='A', JOBVT='S'
    *                         or 'A')
    *                 M left singular vectors to be computed in U and
    *                 N right singular vectors to be computed in VT
    *
                      IF( LWORK.GE.N*N+MAX( N+M, 4*N, BDSPAC ) ) THEN
    *
    *                    Sufficient workspace for a fast algorithm
    *
                         IU = 1
                         IF( LWORK.GE.WRKBL+LDA*N ) THEN
    *
    *                       WORK(IU) is LDA by N
    *
                            LDWRKU = LDA
                         ELSE
    *
    *                       WORK(IU) is N by N
    *
                            LDWRKU = N
                         END IF
                         ITAU = IU + LDWRKU*N
                         IWORK = ITAU + N
    *
    *                    Compute A=Q*R, copying result to U
    *                    (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
    *
                         CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
    *
    *                    Generate Q in U
    *                    (Workspace: need N*N+N+M, prefer N*N+N+M*NB)
    *
                         CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy R to WORK(IU), zeroing out below it
    *
                         CALL DLACPY( 'U', N, N, A, LDA, WORK( IU ),
         $                            LDWRKU )
                         CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
         $                            WORK( IU+1 ), LDWRKU )
                         IE = ITAU
                         ITAUQ = IE + N
                         ITAUP = ITAUQ + N
                         IWORK = ITAUP + N
    *
    *                    Bidiagonalize R in WORK(IU), copying result to VT
    *                    (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB)
    *
                         CALL DGEBRD( N, N, WORK( IU ), LDWRKU, S,
         $                            WORK( IE ), WORK( ITAUQ ),
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'U', N, N, WORK( IU ), LDWRKU, VT,
         $                            LDVT )
    *
    *                    Generate left bidiagonalizing vectors in WORK(IU)
    *                    (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB)
    *
                         CALL DORGBR( 'Q', N, N, N, WORK( IU ), LDWRKU,
         $                            WORK( ITAUQ ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate right bidiagonalizing vectors in VT
    *                    (Workspace: need N*N+4*N-1,
    *                                prefer N*N+3*N+(N-1)*NB)
    *
                         CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + N
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of R in WORK(IU) and computing
    *                    right singular vectors of R in VT
    *                    (Workspace: need N*N+BDSPAC)
    *
                         CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ), VT,
         $                            LDVT, WORK( IU ), LDWRKU, DUM, 1,
         $                            WORK( IWORK ), INFO )
    *
    *                    Multiply Q in U by left singular vectors of R in
    *                    WORK(IU), storing result in A
    *                    (Workspace: need N*N)
    *
                         CALL DGEMM( 'N', 'N', M, N, N, ONE, U, LDU,
         $                           WORK( IU ), LDWRKU, ZERO, A, LDA )
    *
    *                    Copy left singular vectors of A from A to U
    *
                         CALL DLACPY( 'F', M, N, A, LDA, U, LDU )
    *
                      ELSE
    *
    *                    Insufficient workspace for a fast algorithm
    *
                         ITAU = 1
                         IWORK = ITAU + N
    *
    *                    Compute A=Q*R, copying result to U
    *                    (Workspace: need 2*N, prefer N+N*NB)
    *
                         CALL DGEQRF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
    *
    *                    Generate Q in U
    *                    (Workspace: need N+M, prefer N+M*NB)
    *
                         CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy R from A to VT, zeroing out below it
    *
                         CALL DLACPY( 'U', N, N, A, LDA, VT, LDVT )
                         IF( N.GT.1 )
         $                  CALL DLASET( 'L', N-1, N-1, ZERO, ZERO,
         $                               VT( 2, 1 ), LDVT )
                         IE = ITAU
                         ITAUQ = IE + N
                         ITAUP = ITAUQ + N
                         IWORK = ITAUP + N
    *
    *                    Bidiagonalize R in VT
    *                    (Workspace: need 4*N, prefer 3*N+2*N*NB)
    *
                         CALL DGEBRD( N, N, VT, LDVT, S, WORK( IE ),
         $                            WORK( ITAUQ ), WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Multiply Q in U by left bidiagonalizing vectors
    *                    in VT
    *                    (Workspace: need 3*N+M, prefer 3*N+M*NB)
    *
                         CALL DORMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT,
         $                            WORK( ITAUQ ), U, LDU, WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate right bidiagonalizing vectors in VT
    *                    (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
    *
                         CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + N
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of A in U and computing right
    *                    singular vectors of A in VT
    *                    (Workspace: need BDSPAC)
    *
                         CALL DBDSQR( 'U', N, N, M, 0, S, WORK( IE ), VT,
         $                            LDVT, U, LDU, DUM, 1, WORK( IWORK ),
         $                            INFO )
    *
                      END IF
    *
                   END IF
    *
                END IF
    *
             ELSE
    *
    *           M .LT. MNTHR
    *
    *           Path 10 (M at least N, but not much larger)
    *           Reduce to bidiagonal form without QR decomposition
    *
                IE = 1
                ITAUQ = IE + N
                ITAUP = ITAUQ + N
                IWORK = ITAUP + N
    *
    *           Bidiagonalize A
    *           (Workspace: need 3*N+M, prefer 3*N+(M+N)*NB)
    *
                CALL DGEBRD( M, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
         $                   WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
         $                   IERR )
                IF( WNTUAS ) THEN
    *
    *              If left singular vectors desired in U, copy result to U
    *              and generate left bidiagonalizing vectors in U
    *              (Workspace: need 3*N+NCU, prefer 3*N+NCU*NB)
    *
                   CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
                   IF( WNTUS )
         $            NCU = N
                   IF( WNTUA )
         $            NCU = M
                   CALL DORGBR( 'Q', M, NCU, N, U, LDU, WORK( ITAUQ ),
         $                      WORK( IWORK ), LWORK-IWORK+1, IERR )
                END IF
                IF( WNTVAS ) THEN
    *
    *              If right singular vectors desired in VT, copy result to
    *              VT and generate right bidiagonalizing vectors in VT
    *              (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
    *
                   CALL DLACPY( 'U', N, N, A, LDA, VT, LDVT )
                   CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
         $                      WORK( IWORK ), LWORK-IWORK+1, IERR )
                END IF
                IF( WNTUO ) THEN
    *
    *              If left singular vectors desired in A, generate left
    *              bidiagonalizing vectors in A
    *              (Workspace: need 4*N, prefer 3*N+N*NB)
    *
                   CALL DORGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ),
         $                      WORK( IWORK ), LWORK-IWORK+1, IERR )
                END IF
                IF( WNTVO ) THEN
    *
    *              If right singular vectors desired in A, generate right
    *              bidiagonalizing vectors in A
    *              (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB)
    *
                   CALL DORGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ),
         $                      WORK( IWORK ), LWORK-IWORK+1, IERR )
                END IF
                IWORK = IE + N
                IF( WNTUAS .OR. WNTUO )
         $         NRU = M
                IF( WNTUN )
         $         NRU = 0
                IF( WNTVAS .OR. WNTVO )
         $         NCVT = N
                IF( WNTVN )
         $         NCVT = 0
                IF( ( .NOT.WNTUO ) .AND. ( .NOT.WNTVO ) ) THEN
    *
    *              Perform bidiagonal QR iteration, if desired, computing
    *              left singular vectors in U and computing right singular
    *              vectors in VT
    *              (Workspace: need BDSPAC)
    *
                   CALL DBDSQR( 'U', N, NCVT, NRU, 0, S, WORK( IE ), VT,
         $                      LDVT, U, LDU, DUM, 1, WORK( IWORK ), INFO )
                ELSE IF( ( .NOT.WNTUO ) .AND. WNTVO ) THEN
    *
    *              Perform bidiagonal QR iteration, if desired, computing
    *              left singular vectors in U and computing right singular
    *              vectors in A
    *              (Workspace: need BDSPAC)
    *
                   CALL DBDSQR( 'U', N, NCVT, NRU, 0, S, WORK( IE ), A, LDA,
         $                      U, LDU, DUM, 1, WORK( IWORK ), INFO )
                ELSE
    *
    *              Perform bidiagonal QR iteration, if desired, computing
    *              left singular vectors in A and computing right singular
    *              vectors in VT
    *              (Workspace: need BDSPAC)
    *
                   CALL DBDSQR( 'U', N, NCVT, NRU, 0, S, WORK( IE ), VT,
         $                      LDVT, A, LDA, DUM, 1, WORK( IWORK ), INFO )
                END IF
    *
             END IF
    *
          ELSE
    *
    *        A has more columns than rows. If A has sufficiently more
    *        columns than rows, first reduce using the LQ decomposition (if
    *        sufficient workspace available)
    *
             IF( N.GE.MNTHR ) THEN
    *
                IF( WNTVN ) THEN
    *
    *              Path 1t(N much larger than M, JOBVT='N')
    *              No right singular vectors to be computed
    *
                   ITAU = 1
                   IWORK = ITAU + M
    *
    *              Compute A=L*Q
    *              (Workspace: need 2*M, prefer M+M*NB)
    *
                   CALL DGELQF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ),
         $                      LWORK-IWORK+1, IERR )
    *
    *              Zero out above L
    *
                   CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, A( 1, 2 ), LDA )
                   IE = 1
                   ITAUQ = IE + M
                   ITAUP = ITAUQ + M
                   IWORK = ITAUP + M
    *
    *              Bidiagonalize L in A
    *              (Workspace: need 4*M, prefer 3*M+2*M*NB)
    *
                   CALL DGEBRD( M, M, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
         $                      WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
         $                      IERR )
                   IF( WNTUO .OR. WNTUAS ) THEN
    *
    *                 If left singular vectors desired, generate Q
    *                 (Workspace: need 4*M, prefer 3*M+M*NB)
    *
                      CALL DORGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                   END IF
                   IWORK = IE + M
                   NRU = 0
                   IF( WNTUO .OR. WNTUAS )
         $            NRU = M
    *
    *              Perform bidiagonal QR iteration, computing left singular
    *              vectors of A in A if desired
    *              (Workspace: need BDSPAC)
    *
                   CALL DBDSQR( 'U', M, 0, NRU, 0, S, WORK( IE ), DUM, 1, A,
         $                      LDA, DUM, 1, WORK( IWORK ), INFO )
    *
    *              If left singular vectors desired in U, copy them there
    *
                   IF( WNTUAS )
         $            CALL DLACPY( 'F', M, M, A, LDA, U, LDU )
    *
                ELSE IF( WNTVO .AND. WNTUN ) THEN
    *
    *              Path 2t(N much larger than M, JOBU='N', JOBVT='O')
    *              M right singular vectors to be overwritten on A and
    *              no left singular vectors to be computed
    *
                   IF( LWORK.GE.M*M+MAX( 4*M, BDSPAC ) ) THEN
    *
    *                 Sufficient workspace for a fast algorithm
    *
                      IR = 1
                      IF( LWORK.GE.MAX( WRKBL, LDA*N+M )+LDA*M ) THEN
    *
    *                    WORK(IU) is LDA by N and WORK(IR) is LDA by M
    *
                         LDWRKU = LDA
                         CHUNK = N
                         LDWRKR = LDA
                      ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N+M )+M*M ) THEN
    *
    *                    WORK(IU) is LDA by N and WORK(IR) is M by M
    *
                         LDWRKU = LDA
                         CHUNK = N
                         LDWRKR = M
                      ELSE
    *
    *                    WORK(IU) is M by CHUNK and WORK(IR) is M by M
    *
                         LDWRKU = M
                         CHUNK = ( LWORK-M*M-M ) / M
                         LDWRKR = M
                      END IF
                      ITAU = IR + LDWRKR*M
                      IWORK = ITAU + M
    *
    *                 Compute A=L*Q
    *                 (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
    *
                      CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                 Copy L to WORK(IR) and zero out above it
    *
                      CALL DLACPY( 'L', M, M, A, LDA, WORK( IR ), LDWRKR )
                      CALL DLASET( 'U', M-1, M-1, ZERO, ZERO,
         $                         WORK( IR+LDWRKR ), LDWRKR )
    *
    *                 Generate Q in A
    *                 (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
    *
                      CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      IE = ITAU
                      ITAUQ = IE + M
                      ITAUP = ITAUQ + M
                      IWORK = ITAUP + M
    *
    *                 Bidiagonalize L in WORK(IR)
    *                 (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
    *
                      CALL DGEBRD( M, M, WORK( IR ), LDWRKR, S, WORK( IE ),
         $                         WORK( ITAUQ ), WORK( ITAUP ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                 Generate right vectors bidiagonalizing L
    *                 (Workspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB)
    *
                      CALL DORGBR( 'P', M, M, M, WORK( IR ), LDWRKR,
         $                         WORK( ITAUP ), WORK( IWORK ),
         $                         LWORK-IWORK+1, IERR )
                      IWORK = IE + M
    *
    *                 Perform bidiagonal QR iteration, computing right
    *                 singular vectors of L in WORK(IR)
    *                 (Workspace: need M*M+BDSPAC)
    *
                      CALL DBDSQR( 'U', M, M, 0, 0, S, WORK( IE ),
         $                         WORK( IR ), LDWRKR, DUM, 1, DUM, 1,
         $                         WORK( IWORK ), INFO )
                      IU = IE + M
    *
    *                 Multiply right singular vectors of L in WORK(IR) by Q
    *                 in A, storing result in WORK(IU) and copying to A
    *                 (Workspace: need M*M+2*M, prefer M*M+M*N+M)
    *
                      DO 30 I = 1, N, CHUNK
                         BLK = MIN( N-I+1, CHUNK )
                         CALL DGEMM( 'N', 'N', M, BLK, M, ONE, WORK( IR ),
         $                           LDWRKR, A( 1, I ), LDA, ZERO,
         $                           WORK( IU ), LDWRKU )
                         CALL DLACPY( 'F', M, BLK, WORK( IU ), LDWRKU,
         $                            A( 1, I ), LDA )
       30             CONTINUE
    *
                   ELSE
    *
    *                 Insufficient workspace for a fast algorithm
    *
                      IE = 1
                      ITAUQ = IE + M
                      ITAUP = ITAUQ + M
                      IWORK = ITAUP + M
    *
    *                 Bidiagonalize A
    *                 (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB)
    *
                      CALL DGEBRD( M, N, A, LDA, S, WORK( IE ),
         $                         WORK( ITAUQ ), WORK( ITAUP ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                 Generate right vectors bidiagonalizing A
    *                 (Workspace: need 4*M, prefer 3*M+M*NB)
    *
                      CALL DORGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      IWORK = IE + M
    *
    *                 Perform bidiagonal QR iteration, computing right
    *                 singular vectors of A in A
    *                 (Workspace: need BDSPAC)
    *
                      CALL DBDSQR( 'L', M, N, 0, 0, S, WORK( IE ), A, LDA,
         $                         DUM, 1, DUM, 1, WORK( IWORK ), INFO )
    *
                   END IF
    *
                ELSE IF( WNTVO .AND. WNTUAS ) THEN
    *
    *              Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O')
    *              M right singular vectors to be overwritten on A and
    *              M left singular vectors to be computed in U
    *
                   IF( LWORK.GE.M*M+MAX( 4*M, BDSPAC ) ) THEN
    *
    *                 Sufficient workspace for a fast algorithm
    *
                      IR = 1
                      IF( LWORK.GE.MAX( WRKBL, LDA*N+M )+LDA*M ) THEN
    *
    *                    WORK(IU) is LDA by N and WORK(IR) is LDA by M
    *
                         LDWRKU = LDA
                         CHUNK = N
                         LDWRKR = LDA
                      ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N+M )+M*M ) THEN
    *
    *                    WORK(IU) is LDA by N and WORK(IR) is M by M
    *
                         LDWRKU = LDA
                         CHUNK = N
                         LDWRKR = M
                      ELSE
    *
    *                    WORK(IU) is M by CHUNK and WORK(IR) is M by M
    *
                         LDWRKU = M
                         CHUNK = ( LWORK-M*M-M ) / M
                         LDWRKR = M
                      END IF
                      ITAU = IR + LDWRKR*M
                      IWORK = ITAU + M
    *
    *                 Compute A=L*Q
    *                 (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
    *
                      CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                 Copy L to U, zeroing about above it
    *
                      CALL DLACPY( 'L', M, M, A, LDA, U, LDU )
                      CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, U( 1, 2 ),
         $                         LDU )
    *
    *                 Generate Q in A
    *                 (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
    *
                      CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      IE = ITAU
                      ITAUQ = IE + M
                      ITAUP = ITAUQ + M
                      IWORK = ITAUP + M
    *
    *                 Bidiagonalize L in U, copying result to WORK(IR)
    *                 (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
    *
                      CALL DGEBRD( M, M, U, LDU, S, WORK( IE ),
         $                         WORK( ITAUQ ), WORK( ITAUP ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      CALL DLACPY( 'U', M, M, U, LDU, WORK( IR ), LDWRKR )
    *
    *                 Generate right vectors bidiagonalizing L in WORK(IR)
    *                 (Workspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB)
    *
                      CALL DORGBR( 'P', M, M, M, WORK( IR ), LDWRKR,
         $                         WORK( ITAUP ), WORK( IWORK ),
         $                         LWORK-IWORK+1, IERR )
    *
    *                 Generate left vectors bidiagonalizing L in U
    *                 (Workspace: need M*M+4*M, prefer M*M+3*M+M*NB)
    *
                      CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      IWORK = IE + M
    *
    *                 Perform bidiagonal QR iteration, computing left
    *                 singular vectors of L in U, and computing right
    *                 singular vectors of L in WORK(IR)
    *                 (Workspace: need M*M+BDSPAC)
    *
                      CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ),
         $                         WORK( IR ), LDWRKR, U, LDU, DUM, 1,
         $                         WORK( IWORK ), INFO )
                      IU = IE + M
    *
    *                 Multiply right singular vectors of L in WORK(IR) by Q
    *                 in A, storing result in WORK(IU) and copying to A
    *                 (Workspace: need M*M+2*M, prefer M*M+M*N+M))
    *
                      DO 40 I = 1, N, CHUNK
                         BLK = MIN( N-I+1, CHUNK )
                         CALL DGEMM( 'N', 'N', M, BLK, M, ONE, WORK( IR ),
         $                           LDWRKR, A( 1, I ), LDA, ZERO,
         $                           WORK( IU ), LDWRKU )
                         CALL DLACPY( 'F', M, BLK, WORK( IU ), LDWRKU,
         $                            A( 1, I ), LDA )
       40             CONTINUE
    *
                   ELSE
    *
    *                 Insufficient workspace for a fast algorithm
    *
                      ITAU = 1
                      IWORK = ITAU + M
    *
    *                 Compute A=L*Q
    *                 (Workspace: need 2*M, prefer M+M*NB)
    *
                      CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                 Copy L to U, zeroing out above it
    *
                      CALL DLACPY( 'L', M, M, A, LDA, U, LDU )
                      CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, U( 1, 2 ),
         $                         LDU )
    *
    *                 Generate Q in A
    *                 (Workspace: need 2*M, prefer M+M*NB)
    *
                      CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      IE = ITAU
                      ITAUQ = IE + M
                      ITAUP = ITAUQ + M
                      IWORK = ITAUP + M
    *
    *                 Bidiagonalize L in U
    *                 (Workspace: need 4*M, prefer 3*M+2*M*NB)
    *
                      CALL DGEBRD( M, M, U, LDU, S, WORK( IE ),
         $                         WORK( ITAUQ ), WORK( ITAUP ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                 Multiply right vectors bidiagonalizing L by Q in A
    *                 (Workspace: need 3*M+N, prefer 3*M+N*NB)
    *
                      CALL DORMBR( 'P', 'L', 'T', M, N, M, U, LDU,
         $                         WORK( ITAUP ), A, LDA, WORK( IWORK ),
         $                         LWORK-IWORK+1, IERR )
    *
    *                 Generate left vectors bidiagonalizing L in U
    *                 (Workspace: need 4*M, prefer 3*M+M*NB)
    *
                      CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ),
         $                         WORK( IWORK ), LWORK-IWORK+1, IERR )
                      IWORK = IE + M
    *
    *                 Perform bidiagonal QR iteration, computing left
    *                 singular vectors of A in U and computing right
    *                 singular vectors of A in A
    *                 (Workspace: need BDSPAC)
    *
                      CALL DBDSQR( 'U', M, N, M, 0, S, WORK( IE ), A, LDA,
         $                         U, LDU, DUM, 1, WORK( IWORK ), INFO )
    *
                   END IF
    *
                ELSE IF( WNTVS ) THEN
    *
                   IF( WNTUN ) THEN
    *
    *                 Path 4t(N much larger than M, JOBU='N', JOBVT='S')
    *                 M right singular vectors to be computed in VT and
    *                 no left singular vectors to be computed
    *
                      IF( LWORK.GE.M*M+MAX( 4*M, BDSPAC ) ) THEN
    *
    *                    Sufficient workspace for a fast algorithm
    *
                         IR = 1
                         IF( LWORK.GE.WRKBL+LDA*M ) THEN
    *
    *                       WORK(IR) is LDA by M
    *
                            LDWRKR = LDA
                         ELSE
    *
    *                       WORK(IR) is M by M
    *
                            LDWRKR = M
                         END IF
                         ITAU = IR + LDWRKR*M
                         IWORK = ITAU + M
    *
    *                    Compute A=L*Q
    *                    (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
    *
                         CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy L to WORK(IR), zeroing out above it
    *
                         CALL DLACPY( 'L', M, M, A, LDA, WORK( IR ),
         $                            LDWRKR )
                         CALL DLASET( 'U', M-1, M-1, ZERO, ZERO,
         $                            WORK( IR+LDWRKR ), LDWRKR )
    *
    *                    Generate Q in A
    *                    (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
    *
                         CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + M
                         ITAUP = ITAUQ + M
                         IWORK = ITAUP + M
    *
    *                    Bidiagonalize L in WORK(IR)
    *                    (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
    *
                         CALL DGEBRD( M, M, WORK( IR ), LDWRKR, S,
         $                            WORK( IE ), WORK( ITAUQ ),
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate right vectors bidiagonalizing L in
    *                    WORK(IR)
    *                    (Workspace: need M*M+4*M, prefer M*M+3*M+(M-1)*NB)
    *
                         CALL DORGBR( 'P', M, M, M, WORK( IR ), LDWRKR,
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         IWORK = IE + M
    *
    *                    Perform bidiagonal QR iteration, computing right
    *                    singular vectors of L in WORK(IR)
    *                    (Workspace: need M*M+BDSPAC)
    *
                         CALL DBDSQR( 'U', M, M, 0, 0, S, WORK( IE ),
         $                            WORK( IR ), LDWRKR, DUM, 1, DUM, 1,
         $                            WORK( IWORK ), INFO )
    *
    *                    Multiply right singular vectors of L in WORK(IR) by
    *                    Q in A, storing result in VT
    *                    (Workspace: need M*M)
    *
                         CALL DGEMM( 'N', 'N', M, N, M, ONE, WORK( IR ),
         $                           LDWRKR, A, LDA, ZERO, VT, LDVT )
    *
                      ELSE
    *
    *                    Insufficient workspace for a fast algorithm
    *
                         ITAU = 1
                         IWORK = ITAU + M
    *
    *                    Compute A=L*Q
    *                    (Workspace: need 2*M, prefer M+M*NB)
    *
                         CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy result to VT
    *
                         CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
    *
    *                    Generate Q in VT
    *                    (Workspace: need 2*M, prefer M+M*NB)
    *
                         CALL DORGLQ( M, N, M, VT, LDVT, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + M
                         ITAUP = ITAUQ + M
                         IWORK = ITAUP + M
    *
    *                    Zero out above L in A
    *
                         CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, A( 1, 2 ),
         $                            LDA )
    *
    *                    Bidiagonalize L in A
    *                    (Workspace: need 4*M, prefer 3*M+2*M*NB)
    *
                         CALL DGEBRD( M, M, A, LDA, S, WORK( IE ),
         $                            WORK( ITAUQ ), WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Multiply right vectors bidiagonalizing L by Q in VT
    *                    (Workspace: need 3*M+N, prefer 3*M+N*NB)
    *
                         CALL DORMBR( 'P', 'L', 'T', M, N, M, A, LDA,
         $                            WORK( ITAUP ), VT, LDVT,
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + M
    *
    *                    Perform bidiagonal QR iteration, computing right
    *                    singular vectors of A in VT
    *                    (Workspace: need BDSPAC)
    *
                         CALL DBDSQR( 'U', M, N, 0, 0, S, WORK( IE ), VT,
         $                            LDVT, DUM, 1, DUM, 1, WORK( IWORK ),
         $                            INFO )
    *
                      END IF
    *
                   ELSE IF( WNTUO ) THEN
    *
    *                 Path 5t(N much larger than M, JOBU='O', JOBVT='S')
    *                 M right singular vectors to be computed in VT and
    *                 M left singular vectors to be overwritten on A
    *
                      IF( LWORK.GE.2*M*M+MAX( 4*M, BDSPAC ) ) THEN
    *
    *                    Sufficient workspace for a fast algorithm
    *
                         IU = 1
                         IF( LWORK.GE.WRKBL+2*LDA*M ) THEN
    *
    *                       WORK(IU) is LDA by M and WORK(IR) is LDA by M
    *
                            LDWRKU = LDA
                            IR = IU + LDWRKU*M
                            LDWRKR = LDA
                         ELSE IF( LWORK.GE.WRKBL+( LDA+M )*M ) THEN
    *
    *                       WORK(IU) is LDA by M and WORK(IR) is M by M
    *
                            LDWRKU = LDA
                            IR = IU + LDWRKU*M
                            LDWRKR = M
                         ELSE
    *
    *                       WORK(IU) is M by M and WORK(IR) is M by M
    *
                            LDWRKU = M
                            IR = IU + LDWRKU*M
                            LDWRKR = M
                         END IF
                         ITAU = IR + LDWRKR*M
                         IWORK = ITAU + M
    *
    *                    Compute A=L*Q
    *                    (Workspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB)
    *
                         CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy L to WORK(IU), zeroing out below it
    *
                         CALL DLACPY( 'L', M, M, A, LDA, WORK( IU ),
         $                            LDWRKU )
                         CALL DLASET( 'U', M-1, M-1, ZERO, ZERO,
         $                            WORK( IU+LDWRKU ), LDWRKU )
    *
    *                    Generate Q in A
    *                    (Workspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB)
    *
                         CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + M
                         ITAUP = ITAUQ + M
                         IWORK = ITAUP + M
    *
    *                    Bidiagonalize L in WORK(IU), copying result to
    *                    WORK(IR)
    *                    (Workspace: need 2*M*M+4*M,
    *                                prefer 2*M*M+3*M+2*M*NB)
    *
                         CALL DGEBRD( M, M, WORK( IU ), LDWRKU, S,
         $                            WORK( IE ), WORK( ITAUQ ),
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'L', M, M, WORK( IU ), LDWRKU,
         $                            WORK( IR ), LDWRKR )
    *
    *                    Generate right bidiagonalizing vectors in WORK(IU)
    *                    (Workspace: need 2*M*M+4*M-1,
    *                                prefer 2*M*M+3*M+(M-1)*NB)
    *
                         CALL DORGBR( 'P', M, M, M, WORK( IU ), LDWRKU,
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate left bidiagonalizing vectors in WORK(IR)
    *                    (Workspace: need 2*M*M+4*M, prefer 2*M*M+3*M+M*NB)
    *
                         CALL DORGBR( 'Q', M, M, M, WORK( IR ), LDWRKR,
         $                            WORK( ITAUQ ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         IWORK = IE + M
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of L in WORK(IR) and computing
    *                    right singular vectors of L in WORK(IU)
    *                    (Workspace: need 2*M*M+BDSPAC)
    *
                         CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ),
         $                            WORK( IU ), LDWRKU, WORK( IR ),
         $                            LDWRKR, DUM, 1, WORK( IWORK ), INFO )
    *
    *                    Multiply right singular vectors of L in WORK(IU) by
    *                    Q in A, storing result in VT
    *                    (Workspace: need M*M)
    *
                         CALL DGEMM( 'N', 'N', M, N, M, ONE, WORK( IU ),
         $                           LDWRKU, A, LDA, ZERO, VT, LDVT )
    *
    *                    Copy left singular vectors of L to A
    *                    (Workspace: need M*M)
    *
                         CALL DLACPY( 'F', M, M, WORK( IR ), LDWRKR, A,
         $                            LDA )
    *
                      ELSE
    *
    *                    Insufficient workspace for a fast algorithm
    *
                         ITAU = 1
                         IWORK = ITAU + M
    *
    *                    Compute A=L*Q, copying result to VT
    *                    (Workspace: need 2*M, prefer M+M*NB)
    *
                         CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
    *
    *                    Generate Q in VT
    *                    (Workspace: need 2*M, prefer M+M*NB)
    *
                         CALL DORGLQ( M, N, M, VT, LDVT, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + M
                         ITAUP = ITAUQ + M
                         IWORK = ITAUP + M
    *
    *                    Zero out above L in A
    *
                         CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, A( 1, 2 ),
         $                            LDA )
    *
    *                    Bidiagonalize L in A
    *                    (Workspace: need 4*M, prefer 3*M+2*M*NB)
    *
                         CALL DGEBRD( M, M, A, LDA, S, WORK( IE ),
         $                            WORK( ITAUQ ), WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Multiply right vectors bidiagonalizing L by Q in VT
    *                    (Workspace: need 3*M+N, prefer 3*M+N*NB)
    *
                         CALL DORMBR( 'P', 'L', 'T', M, N, M, A, LDA,
         $                            WORK( ITAUP ), VT, LDVT,
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Generate left bidiagonalizing vectors of L in A
    *                    (Workspace: need 4*M, prefer 3*M+M*NB)
    *
                         CALL DORGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + M
    *
    *                    Perform bidiagonal QR iteration, compute left
    *                    singular vectors of A in A and compute right
    *                    singular vectors of A in VT
    *                    (Workspace: need BDSPAC)
    *
                         CALL DBDSQR( 'U', M, N, M, 0, S, WORK( IE ), VT,
         $                            LDVT, A, LDA, DUM, 1, WORK( IWORK ),
         $                            INFO )
    *
                      END IF
    *
                   ELSE IF( WNTUAS ) THEN
    *
    *                 Path 6t(N much larger than M, JOBU='S' or 'A',
    *                         JOBVT='S')
    *                 M right singular vectors to be computed in VT and
    *                 M left singular vectors to be computed in U
    *
                      IF( LWORK.GE.M*M+MAX( 4*M, BDSPAC ) ) THEN
    *
    *                    Sufficient workspace for a fast algorithm
    *
                         IU = 1
                         IF( LWORK.GE.WRKBL+LDA*M ) THEN
    *
    *                       WORK(IU) is LDA by N
    *
                            LDWRKU = LDA
                         ELSE
    *
    *                       WORK(IU) is LDA by M
    *
                            LDWRKU = M
                         END IF
                         ITAU = IU + LDWRKU*M
                         IWORK = ITAU + M
    *
    *                    Compute A=L*Q
    *                    (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
    *
                         CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy L to WORK(IU), zeroing out above it
    *
                         CALL DLACPY( 'L', M, M, A, LDA, WORK( IU ),
         $                            LDWRKU )
                         CALL DLASET( 'U', M-1, M-1, ZERO, ZERO,
         $                            WORK( IU+LDWRKU ), LDWRKU )
    *
    *                    Generate Q in A
    *                    (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
    *
                         CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + M
                         ITAUP = ITAUQ + M
                         IWORK = ITAUP + M
    *
    *                    Bidiagonalize L in WORK(IU), copying result to U
    *                    (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
    *
                         CALL DGEBRD( M, M, WORK( IU ), LDWRKU, S,
         $                            WORK( IE ), WORK( ITAUQ ),
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'L', M, M, WORK( IU ), LDWRKU, U,
         $                            LDU )
    *
    *                    Generate right bidiagonalizing vectors in WORK(IU)
    *                    (Workspace: need M*M+4*M-1,
    *                                prefer M*M+3*M+(M-1)*NB)
    *
                         CALL DORGBR( 'P', M, M, M, WORK( IU ), LDWRKU,
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate left bidiagonalizing vectors in U
    *                    (Workspace: need M*M+4*M, prefer M*M+3*M+M*NB)
    *
                         CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + M
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of L in U and computing right
    *                    singular vectors of L in WORK(IU)
    *                    (Workspace: need M*M+BDSPAC)
    *
                         CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ),
         $                            WORK( IU ), LDWRKU, U, LDU, DUM, 1,
         $                            WORK( IWORK ), INFO )
    *
    *                    Multiply right singular vectors of L in WORK(IU) by
    *                    Q in A, storing result in VT
    *                    (Workspace: need M*M)
    *
                         CALL DGEMM( 'N', 'N', M, N, M, ONE, WORK( IU ),
         $                           LDWRKU, A, LDA, ZERO, VT, LDVT )
    *
                      ELSE
    *
    *                    Insufficient workspace for a fast algorithm
    *
                         ITAU = 1
                         IWORK = ITAU + M
    *
    *                    Compute A=L*Q, copying result to VT
    *                    (Workspace: need 2*M, prefer M+M*NB)
    *
                         CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
    *
    *                    Generate Q in VT
    *                    (Workspace: need 2*M, prefer M+M*NB)
    *
                         CALL DORGLQ( M, N, M, VT, LDVT, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy L to U, zeroing out above it
    *
                         CALL DLACPY( 'L', M, M, A, LDA, U, LDU )
                         CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, U( 1, 2 ),
         $                            LDU )
                         IE = ITAU
                         ITAUQ = IE + M
                         ITAUP = ITAUQ + M
                         IWORK = ITAUP + M
    *
    *                    Bidiagonalize L in U
    *                    (Workspace: need 4*M, prefer 3*M+2*M*NB)
    *
                         CALL DGEBRD( M, M, U, LDU, S, WORK( IE ),
         $                            WORK( ITAUQ ), WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Multiply right bidiagonalizing vectors in U by Q
    *                    in VT
    *                    (Workspace: need 3*M+N, prefer 3*M+N*NB)
    *
                         CALL DORMBR( 'P', 'L', 'T', M, N, M, U, LDU,
         $                            WORK( ITAUP ), VT, LDVT,
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Generate left bidiagonalizing vectors in U
    *                    (Workspace: need 4*M, prefer 3*M+M*NB)
    *
                         CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + M
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of A in U and computing right
    *                    singular vectors of A in VT
    *                    (Workspace: need BDSPAC)
    *
                         CALL DBDSQR( 'U', M, N, M, 0, S, WORK( IE ), VT,
         $                            LDVT, U, LDU, DUM, 1, WORK( IWORK ),
         $                            INFO )
    *
                      END IF
    *
                   END IF
    *
                ELSE IF( WNTVA ) THEN
    *
                   IF( WNTUN ) THEN
    *
    *                 Path 7t(N much larger than M, JOBU='N', JOBVT='A')
    *                 N right singular vectors to be computed in VT and
    *                 no left singular vectors to be computed
    *
                      IF( LWORK.GE.M*M+MAX( N+M, 4*M, BDSPAC ) ) THEN
    *
    *                    Sufficient workspace for a fast algorithm
    *
                         IR = 1
                         IF( LWORK.GE.WRKBL+LDA*M ) THEN
    *
    *                       WORK(IR) is LDA by M
    *
                            LDWRKR = LDA
                         ELSE
    *
    *                       WORK(IR) is M by M
    *
                            LDWRKR = M
                         END IF
                         ITAU = IR + LDWRKR*M
                         IWORK = ITAU + M
    *
    *                    Compute A=L*Q, copying result to VT
    *                    (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
    *
                         CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
    *
    *                    Copy L to WORK(IR), zeroing out above it
    *
                         CALL DLACPY( 'L', M, M, A, LDA, WORK( IR ),
         $                            LDWRKR )
                         CALL DLASET( 'U', M-1, M-1, ZERO, ZERO,
         $                            WORK( IR+LDWRKR ), LDWRKR )
    *
    *                    Generate Q in VT
    *                    (Workspace: need M*M+M+N, prefer M*M+M+N*NB)
    *
                         CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + M
                         ITAUP = ITAUQ + M
                         IWORK = ITAUP + M
    *
    *                    Bidiagonalize L in WORK(IR)
    *                    (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
    *
                         CALL DGEBRD( M, M, WORK( IR ), LDWRKR, S,
         $                            WORK( IE ), WORK( ITAUQ ),
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate right bidiagonalizing vectors in WORK(IR)
    *                    (Workspace: need M*M+4*M-1,
    *                                prefer M*M+3*M+(M-1)*NB)
    *
                         CALL DORGBR( 'P', M, M, M, WORK( IR ), LDWRKR,
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         IWORK = IE + M
    *
    *                    Perform bidiagonal QR iteration, computing right
    *                    singular vectors of L in WORK(IR)
    *                    (Workspace: need M*M+BDSPAC)
    *
                         CALL DBDSQR( 'U', M, M, 0, 0, S, WORK( IE ),
         $                            WORK( IR ), LDWRKR, DUM, 1, DUM, 1,
         $                            WORK( IWORK ), INFO )
    *
    *                    Multiply right singular vectors of L in WORK(IR) by
    *                    Q in VT, storing result in A
    *                    (Workspace: need M*M)
    *
                         CALL DGEMM( 'N', 'N', M, N, M, ONE, WORK( IR ),
         $                           LDWRKR, VT, LDVT, ZERO, A, LDA )
    *
    *                    Copy right singular vectors of A from A to VT
    *
                         CALL DLACPY( 'F', M, N, A, LDA, VT, LDVT )
    *
                      ELSE
    *
    *                    Insufficient workspace for a fast algorithm
    *
                         ITAU = 1
                         IWORK = ITAU + M
    *
    *                    Compute A=L*Q, copying result to VT
    *                    (Workspace: need 2*M, prefer M+M*NB)
    *
                         CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
    *
    *                    Generate Q in VT
    *                    (Workspace: need M+N, prefer M+N*NB)
    *
                         CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + M
                         ITAUP = ITAUQ + M
                         IWORK = ITAUP + M
    *
    *                    Zero out above L in A
    *
                         CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, A( 1, 2 ),
         $                            LDA )
    *
    *                    Bidiagonalize L in A
    *                    (Workspace: need 4*M, prefer 3*M+2*M*NB)
    *
                         CALL DGEBRD( M, M, A, LDA, S, WORK( IE ),
         $                            WORK( ITAUQ ), WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Multiply right bidiagonalizing vectors in A by Q
    *                    in VT
    *                    (Workspace: need 3*M+N, prefer 3*M+N*NB)
    *
                         CALL DORMBR( 'P', 'L', 'T', M, N, M, A, LDA,
         $                            WORK( ITAUP ), VT, LDVT,
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + M
    *
    *                    Perform bidiagonal QR iteration, computing right
    *                    singular vectors of A in VT
    *                    (Workspace: need BDSPAC)
    *
                         CALL DBDSQR( 'U', M, N, 0, 0, S, WORK( IE ), VT,
         $                            LDVT, DUM, 1, DUM, 1, WORK( IWORK ),
         $                            INFO )
    *
                      END IF
    *
                   ELSE IF( WNTUO ) THEN
    *
    *                 Path 8t(N much larger than M, JOBU='O', JOBVT='A')
    *                 N right singular vectors to be computed in VT and
    *                 M left singular vectors to be overwritten on A
    *
                      IF( LWORK.GE.2*M*M+MAX( N+M, 4*M, BDSPAC ) ) THEN
    *
    *                    Sufficient workspace for a fast algorithm
    *
                         IU = 1
                         IF( LWORK.GE.WRKBL+2*LDA*M ) THEN
    *
    *                       WORK(IU) is LDA by M and WORK(IR) is LDA by M
    *
                            LDWRKU = LDA
                            IR = IU + LDWRKU*M
                            LDWRKR = LDA
                         ELSE IF( LWORK.GE.WRKBL+( LDA+M )*M ) THEN
    *
    *                       WORK(IU) is LDA by M and WORK(IR) is M by M
    *
                            LDWRKU = LDA
                            IR = IU + LDWRKU*M
                            LDWRKR = M
                         ELSE
    *
    *                       WORK(IU) is M by M and WORK(IR) is M by M
    *
                            LDWRKU = M
                            IR = IU + LDWRKU*M
                            LDWRKR = M
                         END IF
                         ITAU = IR + LDWRKR*M
                         IWORK = ITAU + M
    *
    *                    Compute A=L*Q, copying result to VT
    *                    (Workspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB)
    *
                         CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
    *
    *                    Generate Q in VT
    *                    (Workspace: need 2*M*M+M+N, prefer 2*M*M+M+N*NB)
    *
                         CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy L to WORK(IU), zeroing out above it
    *
                         CALL DLACPY( 'L', M, M, A, LDA, WORK( IU ),
         $                            LDWRKU )
                         CALL DLASET( 'U', M-1, M-1, ZERO, ZERO,
         $                            WORK( IU+LDWRKU ), LDWRKU )
                         IE = ITAU
                         ITAUQ = IE + M
                         ITAUP = ITAUQ + M
                         IWORK = ITAUP + M
    *
    *                    Bidiagonalize L in WORK(IU), copying result to
    *                    WORK(IR)
    *                    (Workspace: need 2*M*M+4*M,
    *                                prefer 2*M*M+3*M+2*M*NB)
    *
                         CALL DGEBRD( M, M, WORK( IU ), LDWRKU, S,
         $                            WORK( IE ), WORK( ITAUQ ),
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'L', M, M, WORK( IU ), LDWRKU,
         $                            WORK( IR ), LDWRKR )
    *
    *                    Generate right bidiagonalizing vectors in WORK(IU)
    *                    (Workspace: need 2*M*M+4*M-1,
    *                                prefer 2*M*M+3*M+(M-1)*NB)
    *
                         CALL DORGBR( 'P', M, M, M, WORK( IU ), LDWRKU,
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate left bidiagonalizing vectors in WORK(IR)
    *                    (Workspace: need 2*M*M+4*M, prefer 2*M*M+3*M+M*NB)
    *
                         CALL DORGBR( 'Q', M, M, M, WORK( IR ), LDWRKR,
         $                            WORK( ITAUQ ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         IWORK = IE + M
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of L in WORK(IR) and computing
    *                    right singular vectors of L in WORK(IU)
    *                    (Workspace: need 2*M*M+BDSPAC)
    *
                         CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ),
         $                            WORK( IU ), LDWRKU, WORK( IR ),
         $                            LDWRKR, DUM, 1, WORK( IWORK ), INFO )
    *
    *                    Multiply right singular vectors of L in WORK(IU) by
    *                    Q in VT, storing result in A
    *                    (Workspace: need M*M)
    *
                         CALL DGEMM( 'N', 'N', M, N, M, ONE, WORK( IU ),
         $                           LDWRKU, VT, LDVT, ZERO, A, LDA )
    *
    *                    Copy right singular vectors of A from A to VT
    *
                         CALL DLACPY( 'F', M, N, A, LDA, VT, LDVT )
    *
    *                    Copy left singular vectors of A from WORK(IR) to A
    *
                         CALL DLACPY( 'F', M, M, WORK( IR ), LDWRKR, A,
         $                            LDA )
    *
                      ELSE
    *
    *                    Insufficient workspace for a fast algorithm
    *
                         ITAU = 1
                         IWORK = ITAU + M
    *
    *                    Compute A=L*Q, copying result to VT
    *                    (Workspace: need 2*M, prefer M+M*NB)
    *
                         CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
    *
    *                    Generate Q in VT
    *                    (Workspace: need M+N, prefer M+N*NB)
    *
                         CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IE = ITAU
                         ITAUQ = IE + M
                         ITAUP = ITAUQ + M
                         IWORK = ITAUP + M
    *
    *                    Zero out above L in A
    *
                         CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, A( 1, 2 ),
         $                            LDA )
    *
    *                    Bidiagonalize L in A
    *                    (Workspace: need 4*M, prefer 3*M+2*M*NB)
    *
                         CALL DGEBRD( M, M, A, LDA, S, WORK( IE ),
         $                            WORK( ITAUQ ), WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Multiply right bidiagonalizing vectors in A by Q
    *                    in VT
    *                    (Workspace: need 3*M+N, prefer 3*M+N*NB)
    *
                         CALL DORMBR( 'P', 'L', 'T', M, N, M, A, LDA,
         $                            WORK( ITAUP ), VT, LDVT,
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Generate left bidiagonalizing vectors in A
    *                    (Workspace: need 4*M, prefer 3*M+M*NB)
    *
                         CALL DORGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + M
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of A in A and computing right
    *                    singular vectors of A in VT
    *                    (Workspace: need BDSPAC)
    *
                         CALL DBDSQR( 'U', M, N, M, 0, S, WORK( IE ), VT,
         $                            LDVT, A, LDA, DUM, 1, WORK( IWORK ),
         $                            INFO )
    *
                      END IF
    *
                   ELSE IF( WNTUAS ) THEN
    *
    *                 Path 9t(N much larger than M, JOBU='S' or 'A',
    *                         JOBVT='A')
    *                 N right singular vectors to be computed in VT and
    *                 M left singular vectors to be computed in U
    *
                      IF( LWORK.GE.M*M+MAX( N+M, 4*M, BDSPAC ) ) THEN
    *
    *                    Sufficient workspace for a fast algorithm
    *
                         IU = 1
                         IF( LWORK.GE.WRKBL+LDA*M ) THEN
    *
    *                       WORK(IU) is LDA by M
    *
                            LDWRKU = LDA
                         ELSE
    *
    *                       WORK(IU) is M by M
    *
                            LDWRKU = M
                         END IF
                         ITAU = IU + LDWRKU*M
                         IWORK = ITAU + M
    *
    *                    Compute A=L*Q, copying result to VT
    *                    (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
    *
                         CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
    *
    *                    Generate Q in VT
    *                    (Workspace: need M*M+M+N, prefer M*M+M+N*NB)
    *
                         CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy L to WORK(IU), zeroing out above it
    *
                         CALL DLACPY( 'L', M, M, A, LDA, WORK( IU ),
         $                            LDWRKU )
                         CALL DLASET( 'U', M-1, M-1, ZERO, ZERO,
         $                            WORK( IU+LDWRKU ), LDWRKU )
                         IE = ITAU
                         ITAUQ = IE + M
                         ITAUP = ITAUQ + M
                         IWORK = ITAUP + M
    *
    *                    Bidiagonalize L in WORK(IU), copying result to U
    *                    (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
    *
                         CALL DGEBRD( M, M, WORK( IU ), LDWRKU, S,
         $                            WORK( IE ), WORK( ITAUQ ),
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'L', M, M, WORK( IU ), LDWRKU, U,
         $                            LDU )
    *
    *                    Generate right bidiagonalizing vectors in WORK(IU)
    *                    (Workspace: need M*M+4*M, prefer M*M+3*M+(M-1)*NB)
    *
                         CALL DORGBR( 'P', M, M, M, WORK( IU ), LDWRKU,
         $                            WORK( ITAUP ), WORK( IWORK ),
         $                            LWORK-IWORK+1, IERR )
    *
    *                    Generate left bidiagonalizing vectors in U
    *                    (Workspace: need M*M+4*M, prefer M*M+3*M+M*NB)
    *
                         CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + M
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of L in U and computing right
    *                    singular vectors of L in WORK(IU)
    *                    (Workspace: need M*M+BDSPAC)
    *
                         CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ),
         $                            WORK( IU ), LDWRKU, U, LDU, DUM, 1,
         $                            WORK( IWORK ), INFO )
    *
    *                    Multiply right singular vectors of L in WORK(IU) by
    *                    Q in VT, storing result in A
    *                    (Workspace: need M*M)
    *
                         CALL DGEMM( 'N', 'N', M, N, M, ONE, WORK( IU ),
         $                           LDWRKU, VT, LDVT, ZERO, A, LDA )
    *
    *                    Copy right singular vectors of A from A to VT
    *
                         CALL DLACPY( 'F', M, N, A, LDA, VT, LDVT )
    *
                      ELSE
    *
    *                    Insufficient workspace for a fast algorithm
    *
                         ITAU = 1
                         IWORK = ITAU + M
    *
    *                    Compute A=L*Q, copying result to VT
    *                    (Workspace: need 2*M, prefer M+M*NB)
    *
                         CALL DGELQF( M, N, A, LDA, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
    *
    *                    Generate Q in VT
    *                    (Workspace: need M+N, prefer M+N*NB)
    *
                         CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Copy L to U, zeroing out above it
    *
                         CALL DLACPY( 'L', M, M, A, LDA, U, LDU )
                         CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, U( 1, 2 ),
         $                            LDU )
                         IE = ITAU
                         ITAUQ = IE + M
                         ITAUP = ITAUQ + M
                         IWORK = ITAUP + M
    *
    *                    Bidiagonalize L in U
    *                    (Workspace: need 4*M, prefer 3*M+2*M*NB)
    *
                         CALL DGEBRD( M, M, U, LDU, S, WORK( IE ),
         $                            WORK( ITAUQ ), WORK( ITAUP ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Multiply right bidiagonalizing vectors in U by Q
    *                    in VT
    *                    (Workspace: need 3*M+N, prefer 3*M+N*NB)
    *
                         CALL DORMBR( 'P', 'L', 'T', M, N, M, U, LDU,
         $                            WORK( ITAUP ), VT, LDVT,
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
    *
    *                    Generate left bidiagonalizing vectors in U
    *                    (Workspace: need 4*M, prefer 3*M+M*NB)
    *
                         CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ),
         $                            WORK( IWORK ), LWORK-IWORK+1, IERR )
                         IWORK = IE + M
    *
    *                    Perform bidiagonal QR iteration, computing left
    *                    singular vectors of A in U and computing right
    *                    singular vectors of A in VT
    *                    (Workspace: need BDSPAC)
    *
                         CALL DBDSQR( 'U', M, N, M, 0, S, WORK( IE ), VT,
         $                            LDVT, U, LDU, DUM, 1, WORK( IWORK ),
         $                            INFO )
    *
                      END IF
    *
                   END IF
    *
                END IF
    *
             ELSE
    *
    *           N .LT. MNTHR
    *
    *           Path 10t(N greater than M, but not much larger)
    *           Reduce to bidiagonal form without LQ decomposition
    *
                IE = 1
                ITAUQ = IE + M
                ITAUP = ITAUQ + M
                IWORK = ITAUP + M
    *
    *           Bidiagonalize A
    *           (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB)
    *
                CALL DGEBRD( M, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ),
         $                   WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
         $                   IERR )
                IF( WNTUAS ) THEN
    *
    *              If left singular vectors desired in U, copy result to U
    *              and generate left bidiagonalizing vectors in U
    *              (Workspace: need 4*M-1, prefer 3*M+(M-1)*NB)
    *
                   CALL DLACPY( 'L', M, M, A, LDA, U, LDU )
                   CALL DORGBR( 'Q', M, M, N, U, LDU, WORK( ITAUQ ),
         $                      WORK( IWORK ), LWORK-IWORK+1, IERR )
                END IF
                IF( WNTVAS ) THEN
    *
    *              If right singular vectors desired in VT, copy result to
    *              VT and generate right bidiagonalizing vectors in VT
    *              (Workspace: need 3*M+NRVT, prefer 3*M+NRVT*NB)
    *
                   CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
                   IF( WNTVA )
         $            NRVT = N
                   IF( WNTVS )
         $            NRVT = M
                   CALL DORGBR( 'P', NRVT, N, M, VT, LDVT, WORK( ITAUP ),
         $                      WORK( IWORK ), LWORK-IWORK+1, IERR )
                END IF
                IF( WNTUO ) THEN
    *
    *              If left singular vectors desired in A, generate left
    *              bidiagonalizing vectors in A
    *              (Workspace: need 4*M-1, prefer 3*M+(M-1)*NB)
    *
                   CALL DORGBR( 'Q', M, M, N, A, LDA, WORK( ITAUQ ),
         $                      WORK( IWORK ), LWORK-IWORK+1, IERR )
                END IF
                IF( WNTVO ) THEN
    *
    *              If right singular vectors desired in A, generate right
    *              bidiagonalizing vectors in A
    *              (Workspace: need 4*M, prefer 3*M+M*NB)
    *
                   CALL DORGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ),
         $                      WORK( IWORK ), LWORK-IWORK+1, IERR )
                END IF
                IWORK = IE + M
                IF( WNTUAS .OR. WNTUO )
         $         NRU = M
                IF( WNTUN )
         $         NRU = 0
                IF( WNTVAS .OR. WNTVO )
         $         NCVT = N
                IF( WNTVN )
         $         NCVT = 0
                IF( ( .NOT.WNTUO ) .AND. ( .NOT.WNTVO ) ) THEN
    *
    *              Perform bidiagonal QR iteration, if desired, computing
    *              left singular vectors in U and computing right singular
    *              vectors in VT
    *              (Workspace: need BDSPAC)
    *
                   CALL DBDSQR( 'L', M, NCVT, NRU, 0, S, WORK( IE ), VT,
         $                      LDVT, U, LDU, DUM, 1, WORK( IWORK ), INFO )
                ELSE IF( ( .NOT.WNTUO ) .AND. WNTVO ) THEN
    *
    *              Perform bidiagonal QR iteration, if desired, computing
    *              left singular vectors in U and computing right singular
    *              vectors in A
    *              (Workspace: need BDSPAC)
    *
                   CALL DBDSQR( 'L', M, NCVT, NRU, 0, S, WORK( IE ), A, LDA,
         $                      U, LDU, DUM, 1, WORK( IWORK ), INFO )
                ELSE
    *
    *              Perform bidiagonal QR iteration, if desired, computing
    *              left singular vectors in A and computing right singular
    *              vectors in VT
    *              (Workspace: need BDSPAC)
    *
                   CALL DBDSQR( 'L', M, NCVT, NRU, 0, S, WORK( IE ), VT,
         $                      LDVT, A, LDA, DUM, 1, WORK( IWORK ), INFO )
                END IF
    *
             END IF
    *
          END IF
    *
    *     If DBDSQR failed to converge, copy unconverged superdiagonals
    *     to WORK( 2:MINMN )
    *
          IF( INFO.NE.0 ) THEN
             IF( IE.GT.2 ) THEN
                DO 50 I = 1, MINMN - 1
                   WORK( I+1 ) = WORK( I+IE-1 )
       50       CONTINUE
             END IF
             IF( IE.LT.2 ) THEN
                DO 60 I = MINMN - 1, 1, -1
                   WORK( I+1 ) = WORK( I+IE-1 )
       60       CONTINUE
             END IF
          END IF
    *
    *     Undo scaling if necessary
    *
          IF( ISCL.EQ.1 ) THEN
             IF( ANRM.GT.BIGNUM )
         $      CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN,
         $                   IERR )
             IF( INFO.NE.0 .AND. ANRM.GT.BIGNUM )
         $      CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN-1, 1, WORK( 2 ),
         $                   MINMN, IERR )
             IF( ANRM.LT.SMLNUM )
         $      CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN,
         $                   IERR )
             IF( INFO.NE.0 .AND. ANRM.LT.SMLNUM )
         $      CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN-1, 1, WORK( 2 ),
         $                   MINMN, IERR )
          END IF
    *
    *     Return optimal workspace in WORK(1)
    *
          WORK( 1 ) = MAXWRK
    *
          RETURN
    *
    *     End of DGESVD
    *
          END