zgesdd.f

          SUBROUTINE ZGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
         $                   LWORK, RWORK, IWORK, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *     8-15-00:  Improve consistency of WS calculations (eca)
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBZ
          INTEGER            INFO, LDA, LDU, LDVT, LWORK, M, N
    *     ..
    *     .. Array Arguments ..
          INTEGER            IWORK( * )
          DOUBLE PRECISION   RWORK( * ), S( * )
          COMPLEX*16         A( LDA, * ), U( LDU, * ), VT( LDVT, * ),
         $                   WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZGESDD computes the singular value decomposition (SVD) of a complex
    *  M-by-N matrix A, optionally computing the left and/or right singular
    *  vectors, by using divide-and-conquer method. The SVD is written
    *
    *       A = U * SIGMA * conjugate-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 unitary matrix, and
    *  V is an N-by-N unitary 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 VT = V**H, not V.
    *
    *  The divide and conquer algorithm makes very mild assumptions about
    *  floating point arithmetic. It will work on machines with a guard
    *  digit in add/subtract, or on those binary machines without guard
    *  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
    *  Cray-2. It could conceivably fail on hexadecimal or decimal machines
    *  without guard digits, but we know of none.
    *
    *  Arguments
    *  =========
    *
    *  JOBZ    (input) CHARACTER*1
    *          Specifies options for computing all or part of the matrix U:
    *          = 'A':  all M columns of U and all N rows of V**H are
    *                  returned in the arrays U and VT;
    *          = 'S':  the first min(M,N) columns of U and the first
    *                  min(M,N) rows of V**H are returned in the arrays U
    *                  and VT;
    *          = 'O':  If M >= N, the first N columns of U are overwritten
    *                  in the array A and all rows of V**H are returned in
    *                  the array VT;
    *                  otherwise, all columns of U are returned in the
    *                  array U and the first M rows of V**H are overwritten
    *                  in the array A;
    *          = 'N':  no columns of U or rows of V**H are computed.
    *
    *  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) COMPLEX*16 array, dimension (LDA,N)
    *          On entry, the M-by-N matrix A.
    *          On exit,
    *          if JOBZ = 'O',  A is overwritten with the first N columns
    *                          of U (the left singular vectors, stored
    *                          columnwise) if M >= N;
    *                          A is overwritten with the first M rows
    *                          of V**H (the right singular vectors, stored
    *                          rowwise) otherwise.
    *          if JOBZ .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) COMPLEX*16 array, dimension (LDU,UCOL)
    *          UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
    *          UCOL = min(M,N) if JOBZ = 'S'.
    *          If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
    *          unitary matrix U;
    *          if JOBZ = 'S', U contains the first min(M,N) columns of U
    *          (the left singular vectors, stored columnwise);
    *          if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
    *
    *  LDU     (input) INTEGER
    *          The leading dimension of the array U.  LDU >= 1; if
    *          JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
    *
    *  VT      (output) COMPLEX*16 array, dimension (LDVT,N)
    *          If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
    *          N-by-N unitary matrix V**H;
    *          if JOBZ = 'S', VT contains the first min(M,N) rows of
    *          V**H (the right singular vectors, stored rowwise);
    *          if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
    *
    *  LDVT    (input) INTEGER
    *          The leading dimension of the array VT.  LDVT >= 1; if
    *          JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
    *          if JOBZ = 'S', LDVT >= min(M,N).
    *
    *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) INTEGER
    *          The dimension of the array WORK. LWORK >= 1.
    *          if JOBZ = 'N', LWORK >= 2*min(M,N)+max(M,N).
    *          if JOBZ = 'O',
    *                LWORK >= 2*min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
    *          if JOBZ = 'S' or 'A',
    *                LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
    *          For good performance, LWORK should generally be larger.
    *
    *          If LWORK = -1, a workspace query is assumed.  The optimal
    *          size for the WORK array is calculated and stored in WORK(1),
    *          and no other work except argument checking is performed.
    *
    *  RWORK   (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
    *          If JOBZ = 'N', LRWORK >= 5*min(M,N).
    *          Otherwise, LRWORK >= 5*min(M,N)*min(M,N) + 7*min(M,N)
    *
    *  IWORK   (workspace) INTEGER array, dimension (8*min(M,N))
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit.
    *          < 0:  if INFO = -i, the i-th argument had an illegal value.
    *          > 0:  The updating process of DBDSDC did not converge.
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *     Ming Gu and Huan Ren, Computer Science Division, University of
    *     California at Berkeley, USA
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          INTEGER            LQUERV
          PARAMETER          ( LQUERV = -1 )
          COMPLEX*16         CZERO, CONE
          PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
         $                   CONE = ( 1.0D+0, 0.0D+0 ) )
          DOUBLE PRECISION   ZERO, ONE
          PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            WNTQA, WNTQAS, WNTQN, WNTQO, WNTQS
          INTEGER            BLK, CHUNK, I, IE, IERR, IL, IR, IRU, IRVT,
         $                   ISCL, ITAU, ITAUP, ITAUQ, IU, IVT, LDWKVT,
         $                   LDWRKL, LDWRKR, LDWRKU, MAXWRK, MINMN, MINWRK,
         $                   MNTHR1, MNTHR2, NRWORK, NWORK, WRKBL
          DOUBLE PRECISION   ANRM, BIGNUM, EPS, SMLNUM
    *     ..
    *     .. Local Arrays ..
          INTEGER            IDUM( 1 )
          DOUBLE PRECISION   DUM( 1 )
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DBDSDC, DLASCL, XERBLA, ZGEBRD, ZGELQF, ZGEMM,
         $                   ZGEQRF, ZLACP2, ZLACPY, ZLACRM, ZLARCM, ZLASCL,
         $                   ZLASET, ZUNGBR, ZUNGLQ, ZUNGQR, ZUNMBR
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          DOUBLE PRECISION   DLAMCH, ZLANGE
          EXTERNAL           LSAME, ILAENV, DLAMCH, ZLANGE
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          INT, MAX, MIN, SQRT
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input arguments
    *
          INFO = 0
          MINMN = MIN( M, N )
          MNTHR1 = INT( MINMN*17.0D0 / 9.0D0 )
          MNTHR2 = INT( MINMN*5.0D0 / 3.0D0 )
          WNTQA = LSAME( JOBZ, 'A' )
          WNTQS = LSAME( JOBZ, 'S' )
          WNTQAS = WNTQA .OR. WNTQS
          WNTQO = LSAME( JOBZ, 'O' )
          WNTQN = LSAME( JOBZ, 'N' )
          MINWRK = 1
          MAXWRK = 1
    *
          IF( .NOT.( WNTQA .OR. WNTQS .OR. WNTQO .OR. WNTQN ) ) THEN
             INFO = -1
          ELSE IF( M.LT.0 ) THEN
             INFO = -2
          ELSE IF( N.LT.0 ) THEN
             INFO = -3
          ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
             INFO = -5
          ELSE IF( LDU.LT.1 .OR. ( WNTQAS .AND. LDU.LT.M ) .OR.
         $         ( WNTQO .AND. M.LT.N .AND. LDU.LT.M ) ) THEN
             INFO = -8
          ELSE IF( LDVT.LT.1 .OR. ( WNTQA .AND. LDVT.LT.N ) .OR.
         $         ( WNTQS .AND. LDVT.LT.MINMN ) .OR.
         $         ( WNTQO .AND. M.GE.N .AND. LDVT.LT.N ) ) THEN
             INFO = -10
          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.
    *       CWorkspace refers to complex workspace, and RWorkspace to
    *       real workspace. NB refers to the optimal block size for the
    *       immediately following subroutine, as returned by ILAENV.)
    *
          IF( INFO.EQ.0 .AND. M.GT.0 .AND. N.GT.0 ) THEN
             IF( M.GE.N ) THEN
    *
    *           There is no complex work space needed for bidiagonal SVD
    *           The real work space needed for bidiagonal SVD is BDSPAC
    *           for computing singular values and singular vectors; BDSPAN
    *           for computing singular values only.
    *           BDSPAC = 5*N*N + 7*N
    *           BDSPAN = MAX(7*N+4, 3*N+2+SMLSIZ*(SMLSIZ+8))
    *
                IF( M.GE.MNTHR1 ) THEN
                   IF( WNTQN ) THEN
    *
    *                 Path 1 (M much larger than N, JOBZ='N')
    *
                      MAXWRK = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1,
         $                     -1 )
                      MAXWRK = MAX( MAXWRK, 2*N+2*N*
         $                     ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) )
                      MINWRK = 3*N
                   ELSE IF( WNTQO ) THEN
    *
    *                 Path 2 (M much larger than N, JOBZ='O')
    *
                      WRKBL = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'ZUNGQR', ' ', M,
         $                    N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 2*N+2*N*
         $                    ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 2*N+N*
         $                    ILAENV( 1, 'ZUNMBR', 'QLN', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 2*N+N*
         $                    ILAENV( 1, 'ZUNMBR', 'PRC', N, N, N, -1 ) )
                      MAXWRK = M*N + N*N + WRKBL
                      MINWRK = 2*N*N + 3*N
                   ELSE IF( WNTQS ) THEN
    *
    *                 Path 3 (M much larger than N, JOBZ='S')
    *
                      WRKBL = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, N+N*ILAENV( 1, 'ZUNGQR', ' ', M,
         $                    N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 2*N+2*N*
         $                    ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 2*N+N*
         $                    ILAENV( 1, 'ZUNMBR', 'QLN', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 2*N+N*
         $                    ILAENV( 1, 'ZUNMBR', 'PRC', N, N, N, -1 ) )
                      MAXWRK = N*N + WRKBL
                      MINWRK = N*N + 3*N
                   ELSE IF( WNTQA ) THEN
    *
    *                 Path 4 (M much larger than N, JOBZ='A')
    *
                      WRKBL = N + N*ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, N+M*ILAENV( 1, 'ZUNGQR', ' ', M,
         $                    M, N, -1 ) )
                      WRKBL = MAX( WRKBL, 2*N+2*N*
         $                    ILAENV( 1, 'ZGEBRD', ' ', N, N, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 2*N+N*
         $                    ILAENV( 1, 'ZUNMBR', 'QLN', N, N, N, -1 ) )
                      WRKBL = MAX( WRKBL, 2*N+N*
         $                    ILAENV( 1, 'ZUNMBR', 'PRC', N, N, N, -1 ) )
                      MAXWRK = N*N + WRKBL
                      MINWRK = N*N + 2*N + M
                   END IF
                ELSE IF( M.GE.MNTHR2 ) THEN
    *
    *              Path 5 (M much larger than N, but not as much as MNTHR1)
    *
                   MAXWRK = 2*N + ( M+N )*ILAENV( 1, 'ZGEBRD', ' ', M, N,
         $                  -1, -1 )
                   MINWRK = 2*N + M
                   IF( WNTQO ) THEN
                      MAXWRK = MAX( MAXWRK, 2*N+N*
         $                     ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*N+N*
         $                     ILAENV( 1, 'ZUNGBR', 'Q', M, N, N, -1 ) )
                      MAXWRK = MAXWRK + M*N
                      MINWRK = MINWRK + N*N
                   ELSE IF( WNTQS ) THEN
                      MAXWRK = MAX( MAXWRK, 2*N+N*
         $                     ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*N+N*
         $                     ILAENV( 1, 'ZUNGBR', 'Q', M, N, N, -1 ) )
                   ELSE IF( WNTQA ) THEN
                      MAXWRK = MAX( MAXWRK, 2*N+N*
         $                     ILAENV( 1, 'ZUNGBR', 'P', N, N, N, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*N+M*
         $                     ILAENV( 1, 'ZUNGBR', 'Q', M, M, N, -1 ) )
                   END IF
                ELSE
    *
    *              Path 6 (M at least N, but not much larger)
    *
                   MAXWRK = 2*N + ( M+N )*ILAENV( 1, 'ZGEBRD', ' ', M, N,
         $                  -1, -1 )
                   MINWRK = 2*N + M
                   IF( WNTQO ) THEN
                      MAXWRK = MAX( MAXWRK, 2*N+N*
         $                     ILAENV( 1, 'ZUNMBR', 'PRC', N, N, N, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*N+N*
         $                     ILAENV( 1, 'ZUNMBR', 'QLN', M, N, N, -1 ) )
                      MAXWRK = MAXWRK + M*N
                      MINWRK = MINWRK + N*N
                   ELSE IF( WNTQS ) THEN
                      MAXWRK = MAX( MAXWRK, 2*N+N*
         $                     ILAENV( 1, 'ZUNMBR', 'PRC', N, N, N, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*N+N*
         $                     ILAENV( 1, 'ZUNMBR', 'QLN', M, N, N, -1 ) )
                   ELSE IF( WNTQA ) THEN
                      MAXWRK = MAX( MAXWRK, 2*N+N*
         $                     ILAENV( 1, 'ZUNGBR', 'PRC', N, N, N, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*N+M*
         $                     ILAENV( 1, 'ZUNGBR', 'QLN', M, M, N, -1 ) )
                   END IF
                END IF
             ELSE
    *
    *           There is no complex work space needed for bidiagonal SVD
    *           The real work space needed for bidiagonal SVD is BDSPAC
    *           for computing singular values and singular vectors; BDSPAN
    *           for computing singular values only.
    *           BDSPAC = 5*M*M + 7*M
    *           BDSPAN = MAX(7*M+4, 3*M+2+SMLSIZ*(SMLSIZ+8))
    *
                IF( N.GE.MNTHR1 ) THEN
                   IF( WNTQN ) THEN
    *
    *                 Path 1t (N much larger than M, JOBZ='N')
    *
                      MAXWRK = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1,
         $                     -1 )
                      MAXWRK = MAX( MAXWRK, 2*M+2*M*
         $                     ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
                      MINWRK = 3*M
                   ELSE IF( WNTQO ) THEN
    *
    *                 Path 2t (N much larger than M, JOBZ='O')
    *
                      WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'ZUNGLQ', ' ', M,
         $                    N, M, -1 ) )
                      WRKBL = MAX( WRKBL, 2*M+2*M*
         $                    ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 2*M+M*
         $                    ILAENV( 1, 'ZUNMBR', 'PRC', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, 2*M+M*
         $                    ILAENV( 1, 'ZUNMBR', 'QLN', M, M, M, -1 ) )
                      MAXWRK = M*N + M*M + WRKBL
                      MINWRK = 2*M*M + 3*M
                   ELSE IF( WNTQS ) THEN
    *
    *                 Path 3t (N much larger than M, JOBZ='S')
    *
                      WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, M+M*ILAENV( 1, 'ZUNGLQ', ' ', M,
         $                    N, M, -1 ) )
                      WRKBL = MAX( WRKBL, 2*M+2*M*
         $                    ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 2*M+M*
         $                    ILAENV( 1, 'ZUNMBR', 'PRC', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, 2*M+M*
         $                    ILAENV( 1, 'ZUNMBR', 'QLN', M, M, M, -1 ) )
                      MAXWRK = M*M + WRKBL
                      MINWRK = M*M + 3*M
                   ELSE IF( WNTQA ) THEN
    *
    *                 Path 4t (N much larger than M, JOBZ='A')
    *
                      WRKBL = M + M*ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
                      WRKBL = MAX( WRKBL, M+N*ILAENV( 1, 'ZUNGLQ', ' ', N,
         $                    N, M, -1 ) )
                      WRKBL = MAX( WRKBL, 2*M+2*M*
         $                    ILAENV( 1, 'ZGEBRD', ' ', M, M, -1, -1 ) )
                      WRKBL = MAX( WRKBL, 2*M+M*
         $                    ILAENV( 1, 'ZUNMBR', 'PRC', M, M, M, -1 ) )
                      WRKBL = MAX( WRKBL, 2*M+M*
         $                    ILAENV( 1, 'ZUNMBR', 'QLN', M, M, M, -1 ) )
                      MAXWRK = M*M + WRKBL
                      MINWRK = M*M + 2*M + N
                   END IF
                ELSE IF( N.GE.MNTHR2 ) THEN
    *
    *              Path 5t (N much larger than M, but not as much as MNTHR1)
    *
                   MAXWRK = 2*M + ( M+N )*ILAENV( 1, 'ZGEBRD', ' ', M, N,
         $                  -1, -1 )
                   MINWRK = 2*M + N
                   IF( WNTQO ) THEN
                      MAXWRK = MAX( MAXWRK, 2*M+M*
         $                     ILAENV( 1, 'ZUNGBR', 'P', M, N, M, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*M+M*
         $                     ILAENV( 1, 'ZUNGBR', 'Q', M, M, N, -1 ) )
                      MAXWRK = MAXWRK + M*N
                      MINWRK = MINWRK + M*M
                   ELSE IF( WNTQS ) THEN
                      MAXWRK = MAX( MAXWRK, 2*M+M*
         $                     ILAENV( 1, 'ZUNGBR', 'P', M, N, M, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*M+M*
         $                     ILAENV( 1, 'ZUNGBR', 'Q', M, M, N, -1 ) )
                   ELSE IF( WNTQA ) THEN
                      MAXWRK = MAX( MAXWRK, 2*M+N*
         $                     ILAENV( 1, 'ZUNGBR', 'P', N, N, M, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*M+M*
         $                     ILAENV( 1, 'ZUNGBR', 'Q', M, M, N, -1 ) )
                   END IF
                ELSE
    *
    *              Path 6t (N greater than M, but not much larger)
    *
                   MAXWRK = 2*M + ( M+N )*ILAENV( 1, 'ZGEBRD', ' ', M, N,
         $                  -1, -1 )
                   MINWRK = 2*M + N
                   IF( WNTQO ) THEN
                      MAXWRK = MAX( MAXWRK, 2*M+M*
         $                     ILAENV( 1, 'ZUNMBR', 'PRC', M, N, M, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*M+M*
         $                     ILAENV( 1, 'ZUNMBR', 'QLN', M, M, N, -1 ) )
                      MAXWRK = MAXWRK + M*N
                      MINWRK = MINWRK + M*M
                   ELSE IF( WNTQS ) THEN
                      MAXWRK = MAX( MAXWRK, 2*M+M*
         $                     ILAENV( 1, 'ZUNGBR', 'PRC', M, N, M, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*M+M*
         $                     ILAENV( 1, 'ZUNGBR', 'QLN', M, M, N, -1 ) )
                   ELSE IF( WNTQA ) THEN
                      MAXWRK = MAX( MAXWRK, 2*M+N*
         $                     ILAENV( 1, 'ZUNGBR', 'PRC', N, N, M, -1 ) )
                      MAXWRK = MAX( MAXWRK, 2*M+M*
         $                     ILAENV( 1, 'ZUNGBR', 'QLN', M, M, N, -1 ) )
                   END IF
                END IF
             END IF
             MAXWRK = MAX( MAXWRK, MINWRK )
          END IF
          IF( INFO.EQ.0 ) THEN
             WORK( 1 ) = MAXWRK
             IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
         $      INFO = -13
          END IF
    *
    *     Quick returns
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZGESDD', -INFO )
             RETURN
          END IF
          IF( LWORK.EQ.LQUERV )
         $   RETURN
          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 = ZLANGE( 'M', M, N, A, LDA, DUM )
          ISCL = 0
          IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
             ISCL = 1
             CALL ZLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, IERR )
          ELSE IF( ANRM.GT.BIGNUM ) THEN
             ISCL = 1
             CALL ZLASCL( '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.MNTHR1 ) THEN
    *
                IF( WNTQN ) THEN
    *
    *              Path 1 (M much larger than N, JOBZ='N')
    *              No singular vectors to be computed
    *
                   ITAU = 1
                   NWORK = ITAU + N
    *
    *              Compute A=Q*R
    *              (CWorkspace: need 2*N, prefer N+N*NB)
    *              (RWorkspace: need 0)
    *
                   CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Zero out below R
    *
                   CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, A( 2, 1 ),
         $                      LDA )
                   IE = 1
                   ITAUQ = 1
                   ITAUP = ITAUQ + N
                   NWORK = ITAUP + N
    *
    *              Bidiagonalize R in A
    *              (CWorkspace: need 3*N, prefer 2*N+2*N*NB)
    *              (RWorkspace: need N)
    *
                   CALL ZGEBRD( N, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
         $                      WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
         $                      IERR )
                   NRWORK = IE + N
    *
    *              Perform bidiagonal SVD, compute singular values only
    *              (CWorkspace: 0)
    *              (RWorkspace: need BDSPAN)
    *
                   CALL DBDSDC( 'U', 'N', N, S, RWORK( IE ), DUM, 1, DUM, 1,
         $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
    *
                ELSE IF( WNTQO ) THEN
    *
    *              Path 2 (M much larger than N, JOBZ='O')
    *              N left singular vectors to be overwritten on A and
    *              N right singular vectors to be computed in VT
    *
                   IU = 1
    *
    *              WORK(IU) is N by N
    *
                   LDWRKU = N
                   IR = IU + LDWRKU*N
                   IF( LWORK.GE.M*N+N*N+3*N ) THEN
    *
    *                 WORK(IR) is M by N
    *
                      LDWRKR = M
                   ELSE
                      LDWRKR = ( LWORK-N*N-3*N ) / N
                   END IF
                   ITAU = IR + LDWRKR*N
                   NWORK = ITAU + N
    *
    *              Compute A=Q*R
    *              (CWorkspace: need N*N+2*N, prefer M*N+N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Copy R to WORK( IR ), zeroing out below it
    *
                   CALL ZLACPY( 'U', N, N, A, LDA, WORK( IR ), LDWRKR )
                   CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, WORK( IR+1 ),
         $                      LDWRKR )
    *
    *              Generate Q in A
    *              (CWorkspace: need 2*N, prefer N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
                   IE = 1
                   ITAUQ = ITAU
                   ITAUP = ITAUQ + N
                   NWORK = ITAUP + N
    *
    *              Bidiagonalize R in WORK(IR)
    *              (CWorkspace: need N*N+3*N, prefer M*N+2*N+2*N*NB)
    *              (RWorkspace: need N)
    *
                   CALL ZGEBRD( N, N, WORK( IR ), LDWRKR, S, RWORK( IE ),
         $                      WORK( ITAUQ ), WORK( ITAUP ), WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of R in WORK(IRU) and computing right singular vectors
    *              of R in WORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRU = IE + N
                   IRVT = IRU + N*N
                   NRWORK = IRVT + N*N
                   CALL DBDSDC( 'U', 'I', N, S, RWORK( IE ), RWORK( IRU ),
         $                      N, RWORK( IRVT ), N, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Copy real matrix RWORK(IRU) to complex matrix WORK(IU)
    *              Overwrite WORK(IU) by the left singular vectors of R
    *              (CWorkspace: need 2*N*N+3*N, prefer M*N+N*N+2*N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', N, N, RWORK( IRU ), N, WORK( IU ),
         $                      LDWRKU )
                   CALL ZUNMBR( 'Q', 'L', 'N', N, N, N, WORK( IR ), LDWRKR,
         $                      WORK( ITAUQ ), WORK( IU ), LDWRKU,
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Copy real matrix RWORK(IRVT) to complex matrix VT
    *              Overwrite VT by the right singular vectors of R
    *              (CWorkspace: need N*N+3*N, prefer M*N+2*N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', N, N, RWORK( IRVT ), N, VT, LDVT )
                   CALL ZUNMBR( 'P', 'R', 'C', N, N, N, WORK( IR ), LDWRKR,
         $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Multiply Q in A by left singular vectors of R in
    *              WORK(IU), storing result in WORK(IR) and copying to A
    *              (CWorkspace: need 2*N*N, prefer N*N+M*N)
    *              (RWorkspace: 0)
    *
                   DO 10 I = 1, M, LDWRKR
                      CHUNK = MIN( M-I+1, LDWRKR )
                      CALL ZGEMM( 'N', 'N', CHUNK, N, N, CONE, A( I, 1 ),
         $                        LDA, WORK( IU ), LDWRKU, CZERO,
         $                        WORK( IR ), LDWRKR )
                      CALL ZLACPY( 'F', CHUNK, N, WORK( IR ), LDWRKR,
         $                         A( I, 1 ), LDA )
       10          CONTINUE
    *
                ELSE IF( WNTQS ) THEN
    *
    *              Path 3 (M much larger than N, JOBZ='S')
    *              N left singular vectors to be computed in U and
    *              N right singular vectors to be computed in VT
    *
                   IR = 1
    *
    *              WORK(IR) is N by N
    *
                   LDWRKR = N
                   ITAU = IR + LDWRKR*N
                   NWORK = ITAU + N
    *
    *              Compute A=Q*R
    *              (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Copy R to WORK(IR), zeroing out below it
    *
                   CALL ZLACPY( 'U', N, N, A, LDA, WORK( IR ), LDWRKR )
                   CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, WORK( IR+1 ),
         $                      LDWRKR )
    *
    *              Generate Q in A
    *              (CWorkspace: need 2*N, prefer N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
                   IE = 1
                   ITAUQ = ITAU
                   ITAUP = ITAUQ + N
                   NWORK = ITAUP + N
    *
    *              Bidiagonalize R in WORK(IR)
    *              (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB)
    *              (RWorkspace: need N)
    *
                   CALL ZGEBRD( N, N, WORK( IR ), LDWRKR, S, RWORK( IE ),
         $                      WORK( ITAUQ ), WORK( ITAUP ), WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRU = IE + N
                   IRVT = IRU + N*N
                   NRWORK = IRVT + N*N
                   CALL DBDSDC( 'U', 'I', N, S, RWORK( IE ), RWORK( IRU ),
         $                      N, RWORK( IRVT ), N, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Copy real matrix RWORK(IRU) to complex matrix U
    *              Overwrite U by left singular vectors of R
    *              (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', N, N, RWORK( IRU ), N, U, LDU )
                   CALL ZUNMBR( 'Q', 'L', 'N', N, N, N, WORK( IR ), LDWRKR,
         $                      WORK( ITAUQ ), U, LDU, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Copy real matrix RWORK(IRVT) to complex matrix VT
    *              Overwrite VT by right singular vectors of R
    *              (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', N, N, RWORK( IRVT ), N, VT, LDVT )
                   CALL ZUNMBR( 'P', 'R', 'C', N, N, N, WORK( IR ), LDWRKR,
         $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Multiply Q in A by left singular vectors of R in
    *              WORK(IR), storing result in U
    *              (CWorkspace: need N*N)
    *              (RWorkspace: 0)
    *
                   CALL ZLACPY( 'F', N, N, U, LDU, WORK( IR ), LDWRKR )
                   CALL ZGEMM( 'N', 'N', M, N, N, CONE, A, LDA, WORK( IR ),
         $                     LDWRKR, CZERO, U, LDU )
    *
                ELSE IF( WNTQA ) THEN
    *
    *              Path 4 (M much larger than N, JOBZ='A')
    *              M left singular vectors to be computed in U and
    *              N right singular vectors to be computed in VT
    *
                   IU = 1
    *
    *              WORK(IU) is N by N
    *
                   LDWRKU = N
                   ITAU = IU + LDWRKU*N
                   NWORK = ITAU + N
    *
    *              Compute A=Q*R, copying result to U
    *              (CWorkspace: need 2*N, prefer N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
                   CALL ZLACPY( 'L', M, N, A, LDA, U, LDU )
    *
    *              Generate Q in U
    *              (CWorkspace: need N+M, prefer N+M*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZUNGQR( M, M, N, U, LDU, WORK( ITAU ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Produce R in A, zeroing out below it
    *
                   CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, A( 2, 1 ),
         $                      LDA )
                   IE = 1
                   ITAUQ = ITAU
                   ITAUP = ITAUQ + N
                   NWORK = ITAUP + N
    *
    *              Bidiagonalize R in A
    *              (CWorkspace: need 3*N, prefer 2*N+2*N*NB)
    *              (RWorkspace: need N)
    *
                   CALL ZGEBRD( N, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
         $                      WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
         $                      IERR )
                   IRU = IE + N
                   IRVT = IRU + N*N
                   NRWORK = IRVT + N*N
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   CALL DBDSDC( 'U', 'I', N, S, RWORK( IE ), RWORK( IRU ),
         $                      N, RWORK( IRVT ), N, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Copy real matrix RWORK(IRU) to complex matrix WORK(IU)
    *              Overwrite WORK(IU) by left singular vectors of R
    *              (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', N, N, RWORK( IRU ), N, WORK( IU ),
         $                      LDWRKU )
                   CALL ZUNMBR( 'Q', 'L', 'N', N, N, N, A, LDA,
         $                      WORK( ITAUQ ), WORK( IU ), LDWRKU,
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Copy real matrix RWORK(IRVT) to complex matrix VT
    *              Overwrite VT by right singular vectors of R
    *              (CWorkspace: need 3*N, prefer 2*N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', N, N, RWORK( IRVT ), N, VT, LDVT )
                   CALL ZUNMBR( 'P', 'R', 'C', N, N, N, A, LDA,
         $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Multiply Q in U by left singular vectors of R in
    *              WORK(IU), storing result in A
    *              (CWorkspace: need N*N)
    *              (RWorkspace: 0)
    *
                   CALL ZGEMM( 'N', 'N', M, N, N, CONE, U, LDU, WORK( IU ),
         $                     LDWRKU, CZERO, A, LDA )
    *
    *              Copy left singular vectors of A from A to U
    *
                   CALL ZLACPY( 'F', M, N, A, LDA, U, LDU )
    *
                END IF
    *
             ELSE IF( M.GE.MNTHR2 ) THEN
    *
    *           MNTHR2 <= M < MNTHR1
    *
    *           Path 5 (M much larger than N, but not as much as MNTHR1)
    *           Reduce to bidiagonal form without QR decomposition, use
    *           ZUNGBR and matrix multiplication to compute singular vectors
    *
                IE = 1
                NRWORK = IE + N
                ITAUQ = 1
                ITAUP = ITAUQ + N
                NWORK = ITAUP + N
    *
    *           Bidiagonalize A
    *           (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB)
    *           (RWorkspace: need N)
    *
                CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
         $                   WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
         $                   IERR )
                IF( WNTQN ) THEN
    *
    *              Compute singular values only
    *              (Cworkspace: 0)
    *              (Rworkspace: need BDSPAN)
    *
                   CALL DBDSDC( 'U', 'N', N, S, RWORK( IE ), DUM, 1, DUM, 1,
         $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
                ELSE IF( WNTQO ) THEN
                   IU = NWORK
                   IRU = NRWORK
                   IRVT = IRU + N*N
                   NRWORK = IRVT + N*N
    *
    *              Copy A to VT, generate P**H
    *              (Cworkspace: need 2*N, prefer N+N*NB)
    *              (Rworkspace: 0)
    *
                   CALL ZLACPY( 'U', N, N, A, LDA, VT, LDVT )
                   CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Generate Q in A
    *              (CWorkspace: need 2*N, prefer N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZUNGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
                   IF( LWORK.GE.M*N+3*N ) THEN
    *
    *                 WORK( IU ) is M by N
    *
                      LDWRKU = M
                   ELSE
    *
    *                 WORK(IU) is LDWRKU by N
    *
                      LDWRKU = ( LWORK-3*N ) / N
                   END IF
                   NWORK = IU + LDWRKU*N
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   CALL DBDSDC( 'U', 'I', N, S, RWORK( IE ), RWORK( IRU ),
         $                      N, RWORK( IRVT ), N, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Multiply real matrix RWORK(IRVT) by P**H in VT,
    *              storing the result in WORK(IU), copying to VT
    *              (Cworkspace: need 0)
    *              (Rworkspace: need 3*N*N)
    *
                   CALL ZLARCM( N, N, RWORK( IRVT ), N, VT, LDVT,
         $                      WORK( IU ), LDWRKU, RWORK( NRWORK ) )
                   CALL ZLACPY( 'F', N, N, WORK( IU ), LDWRKU, VT, LDVT )
    *
    *              Multiply Q in A by real matrix RWORK(IRU), storing the
    *              result in WORK(IU), copying to A
    *              (CWorkspace: need N*N, prefer M*N)
    *              (Rworkspace: need 3*N*N, prefer N*N+2*M*N)
    *
                   NRWORK = IRVT
                   DO 20 I = 1, M, LDWRKU
                      CHUNK = MIN( M-I+1, LDWRKU )
                      CALL ZLACRM( CHUNK, N, A( I, 1 ), LDA, RWORK( IRU ),
         $                         N, WORK( IU ), LDWRKU, RWORK( NRWORK ) )
                      CALL ZLACPY( 'F', CHUNK, N, WORK( IU ), LDWRKU,
         $                         A( I, 1 ), LDA )
       20          CONTINUE
    *
                ELSE IF( WNTQS ) THEN
    *
    *              Copy A to VT, generate P**H
    *              (Cworkspace: need 2*N, prefer N+N*NB)
    *              (Rworkspace: 0)
    *
                   CALL ZLACPY( 'U', N, N, A, LDA, VT, LDVT )
                   CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Copy A to U, generate Q
    *              (Cworkspace: need 2*N, prefer N+N*NB)
    *              (Rworkspace: 0)
    *
                   CALL ZLACPY( 'L', M, N, A, LDA, U, LDU )
                   CALL ZUNGBR( 'Q', M, N, N, U, LDU, WORK( ITAUQ ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRU = NRWORK
                   IRVT = IRU + N*N
                   NRWORK = IRVT + N*N
                   CALL DBDSDC( 'U', 'I', N, S, RWORK( IE ), RWORK( IRU ),
         $                      N, RWORK( IRVT ), N, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Multiply real matrix RWORK(IRVT) by P**H in VT,
    *              storing the result in A, copying to VT
    *              (Cworkspace: need 0)
    *              (Rworkspace: need 3*N*N)
    *
                   CALL ZLARCM( N, N, RWORK( IRVT ), N, VT, LDVT, A, LDA,
         $                      RWORK( NRWORK ) )
                   CALL ZLACPY( 'F', N, N, A, LDA, VT, LDVT )
    *
    *              Multiply Q in U by real matrix RWORK(IRU), storing the
    *              result in A, copying to U
    *              (CWorkspace: need 0)
    *              (Rworkspace: need N*N+2*M*N)
    *
                   NRWORK = IRVT
                   CALL ZLACRM( M, N, U, LDU, RWORK( IRU ), N, A, LDA,
         $                      RWORK( NRWORK ) )
                   CALL ZLACPY( 'F', M, N, A, LDA, U, LDU )
                ELSE
    *
    *              Copy A to VT, generate P**H
    *              (Cworkspace: need 2*N, prefer N+N*NB)
    *              (Rworkspace: 0)
    *
                   CALL ZLACPY( 'U', N, N, A, LDA, VT, LDVT )
                   CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Copy A to U, generate Q
    *              (Cworkspace: need 2*N, prefer N+N*NB)
    *              (Rworkspace: 0)
    *
                   CALL ZLACPY( 'L', M, N, A, LDA, U, LDU )
                   CALL ZUNGBR( 'Q', M, M, N, U, LDU, WORK( ITAUQ ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRU = NRWORK
                   IRVT = IRU + N*N
                   NRWORK = IRVT + N*N
                   CALL DBDSDC( 'U', 'I', N, S, RWORK( IE ), RWORK( IRU ),
         $                      N, RWORK( IRVT ), N, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Multiply real matrix RWORK(IRVT) by P**H in VT,
    *              storing the result in A, copying to VT
    *              (Cworkspace: need 0)
    *              (Rworkspace: need 3*N*N)
    *
                   CALL ZLARCM( N, N, RWORK( IRVT ), N, VT, LDVT, A, LDA,
         $                      RWORK( NRWORK ) )
                   CALL ZLACPY( 'F', N, N, A, LDA, VT, LDVT )
    *
    *              Multiply Q in U by real matrix RWORK(IRU), storing the
    *              result in A, copying to U
    *              (CWorkspace: 0)
    *              (Rworkspace: need 3*N*N)
    *
                   NRWORK = IRVT
                   CALL ZLACRM( M, N, U, LDU, RWORK( IRU ), N, A, LDA,
         $                      RWORK( NRWORK ) )
                   CALL ZLACPY( 'F', M, N, A, LDA, U, LDU )
                END IF
    *
             ELSE
    *
    *           M .LT. MNTHR2
    *
    *           Path 6 (M at least N, but not much larger)
    *           Reduce to bidiagonal form without QR decomposition
    *           Use ZUNMBR to compute singular vectors
    *
                IE = 1
                NRWORK = IE + N
                ITAUQ = 1
                ITAUP = ITAUQ + N
                NWORK = ITAUP + N
    *
    *           Bidiagonalize A
    *           (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB)
    *           (RWorkspace: need N)
    *
                CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
         $                   WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
         $                   IERR )
                IF( WNTQN ) THEN
    *
    *              Compute singular values only
    *              (Cworkspace: 0)
    *              (Rworkspace: need BDSPAN)
    *
                   CALL DBDSDC( 'U', 'N', N, S, RWORK( IE ), DUM, 1, DUM, 1,
         $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
                ELSE IF( WNTQO ) THEN
                   IU = NWORK
                   IRU = NRWORK
                   IRVT = IRU + N*N
                   NRWORK = IRVT + N*N
                   IF( LWORK.GE.M*N+3*N ) THEN
    *
    *                 WORK( IU ) is M by N
    *
                      LDWRKU = M
                   ELSE
    *
    *                 WORK( IU ) is LDWRKU by N
    *
                      LDWRKU = ( LWORK-3*N ) / N
                   END IF
                   NWORK = IU + LDWRKU*N
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   CALL DBDSDC( 'U', 'I', N, S, RWORK( IE ), RWORK( IRU ),
         $                      N, RWORK( IRVT ), N, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Copy real matrix RWORK(IRVT) to complex matrix VT
    *              Overwrite VT by right singular vectors of A
    *              (Cworkspace: need 2*N, prefer N+N*NB)
    *              (Rworkspace: need 0)
    *
                   CALL ZLACP2( 'F', N, N, RWORK( IRVT ), N, VT, LDVT )
                   CALL ZUNMBR( 'P', 'R', 'C', N, N, N, A, LDA,
         $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
                   IF( LWORK.GE.M*N+3*N ) THEN
    *
    *              Copy real matrix RWORK(IRU) to complex matrix WORK(IU)
    *              Overwrite WORK(IU) by left singular vectors of A, copying
    *              to A
    *              (Cworkspace: need M*N+2*N, prefer M*N+N+N*NB)
    *              (Rworkspace: need 0)
    *
                      CALL ZLASET( 'F', M, N, CZERO, CZERO, WORK( IU ),
         $                         LDWRKU )
                      CALL ZLACP2( 'F', N, N, RWORK( IRU ), N, WORK( IU ),
         $                         LDWRKU )
                      CALL ZUNMBR( 'Q', 'L', 'N', M, N, N, A, LDA,
         $                         WORK( ITAUQ ), WORK( IU ), LDWRKU,
         $                         WORK( NWORK ), LWORK-NWORK+1, IERR )
                      CALL ZLACPY( 'F', M, N, WORK( IU ), LDWRKU, A, LDA )
                   ELSE
    *
    *                 Generate Q in A
    *                 (Cworkspace: need 2*N, prefer N+N*NB)
    *                 (Rworkspace: need 0)
    *
                      CALL ZUNGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ),
         $                         WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *                 Multiply Q in A by real matrix RWORK(IRU), storing the
    *                 result in WORK(IU), copying to A
    *                 (CWorkspace: need N*N, prefer M*N)
    *                 (Rworkspace: need 3*N*N, prefer N*N+2*M*N)
    *
                      NRWORK = IRVT
                      DO 30 I = 1, M, LDWRKU
                         CHUNK = MIN( M-I+1, LDWRKU )
                         CALL ZLACRM( CHUNK, N, A( I, 1 ), LDA,
         $                            RWORK( IRU ), N, WORK( IU ), LDWRKU,
         $                            RWORK( NRWORK ) )
                         CALL ZLACPY( 'F', CHUNK, N, WORK( IU ), LDWRKU,
         $                            A( I, 1 ), LDA )
       30             CONTINUE
                   END IF
    *
                ELSE IF( WNTQS ) THEN
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRU = NRWORK
                   IRVT = IRU + N*N
                   NRWORK = IRVT + N*N
                   CALL DBDSDC( 'U', 'I', N, S, RWORK( IE ), RWORK( IRU ),
         $                      N, RWORK( IRVT ), N, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Copy real matrix RWORK(IRU) to complex matrix U
    *              Overwrite U by left singular vectors of A
    *              (CWorkspace: need 3*N, prefer 2*N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLASET( 'F', M, N, CZERO, CZERO, U, LDU )
                   CALL ZLACP2( 'F', N, N, RWORK( IRU ), N, U, LDU )
                   CALL ZUNMBR( 'Q', 'L', 'N', M, N, N, A, LDA,
         $                      WORK( ITAUQ ), U, LDU, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Copy real matrix RWORK(IRVT) to complex matrix VT
    *              Overwrite VT by right singular vectors of A
    *              (CWorkspace: need 3*N, prefer 2*N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', N, N, RWORK( IRVT ), N, VT, LDVT )
                   CALL ZUNMBR( 'P', 'R', 'C', N, N, N, A, LDA,
         $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
                ELSE
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRU = NRWORK
                   IRVT = IRU + N*N
                   NRWORK = IRVT + N*N
                   CALL DBDSDC( 'U', 'I', N, S, RWORK( IE ), RWORK( IRU ),
         $                      N, RWORK( IRVT ), N, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Set the right corner of U to identity matrix
    *
                   CALL ZLASET( 'F', M, M, CZERO, CZERO, U, LDU )
                   IF( M.GT.N ) THEN
                      CALL ZLASET( 'F', M-N, M-N, CZERO, CONE,
         $                         U( N+1, N+1 ), LDU )
                   END IF
    *
    *              Copy real matrix RWORK(IRU) to complex matrix U
    *              Overwrite U by left singular vectors of A
    *              (CWorkspace: need 2*N+M, prefer 2*N+M*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', N, N, RWORK( IRU ), N, U, LDU )
                   CALL ZUNMBR( 'Q', 'L', 'N', M, M, N, A, LDA,
         $                      WORK( ITAUQ ), U, LDU, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Copy real matrix RWORK(IRVT) to complex matrix VT
    *              Overwrite VT by right singular vectors of A
    *              (CWorkspace: need 3*N, prefer 2*N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', N, N, RWORK( IRVT ), N, VT, LDVT )
                   CALL ZUNMBR( 'P', 'R', 'C', N, N, N, A, LDA,
         $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
                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.MNTHR1 ) THEN
    *
                IF( WNTQN ) THEN
    *
    *              Path 1t (N much larger than M, JOBZ='N')
    *              No singular vectors to be computed
    *
                   ITAU = 1
                   NWORK = ITAU + M
    *
    *              Compute A=L*Q
    *              (CWorkspace: need 2*M, prefer M+M*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Zero out above L
    *
                   CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, A( 1, 2 ),
         $                      LDA )
                   IE = 1
                   ITAUQ = 1
                   ITAUP = ITAUQ + M
                   NWORK = ITAUP + M
    *
    *              Bidiagonalize L in A
    *              (CWorkspace: need 3*M, prefer 2*M+2*M*NB)
    *              (RWorkspace: need M)
    *
                   CALL ZGEBRD( M, M, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
         $                      WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
         $                      IERR )
                   NRWORK = IE + M
    *
    *              Perform bidiagonal SVD, compute singular values only
    *              (CWorkspace: 0)
    *              (RWorkspace: need BDSPAN)
    *
                   CALL DBDSDC( 'U', 'N', M, S, RWORK( IE ), DUM, 1, DUM, 1,
         $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
    *
                ELSE IF( WNTQO ) THEN
    *
    *              Path 2t (N much larger than M, JOBZ='O')
    *              M right singular vectors to be overwritten on A and
    *              M left singular vectors to be computed in U
    *
                   IVT = 1
                   LDWKVT = M
    *
    *              WORK(IVT) is M by M
    *
                   IL = IVT + LDWKVT*M
                   IF( LWORK.GE.M*N+M*M+3*M ) THEN
    *
    *                 WORK(IL) M by N
    *
                      LDWRKL = M
                      CHUNK = N
                   ELSE
    *
    *                 WORK(IL) is M by CHUNK
    *
                      LDWRKL = M
                      CHUNK = ( LWORK-M*M-3*M ) / M
                   END IF
                   ITAU = IL + LDWRKL*CHUNK
                   NWORK = ITAU + M
    *
    *              Compute A=L*Q
    *              (CWorkspace: need 2*M, prefer M+M*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Copy L to WORK(IL), zeroing about above it
    *
                   CALL ZLACPY( 'L', M, M, A, LDA, WORK( IL ), LDWRKL )
                   CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO,
         $                      WORK( IL+LDWRKL ), LDWRKL )
    *
    *              Generate Q in A
    *              (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
                   IE = 1
                   ITAUQ = ITAU
                   ITAUP = ITAUQ + M
                   NWORK = ITAUP + M
    *
    *              Bidiagonalize L in WORK(IL)
    *              (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB)
    *              (RWorkspace: need M)
    *
                   CALL ZGEBRD( M, M, WORK( IL ), LDWRKL, S, RWORK( IE ),
         $                      WORK( ITAUQ ), WORK( ITAUP ), WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRU = IE + M
                   IRVT = IRU + M*M
                   NRWORK = IRVT + M*M
                   CALL DBDSDC( 'U', 'I', M, S, RWORK( IE ), RWORK( IRU ),
         $                      M, RWORK( IRVT ), M, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Copy real matrix RWORK(IRU) to complex matrix WORK(IU)
    *              Overwrite WORK(IU) by the left singular vectors of L
    *              (CWorkspace: need N*N+3*N, prefer M*N+2*N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', M, M, RWORK( IRU ), M, U, LDU )
                   CALL ZUNMBR( 'Q', 'L', 'N', M, M, M, WORK( IL ), LDWRKL,
         $                      WORK( ITAUQ ), U, LDU, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT)
    *              Overwrite WORK(IVT) by the right singular vectors of L
    *              (CWorkspace: need N*N+3*N, prefer M*N+2*N+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', M, M, RWORK( IRVT ), M, WORK( IVT ),
         $                      LDWKVT )
                   CALL ZUNMBR( 'P', 'R', 'C', M, M, M, WORK( IL ), LDWRKL,
         $                      WORK( ITAUP ), WORK( IVT ), LDWKVT,
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Multiply right singular vectors of L in WORK(IL) by Q
    *              in A, storing result in WORK(IL) and copying to A
    *              (CWorkspace: need 2*M*M, prefer M*M+M*N))
    *              (RWorkspace: 0)
    *
                   DO 40 I = 1, N, CHUNK
                      BLK = MIN( N-I+1, CHUNK )
                      CALL ZGEMM( 'N', 'N', M, BLK, M, CONE, WORK( IVT ), M,
         $                        A( 1, I ), LDA, CZERO, WORK( IL ),
         $                        LDWRKL )
                      CALL ZLACPY( 'F', M, BLK, WORK( IL ), LDWRKL,
         $                         A( 1, I ), LDA )
       40          CONTINUE
    *
                ELSE IF( WNTQS ) THEN
    *
    *             Path 3t (N much larger than M, JOBZ='S')
    *             M right singular vectors to be computed in VT and
    *             M left singular vectors to be computed in U
    *
                   IL = 1
    *
    *              WORK(IL) is M by M
    *
                   LDWRKL = M
                   ITAU = IL + LDWRKL*M
                   NWORK = ITAU + M
    *
    *              Compute A=L*Q
    *              (CWorkspace: need 2*M, prefer M+M*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Copy L to WORK(IL), zeroing out above it
    *
                   CALL ZLACPY( 'L', M, M, A, LDA, WORK( IL ), LDWRKL )
                   CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO,
         $                      WORK( IL+LDWRKL ), LDWRKL )
    *
    *              Generate Q in A
    *              (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
                   IE = 1
                   ITAUQ = ITAU
                   ITAUP = ITAUQ + M
                   NWORK = ITAUP + M
    *
    *              Bidiagonalize L in WORK(IL)
    *              (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB)
    *              (RWorkspace: need M)
    *
                   CALL ZGEBRD( M, M, WORK( IL ), LDWRKL, S, RWORK( IE ),
         $                      WORK( ITAUQ ), WORK( ITAUP ), WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRU = IE + M
                   IRVT = IRU + M*M
                   NRWORK = IRVT + M*M
                   CALL DBDSDC( 'U', 'I', M, S, RWORK( IE ), RWORK( IRU ),
         $                      M, RWORK( IRVT ), M, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Copy real matrix RWORK(IRU) to complex matrix U
    *              Overwrite U by left singular vectors of L
    *              (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', M, M, RWORK( IRU ), M, U, LDU )
                   CALL ZUNMBR( 'Q', 'L', 'N', M, M, M, WORK( IL ), LDWRKL,
         $                      WORK( ITAUQ ), U, LDU, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Copy real matrix RWORK(IRVT) to complex matrix VT
    *              Overwrite VT by left singular vectors of L
    *              (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', M, M, RWORK( IRVT ), M, VT, LDVT )
                   CALL ZUNMBR( 'P', 'R', 'C', M, M, M, WORK( IL ), LDWRKL,
         $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Copy VT to WORK(IL), multiply right singular vectors of L
    *              in WORK(IL) by Q in A, storing result in VT
    *              (CWorkspace: need M*M)
    *              (RWorkspace: 0)
    *
                   CALL ZLACPY( 'F', M, M, VT, LDVT, WORK( IL ), LDWRKL )
                   CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IL ), LDWRKL,
         $                     A, LDA, CZERO, VT, LDVT )
    *
                ELSE IF( WNTQA ) THEN
    *
    *              Path 9t (N much larger than M, JOBZ='A')
    *              N right singular vectors to be computed in VT and
    *              M left singular vectors to be computed in U
    *
                   IVT = 1
    *
    *              WORK(IVT) is M by M
    *
                   LDWKVT = M
                   ITAU = IVT + LDWKVT*M
                   NWORK = ITAU + M
    *
    *              Compute A=L*Q, copying result to VT
    *              (CWorkspace: need 2*M, prefer M+M*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
                   CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT )
    *
    *              Generate Q in VT
    *              (CWorkspace: need M+N, prefer M+N*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Produce L in A, zeroing out above it
    *
                   CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, A( 1, 2 ),
         $                      LDA )
                   IE = 1
                   ITAUQ = ITAU
                   ITAUP = ITAUQ + M
                   NWORK = ITAUP + M
    *
    *              Bidiagonalize L in A
    *              (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB)
    *              (RWorkspace: need M)
    *
                   CALL ZGEBRD( M, M, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
         $                      WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
         $                      IERR )
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRU = IE + M
                   IRVT = IRU + M*M
                   NRWORK = IRVT + M*M
                   CALL DBDSDC( 'U', 'I', M, S, RWORK( IE ), RWORK( IRU ),
         $                      M, RWORK( IRVT ), M, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Copy real matrix RWORK(IRU) to complex matrix U
    *              Overwrite U by left singular vectors of L
    *              (CWorkspace: need 3*M, prefer 2*M+M*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', M, M, RWORK( IRU ), M, U, LDU )
                   CALL ZUNMBR( 'Q', 'L', 'N', M, M, M, A, LDA,
         $                      WORK( ITAUQ ), U, LDU, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT)
    *              Overwrite WORK(IVT) by right singular vectors of L
    *              (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB)
    *              (RWorkspace: 0)
    *
                   CALL ZLACP2( 'F', M, M, RWORK( IRVT ), M, WORK( IVT ),
         $                      LDWKVT )
                   CALL ZUNMBR( 'P', 'R', 'C', M, M, M, A, LDA,
         $                      WORK( ITAUP ), WORK( IVT ), LDWKVT,
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Multiply right singular vectors of L in WORK(IVT) by
    *              Q in VT, storing result in A
    *              (CWorkspace: need M*M)
    *              (RWorkspace: 0)
    *
                   CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IVT ), LDWKVT,
         $                     VT, LDVT, CZERO, A, LDA )
    *
    *              Copy right singular vectors of A from A to VT
    *
                   CALL ZLACPY( 'F', M, N, A, LDA, VT, LDVT )
    *
                END IF
    *
             ELSE IF( N.GE.MNTHR2 ) THEN
    *
    *           MNTHR2 <= N < MNTHR1
    *
    *           Path 5t (N much larger than M, but not as much as MNTHR1)
    *           Reduce to bidiagonal form without QR decomposition, use
    *           ZUNGBR and matrix multiplication to compute singular vectors
    *
    *
                IE = 1
                NRWORK = IE + M
                ITAUQ = 1
                ITAUP = ITAUQ + M
                NWORK = ITAUP + M
    *
    *           Bidiagonalize A
    *           (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB)
    *           (RWorkspace: M)
    *
                CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
         $                   WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
         $                   IERR )
    *
                IF( WNTQN ) THEN
    *
    *              Compute singular values only
    *              (Cworkspace: 0)
    *              (Rworkspace: need BDSPAN)
    *
                   CALL DBDSDC( 'L', 'N', M, S, RWORK( IE ), DUM, 1, DUM, 1,
         $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
                ELSE IF( WNTQO ) THEN
                   IRVT = NRWORK
                   IRU = IRVT + M*M
                   NRWORK = IRU + M*M
                   IVT = NWORK
    *
    *              Copy A to U, generate Q
    *              (Cworkspace: need 2*M, prefer M+M*NB)
    *              (Rworkspace: 0)
    *
                   CALL ZLACPY( 'L', M, M, A, LDA, U, LDU )
                   CALL ZUNGBR( 'Q', M, M, N, U, LDU, WORK( ITAUQ ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Generate P**H in A
    *              (Cworkspace: need 2*M, prefer M+M*NB)
    *              (Rworkspace: 0)
    *
                   CALL ZUNGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
                   LDWKVT = M
                   IF( LWORK.GE.M*N+3*M ) THEN
    *
    *                 WORK( IVT ) is M by N
    *
                      NWORK = IVT + LDWKVT*N
                      CHUNK = N
                   ELSE
    *
    *                 WORK( IVT ) is M by CHUNK
    *
                      CHUNK = ( LWORK-3*M ) / M
                      NWORK = IVT + LDWKVT*CHUNK
                   END IF
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   CALL DBDSDC( 'L', 'I', M, S, RWORK( IE ), RWORK( IRU ),
         $                      M, RWORK( IRVT ), M, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Multiply Q in U by real matrix RWORK(IRVT)
    *              storing the result in WORK(IVT), copying to U
    *              (Cworkspace: need 0)
    *              (Rworkspace: need 2*M*M)
    *
                   CALL ZLACRM( M, M, U, LDU, RWORK( IRU ), M, WORK( IVT ),
         $                      LDWKVT, RWORK( NRWORK ) )
                   CALL ZLACPY( 'F', M, M, WORK( IVT ), LDWKVT, U, LDU )
    *
    *              Multiply RWORK(IRVT) by P**H in A, storing the
    *              result in WORK(IVT), copying to A
    *              (CWorkspace: need M*M, prefer M*N)
    *              (Rworkspace: need 2*M*M, prefer 2*M*N)
    *
                   NRWORK = IRU
                   DO 50 I = 1, N, CHUNK
                      BLK = MIN( N-I+1, CHUNK )
                      CALL ZLARCM( M, BLK, RWORK( IRVT ), M, A( 1, I ), LDA,
         $                         WORK( IVT ), LDWKVT, RWORK( NRWORK ) )
                      CALL ZLACPY( 'F', M, BLK, WORK( IVT ), LDWKVT,
         $                         A( 1, I ), LDA )
       50          CONTINUE
                ELSE IF( WNTQS ) THEN
    *
    *              Copy A to U, generate Q
    *              (Cworkspace: need 2*M, prefer M+M*NB)
    *              (Rworkspace: 0)
    *
                   CALL ZLACPY( 'L', M, M, A, LDA, U, LDU )
                   CALL ZUNGBR( 'Q', M, M, N, U, LDU, WORK( ITAUQ ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Copy A to VT, generate P**H
    *              (Cworkspace: need 2*M, prefer M+M*NB)
    *              (Rworkspace: 0)
    *
                   CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT )
                   CALL ZUNGBR( 'P', M, N, M, VT, LDVT, WORK( ITAUP ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRVT = NRWORK
                   IRU = IRVT + M*M
                   NRWORK = IRU + M*M
                   CALL DBDSDC( 'L', 'I', M, S, RWORK( IE ), RWORK( IRU ),
         $                      M, RWORK( IRVT ), M, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Multiply Q in U by real matrix RWORK(IRU), storing the
    *              result in A, copying to U
    *              (CWorkspace: need 0)
    *              (Rworkspace: need 3*M*M)
    *
                   CALL ZLACRM( M, M, U, LDU, RWORK( IRU ), M, A, LDA,
         $                      RWORK( NRWORK ) )
                   CALL ZLACPY( 'F', M, M, A, LDA, U, LDU )
    *
    *              Multiply real matrix RWORK(IRVT) by P**H in VT,
    *              storing the result in A, copying to VT
    *              (Cworkspace: need 0)
    *              (Rworkspace: need M*M+2*M*N)
    *
                   NRWORK = IRU
                   CALL ZLARCM( M, N, RWORK( IRVT ), M, VT, LDVT, A, LDA,
         $                      RWORK( NRWORK ) )
                   CALL ZLACPY( 'F', M, N, A, LDA, VT, LDVT )
                ELSE
    *
    *              Copy A to U, generate Q
    *              (Cworkspace: need 2*M, prefer M+M*NB)
    *              (Rworkspace: 0)
    *
                   CALL ZLACPY( 'L', M, M, A, LDA, U, LDU )
                   CALL ZUNGBR( 'Q', M, M, N, U, LDU, WORK( ITAUQ ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Copy A to VT, generate P**H
    *              (Cworkspace: need 2*M, prefer M+M*NB)
    *              (Rworkspace: 0)
    *
                   CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT )
                   CALL ZUNGBR( 'P', N, N, M, VT, LDVT, WORK( ITAUP ),
         $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRVT = NRWORK
                   IRU = IRVT + M*M
                   NRWORK = IRU + M*M
                   CALL DBDSDC( 'L', 'I', M, S, RWORK( IE ), RWORK( IRU ),
         $                      M, RWORK( IRVT ), M, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Multiply Q in U by real matrix RWORK(IRU), storing the
    *              result in A, copying to U
    *              (CWorkspace: need 0)
    *              (Rworkspace: need 3*M*M)
    *
                   CALL ZLACRM( M, M, U, LDU, RWORK( IRU ), M, A, LDA,
         $                      RWORK( NRWORK ) )
                   CALL ZLACPY( 'F', M, M, A, LDA, U, LDU )
    *
    *              Multiply real matrix RWORK(IRVT) by P**H in VT,
    *              storing the result in A, copying to VT
    *              (Cworkspace: need 0)
    *              (Rworkspace: need M*M+2*M*N)
    *
                   CALL ZLARCM( M, N, RWORK( IRVT ), M, VT, LDVT, A, LDA,
         $                      RWORK( NRWORK ) )
                   CALL ZLACPY( 'F', M, N, A, LDA, VT, LDVT )
                END IF
    *
             ELSE
    *
    *           N .LT. MNTHR2
    *
    *           Path 6t (N greater than M, but not much larger)
    *           Reduce to bidiagonal form without LQ decomposition
    *           Use ZUNMBR to compute singular vectors
    *
                IE = 1
                NRWORK = IE + M
                ITAUQ = 1
                ITAUP = ITAUQ + M
                NWORK = ITAUP + M
    *
    *           Bidiagonalize A
    *           (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB)
    *           (RWorkspace: M)
    *
                CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
         $                   WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1,
         $                   IERR )
                IF( WNTQN ) THEN
    *
    *              Compute singular values only
    *              (Cworkspace: 0)
    *              (Rworkspace: need BDSPAN)
    *
                   CALL DBDSDC( 'L', 'N', M, S, RWORK( IE ), DUM, 1, DUM, 1,
         $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
                ELSE IF( WNTQO ) THEN
                   LDWKVT = M
                   IVT = NWORK
                   IF( LWORK.GE.M*N+3*M ) THEN
    *
    *                 WORK( IVT ) is M by N
    *
                      CALL ZLASET( 'F', M, N, CZERO, CZERO, WORK( IVT ),
         $                         LDWKVT )
                      NWORK = IVT + LDWKVT*N
                   ELSE
    *
    *                 WORK( IVT ) is M by CHUNK
    *
                      CHUNK = ( LWORK-3*M ) / M
                      NWORK = IVT + LDWKVT*CHUNK
                   END IF
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRVT = NRWORK
                   IRU = IRVT + M*M
                   NRWORK = IRU + M*M
                   CALL DBDSDC( 'L', 'I', M, S, RWORK( IE ), RWORK( IRU ),
         $                      M, RWORK( IRVT ), M, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Copy real matrix RWORK(IRU) to complex matrix U
    *              Overwrite U by left singular vectors of A
    *              (Cworkspace: need 2*M, prefer M+M*NB)
    *              (Rworkspace: need 0)
    *
                   CALL ZLACP2( 'F', M, M, RWORK( IRU ), M, U, LDU )
                   CALL ZUNMBR( 'Q', 'L', 'N', M, M, N, A, LDA,
         $                      WORK( ITAUQ ), U, LDU, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
                   IF( LWORK.GE.M*N+3*M ) THEN
    *
    *              Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT)
    *              Overwrite WORK(IVT) by right singular vectors of A,
    *              copying to A
    *              (Cworkspace: need M*N+2*M, prefer M*N+M+M*NB)
    *              (Rworkspace: need 0)
    *
                      CALL ZLACP2( 'F', M, M, RWORK( IRVT ), M, WORK( IVT ),
         $                         LDWKVT )
                      CALL ZUNMBR( 'P', 'R', 'C', M, N, M, A, LDA,
         $                         WORK( ITAUP ), WORK( IVT ), LDWKVT,
         $                         WORK( NWORK ), LWORK-NWORK+1, IERR )
                      CALL ZLACPY( 'F', M, N, WORK( IVT ), LDWKVT, A, LDA )
                   ELSE
    *
    *                 Generate P**H in A
    *                 (Cworkspace: need 2*M, prefer M+M*NB)
    *                 (Rworkspace: need 0)
    *
                      CALL ZUNGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ),
         $                         WORK( NWORK ), LWORK-NWORK+1, IERR )
    *
    *                 Multiply Q in A by real matrix RWORK(IRU), storing the
    *                 result in WORK(IU), copying to A
    *                 (CWorkspace: need M*M, prefer M*N)
    *                 (Rworkspace: need 3*M*M, prefer M*M+2*M*N)
    *
                      NRWORK = IRU
                      DO 60 I = 1, N, CHUNK
                         BLK = MIN( N-I+1, CHUNK )
                         CALL ZLARCM( M, BLK, RWORK( IRVT ), M, A( 1, I ),
         $                            LDA, WORK( IVT ), LDWKVT,
         $                            RWORK( NRWORK ) )
                         CALL ZLACPY( 'F', M, BLK, WORK( IVT ), LDWKVT,
         $                            A( 1, I ), LDA )
       60             CONTINUE
                   END IF
                ELSE IF( WNTQS ) THEN
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRVT = NRWORK
                   IRU = IRVT + M*M
                   NRWORK = IRU + M*M
                   CALL DBDSDC( 'L', 'I', M, S, RWORK( IE ), RWORK( IRU ),
         $                      M, RWORK( IRVT ), M, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Copy real matrix RWORK(IRU) to complex matrix U
    *              Overwrite U by left singular vectors of A
    *              (CWorkspace: need 3*M, prefer 2*M+M*NB)
    *              (RWorkspace: M*M)
    *
                   CALL ZLACP2( 'F', M, M, RWORK( IRU ), M, U, LDU )
                   CALL ZUNMBR( 'Q', 'L', 'N', M, M, N, A, LDA,
         $                      WORK( ITAUQ ), U, LDU, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Copy real matrix RWORK(IRVT) to complex matrix VT
    *              Overwrite VT by right singular vectors of A
    *              (CWorkspace: need 3*M, prefer 2*M+M*NB)
    *              (RWorkspace: M*M)
    *
                   CALL ZLASET( 'F', M, N, CZERO, CZERO, VT, LDVT )
                   CALL ZLACP2( 'F', M, M, RWORK( IRVT ), M, VT, LDVT )
                   CALL ZUNMBR( 'P', 'R', 'C', M, N, M, A, LDA,
         $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
                ELSE
    *
    *              Perform bidiagonal SVD, computing left singular vectors
    *              of bidiagonal matrix in RWORK(IRU) and computing right
    *              singular vectors of bidiagonal matrix in RWORK(IRVT)
    *              (CWorkspace: need 0)
    *              (RWorkspace: need BDSPAC)
    *
                   IRVT = NRWORK
                   IRU = IRVT + M*M
                   NRWORK = IRU + M*M
    *
                   CALL DBDSDC( 'L', 'I', M, S, RWORK( IE ), RWORK( IRU ),
         $                      M, RWORK( IRVT ), M, DUM, IDUM,
         $                      RWORK( NRWORK ), IWORK, INFO )
    *
    *              Copy real matrix RWORK(IRU) to complex matrix U
    *              Overwrite U by left singular vectors of A
    *              (CWorkspace: need 3*M, prefer 2*M+M*NB)
    *              (RWorkspace: M*M)
    *
                   CALL ZLACP2( 'F', M, M, RWORK( IRU ), M, U, LDU )
                   CALL ZUNMBR( 'Q', 'L', 'N', M, M, N, A, LDA,
         $                      WORK( ITAUQ ), U, LDU, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
    *
    *              Set all of VT to identity matrix
    *
                   CALL ZLASET( 'F', N, N, CZERO, CONE, VT, LDVT )
    *
    *              Copy real matrix RWORK(IRVT) to complex matrix VT
    *              Overwrite VT by right singular vectors of A
    *              (CWorkspace: need 2*M+N, prefer 2*M+N*NB)
    *              (RWorkspace: M*M)
    *
                   CALL ZLACP2( 'F', M, M, RWORK( IRVT ), M, VT, LDVT )
                   CALL ZUNMBR( 'P', 'R', 'C', N, N, M, A, LDA,
         $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
         $                      LWORK-NWORK+1, IERR )
                END IF
    *
             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,
         $                   RWORK( IE ), 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,
         $                   RWORK( IE ), MINMN, IERR )
          END IF
    *
    *     Return optimal workspace in WORK(1)
    *
          WORK( 1 ) = MAXWRK
    *
          RETURN
    *
    *     End of ZGESDD
    *
          END