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-version 1.5, 2017/06/17 11:06:42
+version 1.6, 2018/05/29 06:55:22
  Line 1
  *> \brief \b ZGEJSV
  *
  *  =========== DOCUMENTATION ===========
  *
  * Online html documentation available at
  *            http://www.netlib.org/lapack/explore-html/
  *
  *> \htmlonly
  *> Download ZGEJSV + dependencies
  *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgejsv.f">
  *> [TGZ]</a>
  *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgejsv.f">
  *> [ZIP]</a>
  *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgejsv.f">
  *> [TXT]</a>
  *> \endhtmlonly
  *
  *  Definition:
  *  ===========
  *
  *     SUBROUTINE ZGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,
  *                         M, N, A, LDA, SVA, U, LDU, V, LDV,
  *                         CWORK, LWORK, RWORK, LRWORK, IWORK, INFO )
  *
  *     .. Scalar Arguments ..
  *     IMPLICIT    NONE
  *     INTEGER     INFO, LDA, LDU, LDV, LWORK, M, N
  *     ..
  *     .. Array Arguments ..
  *     COMPLEX*16     A( LDA, * ),  U( LDU, * ), V( LDV, * ), CWORK( LWORK )
  *     DOUBLE PRECISION   SVA( N ), RWORK( LRWORK )
  *     INTEGER     IWORK( * )
  *     CHARACTER*1 JOBA, JOBP, JOBR, JOBT, JOBU, JOBV
  *       ..
  *
  *
  *> \par Purpose:
  *  =============
  *>
  *> \verbatim
  *>
  *> ZGEJSV computes the singular value decomposition (SVD) of a complex M-by-N
  *> matrix [A], where M >= N. The SVD of [A] is written as
  *>
  *>              [A] = [U] * [SIGMA] * [V]^*,
  *>
  *> where [SIGMA] is an N-by-N (M-by-N) matrix which is zero except for its N
  *> diagonal elements, [U] is an M-by-N (or 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]. The columns of [U] and [V] are the left and
  *> the right singular vectors of [A], respectively. The matrices [U] and [V]
  *> are computed and stored in the arrays U and V, respectively. The diagonal
  *> of [SIGMA] is computed and stored in the array SVA.
  *> \endverbatim
  *>
  *>  Arguments:
  *>  ==========
  *>
  *> \param[in] JOBA
  *> \verbatim
  *>          JOBA is CHARACTER*1
  *>         Specifies the level of accuracy:
  *>       = 'C': This option works well (high relative accuracy) if A = B * D,
  *>              with well-conditioned B and arbitrary diagonal matrix D.
  *>              The accuracy cannot be spoiled by COLUMN scaling. The
  *>              accuracy of the computed output depends on the condition of
  *>              B, and the procedure aims at the best theoretical accuracy.
  *>              The relative error max_{i=1:N}|d sigma_i| / sigma_i is
  *>              bounded by f(M,N)*epsilon* cond(B), independent of D.
  *>              The input matrix is preprocessed with the QRF with column
  *>              pivoting. This initial preprocessing and preconditioning by
  *>              a rank revealing QR factorization is common for all values of
  *>              JOBA. Additional actions are specified as follows:
  *>       = 'E': Computation as with 'C' with an additional estimate of the
  *>              condition number of B. It provides a realistic error bound.
  *>       = 'F': If A = D1 * C * D2 with ill-conditioned diagonal scalings
  *>              D1, D2, and well-conditioned matrix C, this option gives
  *>              higher accuracy than the 'C' option. If the structure of the
  *>              input matrix is not known, and relative accuracy is
  *>              desirable, then this option is advisable. The input matrix A
  *>              is preprocessed with QR factorization with FULL (row and
  *>              column) pivoting.
  *>       = 'G'  Computation as with 'F' with an additional estimate of the
  *>              condition number of B, where A=B*D. If A has heavily weighted
  *>              rows, then using this condition number gives too pessimistic
  *>              error bound.
  *>       = 'A': Small singular values are not well determined by the data
  *>              and are considered as noisy; the matrix is treated as
  *>              numerically rank defficient. The error in the computed
  *>              singular values is bounded by f(m,n)*epsilon*||A||.
  *>              The computed SVD A = U * S * V^* restores A up to
  *>              f(m,n)*epsilon*||A||.
  *>              This gives the procedure the licence to discard (set to zero)
  *>              all singular values below N*epsilon*||A||.
  *>       = 'R': Similar as in 'A'. Rank revealing property of the initial
  *>              QR factorization is used do reveal (using triangular factor)
  *>              a gap sigma_{r+1} < epsilon * sigma_r in which case the
  *>              numerical RANK is declared to be r. The SVD is computed with
  *>              absolute error bounds, but more accurately than with 'A'.
  *> \endverbatim
  *>
  *> \param[in] JOBU
  *> \verbatim
  *>          JOBU is CHARACTER*1
  *>         Specifies whether to compute the columns of U:
  *>       = 'U': N columns of U are returned in the array U.
  *>       = 'F': full set of M left sing. vectors is returned in the array U.
  *>       = 'W': U may be used as workspace of length M*N. See the description
  *>              of U.
  *>       = 'N': U is not computed.
  *> \endverbatim
  *>
  *> \param[in] JOBV
  *> \verbatim
  *>          JOBV is CHARACTER*1
  *>         Specifies whether to compute the matrix V:
  *>       = 'V': N columns of V are returned in the array V; Jacobi rotations
  *>              are not explicitly accumulated.
  *>       = 'J': N columns of V are returned in the array V, but they are
  *>              computed as the product of Jacobi rotations, if JOBT .EQ. 'N'.
  *>       = 'W': V may be used as workspace of length N*N. See the description
  *>              of V.
  *>       = 'N': V is not computed.
  *> \endverbatim
  *>
  *> \param[in] JOBR
  *> \verbatim
  *>          JOBR is CHARACTER*1
  *>         Specifies the RANGE for the singular values. Issues the licence to
  *>         set to zero small positive singular values if they are outside
  *>         specified range. If A .NE. 0 is scaled so that the largest singular
  *>         value of c*A is around SQRT(BIG), BIG=DLAMCH('O'), then JOBR issues
  *>         the licence to kill columns of A whose norm in c*A is less than
  *>         SQRT(SFMIN) (for JOBR.EQ.'R'), or less than SMALL=SFMIN/EPSLN,
  *>         where SFMIN=DLAMCH('S'), EPSLN=DLAMCH('E').
  *>       = 'N': Do not kill small columns of c*A. This option assumes that
  *>              BLAS and QR factorizations and triangular solvers are
  *>              implemented to work in that range. If the condition of A
  *>              is greater than BIG, use ZGESVJ.
  *>       = 'R': RESTRICTED range for sigma(c*A) is [SQRT(SFMIN), SQRT(BIG)]
  *>              (roughly, as described above). This option is recommended.
  *>                                             ===========================
  *>         For computing the singular values in the FULL range [SFMIN,BIG]
  *>         use ZGESVJ.
  *> \endverbatim
  *>
  *> \param[in] JOBT
  *> \verbatim
  *>          JOBT is CHARACTER*1
  *>         If the matrix is square then the procedure may determine to use
  *>         transposed A if A^* seems to be better with respect to convergence.
  *>         If the matrix is not square, JOBT is ignored.
  *>         The decision is based on two values of entropy over the adjoint
  *>         orbit of A^* * A. See the descriptions of WORK(6) and WORK(7).
  *>       = 'T': transpose if entropy test indicates possibly faster
  *>         convergence of Jacobi process if A^* is taken as input. If A is
  *>         replaced with A^*, then the row pivoting is included automatically.
  *>       = 'N': do not speculate.
  *>         The option 'T' can be used to compute only the singular values, or
  *>         the full SVD (U, SIGMA and V). For only one set of singular vectors
  *>         (U or V), the caller should provide both U and V, as one of the
  *>         matrices is used as workspace if the matrix A is transposed.
  *>         The implementer can easily remove this constraint and make the
  *>         code more complicated. See the descriptions of U and V.
  *>         In general, this option is considered experimental, and 'N'; should
  *>         be preferred. This is subject to changes in the future.
  *> \endverbatim
  *>
  *> \param[in] JOBP
  *> \verbatim
  *>          JOBP is CHARACTER*1
  *>         Issues the licence to introduce structured perturbations to drown
  *>         denormalized numbers. This licence should be active if the
  *>         denormals are poorly implemented, causing slow computation,
  *>         especially in cases of fast convergence (!). For details see [1,2].
  *>         For the sake of simplicity, this perturbations are included only
  *>         when the full SVD or only the singular values are requested. The
  *>         implementer/user can easily add the perturbation for the cases of
  *>         computing one set of singular vectors.
  *>       = 'P': introduce perturbation
  *>       = 'N': do not perturb
  *> \endverbatim
  *>
  *> \param[in] M
  *> \verbatim
  *>          M is INTEGER
  *>         The number of rows of the input matrix A.  M >= 0.
  *> \endverbatim
  *>
  *> \param[in] N
  *> \verbatim
  *>          N is INTEGER
  *>         The number of columns of the input matrix A. M >= N >= 0.
  *> \endverbatim
  *>
  *> \param[in,out] A
  *> \verbatim
  *>          A is COMPLEX*16 array, dimension (LDA,N)
  *>          On entry, the M-by-N matrix A.
  *> \endverbatim
  *>
  *> \param[in] LDA
  *> \verbatim
  *>          LDA is INTEGER
  *>          The leading dimension of the array A.  LDA >= max(1,M).
  *> \endverbatim
  *>
  *> \param[out] SVA
  *> \verbatim
  *>          SVA is DOUBLE PRECISION array, dimension (N)
  *>          On exit,
  *>          - For WORK(1)/WORK(2) = ONE: The singular values of A. During the
  *>            computation SVA contains Euclidean column norms of the
  *>            iterated matrices in the array A.
  *>          - For WORK(1) .NE. WORK(2): The singular values of A are
  *>            (WORK(1)/WORK(2)) * SVA(1:N). This factored form is used if
  *>            sigma_max(A) overflows or if small singular values have been
  *>            saved from underflow by scaling the input matrix A.
  *>          - If JOBR='R' then some of the singular values may be returned
  *>            as exact zeros obtained by "set to zero" because they are
  *>            below the numerical rank threshold or are denormalized numbers.
  *> \endverbatim
  *>
  *> \param[out] U
  *> \verbatim
  *>          U is COMPLEX*16 array, dimension ( LDU, N )
  *>          If JOBU = 'U', then U contains on exit the M-by-N matrix of
  *>                         the left singular vectors.
  *>          If JOBU = 'F', then U contains on exit the M-by-M matrix of
  *>                         the left singular vectors, including an ONB
  *>                         of the orthogonal complement of the Range(A).
  *>          If JOBU = 'W'  .AND. (JOBV.EQ.'V' .AND. JOBT.EQ.'T' .AND. M.EQ.N),
  *>                         then U is used as workspace if the procedure
  *>                         replaces A with A^*. In that case, [V] is computed
  *>                         in U as left singular vectors of A^* and then
  *>                         copied back to the V array. This 'W' option is just
  *>                         a reminder to the caller that in this case U is
  *>                         reserved as workspace of length N*N.
  *>          If JOBU = 'N'  U is not referenced, unless JOBT='T'.
  *> \endverbatim
  *>
  *> \param[in] LDU
  *> \verbatim
  *>          LDU is INTEGER
  *>          The leading dimension of the array U,  LDU >= 1.
  *>          IF  JOBU = 'U' or 'F' or 'W',  then LDU >= M.
  *> \endverbatim
  *>
  *> \param[out] V
  *> \verbatim
  *>          V is COMPLEX*16 array, dimension ( LDV, N )
  *>          If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of
  *>                         the right singular vectors;
  *>          If JOBV = 'W', AND (JOBU.EQ.'U' AND JOBT.EQ.'T' AND M.EQ.N),
  *>                         then V is used as workspace if the pprocedure
  *>                         replaces A with A^*. In that case, [U] is computed
  *>                         in V as right singular vectors of A^* and then
  *>                         copied back to the U array. This 'W' option is just
  *>                         a reminder to the caller that in this case V is
  *>                         reserved as workspace of length N*N.
  *>          If JOBV = 'N'  V is not referenced, unless JOBT='T'.
  *> \endverbatim
  *>
  *> \param[in] LDV
  *> \verbatim
  *>          LDV is INTEGER
  *>          The leading dimension of the array V,  LDV >= 1.
  *>          If JOBV = 'V' or 'J' or 'W', then LDV >= N.
  *> \endverbatim
  *>
  *> \param[out] CWORK
  *> \verbatim
  *>          CWORK is COMPLEX*16 array, dimension (MAX(2,LWORK))
  *>          If the call to ZGEJSV is a workspace query (indicated by LWORK=-1 or
  *>          LRWORK=-1), then on exit CWORK(1) contains the required length of
  *>          CWORK for the job parameters used in the call.
  *> \endverbatim
  *>
  *> \param[in] LWORK
  *> \verbatim
  *>          LWORK is INTEGER
  *>          Length of CWORK to confirm proper allocation of workspace.
  *>          LWORK depends on the job:
  *>
  *>          1. If only SIGMA is needed ( JOBU.EQ.'N', JOBV.EQ.'N' ) and
  *>            1.1 .. no scaled condition estimate required (JOBA.NE.'E'.AND.JOBA.NE.'G'):
  *>               LWORK >= 2*N+1. This is the minimal requirement.
  *>               ->> For optimal performance (blocked code) the optimal value
  *>               is LWORK >= N + (N+1)*NB. Here NB is the optimal
  *>               block size for ZGEQP3 and ZGEQRF.
  *>               In general, optimal LWORK is computed as
  *>               LWORK >= max(N+LWORK(ZGEQP3),N+LWORK(ZGEQRF), LWORK(ZGESVJ)).
  *>            1.2. .. an estimate of the scaled condition number of A is
  *>               required (JOBA='E', or 'G'). In this case, LWORK the minimal
  *>               requirement is LWORK >= N*N + 2*N.
  *>               ->> For optimal performance (blocked code) the optimal value
  *>               is LWORK >= max(N+(N+1)*NB, N*N+2*N)=N**2+2*N.
  *>               In general, the optimal length LWORK is computed as
  *>               LWORK >= max(N+LWORK(ZGEQP3),N+LWORK(ZGEQRF), LWORK(ZGESVJ),
  *>                            N*N+LWORK(ZPOCON)).
  *>          2. If SIGMA and the right singular vectors are needed (JOBV.EQ.'V'),
  *>             (JOBU.EQ.'N')
  *>            2.1   .. no scaled condition estimate requested (JOBE.EQ.'N'):
  *>            -> the minimal requirement is LWORK >= 3*N.
  *>            -> For optimal performance,
  *>               LWORK >= max(N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
  *>               where NB is the optimal block size for ZGEQP3, ZGEQRF, ZGELQ,
  *>               ZUNMLQ. In general, the optimal length LWORK is computed as
  *>               LWORK >= max(N+LWORK(ZGEQP3), N+LWORK(ZGESVJ),
  *>                       N+LWORK(ZGELQF), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMLQ)).
  *>            2.2 .. an estimate of the scaled condition number of A is
  *>               required (JOBA='E', or 'G').
  *>            -> the minimal requirement is LWORK >= 3*N.
  *>            -> For optimal performance,
  *>               LWORK >= max(N+(N+1)*NB, 2*N,2*N+N*NB)=2*N+N*NB,
  *>               where NB is the optimal block size for ZGEQP3, ZGEQRF, ZGELQ,
  *>               ZUNMLQ. In general, the optimal length LWORK is computed as
  *>               LWORK >= max(N+LWORK(ZGEQP3), LWORK(ZPOCON), N+LWORK(ZGESVJ),
  *>                       N+LWORK(ZGELQF), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMLQ)).
  *>          3. If SIGMA and the left singular vectors are needed
  *>            3.1  .. no scaled condition estimate requested (JOBE.EQ.'N'):
  *>            -> the minimal requirement is LWORK >= 3*N.
  *>            -> For optimal performance:
  *>               if JOBU.EQ.'U' :: LWORK >= max(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
  *>               where NB is the optimal block size for ZGEQP3, ZGEQRF, ZUNMQR.
  *>               In general, the optimal length LWORK is computed as
  *>               LWORK >= max(N+LWORK(ZGEQP3), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMQR)).
  *>            3.2  .. an estimate of the scaled condition number of A is
  *>               required (JOBA='E', or 'G').
  *>            -> the minimal requirement is LWORK >= 3*N.
  *>            -> For optimal performance:
  *>               if JOBU.EQ.'U' :: LWORK >= max(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
  *>               where NB is the optimal block size for ZGEQP3, ZGEQRF, ZUNMQR.
  *>               In general, the optimal length LWORK is computed as
  *>               LWORK >= max(N+LWORK(ZGEQP3),N+LWORK(ZPOCON),
  *>                        2*N+LWORK(ZGEQRF), N+LWORK(ZUNMQR)).
  *>          4. If the full SVD is needed: (JOBU.EQ.'U' or JOBU.EQ.'F') and
  *>            4.1. if JOBV.EQ.'V'
  *>               the minimal requirement is LWORK >= 5*N+2*N*N.
  *>            4.2. if JOBV.EQ.'J' the minimal requirement is
  *>               LWORK >= 4*N+N*N.
- *>            In both cases, the allocated CWORK can accomodate blocked runs
+ *>            In both cases, the allocated CWORK can accommodate blocked runs
  *>            of ZGEQP3, ZGEQRF, ZGELQF, SUNMQR, ZUNMLQ.
  *>
  *>          If the call to ZGEJSV is a workspace query (indicated by LWORK=-1 or
  *>          LRWORK=-1), then on exit CWORK(1) contains the optimal and CWORK(2) contains the
  *>          minimal length of CWORK for the job parameters used in the call.
  *> \endverbatim
  *>
  *> \param[out] RWORK
  *> \verbatim
  *>          RWORK is DOUBLE PRECISION array, dimension (MAX(7,LWORK))
  *>          On exit,
  *>          RWORK(1) = Determines the scaling factor SCALE = RWORK(2) / RWORK(1)
  *>                    such that SCALE*SVA(1:N) are the computed singular values
  *>                    of A. (See the description of SVA().)
  *>          RWORK(2) = See the description of RWORK(1).
  *>          RWORK(3) = SCONDA is an estimate for the condition number of
  *>                    column equilibrated A. (If JOBA .EQ. 'E' or 'G')
  *>                    SCONDA is an estimate of SQRT(||(R^* * R)^(-1)||_1).
  *>                    It is computed using SPOCON. It holds
  *>                    N^(-1/4) * SCONDA <= ||R^(-1)||_2 <= N^(1/4) * SCONDA
  *>                    where R is the triangular factor from the QRF of A.
  *>                    However, if R is truncated and the numerical rank is
  *>                    determined to be strictly smaller than N, SCONDA is
  *>                    returned as -1, thus indicating that the smallest
  *>                    singular values might be lost.
  *>
  *>          If full SVD is needed, the following two condition numbers are
  *>          useful for the analysis of the algorithm. They are provied for
  *>          a developer/implementer who is familiar with the details of
  *>          the method.
  *>
  *>          RWORK(4) = an estimate of the scaled condition number of the
  *>                    triangular factor in the first QR factorization.
  *>          RWORK(5) = an estimate of the scaled condition number of the
  *>                    triangular factor in the second QR factorization.
  *>          The following two parameters are computed if JOBT .EQ. 'T'.
  *>          They are provided for a developer/implementer who is familiar
  *>          with the details of the method.
  *>          RWORK(6) = the entropy of A^* * A :: this is the Shannon entropy
  *>                    of diag(A^* * A) / Trace(A^* * A) taken as point in the
  *>                    probability simplex.
  *>          RWORK(7) = the entropy of A * A^*. (See the description of RWORK(6).)
  *>          If the call to ZGEJSV is a workspace query (indicated by LWORK=-1 or
  *>          LRWORK=-1), then on exit RWORK(1) contains the required length of
  *>          RWORK for the job parameters used in the call.
  *> \endverbatim
  *>
  *> \param[in] LRWORK
  *> \verbatim
  *>          LRWORK is INTEGER
  *>          Length of RWORK to confirm proper allocation of workspace.
  *>          LRWORK depends on the job:
  *>
  *>       1. If only the singular values are requested i.e. if
  *>          LSAME(JOBU,'N') .AND. LSAME(JOBV,'N')
  *>          then:
  *>          1.1. If LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G'),
  *>               then: LRWORK = max( 7, 2 * M ).
  *>          1.2. Otherwise, LRWORK  = max( 7,  N ).
  *>       2. If singular values with the right singular vectors are requested
  *>          i.e. if
  *>          (LSAME(JOBV,'V').OR.LSAME(JOBV,'J')) .AND.
  *>          .NOT.(LSAME(JOBU,'U').OR.LSAME(JOBU,'F'))
  *>          then:
  *>          2.1. If LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G'),
  *>          then LRWORK = max( 7, 2 * M ).
  *>          2.2. Otherwise, LRWORK  = max( 7,  N ).
  *>       3. If singular values with the left singular vectors are requested, i.e. if
  *>          (LSAME(JOBU,'U').OR.LSAME(JOBU,'F')) .AND.
  *>          .NOT.(LSAME(JOBV,'V').OR.LSAME(JOBV,'J'))
  *>          then:
  *>          3.1. If LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G'),
  *>          then LRWORK = max( 7, 2 * M ).
  *>          3.2. Otherwise, LRWORK  = max( 7,  N ).
  *>       4. If singular values with both the left and the right singular vectors
  *>          are requested, i.e. if
  *>          (LSAME(JOBU,'U').OR.LSAME(JOBU,'F')) .AND.
  *>          (LSAME(JOBV,'V').OR.LSAME(JOBV,'J'))
  *>          then:
  *>          4.1. If LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G'),
  *>          then LRWORK = max( 7, 2 * M ).
  *>          4.2. Otherwise, LRWORK  = max( 7, N ).
  *>
- *>          If, on entry, LRWORK = -1 ot LWORK=-1, a workspace query is assumed and
+ *>          If, on entry, LRWORK = -1 or LWORK=-1, a workspace query is assumed and
  *>          the length of RWORK is returned in RWORK(1).
  *> \endverbatim
  *>
  *> \param[out] IWORK
  *> \verbatim
  *>          IWORK is INTEGER array, of dimension at least 4, that further depends
  *>          on the job:
  *>
  *>          1. If only the singular values are requested then:
  *>             If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') )
  *>             then the length of IWORK is N+M; otherwise the length of IWORK is N.
  *>          2. If the singular values and the right singular vectors are requested then:
  *>             If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') )
  *>             then the length of IWORK is N+M; otherwise the length of IWORK is N.
  *>          3. If the singular values and the left singular vectors are requested then:
  *>             If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') )
  *>             then the length of IWORK is N+M; otherwise the length of IWORK is N.
  *>          4. If the singular values with both the left and the right singular vectors
  *>             are requested, then:
  *>             4.1. If LSAME(JOBV,'J') the length of IWORK is determined as follows:
  *>                  If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') )
  *>                  then the length of IWORK is N+M; otherwise the length of IWORK is N.
  *>             4.2. If LSAME(JOBV,'V') the length of IWORK is determined as follows:
  *>                  If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') )
  *>                  then the length of IWORK is 2*N+M; otherwise the length of IWORK is 2*N.
  *>
  *>          On exit,
  *>          IWORK(1) = the numerical rank determined after the initial
  *>                     QR factorization with pivoting. See the descriptions
  *>                     of JOBA and JOBR.
  *>          IWORK(2) = the number of the computed nonzero singular values
  *>          IWORK(3) = if nonzero, a warning message:
  *>                     If IWORK(3).EQ.1 then some of the column norms of A
  *>                     were denormalized floats. The requested high accuracy
  *>                     is not warranted by the data.
  *>          IWORK(4) = 1 or -1. If IWORK(4) .EQ. 1, then the procedure used A^* to
  *>                     do the job as specified by the JOB parameters.
  *>          If the call to ZGEJSV is a workspace query (indicated by LWORK .EQ. -1 or
  *>          LRWORK .EQ. -1), then on exit IWORK(1) contains the required length of
  *>          IWORK for the job parameters used in the call.
  *> \endverbatim
  *>
  *> \param[out] INFO
  *> \verbatim
  *>          INFO is INTEGER
  *>           < 0  : if INFO = -i, then the i-th argument had an illegal value.
  *>           = 0 :  successful exit;
  *>           > 0 :  ZGEJSV  did not converge in the maximal allowed number
  *>                  of sweeps. The computed values may be inaccurate.
  *> \endverbatim
  *
  *  Authors:
  *  ========
  *
  *> \author Univ. of Tennessee
  *> \author Univ. of California Berkeley
  *> \author Univ. of Colorado Denver
  *> \author NAG Ltd.
  *
  *> \date June 2016
  *
  *> \ingroup complex16GEsing
  *
  *> \par Further Details:
  *  =====================
  *>
  *> \verbatim
  *>
  *>  ZGEJSV implements a preconditioned Jacobi SVD algorithm. It uses ZGEQP3,
  *>  ZGEQRF, and ZGELQF as preprocessors and preconditioners. Optionally, an
  *>  additional row pivoting can be used as a preprocessor, which in some
  *>  cases results in much higher accuracy. An example is matrix A with the
  *>  structure A = D1 * C * D2, where D1, D2 are arbitrarily ill-conditioned
  *>  diagonal matrices and C is well-conditioned matrix. In that case, complete
  *>  pivoting in the first QR factorizations provides accuracy dependent on the
  *>  condition number of C, and independent of D1, D2. Such higher accuracy is
  *>  not completely understood theoretically, but it works well in practice.
  *>  Further, if A can be written as A = B*D, with well-conditioned B and some
  *>  diagonal D, then the high accuracy is guaranteed, both theoretically and
  *>  in software, independent of D. For more details see [1], [2].
  *>     The computational range for the singular values can be the full range
  *>  ( UNDERFLOW,OVERFLOW ), provided that the machine arithmetic and the BLAS
  *>  & LAPACK routines called by ZGEJSV are implemented to work in that range.
  *>  If that is not the case, then the restriction for safe computation with
  *>  the singular values in the range of normalized IEEE numbers is that the
  *>  spectral condition number kappa(A)=sigma_max(A)/sigma_min(A) does not
  *>  overflow. This code (ZGEJSV) is best used in this restricted range,
  *>  meaning that singular values of magnitude below ||A||_2 / DLAMCH('O') are
  *>  returned as zeros. See JOBR for details on this.
  *>     Further, this implementation is somewhat slower than the one described
  *>  in [1,2] due to replacement of some non-LAPACK components, and because
  *>  the choice of some tuning parameters in the iterative part (ZGESVJ) is
  *>  left to the implementer on a particular machine.
  *>     The rank revealing QR factorization (in this code: ZGEQP3) should be
  *>  implemented as in [3]. We have a new version of ZGEQP3 under development
  *>  that is more robust than the current one in LAPACK, with a cleaner cut in
  *>  rank deficient cases. It will be available in the SIGMA library [4].
  *>  If M is much larger than N, it is obvious that the initial QRF with
  *>  column pivoting can be preprocessed by the QRF without pivoting. That
  *>  well known trick is not used in ZGEJSV because in some cases heavy row
  *>  weighting can be treated with complete pivoting. The overhead in cases
  *>  M much larger than N is then only due to pivoting, but the benefits in
  *>  terms of accuracy have prevailed. The implementer/user can incorporate
  *>  this extra QRF step easily. The implementer can also improve data movement
  *>  (matrix transpose, matrix copy, matrix transposed copy) - this
  *>  implementation of ZGEJSV uses only the simplest, naive data movement.
  *> \endverbatim
  *
  *> \par Contributor:
  *  ==================
  *>
  *>  Zlatko Drmac, Department of Mathematics, Faculty of Science,
  *>  University of Zagreb (Zagreb, Croatia); drmac@math.hr
  *
  *> \par References:
  *  ================
  *>
  *> \verbatim
  *>
  *> [1] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm I.
  *>     SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1322-1342.
  *>     LAPACK Working note 169.
  *> [2] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm II.
  *>     SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1343-1362.
  *>     LAPACK Working note 170.
  *> [3] Z. Drmac and Z. Bujanovic: On the failure of rank-revealing QR
  *>     factorization software - a case study.
  *>     ACM Trans. Math. Softw. Vol. 35, No 2 (2008), pp. 1-28.
  *>     LAPACK Working note 176.
  *> [4] Z. Drmac: SIGMA - mathematical software library for accurate SVD, PSV,
  *>     QSVD, (H,K)-SVD computations.
  *>     Department of Mathematics, University of Zagreb, 2008, 2016.
  *> \endverbatim
  *
  *>  \par Bugs, examples and comments:
  *   =================================
  *>
  *>  Please report all bugs and send interesting examples and/or comments to
  *>  drmac@math.hr. Thank you.
  *>
  *  =====================================================================
        SUBROUTINE ZGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,
       $                   M, N, A, LDA, SVA, U, LDU, V, LDV,
       $                   CWORK, LWORK, RWORK, LRWORK, IWORK, INFO )
  *
- *  -- LAPACK computational routine (version 3.7.0) --
+ *  -- LAPACK computational routine (version 3.7.1) --
  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
- *     December 2016
+ *     June 2017
  *
  *     .. Scalar Arguments ..
        IMPLICIT    NONE
        INTEGER     INFO, LDA, LDU, LDV, LWORK, LRWORK, M, N
  *     ..
  *     .. Array Arguments ..
        COMPLEX*16       A( LDA, * ), U( LDU, * ), V( LDV, * ),
       $                 CWORK( LWORK )
        DOUBLE PRECISION SVA( N ), RWORK( LRWORK )
        INTEGER          IWORK( * )
        CHARACTER*1      JOBA, JOBP, JOBR, JOBT, JOBU, JOBV
  *     ..
  *
  *  ===========================================================================
  *
  *     .. Local Parameters ..
        DOUBLE PRECISION ZERO, ONE
        PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
        COMPLEX*16 CZERO, CONE
        PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ), CONE = ( 1.0D0, 0.0D0 ) )
  *     ..
  *     .. Local Scalars ..
        COMPLEX*16       CTEMP
        DOUBLE PRECISION AAPP,    AAQQ,   AATMAX, AATMIN, BIG,    BIG1,
       $                 COND_OK, CONDR1, CONDR2, ENTRA,  ENTRAT, EPSLN,
       $                 MAXPRJ,  SCALEM, SCONDA, SFMIN,  SMALL,  TEMP1,
       $                 USCAL1,  USCAL2, XSC
        INTEGER IERR,   N1,     NR,     NUMRANK,        p, q,   WARNING
        LOGICAL ALMORT, DEFR,   ERREST, GOSCAL,  JRACC,  KILL,   LQUERY,
       $        LSVEC,  L2ABER, L2KILL, L2PERT,  L2RANK, L2TRAN, NOSCAL,
       $        ROWPIV, RSVEC,  TRANSP
  *
        INTEGER OPTWRK, MINWRK, MINRWRK, MINIWRK
        INTEGER LWCON,  LWLQF, LWQP3, LWQRF, LWUNMLQ, LWUNMQR, LWUNMQRM,
       $        LWSVDJ, LWSVDJV, LRWQP3, LRWCON, LRWSVDJ, IWOFF
        INTEGER LWRK_ZGELQF, LWRK_ZGEQP3,  LWRK_ZGEQP3N, LWRK_ZGEQRF,
       $        LWRK_ZGESVJ, LWRK_ZGESVJV, LWRK_ZGESVJU, LWRK_ZUNMLQ,
       $        LWRK_ZUNMQR, LWRK_ZUNMQRM
  *     ..
  *     .. Local Arrays
        COMPLEX*16         CDUMMY(1)
        DOUBLE PRECISION   RDUMMY(1)
  *
  *     .. Intrinsic Functions ..
        INTRINSIC ABS, DCMPLX, CONJG, DLOG, MAX, MIN, DBLE, NINT, SQRT
  *     ..
  *     .. External Functions ..
        DOUBLE PRECISION      DLAMCH, DZNRM2
        INTEGER   IDAMAX, IZAMAX
        LOGICAL   LSAME
        EXTERNAL  IDAMAX, IZAMAX, LSAME, DLAMCH, DZNRM2
  *     ..
  *     .. External Subroutines ..
        EXTERNAL  DLASSQ, ZCOPY,  ZGELQF, ZGEQP3, ZGEQRF, ZLACPY, ZLAPMR,
       $          ZLASCL, DLASCL, ZLASET, ZLASSQ, ZLASWP, ZUNGQR, ZUNMLQ,
       $          ZUNMQR, ZPOCON, DSCAL,  ZDSCAL, ZSWAP,  ZTRSM,  ZLACGV,
       $          XERBLA
  *
        EXTERNAL  ZGESVJ
  *     ..
  *
  *     Test the input arguments
  *
        LSVEC  = LSAME( JOBU, 'U' ) .OR. LSAME( JOBU, 'F' )
        JRACC  = LSAME( JOBV, 'J' )
        RSVEC  = LSAME( JOBV, 'V' ) .OR. JRACC
        ROWPIV = LSAME( JOBA, 'F' ) .OR. LSAME( JOBA, 'G' )
        L2RANK = LSAME( JOBA, 'R' )
        L2ABER = LSAME( JOBA, 'A' )
        ERREST = LSAME( JOBA, 'E' ) .OR. LSAME( JOBA, 'G' )
        L2TRAN = LSAME( JOBT, 'T' ) .AND. ( M .EQ. N )
        L2KILL = LSAME( JOBR, 'R' )
        DEFR   = LSAME( JOBR, 'N' )
        L2PERT = LSAME( JOBP, 'P' )
  *
        LQUERY = ( LWORK .EQ. -1 ) .OR. ( LRWORK .EQ. -1 )
  *
        IF ( .NOT.(ROWPIV .OR. L2RANK .OR. L2ABER .OR.
       $     ERREST .OR. LSAME( JOBA, 'C' ) )) THEN
           INFO = - 1
        ELSE IF ( .NOT.( LSVEC .OR. LSAME( JOBU, 'N' ) .OR.
       $   ( LSAME( JOBU, 'W' ) .AND. RSVEC .AND. L2TRAN ) ) ) THEN
           INFO = - 2
        ELSE IF ( .NOT.( RSVEC .OR. LSAME( JOBV, 'N' ) .OR.
       $   ( LSAME( JOBV, 'W' ) .AND. LSVEC .AND. L2TRAN ) ) ) THEN
           INFO = - 3
        ELSE IF ( .NOT. ( L2KILL .OR. DEFR ) )    THEN
           INFO = - 4
        ELSE IF ( .NOT. ( LSAME(JOBT,'T') .OR. LSAME(JOBT,'N') ) ) THEN
           INFO = - 5
        ELSE IF ( .NOT. ( L2PERT .OR. LSAME( JOBP, 'N' ) ) ) THEN
           INFO = - 6
        ELSE IF ( M .LT. 0 ) THEN
           INFO = - 7
        ELSE IF ( ( N .LT. 0 ) .OR. ( N .GT. M ) ) THEN
           INFO = - 8
        ELSE IF ( LDA .LT. M ) THEN
           INFO = - 10
        ELSE IF ( LSVEC .AND. ( LDU .LT. M ) ) THEN
           INFO = - 13
        ELSE IF ( RSVEC .AND. ( LDV .LT. N ) ) THEN
           INFO = - 15
        ELSE
  *        #:)
           INFO = 0
        END IF
  *
        IF ( INFO .EQ. 0 ) THEN
  *         .. compute the minimal and the optimal workspace lengths
  *         [[The expressions for computing the minimal and the optimal
  *         values of LCWORK, LRWORK are written with a lot of redundancy and
  *         can be simplified. However, this verbose form is useful for
  *         maintenance and modifications of the code.]]
  *
  *        .. minimal workspace length for ZGEQP3 of an M x N matrix,
  *         ZGEQRF of an N x N matrix, ZGELQF of an N x N matrix,
  *         ZUNMLQ for computing N x N matrix, ZUNMQR for computing N x N
  *         matrix, ZUNMQR for computing M x N matrix, respectively.
            LWQP3 = N+1
            LWQRF = MAX( 1, N )
            LWLQF = MAX( 1, N )
            LWUNMLQ  = MAX( 1, N )
            LWUNMQR  = MAX( 1, N )
            LWUNMQRM = MAX( 1, M )
  *        .. minimal workspace length for ZPOCON of an N x N matrix
            LWCON = 2 * N
  *        .. minimal workspace length for ZGESVJ of an N x N matrix,
  *         without and with explicit accumulation of Jacobi rotations
            LWSVDJ  = MAX( 2 * N, 1 )
            LWSVDJV = MAX( 2 * N, 1 )
  *         .. minimal REAL workspace length for ZGEQP3, ZPOCON, ZGESVJ
            LRWQP3  = N
            LRWCON  = N
            LRWSVDJ = N
            IF ( LQUERY ) THEN
                CALL ZGEQP3( M, N, A, LDA, IWORK, CDUMMY, CDUMMY, -1,
       $             RDUMMY, IERR )
                LWRK_ZGEQP3 = CDUMMY(1)
                CALL ZGEQRF( N, N, A, LDA, CDUMMY, CDUMMY,-1, IERR )
                LWRK_ZGEQRF = CDUMMY(1)
                CALL ZGELQF( N, N, A, LDA, CDUMMY, CDUMMY,-1, IERR )
                LWRK_ZGELQF = CDUMMY(1)
            END IF
            MINWRK  = 2
            OPTWRK  = 2
            MINIWRK = N
            IF ( .NOT. (LSVEC .OR. RSVEC ) ) THEN
  *             .. minimal and optimal sizes of the complex workspace if
  *             only the singular values are requested
                IF ( ERREST ) THEN
                    MINWRK = MAX( N+LWQP3, N**2+LWCON, N+LWQRF, LWSVDJ )
                ELSE
                    MINWRK = MAX( N+LWQP3, N+LWQRF, LWSVDJ )
                END IF
                IF ( LQUERY ) THEN
                    CALL ZGESVJ( 'L', 'N', 'N', N, N, A, LDA, SVA, N, V,
       $                 LDV, CDUMMY, -1, RDUMMY, -1, IERR )
                    LWRK_ZGESVJ = CDUMMY(1)
                    IF ( ERREST ) THEN
                        OPTWRK = MAX( N+LWRK_ZGEQP3, N**2+LWCON,
       $                              N+LWRK_ZGEQRF, LWRK_ZGESVJ )
                    ELSE
                        OPTWRK = MAX( N+LWRK_ZGEQP3, N+LWRK_ZGEQRF,
       $                              LWRK_ZGESVJ )
                    END IF
                END IF
                IF ( L2TRAN .OR. ROWPIV ) THEN
                    IF ( ERREST ) THEN
                       MINRWRK = MAX( 7, 2*M,  LRWQP3, LRWCON, LRWSVDJ )
                    ELSE
                       MINRWRK = MAX( 7, 2*M,  LRWQP3, LRWSVDJ )
                    END IF
                ELSE
                    IF ( ERREST ) THEN
                       MINRWRK = MAX( 7, LRWQP3, LRWCON, LRWSVDJ )
                    ELSE
                       MINRWRK = MAX( 7, LRWQP3, LRWSVDJ )
                    END IF
                END IF
                IF ( ROWPIV .OR. L2TRAN ) MINIWRK = MINIWRK + M
            ELSE IF ( RSVEC .AND. (.NOT.LSVEC) ) THEN
  *            .. minimal and optimal sizes of the complex workspace if the
  *            singular values and the right singular vectors are requested
               IF ( ERREST ) THEN
                   MINWRK = MAX( N+LWQP3, LWCON, LWSVDJ, N+LWLQF,
       $                         2*N+LWQRF, N+LWSVDJ, N+LWUNMLQ )
               ELSE
                   MINWRK = MAX( N+LWQP3, LWSVDJ, N+LWLQF, 2*N+LWQRF,
       $                         N+LWSVDJ, N+LWUNMLQ )
               END IF
               IF ( LQUERY ) THEN
                   CALL ZGESVJ( 'L', 'U', 'N', N,N, U, LDU, SVA, N, A,
       $                LDA, CDUMMY, -1, RDUMMY, -1, IERR )
                   LWRK_ZGESVJ = CDUMMY(1)
                   CALL ZUNMLQ( 'L', 'C', N, N, N, A, LDA, CDUMMY,
       $                V, LDV, CDUMMY, -1, IERR )
                   LWRK_ZUNMLQ = CDUMMY(1)
                   IF ( ERREST ) THEN
                   OPTWRK = MAX( N+LWRK_ZGEQP3, LWCON, LWRK_ZGESVJ,
       $                         N+LWRK_ZGELQF, 2*N+LWRK_ZGEQRF,
       $                         N+LWRK_ZGESVJ,  N+LWRK_ZUNMLQ )
                   ELSE
                   OPTWRK = MAX( N+LWRK_ZGEQP3, LWRK_ZGESVJ,N+LWRK_ZGELQF,
       $                         2*N+LWRK_ZGEQRF, N+LWRK_ZGESVJ,
       $                         N+LWRK_ZUNMLQ )
                   END IF
               END IF
               IF ( L2TRAN .OR. ROWPIV ) THEN
                    IF ( ERREST ) THEN
                       MINRWRK = MAX( 7, 2*M,  LRWQP3, LRWSVDJ, LRWCON )
                    ELSE
                       MINRWRK = MAX( 7, 2*M,  LRWQP3, LRWSVDJ )
                    END IF
               ELSE
                    IF ( ERREST ) THEN
                       MINRWRK = MAX( 7, LRWQP3, LRWSVDJ, LRWCON )
                    ELSE
                       MINRWRK = MAX( 7, LRWQP3, LRWSVDJ )
                    END IF
               END IF
               IF ( ROWPIV .OR. L2TRAN ) MINIWRK = MINIWRK + M
            ELSE IF ( LSVEC .AND. (.NOT.RSVEC) ) THEN
  *            .. minimal and optimal sizes of the complex workspace if the
  *            singular values and the left singular vectors are requested
               IF ( ERREST ) THEN
                   MINWRK = N + MAX( LWQP3,LWCON,N+LWQRF,LWSVDJ,LWUNMQRM )
               ELSE
                   MINWRK = N + MAX( LWQP3, N+LWQRF, LWSVDJ, LWUNMQRM )
               END IF
               IF ( LQUERY ) THEN
                   CALL ZGESVJ( 'L', 'U', 'N', N,N, U, LDU, SVA, N, A,
       $                LDA, CDUMMY, -1, RDUMMY, -1, IERR )
                   LWRK_ZGESVJ = CDUMMY(1)
                   CALL ZUNMQR( 'L', 'N', M, N, N, A, LDA, CDUMMY, U,
       $               LDU, CDUMMY, -1, IERR )
                   LWRK_ZUNMQRM = CDUMMY(1)
                   IF ( ERREST ) THEN
                   OPTWRK = N + MAX( LWRK_ZGEQP3, LWCON, N+LWRK_ZGEQRF,
       $                             LWRK_ZGESVJ, LWRK_ZUNMQRM )
                   ELSE
                   OPTWRK = N + MAX( LWRK_ZGEQP3, N+LWRK_ZGEQRF,
       $                             LWRK_ZGESVJ, LWRK_ZUNMQRM )
                   END IF
               END IF
               IF ( L2TRAN .OR. ROWPIV ) THEN
                   IF ( ERREST ) THEN
                      MINRWRK = MAX( 7, 2*M,  LRWQP3, LRWSVDJ, LRWCON )
                   ELSE
                      MINRWRK = MAX( 7, 2*M,  LRWQP3, LRWSVDJ )
                   END IF
               ELSE
                   IF ( ERREST ) THEN
                      MINRWRK = MAX( 7, LRWQP3, LRWSVDJ, LRWCON )
                   ELSE
                      MINRWRK = MAX( 7, LRWQP3, LRWSVDJ )
                   END IF
               END IF
               IF ( ROWPIV .OR. L2TRAN ) MINIWRK = MINIWRK + M
            ELSE
  *            .. minimal and optimal sizes of the complex workspace if the
  *            full SVD is requested
               IF ( .NOT. JRACC ) THEN
                   IF ( ERREST ) THEN
                      MINWRK = MAX( N+LWQP3, N+LWCON,  2*N+N**2+LWCON,
       $                         2*N+LWQRF,         2*N+LWQP3,
       $                         2*N+N**2+N+LWLQF,  2*N+N**2+N+N**2+LWCON,
       $                         2*N+N**2+N+LWSVDJ, 2*N+N**2+N+LWSVDJV,
       $                         2*N+N**2+N+LWUNMQR,2*N+N**2+N+LWUNMLQ,
       $                         N+N**2+LWSVDJ,   N+LWUNMQRM )
                   ELSE
                      MINWRK = MAX( N+LWQP3,        2*N+N**2+LWCON,
       $                         2*N+LWQRF,         2*N+LWQP3,
       $                         2*N+N**2+N+LWLQF,  2*N+N**2+N+N**2+LWCON,
       $                         2*N+N**2+N+LWSVDJ, 2*N+N**2+N+LWSVDJV,
       $                         2*N+N**2+N+LWUNMQR,2*N+N**2+N+LWUNMLQ,
       $                         N+N**2+LWSVDJ,      N+LWUNMQRM )
                   END IF
                   MINIWRK = MINIWRK + N
                   IF ( ROWPIV .OR. L2TRAN ) MINIWRK = MINIWRK + M
               ELSE
                   IF ( ERREST ) THEN
                      MINWRK = MAX( N+LWQP3, N+LWCON, 2*N+LWQRF,
       $                         2*N+N**2+LWSVDJV, 2*N+N**2+N+LWUNMQR,
       $                         N+LWUNMQRM )
                   ELSE
                      MINWRK = MAX( N+LWQP3, 2*N+LWQRF,
       $                         2*N+N**2+LWSVDJV, 2*N+N**2+N+LWUNMQR,
       $                         N+LWUNMQRM )
                   END IF
                   IF ( ROWPIV .OR. L2TRAN ) MINIWRK = MINIWRK + M
               END IF
               IF ( LQUERY ) THEN
                   CALL ZUNMQR( 'L', 'N', M, N, N, A, LDA, CDUMMY, U,
       $                LDU, CDUMMY, -1, IERR )
                   LWRK_ZUNMQRM = CDUMMY(1)
                   CALL ZUNMQR( 'L', 'N', N, N, N, A, LDA, CDUMMY, U,
       $                LDU, CDUMMY, -1, IERR )
                   LWRK_ZUNMQR = CDUMMY(1)
                   IF ( .NOT. JRACC ) THEN
                       CALL ZGEQP3( N,N, A, LDA, IWORK, CDUMMY,CDUMMY, -1,
       $                    RDUMMY, IERR )
                       LWRK_ZGEQP3N = CDUMMY(1)
                       CALL ZGESVJ( 'L', 'U', 'N', N, N, U, LDU, SVA,
       $                    N, V, LDV, CDUMMY, -1, RDUMMY, -1, IERR )
                       LWRK_ZGESVJ = CDUMMY(1)
                       CALL ZGESVJ( 'U', 'U', 'N', N, N, U, LDU, SVA,
       $                    N, V, LDV, CDUMMY, -1, RDUMMY, -1, IERR )
                       LWRK_ZGESVJU = CDUMMY(1)
                       CALL ZGESVJ( 'L', 'U', 'V', N, N, U, LDU, SVA,
       $                    N, V, LDV, CDUMMY, -1, RDUMMY, -1, IERR )
                       LWRK_ZGESVJV = CDUMMY(1)
                       CALL ZUNMLQ( 'L', 'C', N, N, N, A, LDA, CDUMMY,
       $                    V, LDV, CDUMMY, -1, IERR )
                       LWRK_ZUNMLQ = CDUMMY(1)
                       IF ( ERREST ) THEN
                         OPTWRK = MAX( N+LWRK_ZGEQP3, N+LWCON,
       $                          2*N+N**2+LWCON, 2*N+LWRK_ZGEQRF,
       $                          2*N+LWRK_ZGEQP3N,
       $                          2*N+N**2+N+LWRK_ZGELQF,
       $                          2*N+N**2+N+N**2+LWCON,
       $                          2*N+N**2+N+LWRK_ZGESVJ,
       $                          2*N+N**2+N+LWRK_ZGESVJV,
       $                          2*N+N**2+N+LWRK_ZUNMQR,
       $                          2*N+N**2+N+LWRK_ZUNMLQ,
       $                          N+N**2+LWRK_ZGESVJU,
       $                          N+LWRK_ZUNMQRM )
                       ELSE
                         OPTWRK = MAX( N+LWRK_ZGEQP3,
       $                          2*N+N**2+LWCON, 2*N+LWRK_ZGEQRF,
       $                          2*N+LWRK_ZGEQP3N,
       $                          2*N+N**2+N+LWRK_ZGELQF,
       $                          2*N+N**2+N+N**2+LWCON,
       $                          2*N+N**2+N+LWRK_ZGESVJ,
       $                          2*N+N**2+N+LWRK_ZGESVJV,
       $                          2*N+N**2+N+LWRK_ZUNMQR,
       $                          2*N+N**2+N+LWRK_ZUNMLQ,
       $                          N+N**2+LWRK_ZGESVJU,
       $                          N+LWRK_ZUNMQRM )
                       END IF
                   ELSE
                       CALL ZGESVJ( 'L', 'U', 'V', N, N, U, LDU, SVA,
       $                    N, V, LDV, CDUMMY, -1, RDUMMY, -1, IERR )
                       LWRK_ZGESVJV = CDUMMY(1)
                       CALL ZUNMQR( 'L', 'N', N, N, N, CDUMMY, N, CDUMMY,
       $                    V, LDV, CDUMMY, -1, IERR )
                       LWRK_ZUNMQR = CDUMMY(1)
                       CALL ZUNMQR( 'L', 'N', M, N, N, A, LDA, CDUMMY, U,
       $                    LDU, CDUMMY, -1, IERR )
                       LWRK_ZUNMQRM = CDUMMY(1)
                       IF ( ERREST ) THEN
                          OPTWRK = MAX( N+LWRK_ZGEQP3, N+LWCON,
       $                           2*N+LWRK_ZGEQRF, 2*N+N**2,
       $                           2*N+N**2+LWRK_ZGESVJV,
       $                           2*N+N**2+N+LWRK_ZUNMQR,N+LWRK_ZUNMQRM )
                       ELSE
                          OPTWRK = MAX( N+LWRK_ZGEQP3, 2*N+LWRK_ZGEQRF,
       $                           2*N+N**2, 2*N+N**2+LWRK_ZGESVJV,
       $                           2*N+N**2+N+LWRK_ZUNMQR,
       $                           N+LWRK_ZUNMQRM )
                       END IF
                   END IF
               END IF
               IF ( L2TRAN .OR. ROWPIV ) THEN
                   MINRWRK = MAX( 7, 2*M,  LRWQP3, LRWSVDJ, LRWCON )
               ELSE
                   MINRWRK = MAX( 7, LRWQP3, LRWSVDJ, LRWCON )
               END IF
            END IF
            MINWRK = MAX( 2, MINWRK )
            OPTWRK = MAX( 2, OPTWRK )
            IF ( LWORK  .LT. MINWRK  .AND. (.NOT.LQUERY) ) INFO = - 17
            IF ( LRWORK .LT. MINRWRK .AND. (.NOT.LQUERY) ) INFO = - 19
        END IF
  *
        IF ( INFO .NE. 0 ) THEN
  *       #:(
           CALL XERBLA( 'ZGEJSV', - INFO )
           RETURN
        ELSE IF ( LQUERY ) THEN
            CWORK(1) = OPTWRK
            CWORK(2) = MINWRK
            RWORK(1) = MINRWRK
            IWORK(1) = MAX( 4, MINIWRK )
            RETURN
        END IF
  *
  *     Quick return for void matrix (Y3K safe)
  * #:)
        IF ( ( M .EQ. 0 ) .OR. ( N .EQ. 0 ) ) THEN
           IWORK(1:4) = 0
           RWORK(1:7) = 0
           RETURN
        ENDIF
  *
  *     Determine whether the matrix U should be M x N or M x M
  *
        IF ( LSVEC ) THEN
           N1 = N
           IF ( LSAME( JOBU, 'F' ) ) N1 = M
        END IF
  *
  *     Set numerical parameters
  *
  *!    NOTE: Make sure DLAMCH() does not fail on the target architecture.
  *
        EPSLN = DLAMCH('Epsilon')
        SFMIN = DLAMCH('SafeMinimum')
        SMALL = SFMIN / EPSLN
        BIG   = DLAMCH('O')
  *     BIG   = ONE / SFMIN
  *
  *     Initialize SVA(1:N) = diag( ||A e_i||_2 )_1^N
  *
  *(!)  If necessary, scale SVA() to protect the largest norm from
  *     overflow. It is possible that this scaling pushes the smallest
  *     column norm left from the underflow threshold (extreme case).
  *
        SCALEM  = ONE / SQRT(DBLE(M)*DBLE(N))
        NOSCAL  = .TRUE.
        GOSCAL  = .TRUE.
        DO 1874 p = 1, N
           AAPP = ZERO
           AAQQ = ONE
           CALL ZLASSQ( M, A(1,p), 1, AAPP, AAQQ )
           IF ( AAPP .GT. BIG ) THEN
              INFO = - 9
              CALL XERBLA( 'ZGEJSV', -INFO )
              RETURN
           END IF
           AAQQ = SQRT(AAQQ)
           IF ( ( AAPP .LT. (BIG / AAQQ) ) .AND. NOSCAL  ) THEN
              SVA(p)  = AAPP * AAQQ
           ELSE
              NOSCAL  = .FALSE.
              SVA(p)  = AAPP * ( AAQQ * SCALEM )
              IF ( GOSCAL ) THEN
                 GOSCAL = .FALSE.
                 CALL DSCAL( p-1, SCALEM, SVA, 1 )
              END IF
           END IF
 CONTINUE
  *
        IF ( NOSCAL ) SCALEM = ONE
  *
        AAPP = ZERO
        AAQQ = BIG
        DO 4781 p = 1, N
           AAPP = MAX( AAPP, SVA(p) )
           IF ( SVA(p) .NE. ZERO ) AAQQ = MIN( AAQQ, SVA(p) )
 CONTINUE
  *
  *     Quick return for zero M x N matrix
  * #:)
        IF ( AAPP .EQ. ZERO ) THEN
           IF ( LSVEC ) CALL ZLASET( 'G', M, N1, CZERO, CONE, U, LDU )
           IF ( RSVEC ) CALL ZLASET( 'G', N, N,  CZERO, CONE, V, LDV )
           RWORK(1) = ONE
           RWORK(2) = ONE
           IF ( ERREST ) RWORK(3) = ONE
           IF ( LSVEC .AND. RSVEC ) THEN
              RWORK(4) = ONE
              RWORK(5) = ONE
           END IF
           IF ( L2TRAN ) THEN
              RWORK(6) = ZERO
              RWORK(7) = ZERO
           END IF
           IWORK(1) = 0
           IWORK(2) = 0
           IWORK(3) = 0
           IWORK(4) = -1
           RETURN
        END IF
  *
  *     Issue warning if denormalized column norms detected. Override the
  *     high relative accuracy request. Issue licence to kill nonzero columns
  *     (set them to zero) whose norm is less than sigma_max / BIG (roughly).
  * #:(
        WARNING = 0
        IF ( AAQQ .LE. SFMIN ) THEN
           L2RANK = .TRUE.
           L2KILL = .TRUE.
           WARNING = 1
        END IF
  *
  *     Quick return for one-column matrix
  * #:)
        IF ( N .EQ. 1 ) THEN
  *
           IF ( LSVEC ) THEN
              CALL ZLASCL( 'G',0,0,SVA(1),SCALEM, M,1,A(1,1),LDA,IERR )
              CALL ZLACPY( 'A', M, 1, A, LDA, U, LDU )
  *           computing all M left singular vectors of the M x 1 matrix
              IF ( N1 .NE. N  ) THEN
                CALL ZGEQRF( M, N, U,LDU, CWORK, CWORK(N+1),LWORK-N,IERR )
                CALL ZUNGQR( M,N1,1, U,LDU,CWORK,CWORK(N+1),LWORK-N,IERR )
                CALL ZCOPY( M, A(1,1), 1, U(1,1), 1 )
              END IF
           END IF
           IF ( RSVEC ) THEN
               V(1,1) = CONE
           END IF
           IF ( SVA(1) .LT. (BIG*SCALEM) ) THEN
              SVA(1)  = SVA(1) / SCALEM
              SCALEM  = ONE
           END IF
           RWORK(1) = ONE / SCALEM
           RWORK(2) = ONE
           IF ( SVA(1) .NE. ZERO ) THEN
              IWORK(1) = 1
              IF ( ( SVA(1) / SCALEM) .GE. SFMIN ) THEN
                 IWORK(2) = 1
              ELSE
                 IWORK(2) = 0
              END IF
           ELSE
              IWORK(1) = 0
              IWORK(2) = 0
           END IF
           IWORK(3) = 0
           IWORK(4) = -1
           IF ( ERREST ) RWORK(3) = ONE
           IF ( LSVEC .AND. RSVEC ) THEN
              RWORK(4) = ONE
              RWORK(5) = ONE
           END IF
           IF ( L2TRAN ) THEN
              RWORK(6) = ZERO
              RWORK(7) = ZERO
           END IF
           RETURN
  *
        END IF
  *
        TRANSP = .FALSE.
  *
        AATMAX = -ONE
        AATMIN =  BIG
        IF ( ROWPIV .OR. L2TRAN ) THEN
  *
  *     Compute the row norms, needed to determine row pivoting sequence
  *     (in the case of heavily row weighted A, row pivoting is strongly
  *     advised) and to collect information needed to compare the
  *     structures of A * A^* and A^* * A (in the case L2TRAN.EQ..TRUE.).
  *
           IF ( L2TRAN ) THEN
              DO 1950 p = 1, M
                 XSC   = ZERO
                 TEMP1 = ONE
                 CALL ZLASSQ( N, A(p,1), LDA, XSC, TEMP1 )
  *              ZLASSQ gets both the ell_2 and the ell_infinity norm
  *              in one pass through the vector
                 RWORK(M+p)  = XSC * SCALEM
                 RWORK(p)    = XSC * (SCALEM*SQRT(TEMP1))
                 AATMAX = MAX( AATMAX, RWORK(p) )
                 IF (RWORK(p) .NE. ZERO)
       $            AATMIN = MIN(AATMIN,RWORK(p))
       CONTINUE
           ELSE
              DO 1904 p = 1, M
                 RWORK(M+p) = SCALEM*ABS( A(p,IZAMAX(N,A(p,1),LDA)) )
                 AATMAX = MAX( AATMAX, RWORK(M+p) )
                 AATMIN = MIN( AATMIN, RWORK(M+p) )
       CONTINUE
           END IF
  *
        END IF
  *
  *     For square matrix A try to determine whether A^*  would be better
  *     input for the preconditioned Jacobi SVD, with faster convergence.
  *     The decision is based on an O(N) function of the vector of column
  *     and row norms of A, based on the Shannon entropy. This should give
  *     the right choice in most cases when the difference actually matters.
  *     It may fail and pick the slower converging side.
  *
        ENTRA  = ZERO
        ENTRAT = ZERO
        IF ( L2TRAN ) THEN
  *
           XSC   = ZERO
           TEMP1 = ONE
           CALL DLASSQ( N, SVA, 1, XSC, TEMP1 )
           TEMP1 = ONE / TEMP1
  *
           ENTRA = ZERO
           DO 1113 p = 1, N
              BIG1  = ( ( SVA(p) / XSC )**2 ) * TEMP1
              IF ( BIG1 .NE. ZERO ) ENTRA = ENTRA + BIG1 * DLOG(BIG1)
    CONTINUE
           ENTRA = - ENTRA / DLOG(DBLE(N))
  *
  *        Now, SVA().^2/Trace(A^* * A) is a point in the probability simplex.
  *        It is derived from the diagonal of  A^* * A.  Do the same with the
  *        diagonal of A * A^*, compute the entropy of the corresponding
  *        probability distribution. Note that A * A^* and A^* * A have the
  *        same trace.
  *
           ENTRAT = ZERO
           DO 1114 p = 1, M
              BIG1 = ( ( RWORK(p) / XSC )**2 ) * TEMP1
              IF ( BIG1 .NE. ZERO ) ENTRAT = ENTRAT + BIG1 * DLOG(BIG1)
    CONTINUE
           ENTRAT = - ENTRAT / DLOG(DBLE(M))
  *
  *        Analyze the entropies and decide A or A^*. Smaller entropy
  *        usually means better input for the algorithm.
  *
           TRANSP = ( ENTRAT .LT. ENTRA )
  *
  *        If A^* is better than A, take the adjoint of A. This is allowed
  *        only for square matrices, M=N.
           IF ( TRANSP ) THEN
  *           In an optimal implementation, this trivial transpose
  *           should be replaced with faster transpose.
              DO 1115 p = 1, N - 1
                 A(p,p) = CONJG(A(p,p))
                 DO 1116 q = p + 1, N
                     CTEMP = CONJG(A(q,p))
                    A(q,p) = CONJG(A(p,q))
                    A(p,q) = CTEMP
          CONTINUE
       CONTINUE
              A(N,N) = CONJG(A(N,N))
              DO 1117 p = 1, N
                 RWORK(M+p) = SVA(p)
                 SVA(p)     = RWORK(p)
  *              previously computed row 2-norms are now column 2-norms
  *              of the transposed matrix
       CONTINUE
              TEMP1  = AAPP
              AAPP   = AATMAX
              AATMAX = TEMP1
              TEMP1  = AAQQ
              AAQQ   = AATMIN
              AATMIN = TEMP1
              KILL   = LSVEC
              LSVEC  = RSVEC
              RSVEC  = KILL
              IF ( LSVEC ) N1 = N
  *
              ROWPIV = .TRUE.
           END IF
  *
        END IF
  *     END IF L2TRAN
  *
  *     Scale the matrix so that its maximal singular value remains less
  *     than SQRT(BIG) -- the matrix is scaled so that its maximal column
  *     has Euclidean norm equal to SQRT(BIG/N). The only reason to keep
  *     SQRT(BIG) instead of BIG is the fact that ZGEJSV uses LAPACK and
  *     BLAS routines that, in some implementations, are not capable of
  *     working in the full interval [SFMIN,BIG] and that they may provoke
  *     overflows in the intermediate results. If the singular values spread
  *     from SFMIN to BIG, then ZGESVJ will compute them. So, in that case,
  *     one should use ZGESVJ instead of ZGEJSV.
  *     >> change in the April 2016 update: allow bigger range, i.e. the
  *     largest column is allowed up to BIG/N and ZGESVJ will do the rest.
        BIG1   = SQRT( BIG )
        TEMP1  = SQRT( BIG / DBLE(N) )
  *      TEMP1  = BIG/DBLE(N)
  *
        CALL DLASCL( 'G', 0, 0, AAPP, TEMP1, N, 1, SVA, N, IERR )
        IF ( AAQQ .GT. (AAPP * SFMIN) ) THEN
            AAQQ = ( AAQQ / AAPP ) * TEMP1
        ELSE
            AAQQ = ( AAQQ * TEMP1 ) / AAPP
        END IF
        TEMP1 = TEMP1 * SCALEM
        CALL ZLASCL( 'G', 0, 0, AAPP, TEMP1, M, N, A, LDA, IERR )
  *
  *     To undo scaling at the end of this procedure, multiply the
  *     computed singular values with USCAL2 / USCAL1.
  *
        USCAL1 = TEMP1
        USCAL2 = AAPP
  *
        IF ( L2KILL ) THEN
  *        L2KILL enforces computation of nonzero singular values in
  *        the restricted range of condition number of the initial A,
  *        sigma_max(A) / sigma_min(A) approx. SQRT(BIG)/SQRT(SFMIN).
           XSC = SQRT( SFMIN )
        ELSE
           XSC = SMALL
  *
  *        Now, if the condition number of A is too big,
  *        sigma_max(A) / sigma_min(A) .GT. SQRT(BIG/N) * EPSLN / SFMIN,
  *        as a precaution measure, the full SVD is computed using ZGESVJ
  *        with accumulated Jacobi rotations. This provides numerically
  *        more robust computation, at the cost of slightly increased run
  *        time. Depending on the concrete implementation of BLAS and LAPACK
  *        (i.e. how they behave in presence of extreme ill-conditioning) the
  *        implementor may decide to remove this switch.
           IF ( ( AAQQ.LT.SQRT(SFMIN) ) .AND. LSVEC .AND. RSVEC ) THEN
              JRACC = .TRUE.
           END IF
  *
        END IF
        IF ( AAQQ .LT. XSC ) THEN
           DO 700 p = 1, N
              IF ( SVA(p) .LT. XSC ) THEN
                 CALL ZLASET( 'A', M, 1, CZERO, CZERO, A(1,p), LDA )
                 SVA(p) = ZERO
              END IF
     CONTINUE
        END IF
  *
  *     Preconditioning using QR factorization with pivoting
  *
        IF ( ROWPIV ) THEN
  *        Optional row permutation (Bjoerck row pivoting):
  *        A result by Cox and Higham shows that the Bjoerck's
  *        row pivoting combined with standard column pivoting
  *        has similar effect as Powell-Reid complete pivoting.
  *        The ell-infinity norms of A are made nonincreasing.
           IF ( ( LSVEC .AND. RSVEC ) .AND. .NOT.( JRACC ) ) THEN
                IWOFF = 2*N
           ELSE
                IWOFF = N
           END IF
           DO 1952 p = 1, M - 1
              q = IDAMAX( M-p+1, RWORK(M+p), 1 ) + p - 1
              IWORK(IWOFF+p) = q
              IF ( p .NE. q ) THEN
                 TEMP1      = RWORK(M+p)
                 RWORK(M+p) = RWORK(M+q)
                 RWORK(M+q) = TEMP1
              END IF
    CONTINUE
           CALL ZLASWP( N, A, LDA, 1, M-1, IWORK(IWOFF+1), 1 )
        END IF
  *
  *     End of the preparation phase (scaling, optional sorting and
  *     transposing, optional flushing of small columns).
  *
  *     Preconditioning
  *
  *     If the full SVD is needed, the right singular vectors are computed
  *     from a matrix equation, and for that we need theoretical analysis
  *     of the Businger-Golub pivoting. So we use ZGEQP3 as the first RR QRF.
  *     In all other cases the first RR QRF can be chosen by other criteria
  *     (eg speed by replacing global with restricted window pivoting, such
  *     as in xGEQPX from TOMS # 782). Good results will be obtained using
  *     xGEQPX with properly (!) chosen numerical parameters.
  *     Any improvement of ZGEQP3 improves overal performance of ZGEJSV.
  *
  *     A * P1 = Q1 * [ R1^* 0]^*:
        DO 1963 p = 1, N
  *        .. all columns are free columns
           IWORK(p) = 0
 CONTINUE
        CALL ZGEQP3( M, N, A, LDA, IWORK, CWORK, CWORK(N+1), LWORK-N,
       $             RWORK, IERR )
  *
  *     The upper triangular matrix R1 from the first QRF is inspected for
  *     rank deficiency and possibilities for deflation, or possible
  *     ill-conditioning. Depending on the user specified flag L2RANK,
  *     the procedure explores possibilities to reduce the numerical
  *     rank by inspecting the computed upper triangular factor. If
  *     L2RANK or L2ABER are up, then ZGEJSV will compute the SVD of
  *     A + dA, where ||dA|| <= f(M,N)*EPSLN.
  *
        NR = 1
        IF ( L2ABER ) THEN
  *        Standard absolute error bound suffices. All sigma_i with
  *        sigma_i < N*EPSLN*||A|| are flushed to zero. This is an
  *        agressive enforcement of lower numerical rank by introducing a
  *        backward error of the order of N*EPSLN*||A||.
           TEMP1 = SQRT(DBLE(N))*EPSLN
           DO 3001 p = 2, N
              IF ( ABS(A(p,p)) .GE. (TEMP1*ABS(A(1,1))) ) THEN
                 NR = NR + 1
              ELSE
                 GO TO 3002
              END IF
    CONTINUE
    CONTINUE
        ELSE IF ( L2RANK ) THEN
  *        .. similarly as above, only slightly more gentle (less agressive).
  *        Sudden drop on the diagonal of R1 is used as the criterion for
  *        close-to-rank-deficient.
           TEMP1 = SQRT(SFMIN)
           DO 3401 p = 2, N
              IF ( ( ABS(A(p,p)) .LT. (EPSLN*ABS(A(p-1,p-1))) ) .OR.
       $           ( ABS(A(p,p)) .LT. SMALL ) .OR.
       $           ( L2KILL .AND. (ABS(A(p,p)) .LT. TEMP1) ) ) GO TO 3402
              NR = NR + 1
    CONTINUE
    CONTINUE
  *
        ELSE
  *        The goal is high relative accuracy. However, if the matrix
  *        has high scaled condition number the relative accuracy is in
  *        general not feasible. Later on, a condition number estimator
  *        will be deployed to estimate the scaled condition number.
  *        Here we just remove the underflowed part of the triangular
  *        factor. This prevents the situation in which the code is
  *        working hard to get the accuracy not warranted by the data.
           TEMP1  = SQRT(SFMIN)
           DO 3301 p = 2, N
              IF ( ( ABS(A(p,p)) .LT. SMALL ) .OR.
       $           ( L2KILL .AND. (ABS(A(p,p)) .LT. TEMP1) ) ) GO TO 3302
              NR = NR + 1
    CONTINUE
    CONTINUE
  *
        END IF
  *
        ALMORT = .FALSE.
        IF ( NR .EQ. N ) THEN
           MAXPRJ = ONE
           DO 3051 p = 2, N
              TEMP1  = ABS(A(p,p)) / SVA(IWORK(p))
              MAXPRJ = MIN( MAXPRJ, TEMP1 )
    CONTINUE
           IF ( MAXPRJ**2 .GE. ONE - DBLE(N)*EPSLN ) ALMORT = .TRUE.
        END IF
  *
  *
        SCONDA = - ONE
        CONDR1 = - ONE
        CONDR2 = - ONE
  *
        IF ( ERREST ) THEN
           IF ( N .EQ. NR ) THEN
              IF ( RSVEC ) THEN
  *              .. V is available as workspace
                 CALL ZLACPY( 'U', N, N, A, LDA, V, LDV )
                 DO 3053 p = 1, N
                    TEMP1 = SVA(IWORK(p))
                    CALL ZDSCAL( p, ONE/TEMP1, V(1,p), 1 )
          CONTINUE
                 IF ( LSVEC )THEN
                     CALL ZPOCON( 'U', N, V, LDV, ONE, TEMP1,
       $                  CWORK(N+1), RWORK, IERR )
                 ELSE
                     CALL ZPOCON( 'U', N, V, LDV, ONE, TEMP1,
       $                  CWORK, RWORK, IERR )
                 END IF
  *
              ELSE IF ( LSVEC ) THEN
  *              .. U is available as workspace
                 CALL ZLACPY( 'U', N, N, A, LDA, U, LDU )
                 DO 3054 p = 1, N
                    TEMP1 = SVA(IWORK(p))
                    CALL ZDSCAL( p, ONE/TEMP1, U(1,p), 1 )
          CONTINUE
                 CALL ZPOCON( 'U', N, U, LDU, ONE, TEMP1,
       $              CWORK(N+1), RWORK, IERR )
              ELSE
                 CALL ZLACPY( 'U', N, N, A, LDA, CWORK, N )
  *[]            CALL ZLACPY( 'U', N, N, A, LDA, CWORK(N+1), N )
  *              Change: here index shifted by N to the left, CWORK(1:N)
  *              not needed for SIGMA only computation
                 DO 3052 p = 1, N
                    TEMP1 = SVA(IWORK(p))
  *[]               CALL ZDSCAL( p, ONE/TEMP1, CWORK(N+(p-1)*N+1), 1 )
                    CALL ZDSCAL( p, ONE/TEMP1, CWORK((p-1)*N+1), 1 )
          CONTINUE
  *           .. the columns of R are scaled to have unit Euclidean lengths.
  *[]               CALL ZPOCON( 'U', N, CWORK(N+1), N, ONE, TEMP1,
  *[]     $              CWORK(N+N*N+1), RWORK, IERR )
                 CALL ZPOCON( 'U', N, CWORK, N, ONE, TEMP1,
       $              CWORK(N*N+1), RWORK, IERR )
  *
              END IF
              IF ( TEMP1 .NE. ZERO ) THEN
                 SCONDA = ONE / SQRT(TEMP1)
              ELSE
                 SCONDA = - ONE
              END IF
  *           SCONDA is an estimate of SQRT(||(R^* * R)^(-1)||_1).
  *           N^(-1/4) * SCONDA <= ||R^(-1)||_2 <= N^(1/4) * SCONDA
           ELSE
              SCONDA = - ONE
           END IF
        END IF
  *
        L2PERT = L2PERT .AND. ( ABS( A(1,1)/A(NR,NR) ) .GT. SQRT(BIG1) )
  *     If there is no violent scaling, artificial perturbation is not needed.
  *
  *     Phase 3:
  *
        IF ( .NOT. ( RSVEC .OR. LSVEC ) ) THEN
  *
  *         Singular Values only
  *
  *         .. transpose A(1:NR,1:N)
           DO 1946 p = 1, MIN( N-1, NR )
              CALL ZCOPY( N-p, A(p,p+1), LDA, A(p+1,p), 1 )
              CALL ZLACGV( N-p+1, A(p,p), 1 )
    CONTINUE
           IF ( NR .EQ. N ) A(N,N) = CONJG(A(N,N))
  *
  *        The following two DO-loops introduce small relative perturbation
  *        into the strict upper triangle of the lower triangular matrix.
  *        Small entries below the main diagonal are also changed.
  *        This modification is useful if the computing environment does not
  *        provide/allow FLUSH TO ZERO underflow, for it prevents many
  *        annoying denormalized numbers in case of strongly scaled matrices.
  *        The perturbation is structured so that it does not introduce any
  *        new perturbation of the singular values, and it does not destroy
  *        the job done by the preconditioner.
  *        The licence for this perturbation is in the variable L2PERT, which
  *        should be .FALSE. if FLUSH TO ZERO underflow is active.
  *
           IF ( .NOT. ALMORT ) THEN
  *
              IF ( L2PERT ) THEN
  *              XSC = SQRT(SMALL)
                 XSC = EPSLN / DBLE(N)
                 DO 4947 q = 1, NR
                    CTEMP = DCMPLX(XSC*ABS(A(q,q)),ZERO)
                    DO 4949 p = 1, N
                       IF ( ( (p.GT.q) .AND. (ABS(A(p,q)).LE.TEMP1) )
       $                    .OR. ( p .LT. q ) )
  *     $                     A(p,q) = TEMP1 * ( A(p,q) / ABS(A(p,q)) )
       $                     A(p,q) = CTEMP
             CONTINUE
          CONTINUE
              ELSE
                 CALL ZLASET( 'U', NR-1,NR-1, CZERO,CZERO, A(1,2),LDA )
              END IF
  *
  *            .. second preconditioning using the QR factorization
  *
              CALL ZGEQRF( N,NR, A,LDA, CWORK, CWORK(N+1),LWORK-N, IERR )
  *
  *           .. and transpose upper to lower triangular
              DO 1948 p = 1, NR - 1
                 CALL ZCOPY( NR-p, A(p,p+1), LDA, A(p+1,p), 1 )
                 CALL ZLACGV( NR-p+1, A(p,p), 1 )
       CONTINUE
  *
        END IF
  *
  *           Row-cyclic Jacobi SVD algorithm with column pivoting
  *
  *           .. again some perturbation (a "background noise") is added
  *           to drown denormals
              IF ( L2PERT ) THEN
  *              XSC = SQRT(SMALL)
                 XSC = EPSLN / DBLE(N)
                 DO 1947 q = 1, NR
                    CTEMP = DCMPLX(XSC*ABS(A(q,q)),ZERO)
                    DO 1949 p = 1, NR
                       IF ( ( (p.GT.q) .AND. (ABS(A(p,q)).LE.TEMP1) )
       $                       .OR. ( p .LT. q ) )
  *     $                   A(p,q) = TEMP1 * ( A(p,q) / ABS(A(p,q)) )
       $                   A(p,q) = CTEMP
             CONTINUE
          CONTINUE
              ELSE
                 CALL ZLASET( 'U', NR-1, NR-1, CZERO, CZERO, A(1,2), LDA )
              END IF
  *
  *           .. and one-sided Jacobi rotations are started on a lower
  *           triangular matrix (plus perturbation which is ignored in
  *           the part which destroys triangular form (confusing?!))
  *
              CALL ZGESVJ( 'L', 'N', 'N', NR, NR, A, LDA, SVA,
       $                N, V, LDV, CWORK, LWORK, RWORK, LRWORK, INFO )
  *
              SCALEM  = RWORK(1)
              NUMRANK = NINT(RWORK(2))
  *
  *
        ELSE IF ( ( RSVEC .AND. ( .NOT. LSVEC ) .AND. ( .NOT. JRACC ) )
       $       .OR.
       $   ( JRACC .AND. ( .NOT. LSVEC ) .AND. ( NR .NE. N ) ) ) THEN
  *
  *        -> Singular Values and Right Singular Vectors <-
  *
           IF ( ALMORT ) THEN
  *
  *           .. in this case NR equals N
              DO 1998 p = 1, NR
                 CALL ZCOPY( N-p+1, A(p,p), LDA, V(p,p), 1 )
                 CALL ZLACGV( N-p+1, V(p,p), 1 )
       CONTINUE
              CALL ZLASET( 'U', NR-1,NR-1, CZERO, CZERO, V(1,2), LDV )
  *
              CALL ZGESVJ( 'L','U','N', N, NR, V, LDV, SVA, NR, A, LDA,
       $                  CWORK, LWORK, RWORK, LRWORK, INFO )
              SCALEM  = RWORK(1)
              NUMRANK = NINT(RWORK(2))
           ELSE
  *
  *        .. two more QR factorizations ( one QRF is not enough, two require
  *        accumulated product of Jacobi rotations, three are perfect )
  *
              CALL ZLASET( 'L', NR-1,NR-1, CZERO, CZERO, A(2,1), LDA )
              CALL ZGELQF( NR,N, A, LDA, CWORK, CWORK(N+1), LWORK-N, IERR)
              CALL ZLACPY( 'L', NR, NR, A, LDA, V, LDV )
              CALL ZLASET( 'U', NR-1,NR-1, CZERO, CZERO, V(1,2), LDV )
              CALL ZGEQRF( NR, NR, V, LDV, CWORK(N+1), CWORK(2*N+1),
       $                   LWORK-2*N, IERR )
              DO 8998 p = 1, NR
                 CALL ZCOPY( NR-p+1, V(p,p), LDV, V(p,p), 1 )
                 CALL ZLACGV( NR-p+1, V(p,p), 1 )
       CONTINUE
              CALL ZLASET('U', NR-1, NR-1, CZERO, CZERO, V(1,2), LDV)
  *
              CALL ZGESVJ( 'L', 'U','N', NR, NR, V,LDV, SVA, NR, U,
       $                  LDU, CWORK(N+1), LWORK-N, RWORK, LRWORK, INFO )
              SCALEM  = RWORK(1)
              NUMRANK = NINT(RWORK(2))
              IF ( NR .LT. N ) THEN
                 CALL ZLASET( 'A',N-NR, NR, CZERO,CZERO, V(NR+1,1),  LDV )
                 CALL ZLASET( 'A',NR, N-NR, CZERO,CZERO, V(1,NR+1),  LDV )
                 CALL ZLASET( 'A',N-NR,N-NR,CZERO,CONE, V(NR+1,NR+1),LDV )
              END IF
  *
           CALL ZUNMLQ( 'L', 'C', N, N, NR, A, LDA, CWORK,
       $               V, LDV, CWORK(N+1), LWORK-N, IERR )
  *
           END IF
  *         .. permute the rows of V
  *         DO 8991 p = 1, N
  *            CALL ZCOPY( N, V(p,1), LDV, A(IWORK(p),1), LDA )
  * 8991    CONTINUE
  *         CALL ZLACPY( 'All', N, N, A, LDA, V, LDV )
           CALL ZLAPMR( .FALSE., N, N, V, LDV, IWORK )
  *
            IF ( TRANSP ) THEN
              CALL ZLACPY( 'A', N, N, V, LDV, U, LDU )
            END IF
  *
        ELSE IF ( JRACC .AND. (.NOT. LSVEC) .AND. ( NR.EQ. N ) ) THEN
  *
           CALL ZLASET( 'L', N-1,N-1, CZERO, CZERO, A(2,1), LDA )
  *
           CALL ZGESVJ( 'U','N','V', N, N, A, LDA, SVA, N, V, LDV,
       $               CWORK, LWORK, RWORK, LRWORK, INFO )
            SCALEM  = RWORK(1)
            NUMRANK = NINT(RWORK(2))
            CALL ZLAPMR( .FALSE., N, N, V, LDV, IWORK )
  *
        ELSE IF ( LSVEC .AND. ( .NOT. RSVEC ) ) THEN
  *
  *        .. Singular Values and Left Singular Vectors                 ..
  *
  *        .. second preconditioning step to avoid need to accumulate
  *        Jacobi rotations in the Jacobi iterations.
           DO 1965 p = 1, NR
              CALL ZCOPY( N-p+1, A(p,p), LDA, U(p,p), 1 )
              CALL ZLACGV( N-p+1, U(p,p), 1 )
    CONTINUE
           CALL ZLASET( 'U', NR-1, NR-1, CZERO, CZERO, U(1,2), LDU )
  *
           CALL ZGEQRF( N, NR, U, LDU, CWORK(N+1), CWORK(2*N+1),
       $              LWORK-2*N, IERR )
  *
           DO 1967 p = 1, NR - 1
              CALL ZCOPY( NR-p, U(p,p+1), LDU, U(p+1,p), 1 )
              CALL ZLACGV( N-p+1, U(p,p), 1 )
    CONTINUE
           CALL ZLASET( 'U', NR-1, NR-1, CZERO, CZERO, U(1,2), LDU )
  *
           CALL ZGESVJ( 'L', 'U', 'N', NR,NR, U, LDU, SVA, NR, A,
       $        LDA, CWORK(N+1), LWORK-N, RWORK, LRWORK, INFO )
           SCALEM  = RWORK(1)
           NUMRANK = NINT(RWORK(2))
  *
           IF ( NR .LT. M ) THEN
              CALL ZLASET( 'A',  M-NR, NR,CZERO, CZERO, U(NR+1,1), LDU )
              IF ( NR .LT. N1 ) THEN
                 CALL ZLASET( 'A',NR, N1-NR, CZERO, CZERO, U(1,NR+1),LDU )
                 CALL ZLASET( 'A',M-NR,N1-NR,CZERO,CONE,U(NR+1,NR+1),LDU )
              END IF
           END IF
  *
           CALL ZUNMQR( 'L', 'N', M, N1, N, A, LDA, CWORK, U,
       $               LDU, CWORK(N+1), LWORK-N, IERR )
  *
           IF ( ROWPIV )
       $       CALL ZLASWP( N1, U, LDU, 1, M-1, IWORK(IWOFF+1), -1 )
  *
           DO 1974 p = 1, N1
              XSC = ONE / DZNRM2( M, U(1,p), 1 )
              CALL ZDSCAL( M, XSC, U(1,p), 1 )
    CONTINUE
  *
           IF ( TRANSP ) THEN
              CALL ZLACPY( 'A', N, N, U, LDU, V, LDV )
           END IF
  *
        ELSE
  *
  *        .. Full SVD ..
  *
           IF ( .NOT. JRACC ) THEN
  *
           IF ( .NOT. ALMORT ) THEN
  *
  *           Second Preconditioning Step (QRF [with pivoting])
  *           Note that the composition of TRANSPOSE, QRF and TRANSPOSE is
  *           equivalent to an LQF CALL. Since in many libraries the QRF
  *           seems to be better optimized than the LQF, we do explicit
  *           transpose and use the QRF. This is subject to changes in an
  *           optimized implementation of ZGEJSV.
  *
              DO 1968 p = 1, NR
                 CALL ZCOPY( N-p+1, A(p,p), LDA, V(p,p), 1 )
                 CALL ZLACGV( N-p+1, V(p,p), 1 )
       CONTINUE
  *
  *           .. the following two loops perturb small entries to avoid
  *           denormals in the second QR factorization, where they are
  *           as good as zeros. This is done to avoid painfully slow
  *           computation with denormals. The relative size of the perturbation
  *           is a parameter that can be changed by the implementer.
  *           This perturbation device will be obsolete on machines with
  *           properly implemented arithmetic.
  *           To switch it off, set L2PERT=.FALSE. To remove it from  the
  *           code, remove the action under L2PERT=.TRUE., leave the ELSE part.
  *           The following two loops should be blocked and fused with the
  *           transposed copy above.
  *
              IF ( L2PERT ) THEN
                 XSC = SQRT(SMALL)
                 DO 2969 q = 1, NR
                    CTEMP = DCMPLX(XSC*ABS( V(q,q) ),ZERO)
                    DO 2968 p = 1, N
                       IF ( ( p .GT. q ) .AND. ( ABS(V(p,q)) .LE. TEMP1 )
       $                   .OR. ( p .LT. q ) )
  *     $                   V(p,q) = TEMP1 * ( V(p,q) / ABS(V(p,q)) )
       $                   V(p,q) = CTEMP
                       IF ( p .LT. q ) V(p,q) = - V(p,q)
             CONTINUE
          CONTINUE
              ELSE
                 CALL ZLASET( 'U', NR-1, NR-1, CZERO, CZERO, V(1,2), LDV )
              END IF
  *
  *           Estimate the row scaled condition number of R1
  *           (If R1 is rectangular, N > NR, then the condition number
  *           of the leading NR x NR submatrix is estimated.)
  *
              CALL ZLACPY( 'L', NR, NR, V, LDV, CWORK(2*N+1), NR )
              DO 3950 p = 1, NR
                 TEMP1 = DZNRM2(NR-p+1,CWORK(2*N+(p-1)*NR+p),1)
                 CALL ZDSCAL(NR-p+1,ONE/TEMP1,CWORK(2*N+(p-1)*NR+p),1)
       CONTINUE
              CALL ZPOCON('L',NR,CWORK(2*N+1),NR,ONE,TEMP1,
       $                   CWORK(2*N+NR*NR+1),RWORK,IERR)
              CONDR1 = ONE / SQRT(TEMP1)
  *           .. here need a second oppinion on the condition number
  *           .. then assume worst case scenario
  *           R1 is OK for inverse <=> CONDR1 .LT. DBLE(N)
  *           more conservative    <=> CONDR1 .LT. SQRT(DBLE(N))
  *
              COND_OK = SQRT(SQRT(DBLE(NR)))
  *[TP]       COND_OK is a tuning parameter.
  *
              IF ( CONDR1 .LT. COND_OK ) THEN
  *              .. the second QRF without pivoting. Note: in an optimized
  *              implementation, this QRF should be implemented as the QRF
  *              of a lower triangular matrix.
  *              R1^* = Q2 * R2
                 CALL ZGEQRF( N, NR, V, LDV, CWORK(N+1), CWORK(2*N+1),
       $              LWORK-2*N, IERR )
  *
                 IF ( L2PERT ) THEN
                    XSC = SQRT(SMALL)/EPSLN
                    DO 3959 p = 2, NR
                       DO 3958 q = 1, p - 1
                          CTEMP=DCMPLX(XSC*MIN(ABS(V(p,p)),ABS(V(q,q))),
       $                              ZERO)
                          IF ( ABS(V(q,p)) .LE. TEMP1 )
  *     $                     V(q,p) = TEMP1 * ( V(q,p) / ABS(V(q,p)) )
       $                     V(q,p) = CTEMP
                CONTINUE
             CONTINUE
                 END IF
  *
                 IF ( NR .NE. N )
       $         CALL ZLACPY( 'A', N, NR, V, LDV, CWORK(2*N+1), N )
  *              .. save ...
  *
  *           .. this transposed copy should be better than naive
                 DO 1969 p = 1, NR - 1
                    CALL ZCOPY( NR-p, V(p,p+1), LDV, V(p+1,p), 1 )
                    CALL ZLACGV(NR-p+1, V(p,p), 1 )
          CONTINUE
                 V(NR,NR)=CONJG(V(NR,NR))
  *
                 CONDR2 = CONDR1
  *
              ELSE
  *
  *              .. ill-conditioned case: second QRF with pivoting
  *              Note that windowed pivoting would be equaly good
  *              numerically, and more run-time efficient. So, in
  *              an optimal implementation, the next call to ZGEQP3
  *              should be replaced with eg. CALL ZGEQPX (ACM TOMS #782)
  *              with properly (carefully) chosen parameters.
  *
  *              R1^* * P2 = Q2 * R2
                 DO 3003 p = 1, NR
                    IWORK(N+p) = 0
          CONTINUE
                 CALL ZGEQP3( N, NR, V, LDV, IWORK(N+1), CWORK(N+1),
       $                  CWORK(2*N+1), LWORK-2*N, RWORK, IERR )
  **               CALL ZGEQRF( N, NR, V, LDV, CWORK(N+1), CWORK(2*N+1),
  **     $              LWORK-2*N, IERR )
                 IF ( L2PERT ) THEN
                    XSC = SQRT(SMALL)
                    DO 3969 p = 2, NR
                       DO 3968 q = 1, p - 1
                          CTEMP=DCMPLX(XSC*MIN(ABS(V(p,p)),ABS(V(q,q))),
       $                                ZERO)
                          IF ( ABS(V(q,p)) .LE. TEMP1 )
  *     $                     V(q,p) = TEMP1 * ( V(q,p) / ABS(V(q,p)) )
       $                     V(q,p) = CTEMP
                CONTINUE
             CONTINUE
                 END IF
  *
                 CALL ZLACPY( 'A', N, NR, V, LDV, CWORK(2*N+1), N )
  *
                 IF ( L2PERT ) THEN
                    XSC = SQRT(SMALL)
                    DO 8970 p = 2, NR
                       DO 8971 q = 1, p - 1
                          CTEMP=DCMPLX(XSC*MIN(ABS(V(p,p)),ABS(V(q,q))),
       $                               ZERO)
  *                        V(p,q) = - TEMP1*( V(q,p) / ABS(V(q,p)) )
                          V(p,q) = - CTEMP
                CONTINUE
             CONTINUE
                 ELSE
                    CALL ZLASET( 'L',NR-1,NR-1,CZERO,CZERO,V(2,1),LDV )
                 END IF
  *              Now, compute R2 = L3 * Q3, the LQ factorization.
                 CALL ZGELQF( NR, NR, V, LDV, CWORK(2*N+N*NR+1),
       $               CWORK(2*N+N*NR+NR+1), LWORK-2*N-N*NR-NR, IERR )
  *              .. and estimate the condition number
                 CALL ZLACPY( 'L',NR,NR,V,LDV,CWORK(2*N+N*NR+NR+1),NR )
                 DO 4950 p = 1, NR
                    TEMP1 = DZNRM2( p, CWORK(2*N+N*NR+NR+p), NR )
                    CALL ZDSCAL( p, ONE/TEMP1, CWORK(2*N+N*NR+NR+p), NR )
          CONTINUE
                 CALL ZPOCON( 'L',NR,CWORK(2*N+N*NR+NR+1),NR,ONE,TEMP1,
       $              CWORK(2*N+N*NR+NR+NR*NR+1),RWORK,IERR )
                 CONDR2 = ONE / SQRT(TEMP1)
  *
  *
                 IF ( CONDR2 .GE. COND_OK ) THEN
  *                 .. save the Householder vectors used for Q3
  *                 (this overwrittes the copy of R2, as it will not be
  *                 needed in this branch, but it does not overwritte the
  *                 Huseholder vectors of Q2.).
                    CALL ZLACPY( 'U', NR, NR, V, LDV, CWORK(2*N+1), N )
  *                 .. and the rest of the information on Q3 is in
  *                 WORK(2*N+N*NR+1:2*N+N*NR+N)
                 END IF
  *
              END IF
  *
              IF ( L2PERT ) THEN
                 XSC = SQRT(SMALL)
                 DO 4968 q = 2, NR
                    CTEMP = XSC * V(q,q)
                    DO 4969 p = 1, q - 1
  *                     V(p,q) = - TEMP1*( V(p,q) / ABS(V(p,q)) )
                       V(p,q) = - CTEMP
             CONTINUE
          CONTINUE
              ELSE
                 CALL ZLASET( 'U', NR-1,NR-1, CZERO,CZERO, V(1,2), LDV )
              END IF
  *
  *        Second preconditioning finished; continue with Jacobi SVD
  *        The input matrix is lower trinagular.
  *
  *        Recover the right singular vectors as solution of a well
  *        conditioned triangular matrix equation.
  *
              IF ( CONDR1 .LT. COND_OK ) THEN
  *
                 CALL ZGESVJ( 'L','U','N',NR,NR,V,LDV,SVA,NR,U, LDU,
       $              CWORK(2*N+N*NR+NR+1),LWORK-2*N-N*NR-NR,RWORK,
       $              LRWORK, INFO )
                 SCALEM  = RWORK(1)
                 NUMRANK = NINT(RWORK(2))
                 DO 3970 p = 1, NR
                    CALL ZCOPY(  NR, V(1,p), 1, U(1,p), 1 )
                    CALL ZDSCAL( NR, SVA(p),    V(1,p), 1 )
          CONTINUE
  *        .. pick the right matrix equation and solve it
  *
                 IF ( NR .EQ. N ) THEN
  * :))             .. best case, R1 is inverted. The solution of this matrix
  *                 equation is Q2*V2 = the product of the Jacobi rotations
  *                 used in ZGESVJ, premultiplied with the orthogonal matrix
  *                 from the second QR factorization.
                    CALL ZTRSM('L','U','N','N', NR,NR,CONE, A,LDA, V,LDV)
                 ELSE
  *                 .. R1 is well conditioned, but non-square. Adjoint of R2
  *                 is inverted to get the product of the Jacobi rotations
  *                 used in ZGESVJ. The Q-factor from the second QR
  *                 factorization is then built in explicitly.
                    CALL ZTRSM('L','U','C','N',NR,NR,CONE,CWORK(2*N+1),
       $                 N,V,LDV)
                    IF ( NR .LT. N ) THEN
                    CALL ZLASET('A',N-NR,NR,CZERO,CZERO,V(NR+1,1),LDV)
                    CALL ZLASET('A',NR,N-NR,CZERO,CZERO,V(1,NR+1),LDV)
                    CALL ZLASET('A',N-NR,N-NR,CZERO,CONE,V(NR+1,NR+1),LDV)
                    END IF
                    CALL ZUNMQR('L','N',N,N,NR,CWORK(2*N+1),N,CWORK(N+1),
       $                V,LDV,CWORK(2*N+N*NR+NR+1),LWORK-2*N-N*NR-NR,IERR)
                 END IF
  *
              ELSE IF ( CONDR2 .LT. COND_OK ) THEN
  *
  *              The matrix R2 is inverted. The solution of the matrix equation
  *              is Q3^* * V3 = the product of the Jacobi rotations (appplied to
  *              the lower triangular L3 from the LQ factorization of
  *              R2=L3*Q3), pre-multiplied with the transposed Q3.
                 CALL ZGESVJ( 'L', 'U', 'N', NR, NR, V, LDV, SVA, NR, U,
       $              LDU, CWORK(2*N+N*NR+NR+1), LWORK-2*N-N*NR-NR,
       $              RWORK, LRWORK, INFO )
                 SCALEM  = RWORK(1)
                 NUMRANK = NINT(RWORK(2))
                 DO 3870 p = 1, NR
                    CALL ZCOPY( NR, V(1,p), 1, U(1,p), 1 )
                    CALL ZDSCAL( NR, SVA(p),    U(1,p), 1 )
          CONTINUE
                 CALL ZTRSM('L','U','N','N',NR,NR,CONE,CWORK(2*N+1),N,
       $                    U,LDU)
  *              .. apply the permutation from the second QR factorization
                 DO 873 q = 1, NR
                    DO 872 p = 1, NR
                       CWORK(2*N+N*NR+NR+IWORK(N+p)) = U(p,q)
              CONTINUE
                    DO 874 p = 1, NR
                       U(p,q) = CWORK(2*N+N*NR+NR+p)
              CONTINUE
           CONTINUE
                 IF ( NR .LT. N ) THEN
                    CALL ZLASET( 'A',N-NR,NR,CZERO,CZERO,V(NR+1,1),LDV )
                    CALL ZLASET( 'A',NR,N-NR,CZERO,CZERO,V(1,NR+1),LDV )
                    CALL ZLASET('A',N-NR,N-NR,CZERO,CONE,V(NR+1,NR+1),LDV)
                 END IF
                 CALL ZUNMQR( 'L','N',N,N,NR,CWORK(2*N+1),N,CWORK(N+1),
       $              V,LDV,CWORK(2*N+N*NR+NR+1),LWORK-2*N-N*NR-NR,IERR )
              ELSE
  *              Last line of defense.
  * #:(          This is a rather pathological case: no scaled condition
  *              improvement after two pivoted QR factorizations. Other
  *              possibility is that the rank revealing QR factorization
  *              or the condition estimator has failed, or the COND_OK
  *              is set very close to ONE (which is unnecessary). Normally,
  *              this branch should never be executed, but in rare cases of
  *              failure of the RRQR or condition estimator, the last line of
  *              defense ensures that ZGEJSV completes the task.
  *              Compute the full SVD of L3 using ZGESVJ with explicit
  *              accumulation of Jacobi rotations.
                 CALL ZGESVJ( 'L', 'U', 'V', NR, NR, V, LDV, SVA, NR, U,
       $              LDU, CWORK(2*N+N*NR+NR+1), LWORK-2*N-N*NR-NR,
       $                         RWORK, LRWORK, INFO )
                 SCALEM  = RWORK(1)
                 NUMRANK = NINT(RWORK(2))
                 IF ( NR .LT. N ) THEN
                    CALL ZLASET( 'A',N-NR,NR,CZERO,CZERO,V(NR+1,1),LDV )
                    CALL ZLASET( 'A',NR,N-NR,CZERO,CZERO,V(1,NR+1),LDV )
                    CALL ZLASET('A',N-NR,N-NR,CZERO,CONE,V(NR+1,NR+1),LDV)
                 END IF
                 CALL ZUNMQR( 'L','N',N,N,NR,CWORK(2*N+1),N,CWORK(N+1),
       $              V,LDV,CWORK(2*N+N*NR+NR+1),LWORK-2*N-N*NR-NR,IERR )
  *
                 CALL ZUNMLQ( 'L', 'C', NR, NR, NR, CWORK(2*N+1), N,
       $              CWORK(2*N+N*NR+1), U, LDU, CWORK(2*N+N*NR+NR+1),
       $              LWORK-2*N-N*NR-NR, IERR )
                 DO 773 q = 1, NR
                    DO 772 p = 1, NR
                       CWORK(2*N+N*NR+NR+IWORK(N+p)) = U(p,q)
              CONTINUE
                    DO 774 p = 1, NR
                       U(p,q) = CWORK(2*N+N*NR+NR+p)
              CONTINUE
           CONTINUE
  *
              END IF
  *
  *           Permute the rows of V using the (column) permutation from the
  *           first QRF. Also, scale the columns to make them unit in
  *           Euclidean norm. This applies to all cases.
  *
              TEMP1 = SQRT(DBLE(N)) * EPSLN
              DO 1972 q = 1, N
                 DO 972 p = 1, N
                    CWORK(2*N+N*NR+NR+IWORK(p)) = V(p,q)
          CONTINUE
                 DO 973 p = 1, N
                    V(p,q) = CWORK(2*N+N*NR+NR+p)
          CONTINUE
                 XSC = ONE / DZNRM2( N, V(1,q), 1 )
                 IF ( (XSC .LT. (ONE-TEMP1)) .OR. (XSC .GT. (ONE+TEMP1)) )
       $           CALL ZDSCAL( N, XSC, V(1,q), 1 )
       CONTINUE
  *           At this moment, V contains the right singular vectors of A.
  *           Next, assemble the left singular vector matrix U (M x N).
              IF ( NR .LT. M ) THEN
                 CALL ZLASET('A', M-NR, NR, CZERO, CZERO, U(NR+1,1), LDU)
                 IF ( NR .LT. N1 ) THEN
                    CALL ZLASET('A',NR,N1-NR,CZERO,CZERO,U(1,NR+1),LDU)
                    CALL ZLASET('A',M-NR,N1-NR,CZERO,CONE,
       $                        U(NR+1,NR+1),LDU)
                 END IF
              END IF
  *
  *           The Q matrix from the first QRF is built into the left singular
  *           matrix U. This applies to all cases.
  *
              CALL ZUNMQR( 'L', 'N', M, N1, N, A, LDA, CWORK, U,
       $           LDU, CWORK(N+1), LWORK-N, IERR )
  *           The columns of U are normalized. The cost is O(M*N) flops.
              TEMP1 = SQRT(DBLE(M)) * EPSLN
              DO 1973 p = 1, NR
                 XSC = ONE / DZNRM2( M, U(1,p), 1 )
                 IF ( (XSC .LT. (ONE-TEMP1)) .OR. (XSC .GT. (ONE+TEMP1)) )
       $          CALL ZDSCAL( M, XSC, U(1,p), 1 )
       CONTINUE
  *
  *           If the initial QRF is computed with row pivoting, the left
  *           singular vectors must be adjusted.
  *
              IF ( ROWPIV )
       $          CALL ZLASWP( N1, U, LDU, 1, M-1, IWORK(IWOFF+1), -1 )
  *
           ELSE
  *
  *        .. the initial matrix A has almost orthogonal columns and
  *        the second QRF is not needed
  *
              CALL ZLACPY( 'U', N, N, A, LDA, CWORK(N+1), N )
              IF ( L2PERT ) THEN
                 XSC = SQRT(SMALL)
                 DO 5970 p = 2, N
                    CTEMP = XSC * CWORK( N + (p-1)*N + p )
                    DO 5971 q = 1, p - 1
  *                     CWORK(N+(q-1)*N+p)=-TEMP1 * ( CWORK(N+(p-1)*N+q) /
  *     $                                        ABS(CWORK(N+(p-1)*N+q)) )
                       CWORK(N+(q-1)*N+p)=-CTEMP
             CONTINUE
          CONTINUE
              ELSE
                 CALL ZLASET( 'L',N-1,N-1,CZERO,CZERO,CWORK(N+2),N )
              END IF
  *
              CALL ZGESVJ( 'U', 'U', 'N', N, N, CWORK(N+1), N, SVA,
       $           N, U, LDU, CWORK(N+N*N+1), LWORK-N-N*N, RWORK, LRWORK,
       $       INFO )
  *
              SCALEM  = RWORK(1)
              NUMRANK = NINT(RWORK(2))
              DO 6970 p = 1, N
                 CALL ZCOPY( N, CWORK(N+(p-1)*N+1), 1, U(1,p), 1 )
                 CALL ZDSCAL( N, SVA(p), CWORK(N+(p-1)*N+1), 1 )
       CONTINUE
  *
              CALL ZTRSM( 'L', 'U', 'N', 'N', N, N,
       $           CONE, A, LDA, CWORK(N+1), N )
              DO 6972 p = 1, N
                 CALL ZCOPY( N, CWORK(N+p), N, V(IWORK(p),1), LDV )
       CONTINUE
              TEMP1 = SQRT(DBLE(N))*EPSLN
              DO 6971 p = 1, N
                 XSC = ONE / DZNRM2( N, V(1,p), 1 )
                 IF ( (XSC .LT. (ONE-TEMP1)) .OR. (XSC .GT. (ONE+TEMP1)) )
       $            CALL ZDSCAL( N, XSC, V(1,p), 1 )
       CONTINUE
  *
  *           Assemble the left singular vector matrix U (M x N).
  *
              IF ( N .LT. M ) THEN
                 CALL ZLASET( 'A',  M-N, N, CZERO, CZERO, U(N+1,1), LDU )
                 IF ( N .LT. N1 ) THEN
                    CALL ZLASET('A',N,  N1-N, CZERO, CZERO,  U(1,N+1),LDU)
                    CALL ZLASET( 'A',M-N,N1-N, CZERO, CONE,U(N+1,N+1),LDU)
                 END IF
              END IF
              CALL ZUNMQR( 'L', 'N', M, N1, N, A, LDA, CWORK, U,
       $           LDU, CWORK(N+1), LWORK-N, IERR )
              TEMP1 = SQRT(DBLE(M))*EPSLN
              DO 6973 p = 1, N1
                 XSC = ONE / DZNRM2( M, U(1,p), 1 )
                 IF ( (XSC .LT. (ONE-TEMP1)) .OR. (XSC .GT. (ONE+TEMP1)) )
       $            CALL ZDSCAL( M, XSC, U(1,p), 1 )
       CONTINUE
  *
              IF ( ROWPIV )
       $         CALL ZLASWP( N1, U, LDU, 1, M-1, IWORK(IWOFF+1), -1 )
  *
           END IF
  *
  *        end of the  >> almost orthogonal case <<  in the full SVD
  *
           ELSE
  *
  *        This branch deploys a preconditioned Jacobi SVD with explicitly
  *        accumulated rotations. It is included as optional, mainly for
  *        experimental purposes. It does perfom well, and can also be used.
  *        In this implementation, this branch will be automatically activated
  *        if the  condition number sigma_max(A) / sigma_min(A) is predicted
  *        to be greater than the overflow threshold. This is because the
  *        a posteriori computation of the singular vectors assumes robust
  *        implementation of BLAS and some LAPACK procedures, capable of working
  *        in presence of extreme values, e.g. when the singular values spread from
  *        the underflow to the overflow threshold.
  *
           DO 7968 p = 1, NR
              CALL ZCOPY( N-p+1, A(p,p), LDA, V(p,p), 1 )
              CALL ZLACGV( N-p+1, V(p,p), 1 )
    CONTINUE
  *
           IF ( L2PERT ) THEN
              XSC = SQRT(SMALL/EPSLN)
              DO 5969 q = 1, NR
                 CTEMP = DCMPLX(XSC*ABS( V(q,q) ),ZERO)
                 DO 5968 p = 1, N
                    IF ( ( p .GT. q ) .AND. ( ABS(V(p,q)) .LE. TEMP1 )
       $                .OR. ( p .LT. q ) )
  *     $                V(p,q) = TEMP1 * ( V(p,q) / ABS(V(p,q)) )
       $                V(p,q) = CTEMP
                    IF ( p .LT. q ) V(p,q) = - V(p,q)
          CONTINUE
       CONTINUE
           ELSE
              CALL ZLASET( 'U', NR-1, NR-1, CZERO, CZERO, V(1,2), LDV )
           END IF
           CALL ZGEQRF( N, NR, V, LDV, CWORK(N+1), CWORK(2*N+1),
       $        LWORK-2*N, IERR )
           CALL ZLACPY( 'L', N, NR, V, LDV, CWORK(2*N+1), N )
  *
           DO 7969 p = 1, NR
              CALL ZCOPY( NR-p+1, V(p,p), LDV, U(p,p), 1 )
              CALL ZLACGV( NR-p+1, U(p,p), 1 )
    CONTINUE
           IF ( L2PERT ) THEN
              XSC = SQRT(SMALL/EPSLN)
              DO 9970 q = 2, NR
                 DO 9971 p = 1, q - 1
                    CTEMP = DCMPLX(XSC * MIN(ABS(U(p,p)),ABS(U(q,q))),
       $                            ZERO)
  *                  U(p,q) = - TEMP1 * ( U(q,p) / ABS(U(q,p)) )
                    U(p,q) = - CTEMP
          CONTINUE
       CONTINUE
           ELSE
              CALL ZLASET('U', NR-1, NR-1, CZERO, CZERO, U(1,2), LDU )
           END IF
           CALL ZGESVJ( 'L', 'U', 'V', NR, NR, U, LDU, SVA,
       $        N, V, LDV, CWORK(2*N+N*NR+1), LWORK-2*N-N*NR,
       $         RWORK, LRWORK, INFO )
           SCALEM  = RWORK(1)
           NUMRANK = NINT(RWORK(2))
           IF ( NR .LT. N ) THEN
              CALL ZLASET( 'A',N-NR,NR,CZERO,CZERO,V(NR+1,1),LDV )
              CALL ZLASET( 'A',NR,N-NR,CZERO,CZERO,V(1,NR+1),LDV )
              CALL ZLASET( 'A',N-NR,N-NR,CZERO,CONE,V(NR+1,NR+1),LDV )
           END IF
           CALL ZUNMQR( 'L','N',N,N,NR,CWORK(2*N+1),N,CWORK(N+1),
       $        V,LDV,CWORK(2*N+N*NR+NR+1),LWORK-2*N-N*NR-NR,IERR )
  *
  *           Permute the rows of V using the (column) permutation from the
  *           first QRF. Also, scale the columns to make them unit in
  *           Euclidean norm. This applies to all cases.
  *
              TEMP1 = SQRT(DBLE(N)) * EPSLN
              DO 7972 q = 1, N
                 DO 8972 p = 1, N
                    CWORK(2*N+N*NR+NR+IWORK(p)) = V(p,q)
          CONTINUE
                 DO 8973 p = 1, N
                    V(p,q) = CWORK(2*N+N*NR+NR+p)
          CONTINUE
                 XSC = ONE / DZNRM2( N, V(1,q), 1 )
                 IF ( (XSC .LT. (ONE-TEMP1)) .OR. (XSC .GT. (ONE+TEMP1)) )
       $           CALL ZDSCAL( N, XSC, V(1,q), 1 )
       CONTINUE
  *
  *           At this moment, V contains the right singular vectors of A.
  *           Next, assemble the left singular vector matrix U (M x N).
  *
           IF ( NR .LT. M ) THEN
              CALL ZLASET( 'A',  M-NR, NR, CZERO, CZERO, U(NR+1,1), LDU )
              IF ( NR .LT. N1 ) THEN
                 CALL ZLASET('A',NR,  N1-NR, CZERO, CZERO,  U(1,NR+1),LDU)
                 CALL ZLASET('A',M-NR,N1-NR, CZERO, CONE,U(NR+1,NR+1),LDU)
              END IF
           END IF
  *
           CALL ZUNMQR( 'L', 'N', M, N1, N, A, LDA, CWORK, U,
       $        LDU, CWORK(N+1), LWORK-N, IERR )
  *
              IF ( ROWPIV )
       $         CALL ZLASWP( N1, U, LDU, 1, M-1, IWORK(IWOFF+1), -1 )
  *
  *
           END IF
           IF ( TRANSP ) THEN
  *           .. swap U and V because the procedure worked on A^*
              DO 6974 p = 1, N
                 CALL ZSWAP( N, U(1,p), 1, V(1,p), 1 )
       CONTINUE
           END IF
  *
        END IF
  *     end of the full SVD
  *
  *     Undo scaling, if necessary (and possible)
  *
        IF ( USCAL2 .LE. (BIG/SVA(1))*USCAL1 ) THEN
           CALL DLASCL( 'G', 0, 0, USCAL1, USCAL2, NR, 1, SVA, N, IERR )
           USCAL1 = ONE
           USCAL2 = ONE
        END IF
  *
        IF ( NR .LT. N ) THEN
           DO 3004 p = NR+1, N
              SVA(p) = ZERO
    CONTINUE
        END IF
  *
        RWORK(1) = USCAL2 * SCALEM
        RWORK(2) = USCAL1
        IF ( ERREST ) RWORK(3) = SCONDA
        IF ( LSVEC .AND. RSVEC ) THEN
           RWORK(4) = CONDR1
           RWORK(5) = CONDR2
        END IF
        IF ( L2TRAN ) THEN
           RWORK(6) = ENTRA
           RWORK(7) = ENTRAT
        END IF
  *
        IWORK(1) = NR
        IWORK(2) = NUMRANK
        IWORK(3) = WARNING
        IF ( TRANSP ) THEN
            IWORK(4) =  1
        ELSE
            IWORK(4) = -1
        END IF
  *
        RETURN
  *     ..
  *     .. END OF ZGEJSV
  *     ..
        END
  *

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