ZGGSVP computes unitary matrices U, V and Q such that

                    N-K-L  K    L
  U**H*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
                 L ( 0     0   A23 )
             M-K-L ( 0     0    0  )

                  N-K-L  K    L
         =     K ( 0    A12  A13 )  if M-K-L < 0;
             M-K ( 0     0   A23 )

                  N-K-L  K    L
  V**H*B*Q =   L ( 0     0   B13 )
             P-L ( 0     0    0  )

 where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
 upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
 otherwise A23 is (M-K)-by-L upper trapezoidal.  K+L = the effective
 numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H. 

 This decomposition is the preprocessing step for computing the
 Generalized Singular Value Decomposition (GSVD), see subroutine
 ZGGSVD.

          JOBU is CHARACTER*1
          = 'U':  Unitary matrix U is computed;
          = 'N':  U is not computed.

          JOBV is CHARACTER*1
          = 'V':  Unitary matrix V is computed;
          = 'N':  V is not computed.

          JOBQ is CHARACTER*1
          = 'Q':  Unitary matrix Q is computed;
          = 'N':  Q is not computed.

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          P is INTEGER
          The number of rows of the matrix B.  P >= 0.

          N is INTEGER
          The number of columns of the matrices A and B.  N >= 0.

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, A contains the triangular (or trapezoidal) matrix
          described in the Purpose section.

          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,M).

          B is COMPLEX*16 array, dimension (LDB,N)
          On entry, the P-by-N matrix B.
          On exit, B contains the triangular matrix described in
          the Purpose section.

          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,P).

          TOLA is DOUBLE PRECISION

          TOLB is DOUBLE PRECISION

          TOLA and TOLB are the thresholds to determine the effective
          numerical rank of matrix B and a subblock of A. Generally,
          they are set to
             TOLA = MAX(M,N)*norm(A)*MAZHEPS,
             TOLB = MAX(P,N)*norm(B)*MAZHEPS.
          The size of TOLA and TOLB may affect the size of backward
          errors of the decomposition.

          K is INTEGER

          L is INTEGER

          On exit, K and L specify the dimension of the subblocks
          described in Purpose section.
          K + L = effective numerical rank of (A**H,B**H)**H.

          U is COMPLEX*16 array, dimension (LDU,M)
          If JOBU = 'U', U contains the unitary matrix U.
          If JOBU = 'N', U is not referenced.

          LDU is INTEGER
          The leading dimension of the array U. LDU >= max(1,M) if
          JOBU = 'U'; LDU >= 1 otherwise.

          V is COMPLEX*16 array, dimension (LDV,P)
          If JOBV = 'V', V contains the unitary matrix V.
          If JOBV = 'N', V is not referenced.

          LDV is INTEGER
          The leading dimension of the array V. LDV >= max(1,P) if
          JOBV = 'V'; LDV >= 1 otherwise.

          Q is COMPLEX*16 array, dimension (LDQ,N)
          If JOBQ = 'Q', Q contains the unitary matrix Q.
          If JOBQ = 'N', Q is not referenced.

          LDQ is INTEGER
          The leading dimension of the array Q. LDQ >= max(1,N) if
          JOBQ = 'Q'; LDQ >= 1 otherwise.

          IWORK is INTEGER array, dimension (N)

          RWORK is DOUBLE PRECISION array, dimension (2*N)

          TAU is COMPLEX*16 array, dimension (N)

          WORK is COMPLEX*16 array, dimension (max(3*N,M,P))

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.

  The subroutine uses LAPACK subroutine ZGEQPF for the QR factorization
  with column pivoting to detect the effective numerical rank of the
  a matrix. It may be replaced by a better rank determination strategy.