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        ZGELQF - compute an LQ factorization of a complex M-by-N matrix A


            INTEGER        INFO, LDA, LWORK, M, N
            COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )


        ZGELQF computes an LQ factorization of a complex M-by-N matrix A: A = L
        * Q.


        M       (input) INTEGER
                The number of rows of the matrix A.  M >= 0.
        N       (input) INTEGER
                The number of columns of the matrix A.  N >= 0.
        A       (input/output) COMPLEX*16 array, dimension (LDA,N)
                On entry, the M-by-N matrix A.  On exit, the  elements  on  and
                below the diagonal of the array contain the m-by-min(m,n) lower
                trapezoidal matrix L (L is lower triangular if  m  <=  n);  the
                elements  above the diagonal, with the array TAU, represent the
                unitary matrix Q as a product  of  elementary  reflectors  (see
                Further  Details).   LDA     (input) INTEGER The leading dimen‐
                sion of the array A.  LDA >= max(1,M).
        TAU     (output) COMPLEX*16 array, dimension (min(M,N))
                The scalar factors of the elementary  reflectors  (see  Further
        WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)
WORK(1) returns the optimal LWORK.
        LWORK   (input) INTEGER
                The dimension of the array WORK.  LWORK >= max(1,M).  For opti‐
                mum performance LWORK >= M*NB, where NB is the  optimal  block‐
                If  LWORK  = -1, then a workspace query is assumed; the routine
                only calculates the optimal size of  the  WORK  array,  returns
                this  value  as the first entry of the WORK array, and no error
                message related to LWORK is issued by XERBLA.
        INFO    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value
        The matrix Q is represented as a product of elementary reflectors
H(1)’, where k = min(m,n).
        Each H(i) has the form
           H(i) = I - tau * v * v’
        where tau is a complex scalar, and v is a complex vector with  v(1:i-1)
        =  0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and
        tau in TAU(i).


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