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


SYNOPSIS

       SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

           INTEGER        INFO, LDA, LWORK, M, N

           COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )


PURPOSE

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


ARGUMENTS

       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  ele­
               ments  on and below the diagonal of the array con­
               tain 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 dimension 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 Details).

       WORK    (workspace/output) COMPLEX*16 array, dimension
               (LWORK)
               On exit, if INFO = 0, WORK(1) returns the  optimal
               LWORK.

       LWORK   (input) INTEGER
               The   dimension  of  the  array  WORK.   LWORK  >=
               max(1,M).  For optimum performance LWORK >=  M*NB,
               where NB is the optimal blocksize.

               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.

               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value


FURTHER DETAILS

       The matrix Q is represented as  a  product  of  elementary
       reflectors

          Q = H(k)' . . . H(2)' 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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