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


SYNOPSIS

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

           INTEGER        INFO, LDA, LWORK, M, N

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


PURPOSE

       CGELQF 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 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 array, dimension (min(M,N))
               The  scalar  factors  of the elementary reflectors
               (see Further Details).

       WORK    (workspace/output) COMPLEX 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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