CGEQL2  -  compute  a QL factorization of a complex m by n
       matrix A


SYNOPSIS

       SUBROUTINE CGEQL2( M, N, A, LDA, TAU, WORK, INFO )

           INTEGER        INFO, LDA, M, N

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


PURPOSE

       CGEQL2 computes a QL factorization of a  complex  m  by  n
       matrix A: A = Q * L.


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, if m >=
               n,  the  lower  triangle  of  the  subarray   A(m-
               n+1:m,1:n)  contains  the  n by n lower triangular
               matrix L; if m <= n, the elements on and below the
               (n-m)-th  superdiagonal  contain  the m by n lower
               trapezoidal matrix L; the remaining elements, 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) COMPLEX array, dimension (N)

       INFO    (output) INTEGER
               = 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


       where  tau  is a complex scalar, and v is a complex vector
       with v(m-k+i+1:m) = 0 and v(m-k+i) =  1;  v(1:m-k+i-1)  is
       stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i).


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