ZGEQLF  -  compute  a QL factorization of a complex M-by-N
       matrix A


SYNOPSIS

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

           INTEGER        INFO, LDA, LWORK, M, N

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


PURPOSE

       ZGEQLF 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*16 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*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,N).   For optimum performance LWORK >= N*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(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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