ZGELQ2  -  compute an LQ factorization of a complex m by n
       matrix A


SYNOPSIS

       SUBROUTINE ZGELQ2( M, N, A, LDA, TAU, WORK, INFO )

           INTEGER        INFO, LDA, M, N

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


PURPOSE

       ZGELQ2 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) COMPLEX*16 array, dimension (M)

       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

          H(i) = I - tau * v * v'

       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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