ZGERQ2  -  compute an RQ factorization of a complex m by n
       matrix A


SYNOPSIS

       SUBROUTINE ZGERQ2( M, N, A, LDA, TAU, WORK, INFO )

           INTEGER        INFO, LDA, M, N

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


PURPOSE

       ZGERQ2 computes an RQ factorization of a complex  m  by  n
       matrix A: A = R * 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, if  m  <=
               n,  the  upper  triangle  of the subarray A(1:m,n-
               m+1:n) contains the m by m upper triangular matrix
               R;  if  m  >= n, the elements on and above the (m-
               n)-th subdiagonal contain the m by n upper  trape­
               zoidal  matrix R; 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) 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(1)' H(2)' . . . H(k)', where k = min(m,n).


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

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


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