ZGERQF  -  compute an RQ factorization of a complex M-by-N
       matrix A


SYNOPSIS

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

           INTEGER        INFO, LDA, LWORK, M, N

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


PURPOSE

       ZGERQF 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  min(m,n)  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,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


       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).

       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(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).


Man(1) output converted with man2html