subroutine hope( gap, h1,h2,hh, t1,t2,tt, a1,a2,aa, p1,p2,pp, known, niter)
integer		h1,h2,h12,  t1,t2,t12,  a1,a2,a12,  p1,p2,p12
integer		i, gap, iter, niter, midpt, nx,nr, px,ax,  qr,tr,hr
real		hh(h1,h2), tt(t1,t2), aa(a1,a2), pp(p1*p2), known(p1*p2), dot
temporary real  x( p1*p2 +a1*a2),  rr( p1*p2 +p1*p2 +t1*t2)
temporary real  g( p1*p2 +a1*a2),  gg( p1*p2 +p1*p2 +t1*t2)
temporary real  s( p1*p2 +a1*a2),  ss( p1*p2 +p1*p2 +t1*t2)
p12 = p1*p2;	a12 = a1*a2;	t12 = t1*t2;	h12= h1*h2;
nx  = p12 + a12;     	  px= 1;	ax= 1+p12
nr  = p12 + p12 + t12;    qr= 1;	hr= 1+p12;	tr= 1+p12+p12
call zero( a12, aa);	midpt= a1/2;	aa( midpt, 1 ) = sqrt( dot( p12,pp,pp))
call zero( nx, x);	call zero( nr, rr);	call copy( p12, pp, x(px))
call zero( nx, g);	call zero( nr, gg);	call copy( a12, aa, x(ax))
do iter= 0, niter {
	call cinloi( 0, 0, midpt,1, a1,a2,aa, p1,p2,pp,    rr(qr))
	call cinloi( 0, 0, midpt,1, h1,h2,hh, p1,p2,pp,    rr(hr))
	call cinloi( 0, 0, midpt,1, a1,a2,aa, t1,t2,tt,    rr(tr))
	call scale (                     -1., nr,          rr    )
	call cinloi( 1, 0, midpt,1, a1,a2,aa, p1,p2,g(px), rr(qr))
	call cinlof( 1, 0, midpt,1, p1,p2,pp, a1,a2,g(ax), rr(qr))
	call cinloi( 1, 1, midpt,1, h1,h2,hh, p1,p2,g(px), rr(hr))
	call cinlof( 1, 1, midpt,1, t1,t2,tt, a1,a2,g(ax), rr(tr))
	do i= 1, p12       { if( known(i) != 0.)    g( i + (px-1)) = 0.}
	do i= 1, midpt+gap { 		            g( i + (ax-1)) = 0.}
	call cinloi( 0, 0, midpt,1, a1,a2,aa, p1,p2,g(px), gg(qr))
	call cinlof( 0, 1, midpt,1, p1,p2,pp, a1,a2,g(ax), gg(qr))
	call cinloi( 0, 0, midpt,1, h1,h2,hh, p1,p2,g(px), gg(hr))
	call cinlof( 0, 0, midpt,1, t1,t2,tt, a1,a2,g(ax), gg(tr))
	call cgstep( iter, nx,  x, g, s,
			   nr, rr,gg,ss )
	call copy( p12, x(px), pp)
	call copy( a12, x(ax), aa)
	}
return; end