function up=pchybsw(au)
% PCHYBSW Hybrid II Schwarz as a precondtioner on an m x m mesh
%
% function up=pchybsw(au)
% 
global ph pv overlap ac zm
[m1,m2]=size(au); m=sqrt(m1);
au2=zeros(m,m); 
au2(:)=au;
%ph=2; pv=2; overlap=max(3,floor(m/5));
up2=addswp(m,au2,overlap,ph,pv,ac,zm);
up=up2(:);
%
% Divide the domain into ph * pv
% subdomains, ph splits in horozontal and pv splits in vertical
%
function u2d=addswp(m,rhs2d,overlap,ph,pv,ac,zm)
[l,r]=partition(m,2,overlap);
[lv,rv]=partition(m,pv,overlap);
[lh,rh]=partition(m,ph,overlap);
h=1/(m+1);
u2d=zeros(m,m);
caph=1/pv; rc=zeros(ph,pv);
%
% This is the one-level additive part. 
%
mr=rv(1);
lr=rv(1)-lv(1)+1;
for ih=1:ph
	for iv=1:pv
		lbh=lh(ih); ubh=rh(ih); lbv=lv(iv); ubv=rv(iv);
		vd=ubv-lbv+1; hd=ubh-lbh+1;
		rsub=rhs2d(lbh:ubh,lbv:ubv);
		ux=subdomain(rsub,hd,vd,h);
		u2d(lbh:ubh,lbv:ubv)=u2d(lbh:ubh,lbv:ubv)+ux;
	end
end
rhsc=hybrid(m,rhs2d,u2d);
u2d=u2d+cmsolv(m,ph/2,rhsc);
%
function rhsc=hybrid(m,rhs2d,u2d);
w=zeros(m*m,1); r1d=w; rhsc=zeros(m,m);
r1d=rhs2d(:); w=u2d(:);
w=r1d-lapmf(w);
rhsc(:)=w;