decode

function xyOut = solver(a, xyIn, wts)

randn('seed',2);

N=length(wts);
    
    deg=diag(sum(a));
    [V,~]=eig(deg-a,deg);
    xyOut=V(:,2:3);

for ncut=1:2
    Mbeta=(0.9*eye(N)+0.1*bsxfun(@rdivide,a+eye(N),sum(a,2)+1))^10;
    for n1=1:119
        xyOut=Mbeta*xyOut;
        [c1,D]=svd(cov(xyOut,1));
        xyOut=(bsxfun(@minus,xyOut,mean(xyOut)))*c1*diag(1./sqrt(.1+diag(D)))*c1';
    end
    [i,j]=find(a>0.009); 
    dd=sum((xyOut(i,:)-xyOut(j,:)).^2,2);
    k=find(dd>3.45*mean(dd));
    if isempty(k), break; end
    a(i(k)+N*(j(k)-1))=0.009;
end

xyOut0=sqrt(N)*detrend(xyOut,'constant')*diag(1./std(xyOut,1,1));
k=5;
[sxyOut0,idxequal]=sortrows(round(15*xyOut0)/15);
idxequal=idxequal(all(~diff(sxyOut0,1,1),2));
xyOut=round(xyOut0);
while size(unique(xyOut,'rows'),1)~=N
    k=k*1.1;
    xyOut=xyOut0*k;
    xyOut(idxequal,:)=(xyOut0(idxequal,:)+randn(numel(idxequal),2)/10)*k;
    xyOut=round(xyOut);
end
if N<35 % small map knot lines
 xyOut=3*xyOut+randi([-1,1],N,2);
end


xyOut = bsxfun(@minus,xyOut,round(wts*(xyOut-xyIn)./sum(wts))); % AV's
end