TLM - Jumping

function xyOut = solver(a, xyIn, wts)
diag(sum(a));
[V,~]=eig(ans-a,ans);
N = length(a);
[p1i,p2i] = find( triu(a,1));
[pickr,pickc] = find(tril(true(nnz(triu(a,1))),-1));

for ss=1:3
    [xy{ss} xy{ss+3}] = solver_alfonsoz (a, ss+1, N, V+rand(size(V))/25); % (Biswas)
end
%[xy{7} xy{8}] = solver_alfonsoz (a, 1, N, V);
xy{7} = solver_hannes(xyIn, N, V(:,2:3),0);

parfor ss=1:7
 NN(ss)=gradeIt(p1i,p2i,pickr,pickc,xy{ss})
end
NN(3)=Inf;
[ZBest,best] = min(NN);
xyOut = xy{best};

xyOut = bsxfun(@minus,xyOut,round(wts*(xyOut-xyIn)./sum(wts)));

sprev = rng(0,'twister');

for ii=1:2
for jiggle=1:15
 xyOutZ=xyOut+randi([-ii ii],N,2);
 grade=gradeIt(p1i,p2i,pickr,pickc,xyOutZ);
 if grade<ZBest && size(unique(xyOutZ,'rows'),1)==N
  xyOut=xyOutZ;
  ZBest=grade;
 end
end
end

rng(sprev);
end

function [xyOut xyOut1] = solver_alfonsoz(a, ss, N, V)
randn('seed',ss);
xyOut=V(:,2:3);
sN=sqrt(N);
for ncut=1:2
    Mbeta=((1-ss/15)*eye(N)+(ss/15)*bsxfun(@rdivide,a+eye(N),sum(a,2)+1))^10;
    for n1=1:(117+ss)
        xyOut=Mbeta*xyOut;
        xc = bsxfun(@minus,xyOut,sum(xyOut)/N);
        [c1,D]=svd(xc');
        xyOut=xc*c1*diag(sN./(.1+D([1 4])))*c1';
    end
    [i,j]=find(a>0.002+ss*5.1e-4);
    sum((xyOut(i,:)-xyOut(j,:)).^2,2);
    k=find(ans>(3.15 + ss*0.102)*mean(ans));
    if isempty(k), break; end
    a(i(k)+N*(j(k)-1))=0.002+ss*5.1e-4;
end

xyOutH=xyOut;
single_idx = find(sum(a)==1);
[singles_link, ~] = find(a(:,single_idx)==1);
xyOut(single_idx,:)=xyOut(singles_link,:);

for zsingle=1:2  
    xyOut0=sqrt(N)*detrend(xyOut,'constant')*diag(1./std(xyOut,1,1));
    k=5;
    [sxyOut0,idxequal]=sortrows(round(15*xyOut0));
    idxequal=idxequal(all(~diff(sxyOut0,1,1),2));
    xyOut=round(xyOut0);
    while size(unique(xyOut,'rows'),1)~=N
        k=k*(1.0+ss*0.055);
        xyOut=xyOut0*k;
        xyOut(idxequal,:)=(xyOut0(idxequal,:)+randn(numel(idxequal),2)/(9+ss))*k;
        xyOut=round(xyOut);
    end
    if zsingle==1
        xyOut1=xyOut;
        xyOut=xyOutH;
    end
end 
end

function xyOut = solver_hannes(xyIn, N, V,xyOut)
mult    = norm(max(xyIn)-min(xyIn))/norm(max(V)-min(V));
%xyOut   = [];
while size(unique(xyOut,'rows'),1)<N
    xyOut       = round(V*mult);
    [~,i]       = unique(xyOut,'rows');
    m           = setdiff(1:N,i);
    xyOut(m,:)  = xyOut(m,:) + randi([-1 1],length(m),2);
    mult        = mult*1.5;
end
end

function ans = gradeIt(p1i,p2i,pickr,pickc,XYnew)
  X = [XYnew(p1i,:) XYnew(p2i,:)];
  xa = X(pickr,:);
  xb = X(pickc,:);
  a = xa(:,1).*xa(:,4) - xa(:,2).*xa(:,3);
  b = xb(:,1).*xb(:,4) - xb(:,2).*xb(:,3);
  Px_n = a.*(xb(:,1) - xb(:,3)) - b.*(xa(:,1) - xa(:,3));
  Py_n = a.*(xb(:,2) - xb(:,4)) - b.*(xa(:,2) - xa(:,4));
  Pxy_d = (xa(:,1) - xa(:,3)).*(xb(:,2) - xb(:,4)) - ...
    (xa(:,2) - xa(:,4)).*(xb(:,1) - xb(:,3));
  
  sum(all([(xa(:,1).*Pxy_d - Px_n).*(Px_n - xa(:,3).*Pxy_d) >=0   ...
    (xa(:,2).*Pxy_d - Py_n).*(Py_n - xa(:,4).*Pxy_d) >=0  ...
    (xb(:,1).*Pxy_d - Px_n).*(Px_n - xb(:,3).*Pxy_d) >=0  ...
    (xb(:,2).*Pxy_d - Py_n).*(Py_n - xb(:,4).*Pxy_d) >=0],2));
end