try71

function xyOut = solver(a, xyIn, wts)

    deg=diag(sum(a));
    [V,~]=eig(deg-a,deg);
    N = length(a);

for ss=1:3
 [xy{ss} xy{ss+3}]     = solver_alfonsoz  (a, xyIn , wts, ss+1, N, V);
 NN(ss)    = gradeIt(a,xy{ss});
 NN(ss+3)      = gradeIt(a,xy{ss+3});
end
xy{7}       = solver_hannes(xyIn, N, V);
NN(7)        = gradeIt(a,xy{7});
[~,best]    = min(NN);
xyOut       = xy{best};

end

function [xyOut xyOut1] = solver_alfonsoz(a, xyIn, wts, ss, N, V)
    randn('seed',ss);
    xyOut=V(:,2:3);

    for ncut=1:2
        Mbeta=((1-ss/10)*eye(N)+(ss/10)*bsxfun(@rdivide,a+eye(N),sum(a,2)+1))^10;
        for n1=1:(117+ss)
            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>0.0075+ss*5.1e-4);
        dd=sum((xyOut(i,:)-xyOut(j,:)).^2,2);
        k=find(dd>(3.15 + ss*0.102)*mean(dd));
        if isempty(k), break; end
        a(i(k)+N*(j(k)-1))=0.0075+ss*5.1e-4;
    end


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

 for zsingle=1:2 % Overlay singletons
  
  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*(1.0+ss*0.055);
    xyOut=xyOut0*k;
    xyOut(idxequal,:)=(xyOut0(idxequal,:)+randn(numel(idxequal),2)/(9+ss))*k;
    xyOut=round(xyOut);
  end

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

  if zsingle==1
   xyOut1=xyOut;
   xyOut=xyOutH;
  end
 end % zsingle

end

function xyOut = solver_hannes(xyIn, N, V)
    %xyOut=0;
    outdiam=sqrt(sum((max(V(:,2:3))-min(V(:,2:3))).^2));
    indiam=sqrt(sum((max(xyIn)-min(xyIn)).^2));
    mult=indiam/outdiam;
    
    while mult==indiam/outdiam || size(unique(xyOut,'rows'),1)<N
        xyOut=round(V(:,2:3)*mult);
        [~,i]=unique(xyOut,'rows');
        m=setdiff(1:N,i);
        xyOut(m,:)=xyOut(m,:)+round(rand(length(m),2))*2-1;
        mult=mult*1.5;
    end
end

function S = gradeIt(a,XYnew)
    A         = triu(a,1);
    nLines    = nnz(A);
    [p1i,p2i] = find(A);
    pick      = tril(true(nLines),-1);

    for nt=1:2
        x1{nt}        = pickCoordinates(XYnew(p1i,nt) ,1,nLines,pick);
        x3{nt}        = pickCoordinates(XYnew(p1i,nt)',nLines,1,pick);
        x2{nt}        = pickCoordinates(XYnew(p2i,nt) ,1,nLines,pick);
        x4{nt}        = pickCoordinates(XYnew(p2i,nt)',nLines,1,pick);
    end

    S = sum(areIntersecting(x1{1},x1{2},x2{1},x2{2},x3{1},x3{2},x4{1},x4{2}));
end

function bool = areIntersecting(x1,y1,x2,y2,x3,y3,x4,y4)
    a = (x1.*y2 - y1.*x2);
    b = (x3.*y4 - y3.*x4);
    Px_n = a.*(x3 - x4) - b.*(x1 - x2);
    Py_n = a.*(y3 - y4) - b.*(y1 - y2);
    Pxy_d = (x1 - x2).*(y3 - y4) - (y1 - y2).*(x3 - x4);

    bool = (isPointBetween(x1, x2, Px_n, Pxy_d) & ...
            isPointBetween(y1, y2, Py_n, Pxy_d) & ...
            isPointBetween(x3, x4, Px_n, Pxy_d) & ...
            isPointBetween(y3, y4, Py_n, Pxy_d));
end

function x = pickCoordinates(xy,n,m,pick)
x         = repmat(xy,n,m);
x         = x(pick);
end

function bool = isPointBetween(pt1, pt2, num, den)

bool = ((pt1.*den <= num) & (num <= pt2.*den)) | ...
       ((pt1.*den >= num) & (num >= pt2.*den));
end