Thankless jiggle

function xyOut = solver(a, xyIn, wts)
deg=diag(sum(a));
[V,~]=eig(deg-a,deg);
N = length(a);
A = triu(a,1);
for ss=1:3
    [xy{ss} xy{ss+3}] = solver_alfonsoz (a, xyIn , wts, ss+1, N, V+rand(size(V))/25); % (Biswas)
    NN(ss) = gradeIt(A,xy{ss});
    NN(ss+3) = gradeIt(A,xy{ss+3});
end
[xy{7} xy{8}] = solver_alfonsoz (a, xyIn , wts, 1, N, V);
NN(7) = gradeIt(A,xy{7});
NN(8) = gradeIt(A,xy{8});
xy{9} = solver_hannes(xyIn, N, V(:,2:3));
NN(9) = gradeIt(A,xy{9});
[ZBest,best] = min(NN);
xyOut = xy{best};

% Jiggle the Best
sprev = rng(0,'twister'); % Non-disturb rng seq by reset post jiggle

for jiggle=1:20
 xyOutZ=xyOut+randi([-1 1],N,2);
 if gradeIt(A,xyOutZ)<ZBest && size(unique(xyOutZ,'rows'),1)==N
  xyOut=xyOutZ; % Use jiggle enhanced for more jiggling
  %break % Faster with Break but not Best Code/Time/Knots Trade
 end
end

rng(sprev) % See a 2 Knot impact w/o any xyOut change

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/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);
        cov_xyOut = (xc'*xc)/N;
        [c1,D]=svd(cov_xyOut);
        xyOut=xc*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);
[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)); % (Biswas)
    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))); 
    if zsingle==1
        xyOut1=xyOut;
        xyOut=xyOutH;
    end
end 
end

function xyOut = solver_hannes(xyIn, N, V)
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,:) + round(rand(length(m),2))*2 - 1;
    mult        = mult*1.5;
end
end

function S = gradeIt(A,XYnew)
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