trulstest_thermal01

function xy = solver(kd,bx)

rand('state',0);
npts = length(kd); 
xy = zeros(npts,1); 
if any(kd(:)>0)
   nones=ones(npts,1); 
   dr=sqrt(bx(2)^2+bx(4)^2);
   kd(kd>dr)=dr;
   [dum,p]=sort(-max(kd));
   kd=kd(p,p);
   S=((kd-eye(npts))>=0); % Remember positive position
   sI=find(S); % Positive index
   strainMatrix = S; % Create strainMatrix;
   mx=-dum(1)*1.21;
   dx=min(bx(2),mx); 
   dy=min(bx(4),mx);
   D=dx+dy;
   d=D/16;
   while max(2,ceil(dx/d))*max(2,ceil(dy/d))<60
      d=d/2;
   end
   x=0:d:dx;
   if x(end)<dx
      x(end+1)=dx;
   end
   y=0:d:dy;
   if y(end)<dy
      y(end+1)=dy;
   end
   
   [x,y]=meshgrid(x,y);
   xy0=x(:)+i*y(:);
   k = length(xy0);
   M=fix(8+npts/4);
   N0=min(M,npts);
   xy(1:N0) = solverl(S(1:N0,1:N0),kd(1:N0,1:N0),dx,dy,N0);
   for N=(M+1):npts
      xy(N) = solver2(S(1:N,N),kd(1:N,N),N,xy0,...
         xy(1:N),k,d,dx,dy,4);
   end
   for N=1:N0
      xy(N) = solver2(S(:,N),kd(:,N),N,[xy(N);xy0],xy,k+1,d,dx,dy,5);
   end
   m=2;
   for f=1:2,
      [XY1,XY2] = meshgrid(xy);
      strainMatrix(sI) = abs(abs(XY1(sI)-XY2(sI))-kd(sI));
      if sum(strainMatrix(sI))<4
         break;
      end
      [sV,sP] = sort(-sum(strainMatrix));
      n=min(fix(npts/m),sum(sV<(sum(sV)*0.98/npts)));
      sN = sP(1:n);
      for i=sN,
         xy(i) = solver2(S(:,i),kd(:,i),i,[xy(i);xy0],xy,k+1,d,dx,dy,5);
         m=m/2;
      end
   end
   [v,w]=sort(p);
   xy=xy(w,:);
end
xy=[real(xy) imag(xy)];

function xy = solverl(S,kd,dx,dy,npts) 
[I,J] = find(triu(S,1)); 
if isempty(I),
   xy = zeros(npts,1);
   return;
end
y = kd(find(triu(S,1)));
k = 450+npts*30; % change k according to memory capacity.
x = zeros(npts,k);
x(:) = rand(npts*k,2)*[dx;i*dy];
[tv,id] = min(sum(abs(abs(x(I,:)-x(J,:))-y(:,ones(1,k)))));
xy=x(:,id);
%xy = freeforce(S,kd,xy,dx,dy,npts,200);

%function xy = freeforce(S,kd,xy,dx,dy,npts,n)
sI=find(S);
fM=S;
d=kd(sI);
[X1,X2]=meshgrid(xy); 
dX=X1(sI)-X2(sI);
strain=sum(abs(abs(dX)-d));
strain0=0;
while strain0<strain,
%for iC=1:n,
   % Direction of force between every point and every other point
   % * magnitude of strain
   % * whether or not S(i,j) contains a don't-care for xy(i) and xy(j)
   
   strain = strain0;
   fM(sI) = dX.*(kd(sI)./(abs(dX)+eps)-1);
   forces = sum(fM,2);
   rand_forces=.1*rand(npts,1).*abs(forces).*exp(-1i*2*pi*rand(npts,1));
   xy0 = xy - .1*(forces+rand_forces);
   xy0=min(dx,max(0,real(xy0)))+1j*min(dy,max(0,imag(xy0)));
   [X1,X2]=meshgrid(xy0); 
   dX=X1(sI)-X2(sI);
   strain0 = sum(abs(abs(dX)-kd(sI)));
   xy = xy0;
end;


function xy1 = solver2(S,kd,N,xy,xy0,k,d,dx,dy,n) 
I = find(S); 
if isempty(I),
   xy1 = xy0(N);
   return;
end 
z = kd(:); 
kones=ones(1,k);
xy=xy(:).';
[tv0,id]=min(sum(abs(abs(xy(ones(size(I)),:)-xy0(I,kones))-z(I,kones)))); 
xy1=xy(id);
for m=1:n
   d0=d;
   d=d0/4;
   [tv,xy1]=finegrid(I,xy1,xy0,d0,d,dx,dy,z);
   if tv0 - tv < 0.1, break, end
   tv0 = tv;
end

function [tv,xy1]=finegrid(I,xy,xy0,d0,d,dx,dy,z);
x1=real(xy); 
y1=imag(xy);
x=max(0,x1-d0):d:min(dx,x1+d0); 
y=(max(0,y1-d0):d:min(dy,y1+d0))'; 
xy=x(ones(size(y)),:)+i*y(:,ones(size(x))); 
xy=xy(:).'; 
kones=ones(size(xy));
[tv,id]=min(sum(abs(abs(xy(ones(size(I)),:)-xy0(I,kones))-z(I,kones)))); 
xy1=xy(id);