function [overlap] = getoverlap(posscores,negscores);

% fits a decision boundary at 45 degrees and, roughly speaking, adds up 
% how far on the wrong side of this boundary the test points are using an
% appropriate scale.

% One of the two classes is called "pos" and the other is "neg"
% It scales the distances to minimize a negative log prob cost, where the 
% probability of giving a datapoint the "pos" label is given by
% 1/(1+exp(-distance/scale))
% and "distance" is how far the point is from the decision boundary on
% the positive side. We want p(pos) to be big for pos cases and small
% for neg cases.

% posscores is the scores under the "pos" model minus the scores under the
% "neg" model for the "pos" cases;
% negscores is the same quantities for the neg cases. 
% If posscores were all positive and negscores were all negative, we
% would make the scale very small so the probabilities were all 1 or 0
% and  the overlap would be zero. If the classes overlap a lot its best to
% use a big scale so that the probabilities are all very soft.


tiny=10^(-50);
adjusttemp=1;

xpos=posscores/2; %the scale should not matter but this prevents problems.
xneg=negscores/2;
%spread=max([xpos;xneg])-min([xpos;xneg]);
%xpos=xpos/spread;
%xneg=xneg/spread;

thresh=0;
z=0;  % temperature=exp(-z);

improvement=1; oldcost=exp(100); %to start the while loop
while improvement>.000001
  beta=exp(z);
  posderiv=sum( 1./(1+exp(-beta*(thresh-xpos))) );
  negderiv= - sum( 1./(1+exp(-beta*(xneg-thresh))) );
  deriv=posderiv+negderiv;
%we ignore a factor of exp(z) in these derivs to help stability;
  thresh=thresh - .01*deriv;

  poscost=sum(-log(tiny+1./(1+exp(-beta*(xpos-thresh)))));
  negcost=sum(-log(tiny+1./(1+exp(-beta*(thresh-xneg)))));
  cost=negcost+poscost;
%  fprintf(1, 'thresh= %4.6f  temp= %4.6f  bits= %4.4f \n', ...
%              thresh,        exp(-z),     cost/log(2));
  improvement=oldcost-cost;
  oldcost=cost;
end;

if adjusttemp==1
improvement=1; oldcost=exp(100); %to start the while loop
while improvement>.00001
  beta=exp(z);
  posderiv=sum( 1./(1+exp(-beta*(thresh-xpos))) );
  negderiv= - sum( 1./(1+exp(-beta*(xneg-thresh))) );
  deriv=posderiv+negderiv;
%we ignore a factor of exp(z) in these derivs to help stability;
  thresh=thresh - .01*deriv;

   poszderiv= sum( beta*(thresh-xpos) .* 1./(1+exp(-beta*(thresh-xpos))) );
  negzderiv= sum( beta*(xneg-thresh) .* 1./(1+exp(-beta*(xneg-thresh))) );
  zderiv=poszderiv+negzderiv;
%we ignore a factor of exp(z) in these derivs to help stability;
  z = z - .01*zderiv;

  poscost=sum(-log(tiny+1./(1+exp(-beta*(xpos-thresh)))));
  negcost=sum(-log(tiny+1./(1+exp(-beta*(thresh-xneg)))));
  cost=negcost+poscost;
%  fprintf(1, 'thresh= %4.6f  temp= %4.6f  bits= %4.4f \n', ...
%              thresh,        exp(-z),     cost/log(2));
  improvement=oldcost-cost;
  oldcost=cost;
end;
end;

overlap= cost/log(2);