logit - expit

%% maps (0,b) into (-inf,inf)
%% inverse of expit
%% usage: logit(x,b) or logit(x) 
%% b defaults to 1
function y = logit(x,b) 
  if nargin<2
    b = 1;
  end
  y = log( x ./ (b - x) );

%% maps (-inf, inf) into (0,b)
%% inverse of logit
%% usage: expit(x,b) or expit(x) 
%% b defaults to 1
function y = expit(x,b) 
  if nargin<2
    b = 1;
  end
  y =  b./(1+exp(-x)) ;