function [lambda, gamma, errorInLambda] = findLambda(classMean, domainVector)
%findLambda - optimize exponent in maxent exponential distribution
% [lambda, gamma, errorInLambda] = findLambda(classMean, domainVector)
% Used the Matlab built-in function fminsearch() to find the optimum value
% of lambda for a mean-constrained maximum entropy problem.
%
% Arguments:
% classMean - mean constraint in maxent problem
% domainVector - vector of possible values taken on by the exponent. Can be
% discrete ordinal or continuous, in which case it should be a vector of
% discretized values over the range of possible values.
%
% Returns the value of the exponent (lambda), the normalization constant
% (gamma) and the estimation error (errorInLambda).

% Written by Maya Gupta, Dept EE, University of Washington.
% Modified by Luca Cazzanti, APL-UW.


[lambda, errorInLambda] = fminsearch(@optLambda, 0);
gamma = 1/ sum(exp(lambda * domainVector));

  function theErr = optLambda(posLambda)
    elambdaVect = exp(posLambda*domainVector);
    meanpmf= sum( domainVector.*elambdaVect )/sum( elambdaVect );
    theErr = abs(meanpmf - classMean);
  end

end