function [estClass] = calcCentroidalParametricClassX(testMat, trainMat, classPriors)
% calcParametricClass
% assumes similarity measure is Hamming similarity
% = counting common features.
% output is a vector of class Labels corresponding to the test points
% which are rows of testMat
%
% models the similarity s(x, mu1) by an exponential distribution 
% (which is max ent/max likelihood distribution)
% then compares log posterior probability of each class.

% test = test feature matrix where each row is a test feature vector
% trainMat = database of all training vectors
%'the right one
[numTrain, prenumFeatures] = size(trainMat);
[numTest, junk] = size(testMat);
numFeatures = prenumFeatures-1;
trainLabel = trainMat(:, prenumFeatures);
numClasses = length(classPriors);

%%%%%%% GET PARAMETRIC MODEL FOR EACH CLASS %%%%%%%%%%%

% first we need a representative guy for each class
    trainMat1 = trainMat(find(trainMat(:, numFeatures+1)==1),1:numFeatures);
    trainMat2 = trainMat(find(trainMat(:, numFeatures+1)==2),1:numFeatures);   
    
    [u1] = getMostRepElement(trainMat1);
    [u2] = getMostRepElement(trainMat2);
    muVect(1,:) = trainMat1(u1, :);
    muVect(2,:) = trainMat2(u2, :);

% now we need to know what the descriptive statistic is.
% for each class
% here we assume the descriptive statistic is 
% mean sim(c1, mu1) for all points c1 in class c1. 
classMean = zeros(numClasses,1); % initialize to zero
countClass = zeros(numClasses, 1); % initialize count to zero

% these are for the "cross" similarities, that is s(c1,mu2) and s(c2, mu1);
classMeanX = zeros(numClasses,1); 
countClassX = zeros(numClasses, 1);
% reverse the class labels
trainLabelX = trainLabel - 1;
trainLabelX(trainLabelX == 0) = 2;

for j= 1:numTrain    
% get the similarity between the jth object in the database and
% its class centroid
classMean(trainLabel(j)) = classMean(trainLabel(j)) + getSimCounting(trainMat(j,1:numFeatures), muVect(trainLabel(j), :));
countClass(trainLabel(j)) = countClass(trainLabel(j)) +1;

% note the trainLabelX at the end
classMeanX(trainLabel(j)) = classMeanX(trainLabel(j)) + getSimCounting(trainMat(j,1:numFeatures), muVect(trainLabelX(j), :));
end
    
% final class means are:
classMean = classMean./countClass;
classMeanX = classMeanX ./ countClass;

% since this is counting measure, the domain of possible
% similarities is 0,1,2, ... numFeatures
domainVector = 0:numFeatures;

% Now numerically optimize the lambda parameter in the 
% exponential model
for g = 1:numClasses
lambda(g) = findLambda(classMean(g), domainVector);
lambdaX(g) = findLambda(classMeanX(g), domainVector);
end

% compute the normalization constants normC as well
for g = 1:numClasses
normC(g) = 1/(sum( exp(lambda(g)*domainVector)));
normCX(g) = 1/(sum(exp(lambdaX(g)*domainVector)));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% check that this is reasonable, normalized.
%psim1 = normC(1)*exp(lambda(1)*domainVector)
%psim2 = normC(2)*exp(lambda(2)*domainVector)


%%%%%% ITERATE THROUGH TEST POINTS %%%%%%%%%%%%
for i = 1:numTest
    
    x = testMat(i, :); % pull off an x. 
        
    % get simTest = s(x, classmean) for each class
    % and figure out how probable that similarity is
    for g = 1:numClasses
     simTest(g) = getSimCounting(x, muVect(g,:));
    end
   
    % Now compute the log posterior for each class:
    logPosteriors = lambda .* simTest + log(normC) + log(classPriors);
    crossTerm = log(normCX) + lambdaX .* simTest(2:-1:1);
    logPosteriors = logPosteriors + crossTerm;
   
    
    % classify as whoever has the largest logPosterior
    % this assumes 0-1 costs
    [who, estClass(i)] = max(logPosteriors);
end %iteration over test points
    
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%