% TODO: create datasets x1 and x2

%% TODO: initialize the weights.  This should be a vector of 3 weights, since we're using 2D data
w =  ... 

% Set this to one in order to check if the gradients are correct.
% Set to zero if you're confident that they're correct and you want to skip the check
checkGradient = 1;

%%%% YOUR MAIN JOB IS TO IMPLEMENT THE FUNCTION logisticNLP THAT TAKES 
%%%% DATA x1 AND x2 FROM THE TWO TRAINING CLASSES, AND THE WEIGHT VECTOR w, AND EVALUATES
%%%% THE NEGATIVE LOG-LIKELIHOOD
%%%%
%%%% YOU SHOULDN'T NEED TO MODIFY ANYTHING FROM HERE UNTIL THE END OF THE INNER LOOP
%%%% BUT YOU SHOULD LOOK IT OVER TO MAKE SURE YOU UNDERSTAND IT

% Initial negative log-likelihood and gradient
[ll,g] = logisticNLP(x1,x2,w);

% Use finite differences to compute the gradient and compare with the analytic value
if checkGradient
	g2 = zeros(size(w));
	h = .001;
	for i=1:length(w)
    	w2 = w;
    	w2(i)=w2(i)+h;
    	g2(i) = (logisticNLP(x1,x2,w2) - ll)/h;
	end
	
	disp('Analytic gradient:')
	disp(g)
	disp('Numerical gradient:')
	disp(g2)
	disp('These two should be nearly identical (i.e., within 1%)')
	pause
end

% Initial step-size
lambda = .001;

% Gradient descent inner-loop
l2 = [];
for t=1:1000
    l2 = [l2;ll];  %keep track of negative log-likelihoods in case you want to plot them
    lambda = lambda * 2;
    e = logisticNLP(x1,x2,w-lambda*g);
    
    if norm(g) < eps
        warning('gradient is zero');
        break;
    end
    if isnan(e) || isinf(e)
        error('nan/inf error');
    end
     
    while (e >= ll) && (lambda > 0)
        lambda = lambda / 2;
        e = logisticNLP(x1,x2,w-lambda*g);
    end
    if (lambda <= eps)
		warning('Infinitesimal lambda')
        fprintf(2,'lambda = %f\n',lambda);
        break;
    end
    
    w = w - lambda*g;
    [ll,g] = logisticNLP(x1,x2,w);
    
    fprintf(2,'step = %d, lambda = %f, ll=%f\n\r',t,lambda,ll);
end

%%%%%%%% GENERATE PLOTS AND/OR SAVE RESULTS HERE