softmaxCost.m

function [cost, grad] = softmaxCost(theta, numClasses, inputSize, lambda, data, labels)

% numClasses - the number of classes 
% inputSize - the size N of the input vector
% lambda - weight decay parameter
% data - the N x M input matrix, where each column data(:, i) corresponds to
%        a single test set
% labels - an M x 1 matrix containing the labels corresponding for the input data
%

% Unroll the parameters from theta

[n,m] = size(data);

theta = reshape(theta, numClasses, inputSize);

numCases = size(data, 2);

groundTruth = full(sparse(labels, 1:numCases, 1));
cost = 0;

%% thetagrad = zeros(numClasses, inputSize);

%% ---------- YOUR CODE HERE --------------------------------------
%  Instructions: Compute the cost and gradient for softmax regression.
%                You need to compute thetagrad and cost.
%                The groundTruth matrix might come in handy.



M = theta * data;
M = bsxfun(@minus, M, max(M, [], 1));
M = exp(M);

h_x = bsxfun(@rdivide,M,sum(M));
cost = sum(log(sum(groundTruth.*h_x))).*(-1/m) + (lambda./2) * sum(theta(:).^2);
%% disp(cost);

thetagrad = (data * (groundTruth - h_x)' )'.*(-1/m) + lambda .* theta;

% ------------------------------------------------------------------
% Unroll the gradient matrices into a vector for minFunc
grad = [thetagrad(:)];
end