function [softmaxModel] = mrTrain(inputSize, outSize, lambda, inputData, labels, options)

%softmaxTrain Train a softmax model with the given parameters on the given

% data. Returns softmaxOptTheta, a vector containing the trained parameters

% for the model.

%

% inputSize: the size of an input vector x^(i)

% numClasses: the number of classes 

% lambda: weight decay parameter

% inputData: an N by M matrix containing the input data, such that

%            inputData(:, c) is the cth input

% labels: M by 1 matrix containing the class labels for the

%            corresponding inputs. labels(c) is the class label for

%            the cth input

% options (optional): options

%   options.maxIter: number of iterations to train for

if ~exist('options', 'var')

    options = struct;

end

if ~isfield(options, 'maxIter')

    options.maxIter = 400;

end

% initialize parameters

theta = 0.005 * randn(outSize * inputSize, 1);

% Use minFunc to minimize the function

addpath minFunc/

options.Method = 'lbfgs'; % Here, we use L-BFGS to optimize our cost

                          % function. Generally, for minFunc to work, you

                          % need a function pointer with two outputs: the

                          % function value and the gradient. In our problem,

                          % softmaxCost.m satisfies this.

options.display = 'on';

[softmaxOptTheta, cost] = minFunc( @(p) mrCost(p, ...

                                   outSize, inputSize, lambda, ...

                                   inputData, labels), ...                                   

                              theta, options);

% Fold softmaxOptTheta into a nicer format

softmaxModel.optTheta = reshape(softmaxOptTheta, outSize, inputSize);

softmaxModel.inputSize = inputSize;

softmaxModel.numClasses = outSize;

end