function [C, sigma] = dataset3Params(X, y, Xval, yval)
%EX6PARAMS returns your choice of C and sigma for Part 3 of the exercise
%where you select the optimal (C, sigma) learning parameters to use for SVM
%with RBF kernel
%   [C, sigma] = EX6PARAMS(X, y, Xval, yval) returns your choice of C and 
%   sigma. You should complete this function to return the optimal C and 
%   sigma based on a cross-validation set.
%

% You need to return the following variables correctly.
C = 1;
sigma = 0.3;

% ====================== YOUR CODE HERE ======================
% Instructions: Fill in this function to return the optimal C and sigma
%               learning parameters found using the cross validation set.
%               You can use svmPredict to predict the labels on the cross
%               validation set. For example, 
%                   predictions = svmPredict(model, Xval);
%               will return the predictions on the cross validation set.
%
%  Note: You can compute the prediction error using 
%        mean(double(predictions ~= yval))
%

% C = best C
% sigma = best Sigma
values = [0.01 0.03 0.1 0.3 1, 3, 10 30]';

% all predictions
predictions = zeros(size(values));

for i=1:size(values,1), % C
    for j=1:size(values,1), % sigma

        model = svmTrain(X, y, values(i), @(x1, x2) gaussianKernel(x1, x2, values(j))); 
        predict = svmPredict(model, Xval);
        predictions(i,j) = mean(double(predict ~= yval));
    
    end
end

[colmin, rowindex] = min(predictions);
[minerror, index] = min(colmin);

C = values(rowindex(index))
sigma = values(index)

% =========================================================================

end
