Neural network in MATLAB

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I wrote a simple example of an XOR network. I used newpr, which defaults to tansig transfer function for both hidden and output layers.

input = [0 0 1 1; 0 1 0 1];               %# each column is an input vector
ouputActual = [0 1 1 0];

net = newpr(input, ouputActual, 2);       %# 1 hidden layer with 2 neurons
net.divideFcn = '';                       %# use the entire input for training

net = init(net);                          %# initialize net
net = train(net, input, ouputActual);     %# train
outputPredicted = sim(net, input);        %# predict

then we check the result by computing the output ourselves. The important thing to remember is that by default, inputs/outputs are scaled to the [-1,1] range:

scaledIn = (2*input - 1);           %# from [0,1] to [-1,1]
for i=1:size(input,2)
    in = scaledIn(:,i);             %# i-th input vector
    hidden(1) = tansig( net.IW{1}(1,1)*in(1) + net.IW{1}(1,2)*in(2) + net.b{1}(1) );
    hidden(2) = tansig( net.IW{1}(2,1)*in(1) + net.IW{1}(2,2)*in(2) + net.b{1}(2) );
    out(i) = tansig( hidden(1)*net.LW{2,1}(1) + hidden(2)*net.LW{2,1}(2) + net.b{2} );
end
scaledOut = (out+1)/2;              %# from [-1,1] to [0,1]

or more efficiently expressed as matrix product in one line:

scaledIn = (2*input - 1);           %# from [0,1] to [-1,1]
out = tansig( net.LW{2,1} * tansig( net.IW{1}*scaledIn + repmat(net.b{1},1,size(input,2)) ) + repmat(net.b{2},1,size(input,2)) );
scaledOut = (1 + out)/2;            %# from [-1,1] to [0,1]

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