/// <summary>
/// Trains the network with inputs and targets.
/// </summary>
/// <param name="input_lst"></param>
/// <param name="targets_lst"></param>
public void Train(List <Double> input_lst, List <Double> targets_lst)
{
// Turn input and target arrays into matrices
Matrix inputs = Matrix.FromList(input_lst);
Matrix targets = Matrix.FromList(targets_lst);
// The input to the hidden layer is the weights (wih) multiplied by inputs
var hidden_inputs = Matrix.MultiplyMatrices(Wih, inputs);
// The outputs of the hidden layer pass through sigmoid activation function
var hidden_outputs = Matrix.Map(hidden_inputs, Activation);
// The input to the output layer is the weights (who) multiplied by hidden layer
var output_inputs = Matrix.MultiplyMatrices(Who, hidden_outputs);
// The output of the network passes through sigmoid activation function
var outputs = Matrix.Map(output_inputs, Activation);
// Error is TARGET - OUTPUT
var output_errors = Matrix.SubtractMatrices(targets, outputs);
// ~ Back prop.
// Transpose hidden <-> output weights
var whoT = Who.Transpose();
// Hidden errors is output error multiplied by weights (who)
var hidden_errors = Matrix.MultiplyMatrices(whoT, output_errors);
// Calculate the gradient, this is much nicer in python!
var gradient_output = Matrix.Map(outputs, Derivative);
// Weight by errors and learing rate
gradient_output.Multiply(output_errors);
gradient_output.Multiply(LearningRate);
// Gradients for next layer, more back propogation!
var gradient_hidden = Matrix.Map(hidden_outputs, Derivative);
// Weight by errors and learning rate
gradient_hidden.Multiply(hidden_errors);
gradient_hidden.Multiply(LearningRate);
// Change in weights from HIDDEN --> OUTPUT
var trans_hidden_outputs = hidden_outputs.Transpose();
var deltaw_output = Matrix.MultiplyMatrices(gradient_output, trans_hidden_outputs);
Who.Add(deltaw_output);
// Change in weights from INPUT --> HIDDEN
var trans_inputs = inputs.Transpose();
var deltaw_hidden = Matrix.MultiplyMatrices(gradient_hidden, trans_inputs);
Wih.Add(deltaw_hidden);
}