% Solve an Autoregression Time-Series Problem with a NAR Neural Network 
  % Script generated by Neural Time Series app 
  % Created 09-Mar-2016 20:04:18 
  % 
  % This script assumes this variable is defined: 
  % 
  %   X - feedback time series. 
   
  T = tonndata(X,false,false); 
   
  % Choose a Training Function 
  % For a list of all training functions type: help nntrain 
  % 'trainlm' is usually fastest. 
  % 'trainbr' takes longer but may be better for challenging problems. 
  % 'trainscg' uses less memory. Suitable in low memory situations. 
  trainFcn = 'trainlm';  % Levenberg-Marquardt backpropagation. 
   
  % Create a Nonlinear Autoregressive Network 
  feedbackDelays = 1:2; 
  hiddenLayerSize = 10; 
  net = narnet(feedbackDelays,hiddenLayerSize,'open',trainFcn); 
   
  % Choose Feedback Pre/Post-Processing Functions 
  % Settings for feedback input are automatically applied to feedback output 
  % For a list of all processing functions type: help nnprocess 
  net.input.processFcns = {'removeconstantrows','mapminmax'}; 
   
  % Prepare the Data for Training and Simulation 
  % The function PREPARETS prepares timeseries data for a particular network, 
  % shifting time by the minimum amount to fill input states and layer 
  % states. Using PREPARETS allows you to keep your original time series data 
  % unchanged, while easily customizing it for networks with differing 
  % numbers of delays, with open loop or closed loop feedback modes. 
  [x,xi,ai,t] = preparets(net,{},{},T); 
   
  % Setup Division of Data for Training, Validation, Testing 
  % For a list of all data division functions type: help nndivide 
  net.divideFcn = 'dividerand';  % Divide data randomly 
  net.divideMode = 'time';  % Divide up every sample 
  net.divideParam.trainRatio = 70/100; 
  net.divideParam.valRatio = 15/100; 
  net.divideParam.testRatio = 15/100; 
   
  % Choose a Performance Function 
  % For a list of all performance functions type: help nnperformance 
  net.performFcn = 'mse';  % Mean Squared Error 
   
  % Choose Plot Functions 
  % For a list of all plot functions type: help nnplot 
  net.plotFcns = {'plotperform','plottrainstate', 'ploterrhist', ... 
      'plotregression', 'plotresponse', 'ploterrcorr', 'plotinerrcorr'}; 
   
  % Train the Network 
  [net,tr] = train(net,x,t,xi,ai); 
   
  % Test the Network 
  y = net(x,xi,ai); 
  e = gsubtract(t,y); 
  performance = perform(net,t,y) 
   
  % Recalculate Training, Validation and Test Performance 
  trainTargets = gmultiply(t,tr.trainMask); 
  valTargets = gmultiply(t,tr.valMask); 
  testTargets = gmultiply(t,tr.testMask); 
  trainPerformance = perform(net,trainTargets,y) 
  valPerformance = perform(net,valTargets,y) 
  testPerformance = perform(net,testTargets,y) 
   
  % View the Network 
  view(net) 
   
  % Plots 
  % Uncomment these lines to enable various plots. 
  %figure, plotperform(tr) 
  %figure, plottrainstate(tr) 
  %figure, ploterrhist(e) 
  %figure, plotregression(t,y) 
  %figure, plotresponse(t,y) 
  %figure, ploterrcorr(e) 
  %figure, plotinerrcorr(x,e) 
   
  % Closed Loop Network 
  % Use this network to do multi-step prediction. 
  % The function CLOSELOOP replaces the feedback input with a direct 
  % connection from the outout layer. 
  netc = closeloop(net); 
  netc.name = [net.name ' - Closed Loop']; 
  view(netc) 
  [xc,xic,aic,tc] = preparets(netc,{},{},T); 
  yc = netc(xc,xic,aic); 
  closedLoopPerformance = perform(net,tc,yc) 
   
  % Multi-step Prediction 
  % Sometimes it is useful to simulate a network in open-loop form for as 
  % long as there is known data T, and then switch to closed-loop to perform 
  % multistep prediction. Here The open-loop network is simulated on the 
  % known output series, then the network and its final delay states are 
  % converted to closed-loop form to produce predictions for 5 more 
  % timesteps. 
  [x1,xio,aio,t] = preparets(net,{},{},T); 
  [y1,xfo,afo] = net(x1,xio,aio); 
  [netc,xic,aic] = closeloop(net,xfo,afo); 
  [y2,xfc,afc] = netc(cell(0,5),xic,aic); 
  % Further predictions can be made by continuing simulation starting with 
  % the final input and layer delay states, xfc and afc. 
   
  % Step-Ahead Prediction Network 
  % For some applications it helps to get the prediction a timestep early. 
  % The original network returns predicted y(t+1) at the same time it is 
  % given y(t+1). For some applications such as decision making, it would 
  % help to have predicted y(t+1) once y(t) is available, but before the 
  % actual y(t+1) occurs. The network can be made to return its output a 
  % timestep early by removing one delay so that its minimal tap delay is now 
  % 0 instead of 1. The new network returns the same outputs as the original 
  % network, but outputs are shifted left one timestep. 
  nets = removedelay(net); 
  nets.name = [net.name ' - Predict One Step Ahead']; 
  view(nets) 
  [xs,xis,ais,ts] = preparets(nets,{},{},T); 
  ys = nets(xs,xis,ais); 
  stepAheadPerformance = perform(nets,ts,ys) 
   
  % Deployment 
  % Change the (false) values to (true) to enable the following code blocks. 
  % See the help for each generation function for more information. 
  if (false) 
      % Generate MATLAB function for neural network for application 
      % deployment in MATLAB scripts or with MATLAB Compiler and Builder 
      % tools, or simply to examine the calculations your trained neural 
      % network performs. 
      genFunction(net,'myNeuralNetworkFunction'); 
      y = myNeuralNetworkFunction(x,xi,ai); 
  end 
  if (false) 
      % Generate a matrix-only MATLAB function for neural network code 
      % generation with MATLAB Coder tools. 
      genFunction(net,'myNeuralNetworkFunction','MatrixOnly','yes'); 
      x1 = cell2mat(x(1,:)); 
      xi1 = cell2mat(xi(1,:)); 
      y = myNeuralNetworkFunction(x1,xi1); 
  end 
  if (false) 
      % Generate a Simulink diagram for simulation or deployment with. 
      % Simulink Coder tools. 
      gensim(net); 
  end