function [net,tr,Ac,El]=trains(net,PD,Tl,Ai,Q,TS,VV,TV)
%TRAINS Sequential order incremental training w/learning functions.
%
%  Syntax
%
%    [net,TR,Ac,El] = trains(net,Pd,Tl,Ai,Q,TS,VV,TV)
%    info = trains(code)
%
%  Description
%
%    TRAINS is not called directly.  Instead it is called by TRAIN for
%    network's whose NET.trainFcn property is set to 'trains'.
%
%    TRAINS trains a network with weight and bias learning rules with
%    sequential updates. The sequence of inputs is presented to the network
%    with updates occuring after each time step.
%
%    This incremental training algorithm is commonly used for adaptive
%    applications.
%
%    TRAINS takes these inputs:
%      NET - Neural network.
%      Pd  - Delayed inputs.
%      Tl  - Layer targets.
%      Ai  - Initial input conditions.
%      Q   - Batch size.
%      TS  - Time steps.
%      VV  - Ignored.
%      TV  - Ignored.
%    and after training the network with its weight and bias
%    learning functions returns:
%      NET - Updated network.
%      TR  - Training record.
%            TR.timesteps - Number of time steps.
%            TR.perf - performance for each time step.
%      Ac  - Collective layer outputs.
%      El  - Layer errors.
%
%    Training occurs according to the TRAINS' training parameter
%    shown here with its default value:
%      net.trainParam.passes    1  Number of times to present sequence
%
%    Dimensions for these variables are:
%      Pd - NoxNixTS cell array, each element P{i,j,ts} is a ZijxQ matrix.
%      Tl - NlxTS cell array, each element P{i,ts} is an VixQ matrix or [].
%    Ai - NlxLD cell array, each element Ai{i,k} is an SixQ matrix.
%      Ac - Nlx(LD+TS) cell array, each element Ac{i,k} is an SixQ matrix.
%      El - NlxTS cell array, each element El{i,k} is an SixQ matrix or [].
%    Where
%      Ni = net.numInputs
%    Nl = net.numLayers
%    LD = net.numLayerDelays
%      Ri = net.inputs{i}.size
%      Si = net.layers{i}.size
%      Vi = net.targets{i}.size
%      Zij = Ri * length(net.inputWeights{i,j}.delays)
%
%    TRAINS(CODE) return useful information for each CODE string:
%      'pnames'    - Names of training parameters.
%      'pdefaults' - Default training parameters.
%
%  Network Use
%
%    You can create a standard network that uses TRAINS for adapting
%    by calling NEWP or NEWLIN.
%
%    To prepare a custom network to adapt with TRAINS:
%    1) Set NET.adaptFcn to 'trains'.
%       (This will set NET.adaptParam to TRAINS' default parameters.)
%    2) Set each NET.inputWeights{i,j}.learnFcn to a learning function.
%       Set each NET.layerWeights{i,j}.learnFcn to a learning function.
%       Set each NET.biases{i}.learnFcn to a learning function.
%       (Weight and bias learning parameters will automatically be
%       set to default values for the given learning function.)
%
%    To allow the network to adapt:
%    1) Set weight and bias learning parameters to desired values.
%    2) Call ADAPT.
%
%    See NEWP and NEWLIN for adaption examples.
%
%  Algorithm
%
%    Each weight and bias is updated according to its learning function
%    after each time step in the input sequence.
%
%  See also NEWP, NEWLIN, TRAIN, TRAINB, TRAINC, TRAINR.

% Mark Beale, 11-31-97
% Copyright 1992-2002 The MathWorks, Inc.
% $Revision: 1.5 $  $Date: 2002/04/14 21:19:06 $

% FUNCTION INFO
% =============

if isstr(net)
  switch (net)
    case 'pnames',
    net = {'passes'};
    case 'pdefaults',
    net.passes = 1;
    otherwise,
    error('Unrecognized code.')
  end
  return
end

% CALCULATION
% ===========

% Parameters
passes = net.adaptParam.passes;

% Parameter Checking
if (~isa(passes,'double')) | (~isreal(passes)) | (any(size(passes)) ~= 1) | ...
  (passes < 1) | (round(passes) ~= passes)
  error('Passes is not a positive integer.')
end

% Constants
numLayers = net.numLayers;
numInputs = net.numInputs;
performFcn = net.performFcn;
if length(performFcn) == 0
  performFcn = 'nullpf';
end
dperformanceFcn = feval(performFcn,'deriv');
needGradient = net.hint.needGradient;
numLayerDelays = net.numLayerDelays;

%Signals
BP = ones(1,Q);
IWLS = cell(net.numLayers,net.numInputs);
LWLS = cell(net.numLayers,net.numLayers);
BLS = cell(net.numLayers,1);
Ac = [Ai cell(net.numLayers,TS)];
El = cell(net.numLayers,TS);
gIW = cell(numLayers,numInputs);
gLW = cell(numLayers,numLayers);
gB = cell(net.numLayers,1);
gA = cell(net.numLayers,1);
AiInd = 0:(numLayerDelays-1);
AcInd = 0:numLayerDelays;

% Initialize
tr.timesteps = 1:TS;
tr.perf = zeros(1,TS);

% Train
for pass=1:passes
  for ts=1:TS
  
    % Simulate
    [Ac(:,ts+numLayerDelays),N,LWZ,IWZ,BZ] = calca1(net,PD(:,:,ts),Ac(:,ts+AiInd),Q);
    El(:,ts) = calce1(net,Ac(:,ts+numLayerDelays),Tl(:,ts));
    tr.perf(ts) = feval(performFcn,El(:,ts),net);
  
    % Gradient
    if (needGradient)
      gE = feval(dperformanceFcn,'e',El(:,ts),net);
      [gB,gIW,gLW,gA] = calcgrad(net,Q,PD(:,:,ts),BZ,IWZ,LWZ,N,Ac(:,ts+AcInd),gE,1);
    end
  
    % Update
    for i=1:net.numLayers
  
      % Update Input Weight Values
      for j=find(net.inputConnect(i,:))
          learnFcn = net.inputWeights{i,j}.learnFcn;
        if length(learnFcn)
          [dw,IWLS{i,j}] = feval(learnFcn,net.IW{i,j}, ...
            PD{i,j,ts},IWZ{i,j},N{i},Ac{i,ts+numLayerDelays},Tl{i,ts},El{i,ts},gIW{i,j},...
            gA{i},net.layers{i}.distances,net.inputWeights{i,j}.learnParam,IWLS{i,j});
          net.IW{i,j} = net.IW{i,j} + dw;
        end
      end
  
      % Update Layer Weight Values
      for j=find(net.layerConnect(i,:))
          learnFcn = net.layerWeights{i,j}.learnFcn;
        if length(learnFcn)
            Ad = cell2mat(Ac(j,ts+numLayerDelays-net.layerWeights{i,j}.delays)');
            [dw,LWLS{i,j}] = feval(learnFcn,net.LW{i,j}, ...
            Ad,LWZ{i,j},N{i},Ac{i,ts+numLayerDelays},Tl{i,ts},El{i,ts},gLW{i,j},...
            gA{i},net.layers{i}.distances,net.layerWeights{i,j}.learnParam,LWLS{i,j});
            net.LW{i,j} = net.LW{i,j} + dw;
        end
      end
  
      % Update Bias Values
      if net.biasConnect(i)
        learnFcn = net.biases{i}.learnFcn;
        if length(learnFcn)
          [db,BLS{i}] = feval(learnFcn,net.b{i}, ...
          BP,BZ{i},N{i},Ac{i,ts+numLayerDelays},Tl{i,ts},El{i,ts},gB{i},...
          gA{i},net.layers{i}.distances,net.biases{i}.learnParam,BLS{i});
          net.b{i} = net.b{i} + db;
        end
      end
    
    end
  end
end

% Finish
tr.timesteps = TS;