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Adapt neural network to data as it is simulated

`[net,Y,E,Pf,Af,tr] = adapt(net,P,T,Pi,Ai)`

This function calculates network outputs and errors after each presentation of an input.

`[net,Y,E,Pf,Af,tr] = adapt(net,P,T,Pi,Ai)` takes

net | Network |

P | Network inputs |

T | Network targets (default = zeros) |

Pi | Initial input delay conditions (default = zeros) |

Ai | Initial layer delay conditions (default = zeros) |

and returns the following after applying the adapt function `net.adaptFcn` with
the adaption parameters `net.adaptParam`:

net | Updated network |

Y | Network outputs |

E | Network errors |

Pf | Final input delay conditions |

Af | Final layer delay conditions |

tr | Training record ( |

Note that `T` is optional and is only needed
for networks that require targets. `Pi` and `Pf` are
also optional and only need to be used for networks that have input
or layer delays.

`adapt`'s signal arguments can have
two formats: cell array or matrix.

The cell array format is easiest to describe. It is most convenient for networks with multiple inputs and outputs, and allows sequences of inputs to be presented,

P |
| Each element |

T |
| Each element |

Pi |
| Each element |

Ai |
| Each element |

Y |
| Each element |

E |
| Each element |

Pf |
| Each element |

Af |
| Each element |

where

Ni | = | net.numInputs |

Nl | = | net.numLayers |

No | = | net.numOutputs |

ID | = | net.numInputDelays |

LD | = | net.numLayerDelays |

TS | = | Number of time steps |

Q | = | Batch size |

Ri | = | net.inputs{i}.size |

Si | = | net.layers{i}.size |

Ui | = | net.outputs{i}.size |

The columns of `Pi`, `Pf`, `Ai`,
and `Af` are ordered from oldest delay condition
to most recent:

Pi{i,k} | = | Input |

Pf{i,k} | = | Input |

Ai{i,k} | = | Layer output |

Af{i,k} | = | Layer output |

The matrix format can be used if only one time step is to be
simulated (`TS = 1`). It is convenient for networks
with only one input and output, but can be used with networks that
have more.

Each matrix argument is found by storing the elements of the corresponding cell array argument in a single matrix:

P | ( |

T | ( |

Pi | ( |

Ai | ( |

Y | ( |

E | ( |

Pf | ( |

Af | ( |

Here two sequences of 12 steps (where `T1` is
known to depend on `P1`) are used to define the operation
of a filter.

p1 = {-1 0 1 0 1 1 -1 0 -1 1 0 1}; t1 = {-1 -1 1 1 1 2 0 -1 -1 0 1 1};

Here `linearlayer` is used
to create a layer with an input range of `[-1 1]`,
one neuron, input delays of 0 and 1, and a learning rate of 0.5. The
linear layer is then simulated.

net =linearlayer([0 1],0.5);

Here the network adapts for one pass through the sequence.

The network's mean squared error is displayed. (Because
this is the first call to `adapt`, the default `Pi` is
used.)

[net,y,e,pf] =adapt(net,p1,t1); mse(e)

Note that the errors are quite large. Here the network adapts
to another 12 time steps (using the previous `Pf` as
the new initial delay conditions).

p2 = {1 -1 -1 1 1 -1 0 0 0 1 -1 -1}; t2 = {2 0 -2 0 2 0 -1 0 0 1 0 -1}; [net,y,e,pf] =adapt(net,p2,t2,pf);mse(e)

Here the network adapts for 100 passes through the entire sequence.

p3 = [p1 p2]; t3 = [t1 t2]; net.adaptParam.passes = 100; [net,y,e] =adapt(net,p3,t3);mse(e)

The error after 100 passes through the sequence is very small. The network has adapted to the relationship between the input and target signals.

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