num5deriv

Numeric five-point stencil neural network derivative function

Syntax

num5deriv('dperf_dwb',net,X,T,Xi,Ai,EW)
num5deriv('de_dwb',net,X,T,Xi,Ai,EW)


Description

This function calculates derivatives using the five-point numeric derivative rule.

$$\begin{array}{l}{y}_1=y(x+2dx)\\ y_2=y(x+dx)\\ y_3=y(x-dx)\\ y_4=y(x-2dx)\\ \frac{dy}{dx}=\frac{-y1+8y_2-8y_3+y_4}{12dx}\end{array}$$

This function is much slower than the analytical (non-numerical) derivative functions, but is provided as a means of checking the analytical derivative functions. The other numerical function, num2deriv, is faster but less accurate.

num5deriv('dperf_dwb',net,X,T,Xi,Ai,EW) takes these arguments,

net	Neural network
X	Inputs, an RxQ matrix (or NxTS cell array of RixQ matrices)
T	Targets, an SxQ matrix (or MxTS cell array of SixQ matrices)
Xi	Initial input delay states (optional)
Ai	Initial layer delay states (optional)
EW	Error weights (optional)

and returns the gradient of performance with respect to the network’s weights and biases, where R and S are the number of input and output elements and Q is the number of samples (and N and M are the number of input and output signals, Ri and Si are the number of each input and outputs elements, and TS is the number of timesteps).

num5deriv('de_dwb',net,X,T,Xi,Ai,EW) returns the Jacobian of errors with respect to the network’s weights and biases.

Examples

Here a feedforward network is trained and both the gradient and Jacobian are calculated.

[x,t] = simplefit_dataset;
net = feedforwardnet(20);
net = train(net,x,t);
y = net(x);
perf = perform(net,t,y);
dwb = num5deriv('dperf_dwb',net,x,t)

Version History

Introduced in R2010b