# Neuronen

(neuron1.sce)

``` //Functions to simulate a neuron
//Author: Gerd Doeben-Henisch
//Version: 7.Jan 2009
//Dependent from: annsvecmtx.sci (Vector and matrix operations)

//*******************************************************
//Function to compute the netsum of a neuron n.j from the outputs of preceding neurons o
// weighted with a vector w of weights

function [s] =net(o,w)

s=vecprod(o,w)

endfunction

//************************************************************
// For the different types of activation functions see e.g. Haykin (1999) pp.12ff
// or Zell (1994) pp.76ff
//****************************************************
//Activation function as Identity (o_j=net_j)
// u := net() sum of net-sum function
// a := activation value

function[a] = actId(u)

a=u

endfunction

//****************************************************
//Activation function as symmetric threshold
//(also called 'signum function')

// u := net() sum of net-sum function
// a := activation value

function[a] = actThresSim(u)

if (u > 0) then a = 1
elseif (u == 0) a = 0
else a = -1
end

endfunction

//****************************************************
//Activation function as asymmetric threshold
// also called 'heavyside'

// u := net() sum of net-sum function
// a := activation value

function[a] = actThresBin(u)

if (u >=0) then a = 1
else a = 0
end

endfunction

//****************************************************
//Activation function as  piecewise linear

// u := net() sum of net-sum function
// a := activation value

function[a] = actPiece(u)

if (u >= 0.5) then a = 1
elseif (u <= -0.5) a = 0
else a  = u
end

endfunction

//****************************************************
//Activation function as logistic function

// u := net() sum of net-sum function
// a := activation value

function[a] = actLog(u)

a=1/(1 + exp(-u))

endfunction

//****************************************************
//Activation function as sinus

// u := net() sum of net-sum function
// a := activation value

function[a] = actSin(u)

a=sin(u)

endfunction

//****************************************************
//Activation function as sigmoid

// u := net() sum of net-sum function
// a := activation value
// s := slope of sigmoid function

function[a] = actSigm(u,s)

a=1/(1 + exp(-s*u))

endfunction
//****************************************************
//Activation function as tangens hyperbolics

// u := net() sum of net-sum function
// a := activation value

function[a] = acttanh(u)

a=tanh(u)

endfunction

//****************************************************
//Activation function as probabilistic function

// u := net() sum of net-sum function
// a := activation value
// T := pseudotemperature

function[a] = actProb(u,T)

a=1/(1 + exp(-u/T))

endfunction

//*******************************************************
//Function to compute the activation a.j of a neuron n.j from the net.j function
//Here we choose a simple binary function with a threshold theta

function [a] =actbin(s,theta)

if s < theta then a = 0,
else a = 1,
end

endfunction

//*******************************************************
//Function to compute the reaction of a neuron n.j with input o and w
//having a simple binary function as activation function

function [o] = neuronbin(in,w,theta)

o = actbin(net(in,w),theta),

endfunction

//*******************************************************
//Function to compute the reaction of a neuron n.j with input vector in
// and weight matrix W with row indicator i and a threshold vector th
// The neuron is assumed to have a simple binary function as activation function

function [o] = neuronbin(in,W,th,i)

o = actbin(net(in,W(i,:)),th(i)),

endfunction
```

Gerd Doeben-Henisch 2013-01-17