MATLABAn Introduction

Imthias Ahamed T. P.Dept. of Electrical Engineering,T.K.M.College of Engineering,

Kollam – 691005,imthiasa@gmail.com

A Glorified Calculator• >> 2*3

• ans =

• 6

• >> 2.5*400

• ans =

• 1000

• >> 2^3

• ans =

• 8

A Glorified Calculator Contd..

>> exp(1)ans = 2.7183>> sin(pi/4)ans = 0.7071

>> exp(-1)*sin(pi/4)ans = 0.2601

• Command window• workspace

plot

• x= [0 1 2 3 4 5 6 7 8 9 10];• d = [0 1 2 3 4 3 2 1 2 3 4];• plot(x,d)

MATrix LABoratory

a=[10 0 0; 0 20 0; 0 0 100];b=[ 1 20 -3; 0.2 100 -4; 25 10 0]c= a+b• d= a-b• e=a*b

MATRIX contd…

• F= inv(a)• H=a*f• Eig(a)

Useful functions

• sin• cos • tan PlotEigInvExp

A PROGRAMMING LANGUAGE

clearclfx= [0 1 2 3 4 5 6 7 8 9 10];d = [0 1 2 3 4 3 2 1 2 3 4];plot(x,d,'x')

X=0:.1:10

clearclfx= 0:.1:.4;y=sin(x)plot(x,y)

hold

clearclfx= 0:.1:10;y1=sin(x);plot(x,y1);y2=cos(x);plot(x,y2);

help

• >> help

• HELP topics:

• matlab\general - General purpose commands.• matlab\ops - Operators and special characters.• matlab\lang - Programming language constructs.• matlab\elmat - Elementary matrices and matrix

manipulation.

help general• >> help general

• General purpose commands.• MATLAB Toolbox Version 6.1 (R12.1) 18-May-2001• • General information• helpbrowser - Bring up the help browser.• doc - Complete on-line help, displayed in the help

browser.• help - M-file help, displayed at the command line. • helpwin

help plot

• PLOT Linear plot. • PLOT(X,Y) plots vector Y versus vector X. If X

or Y is a matrix,• then the vector is plotted versus the rows or

columns of the matrix,• whichever line up. If X is a scalar and Y is a

vector, length(Y)• disconnected points are plotted.

• Command window• Workspace• Edit window• Figer window

Model of a Simple Perceptron

wk1

wk2

wkm

x1

x2

xm

......

S

Biasbk

Summing junction

Synaptic weights

Input signals j(×)

Activation function

vkOutputyk

m

jjkjk xwv

0and ( )kk vy jLet bk=wk0 and x0=+1

Multi Layer Perceptron

18

Back-propagation Algorithm:Summary

1. Initialization. Pick all of

the wji from a uniform

distribution.

2. Presentations of

Training Examples.

3. Forward Computation.

4. Backward

Computation.

5. Iteration.

NN commands

• net = newff([rangep1; rangep2],[8 1],{'logsig' 'logsig'});• Y = sim(net,P)• net = train(net,P,T);• Y = sim(net,P);

Pattern classification problem

• %defines inputs• P = [ 0.8903 0.9574 0.8031 0.9523 0.9517 0.0662 0.1129 0.1560 0.1604 0.0406• 0.8391 0.9237 0.9782 0.9814 0.8761 0.1008 0.1534 0.0968 0.0942 0.1159]• T =[ 0 0 0 0 0 1 1 1 1 1]

creates a feed forward network

• net = newff([-1 1; -1 1],[4 1],{'logsig' 'logsig'});• %creates a feed forward network • %[-1 1;-1 1] represents min and max of

inputs• %[4 1] 4 represents size of hidden layer and

1 size of the output layer• %('logsig' 'logsig') represents transfer

function of output and hidden layer

training

• ybeforetrain = sim(net,P)• % simulates network net.trainParam.epochs = 50;• %network is trained for 50 epochs • net = train(net,P,T);

Testing

• Y = sim(net,P);• plotpv(P,Y)

A function approximation example

• P1=[32.7 43.3 19 5;• 2.3 84.7 11 2;• 0.9 86.1 10 3;• 4.7 83.8 10.5 1;• 42.5 34.3 16.8 6;• 1.1 85.9 11 2;• 5.88 68.7 22.5 3;• 47.6 31.7 11.7 9;• 9.3 61.2 25.5 4;• 13.8 75.6 9.6 1;• 0.3 74.5 23.2 2;

• 0.3 90.9 7.8 1;• 0.3 87.9 10.8 1;• 1.5 91.7 6.3 0.5;• 34.9 28.5 27.6 9;• 8.4 82.7 6.9 2;• 4.5 71 18.5 6;• 3.9 75.9 17.2 3];

target• T1=[0.00025;• 0.009;• 0.009;• 0.025;• 0.00025;• 0.009;• 0.00049;• 0.00009;• 0.00025;• 0.049;• 0.00064;• 0.081;• 0.025;• 0.1;• 0.0000484;• 0.1;• 0.00016;• 0.001];

Initialising the net

• P=P1' T=T1'• net = newff([0 50; 25 95;5 30;0 10],[8 1],

{'logsig' 'logsig'});• Y = sim(net,P)

training

• net.trainParam.epochs = 500;• net.trainParam.goal = 1e-8;• net = train(net,P,T);• save result net• Y = sim(net,P);

testing

• clear• load result % read net from file result.mat

• ptest= [27.5; 44.5; 20; 8]• ytest = sim(net,ptest)•