Introduction to MATLAB

AM 581 Computational Laboratory

Department of Applied Mechanics, IIT Madras

The language of technical computing

MATLAB: technical computing language & interactive environment for

•Algorithm development (writing programs)

•Data visualization (graphs, figures etc)

•Data analysis

•Numerical computations

MATLAB 7.1.lnkClick on the icon

Workspace

Command HistoryCommand window

Path to current directory

To quit type at the prompt

>> exit

or

>> quit

Scalars

(1) Real Numbers (default)

>> 3.1416

(2) Complex Numbers>> 3 + 4*j

>> 3 + 4*i

>> complex(3,4)

• Other Types– strings

>>b = ‘Hello’

– Syms (symbolic expressions)>> syms x alpha real

By default, all computations are in double precisions

>> format long

>> pi

ans =

3.14159265358979

>> format short

>> pi

ans =

3.1416

Arithmetic Operations

• Arithmetic operations (+,-,*,/)>>7/45>>(1+i)*(2+i)

• Exponentiation (^ )>>4^2>>(3+4*j)^2

• Complicated expressions, use parentheses>>((2+3)*3)/10.3

• Multiplication is NOT implicit given parentheses>>3(1+0.7) gives an error

Logical operations

>> a == b, a >= b EQUAL, GREATER OR EQUAL

>> a ~= b, a ~>b NOT EQUAL, NOT GREATER

>> a & b a AND b

>> a | b a OR b

>> a | ~ b a AND NOT b

Answer is either 0 or 1

0 is FALSE

1 is TRUE

Scalar variables• If not assigned, value stored in ans

>>0.5*73

• is the same as>>ans = 0.5*73;

• Once assigned, can use variables >>a=14.5; b=3.7; >>c=a^2-2*b;

• If a variable is not in the environment, an error is returned>>c = A + b gives an error

• variable names are case-sensitive• names must start with a letter

Unlike in Fortran/C, not required to define all variables at the start of the program

Vectors & Matrices

• Row vectors

>> a=[1 2 3 4];

• Column vectors

>> b=[1;2;3;4];

•Matrix (3 x 2)

>> c = [ 1 2*i; 3 4; 5*j 6];

This is equivalent to

>> c = [ 1 2*i;

3 4;

5*j 6];

Vectors & Matrices>> a = linspace(1,10,4)

This is a row vector a = [1 4 7 10 ]

>> b = eye(2)

This is a 2 x 2 identity matrix

>> c = ones(3,4)

>> d = zeros(3,4)

c and d are 3 x 4 matrices whose all elements are unity and zero respectivelyThe general function call is:

var=zeros( M, N);Number of rows Number of columns

Basic matrix operations

• arithmetic operations

>> a+b >> a-b

>> a*b

>> a*inv(b) is the same as

>> a/b

>> size(a) returns the size of matrix a

>> length(a) returns the length if a is a vector

If a is a matrix, this is equivalent to

>> max(size(a))

Matrices a and b should be of equal dimemsions

Element-wise Operations

• All the scalar operators work element-wise also >>t = [1 2 3];

>>f = exp(t);

• is the same as>>f = [exp(1) exp(2) exp(3)];

>> a = [ 1 2; 3 4];

>> a+2

ans =

3 4

5 6

>> a=[1 2;3 4];>> b=[5 6;7 8]; >> c3 = a.*bc3 =

5 1221 32

>> c4 = a./bc4 =

0.2000 0.33330.4286 0.5000

>> size(a)ans =

2 2>> length(b)ans = 2

Matrices a and b should be of equal dimemsions

a = 1 2 b = 5 6

3 4 7 8

Graphics

>> t=linspace(0,10,100);

>> y = sin(pi*t);

>> plot(t,y)

>> y2 =cos(pi*t);

>> hold on

>> plot(t,y2,’r--’)

>>t=0:.01:2*pi;>>polar(t,abs(sin(2*t).*cos(2*t)));

>>t=linspace(0,10,1000);>>y=sin(pi*t);>>z=pi*cos(pi*t);>>plot3(t,y,z);>>xlabel(‘time, t’)>>ylabel(‘displacement’)>>zlabel(‘velocity’)

Plotting a function of two independent variables

z=exp(-x^2-y^2)>> x=linspace(-2,2,10);>> y=linspace(-2,2,20);>> for k1 = 1:length(y)

z(k1,:) = exp(-x.^2-y(k1)^2);end

>> surf(x,y,z)>> xlabel(‘x’)>> ylabel(‘y’)>> zlabel(‘z’)>> size(x) [1 10]>> size(y) [1 20]>> size(z) [20 10]

MATLAB programs (m files)

Script files function files• sequence of MATLAB statements

• Create new functions in addition to already existing MATLAB functions

• Can be called directly in script files

% This is a test program

clear all;

x=-2:0.2:2;

y = -3:0.2:3;

for k1 = 1:length(y)

z(k1,:) = exp(-x.^2+y(k1)^2);

end

figure

surf(x,y,z)

function [mean, stdev] = statistics(x);% returns the mean and standard deviation

n = length(x);mean = sum(x)/n;stdev = sqrt(sum(x-mean).^2)/n;

>> x = rand(1,1000);

>> [mean_x, std_x] = statistics(x);

>> help statistics

returns mean and standard deviation

[out1,out2,…,out_n] = function (arg1,arg2,.., arg_n)

Function files

for <condition>

program

end

for j = 1,100

a(j) = j;

end

if <condition1>program1

elseif <condition2>program2

end

LOOPS

if a > b

c = exp(a-b);

elseif a < b

c = exp(b-a);

else

c = 0;

end

while k < 100

a(k) = exp(-k);

k = k + 1;

end

Writing programs in MATLAB

1. Save the program, for example, as “first.m”

2. Change the working directory to where the program is saved.

3. At the prompt, type

>> first

Some useful commands>> clear c lears the workspace

>> clc clears a cluttered screen

>> cd ../otherdirectory change directory

>> ls displays files in directory

>> who displays variables in workspace

>> whos displays sizes of variables

>> save work.mat saves all the variables in binary

>> load work loads all the variables in workpace

>> more on

>> why Try this !!! Its fun!!!

Demos and online help

Visit the URL www.mathworks.com

academia

tutorial

file exchange

>> demo

>> demo matlab graphics

>> helpwin

>> help plot

>> lookfor plot