Introduction to MATLAB

Transcription

1 Introduction to MATLAB The language of technical computing AM 581 Computational Laboratory Department of Applied Mechanics, IIT Madras

2 MATLAB: technical computing language & interactive environment for Algorithm development (writing programs) Data visualization (graphs, figures etc) Data analysis Numerical computations Click on the icon MATLAB 7.1.lnk

3 Workspace Path to current directory To quit type at the prompt >> exit or >> quit Command History Command window

4 Scalars (1) Real Numbers (default) >> (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 = >> format short >> pi ans =

5 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

6 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

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

8 Vectors & Matrices Row vectors >> a=[ ]; 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];

9 Vectors & Matrices >> a = linspace(1,10,4) This is a row vector a = [ ] >> 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 respectively The general function call is: var=zeros(m,n); Number of rows Number of columns

10 Basic matrix operations arithmetic operations >> a+b >> a-b >> a*b Matrices a and b should be of equal dimemsions >> 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))

11 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 =

12 >> a=[1 2;3 4]; >> b=[5 6;7 8]; >> c3 = a.*b c3 = >> c4 = a./b c4 = >> size(a) ans = 2 2 >> length(b) ans = 2 a = 1 2 b = Matrices a and b should be of equal dimemsions

13 Graphics >> t=linspace(0,10,100); >> y = sin(pi*t); >> plot(t,y) >> y2 =cos(pi*t); >> hold on >> plot(t,y2, r-- )

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

15 >>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 )

16 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]

17 MATLAB programs (m files) Script files sequence of MATLAB statements % 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 files Create new functions in addition to already existing MATLAB functions Can be called directly in script files

18 Function files [out1,out2,,out_n] = function (arg1,arg2,.., arg_n) 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

19 for for j <condition> = 1,100 program a(j) = j; end end LOOPS if <condition1> a > b program1 c = exp(a-b); elseif <condition2> elseif program2a < b endc = exp(b-a); else c = 0; end while k < 100 a(k) = exp(-k); k = k + 1; end

20 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

21 Some useful commands >> clear clears 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!!!

22 Demos and online help Visit the URL academia tutorial file exchange >> demo >> demo matlab graphics >> helpwin >> help plot >> lookfor plot