Matlab Tut 2c361i

ME310 - Matlab Tutorial

ME 310 Useful Matlab Commands Prepared By : Hakan Mencek (C-206) In this tutorial, some of the useful Matlab commands are listed and basic programming using m-files are explained. Note that it is not possible to list all commands of Matlab. If another function or command is required, help commands listed in Section 2 should be used.

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Basic Commands ˆ clc : clear command window ˆ clear : clear variables and functions from the workspace ˆ ctrl + c : stop the execution of Matlab (press control and c keys simultaneously) ˆ close : close the current figure ˆ whos : list current variables ˆ figure : create a new figure window ˆ % : comment

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Getting Help ˆ F1 : pressing F1 key opens the matlab help interface ˆ help : display help topics in command window. General help topics are listed in Table 1. These keywords are used to list the commonly used functions related to the subjects. Execute help keyword command to see the related functions

Table 1: Help keywords and their descriptions Keyword general ops lang elmat elfun specfun matfun polyfun scribe graph2d graph3d

Description General purpose commands Operators and special characters Programming language constructs Elementary matrices and matrix manipulation Elementary math functions Specialized math functions Matrix functions - numerical linear algebra Interpolation and polynomials Annotation and Plot Editing Two dimensional graphs Three dimensional graphs

ˆ lookfor keyword : search all m-files for keyword ˆ help function : display help for function

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ME310 - Matlab Tutorial

3

Variable Declaration

3.1

Single Variables

ˆ a = 4⇒a=4 ˆ b = cos(0) ⇒ b = 1

3.2

Vectors/Arrays

ˆ a = [1 5 7 8] ⇒ a = 1 5 7 8 ˆ b = 1 :

5⇒b = 1 2 3 4 5

ˆ c = 1 :

0.5 :

3 ⇒ c = 1.0000 1.5000 2.0000 2.5000 3.0000

ˆ linspace(x1,x2,N) : generates N equally spaced points between x1 & x2

Elements of an array variable can be extracted via parantheses ( c(3) = 2.0000 )

3.3

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Matrices

ˆ A = [1 5 ; 7 8] ⇒ A =



1 5 7 8



ˆ linspace(x1,x2,N) : generates N equally spaced points between x1 & x2 ˆ zeros(n,m) : creates n×m matrix of zeros ˆ ones(n,m) : creates n×m matrix of ones ˆ eye(n) : n×n identity matrix ˆ transpose(A) or A’ : transpose of A ˆ inv(A) : inverse of square matrix A ˆ det(A) : determinant of square matrix A ˆ size(A) : display the dimensions of a vector or a matrix

Element extraction from a matrix is similar to vectors. As an example consider the following commands. >> A = [1 2 3 4; 5 6 7 8; 9 10 11 12] A = 1 2 3 4 5 6 7 8 9 10 11 12 >> A(2,3) ans = 7 >> A(:,2) ans = 2 6 1

% 3x4 matrix declaration

% extracting the element of A at the 2nd row and 3rd column

% extracting 2nd column

Note that unlike C language, arrays start from 1 in Matlab Page 2 of 7

ME310 - Matlab Tutorial

10 >> A(3,:) % extracting 3rd row ans = 9 10 11 12 >> A(2:3,3:4) ans = 7 8 11 12

% extracting a sub matrix of A

Matlab software has two different types of arithmetic operations as matrix operations and element by element (array) operations. These two operations are distinguished by period (.) character. C = A * B C = A . *B

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% Matrix multiplication of A and B matrices % C(1,1) = A(1,1)*B(1,1) + A(1,2)*B(2,1) % Element by element multiplication of A and B matrices : % C(1,1) = A(1,1)*B(1,1)

Basic Plotting Commands ˆ plot(x,y) : plot variation of y with respect to y ˆ help plot : displays formatting options for plot function ˆ xlim([x1 x2]) : set the horizontal axis limits to x1, x2 ˆ ylim([y1 y2]) : set the vertical axis limits to y1,y2 ˆ grid : displays grid on the plot ˆ title(),xlabel(), ylabel() : annotate the graph ˆ hold on/off : hold current plot in order to add more graph to this plot

Example Matlab commands are given below to illustrate plot command. t = −pi : 0.05 : pi; % defining the plotting range hold on plot(t,sin(t),'.k') % plotting sin(x) plot(t,cos(t),'−r') % plotting cos(x) hold off xlim([−3 3]); % adjusting x and y limits of the plot ylim([−1.2 1.2]); grid % adding grids to the plot title('Variation of Sin(x) and Cos(x) wrt x'); % adding title to the plot

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Script/Function Development

In Matlab, a convenient way of developing programs is using m-files instead of command window. edit command opens the m-file editor. Scripts or functions can be develop by this editor. Scripts are programs, which do not require any inputs. In addition, they cannot give any output at the end of the program. However, in general, functions need some input parameters and can output some results to

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ME310 - Matlab Tutorial

other programs. Another important difference is that, the variables in scripts are not cleared unless specified by the . On the other hand, declared variables in functions are removed after the termination of the function. In order to define a function following syntax should be used. function [out1,out2,out3] = fun1(input1,input2) ... % 2 input / 3 output function declaration end

This function should be saved in the working directory of Matlab with the function name in order to run properly. Then, fun1 can be called similar to built-in functions in Matlab. It is possible to write more than one functions in an m-file. In this case, the upper function becomes the main function and it can be called from command window. However, the remaining functions below become local functions and cannot be called outside this m-file. function [out1,out2,out3] = fun1(input1,input2) ... % main function end function out4 = fun2(input3) ... % sub−function 1 end function out5 = fun3(input4) ... % sub−function 2 end

Here, main function fun1 can be called from command window and from other m-files. But sub-functions, fun2 & fun3 can only be used in this m-file. fun1 can use these functions and fun2 and fun3 can also call each other. These sub-functions cannot be used by other m-files. Because these functions are cleared once the main function is terminated similar to other local variables in a function. Note that the name of this m-file should be fun1.m in order to run properly.

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Basic Control Flow Commands ˆ for : repeat statements a specific number of times ˆ while : repeat statements until a condition is satisfied ˆ break : terminate the execution of a loop ˆ continue : control to the next iteration of a loop ˆ if : conditionally executes a statement. Conditional operations are listed below

1. == : equal to 2. >, >= : greater than, greater than or equal to 3. <, <= : less than, less than or equal to ˆ elseif : executes a statement if a previous IF condition is failed and necessary condition is satisfied ˆ else : execute a statement if a previous IF condition is not satisfied

Example usage of for loop with if structure is given below.

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ME310 - Matlab Tutorial

for i=1:1:10 if i ≥ 5 b = −1*i; elseif i==2 b=20; else b=i; end b end

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% this loop is executed for values of i from 1 to 10 % if condition, satisfied for values of i greater than or equal to 5 % elseif condition, satisfied if i is equal to 2 % else statement, if other conditions are failed, the statements % in else block are executed % print b to the command window

Input / Output Functions

7.1

Reading from and Writing to Command Window

ˆ input : ask for a input % Asks for input and assign the given value to variable a >> a = input(['Please enter a number : ']) Please enter a number : 5.5 a = 5.5000

ˆ disp : display a string in the command window % script a = input('Enter a number to calculate its square root: '); b = sqrt(a); disp(['the square root of ' num2str(a) ' is ' num2str(b)]); % output Enter a number to calculate its square root: 20 the square root of 20 is 4.4721

Note that, in order to display a numerical variable using disp command, this number should be converted to a ‘string’. This conversion be performed by num2str() function.

7.2

Reading from and Writing to a File

ˆ FID = fopen(filename,permission) : Open a file from a specified directory with given permission and assign it to a file ID.

Table 2: File opening permissions Permission ‘r’ ‘w’ ‘a’

Description read write (create if necessary) append (create if necessary)

ˆ fclose(FID) : Close the file assigned to FID ˆ fprintf(FID,’...’,var1,var2) : Write to a file Page 5 of 7

ME310 - Matlab Tutorial

ˆ textscan(FID,’...’) : Read data from a file

Example usage of these I/O functions is shown below. % Opening input and output files. Note that these files must be % in the working directory of Matlab. Otherwise full path should be defined % e.g. : input file = fopen('D/temp/input.txt','r'); input file = fopen('input.txt','r'); output file = fopen('output.txt','w'); % reading data from the input file data = textscan(input file,'%f %f %f'); column1 = data{1}; % Notice that these paranthesis are different !!! column2 = data{2}; column3 = data{3}; % writing to the output file fprintf(output file,' col 1 \t

col 2 \t col 3');

for i = 1:size(column1,1) % here arrays are printed to the file using a for loop. it is possible to % directly write an array or a matrix. check help document of fprintf function fprintf(output file,'\n %f \t %.2f \t %.4f',column1(i),column2(i),column3(i)); end % closing files fclose(input file); fclose(output file);

Necessary input file and the resulting output file input file 0.8147 0.9058 0.1270 0.9134 0.6324

: 0.0975 0.2785 0.5469 0.9575 0.9649

0.1576 0.9706 0.9572 0.4854 0.8003

output file: col 1 col 2 0.814700 0.10 0.905800 0.28 0.127000 0.55 0.913400 0.96 0.632400 0.96

col 3 0.1576 0.9706 0.9572 0.4854 0.8003

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Other Useful Commands ˆ inline : used to define a function quickly >> g = inline('xˆ2+3*x+5') g = Inline function: g(x) = xˆ2+3*x+5 >> g(3) ans = 23

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ME310 - Matlab Tutorial

ˆ eval(’string’) : evaluate the string as a Matlab expression >> s = 'a = 1:0.5:2'; >> eval(s) a = 1.0000 1.5000

% here s is a string variable

2.0000

% effective use of eval function to generate variable names for i = 1:3 eval(['M' num2str(i) ' = i']) end % the for loop above generates 3 variables M1,M2 and M3 with respective values M1 = 1 M2 = 2 M3 = 3

ˆ ezplot(’function’,[xmin xmax] : simple function plotting command % plots f(x) = xˆ2 −2*x +1 wrt. x changing from −10 to 10 ezplot('xˆ2 − 2*x + 1',[−10 10])

ˆ tic/toc : measure elapsed time between them. Write tic at the beginning of a script and toc at the end to measure the execution time of the script.

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