MatLAB Lesson 7 : M-file Programming I

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The Hong Kong Polytechnic UniversityIndustrial Centre

MatLABLesson 7 : M-file Programming I

Edward Cheung

email: icec@polyu.edu.hk

Room W311g

2008

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Types of M-file

• Script M-file doesn’t accept input argument No return output argument Operates on data in the workspace only Useful for the automation of a series of commands that

frequently needed – like macro

• Function M-files Accept input argument and provide output return argument Internal variables are local by default Useful for building function

• Can be include in search path

• fileSet path or >> pathtool

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Example of Script File

%script M-file%This program shows how to create a script filestart_th=0;end_th=2*pi;th=start_th:.1:end_th;x=sin(th);y=cos(th);plot(x,y);axis equaltitle('Sine vs. Cosine','fontsize',18)xlabel('Sine','fontsize',16)ylabel('Cosine','fontsize',16)

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Example of Script File (cont.)

>> save file as script_test.m>> script_test % run script file

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Functions

• Types of functions Built-in function User-defined function

• Function files are created and edited like script files using the editor/debugger window

• fileNewM-file

• First line must be the function’s definition

• Syntax:- function [output_arg]=fun_name (input_arg) [] is not required for single output argument

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Variables

• Local The arguments and variables are valid for the function file

only

• Global We can make a variable recognized in different function

files by using >>global=variable_name

• All the variables in a function file are local

• Good practice is to minimize the use of global variable to avoid conflict with other programmes sharing the environment.

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Example of Functions in Modular Arithmetic

Remainder & Modular Functions >> mod(38,3)ans = 2>> rem(38,3)ans = 2>> rem(38,-3) % rem (x,y) has the same sign as x (36/3)

ans = 2>> mod(38,-3) %mod(x,y) has the same sign as y (39/3)

ans = -1> which modC:\matlab12\toolbox\matlab\elfun\mod.m

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Creating Function M-files

• Must start with a function declaration in first line• Function output=my_function(x)• % suppose we want to create a function to calculate sine

square.• Enter the following in a new m-file and save the file as

sin_square.mfunction x=sin_square(y)x=sin(y)*sin(y)

>> which sin_square %function exist?>> type sin_square %type to screen if needed

>> sin_square(pi/8) %use function>> u=sin_square(pi/8)u = 0.1464

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Application Example: Determine Triangle Area

)(For

))()((

)(2

1

bac

csbsassArea

cbas

• There are different methods to calculate the area of a triangle depending on known parameters

• The Huron formula (Greek 1st century) can be used if the sides of the triangle are known

• where

s= semiperimeter

Area=area of ABC

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Example on Function with More Variables% Calculates Area of a Triangle % Huron Formula :Input 3 sides% Usage: triangle_area(a,b,c)% area=triangle_area(a,b,c)% Example:- % triangle_area(3,4,5)% Area=triangle_area(6,8,10)function x=triangle_area(a,b,c)s=1/2*(a+b+c);x=sqrt(s*(s-a)*(s-b)*(s-c));

You can get help by >>help triangle_area

% print comments after the function declaration

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In-line Functions

• Use when a simple function is needed for many times within a programme

• Reside in the same programme file• Name=inline(‘expression’,’arg1’,’arg2’…)• Create an inline object based on character string

Example:>> sin2_cos2=inline('sin(x)^2+cos(y)^2','x','y')sin2_cos2 = Inline function: sin2_cos2(x,y) = sin(x)^2+cos(y)^2>> which sin2_cos2sin2_cos2 is a variable.>> u=sin2_cos2(pi/2,pi/2)u = 1

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Anonymous Function & Function Handle

• User can define a function at the command line or in M-file using a file handle without an associated file. It is available after MatLab v.6. A function handle is a data type in MatLab containing all the

information for referencing a function. Created by using the @ operator or the str2func function

• Syntax:- handle = @(arglist)anonymous_function

For example, to create a square anonymous function,

y = x2

>> y=@(x)x^2; >> y(4) ans = 16

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Example of Two Variables Anonymous Function

g=@(x,y) (x.^2 + y.^2);ezsurf(g);shading flat;title('f(x,y)=x^2+y^2');

-5

0

5

-5

0

5

0

20

40

60

80

x

f(x,y)=x2+y2

y

• Use function handle to pass function into function for new applications as it is more efficient than string operations. Use inline function if MatLab flags an error.

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Flow Control

• There are 4 flow control statements in MatLab

• If statement

• Switch statement

• While loops

• For loops

• The if statement and the while loops use relational or logical operation to determine programme flow

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Loops

• For loop Use when the number of passes are known ahead of time

• While loop Use when the loop must terminate when a specific condition

is met.

• Automatic indentation is available on the editor/debugger when pressing the enter key until an end statement is reached.

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Relational Operators

Relational Operators Meaning

< Less than

<= Less than or equal

> Greater than

>= Greater than or equal

== Equal to

~= Not equal to

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Example on Relational Operator

Example 1:a=[1 2 4 6 2];b=[2 1 4 5 2];a== b % check if a equals ba>b % check if a greater than b

Example 2:x=1:5;y=4; % y is a scaler x<y % ans is a vectorans = 1 1 1 0 0

• For a comparison to be true for an entire matrix, every element must be true(i.e. all equals to 1).

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Find

• find searches a matrix and identifies which elements in that matrix meet certain criterion.>> x =[7 14 21 28 35]>> find(x>20) % get index of elementans = 3 4 5>> z=find(x>21) % save indices into zz = 4 5

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Example on using find

% ex_find1% Given a matrix x, find & print all elements

with x>50.%x=[20 30 40;89 9 88;33 90 54];disp('Given a matrix x=')disp(x)element=find(x>50);[row,col]=find(x>50);disp('Element in matrix x with value greater than

50 are as follows:-')fprintf('x(%d,%d)=%d\n',[row,col,x(element)]')

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Logical Operators

Logical Operator Meaning

~ Not

& And

| Or

Xor Exclusive or

•Logical operator works element-wise on matrices

•Boolean operation: 1=true and 0=false

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Truth Table

Input Not And Or Xor

x y ~x x&y x|y xor(x,y)

0 0 1 0 0 0

0 1 1 0 1 1

1 0 0 0 1 1

1 1 0 1 1 0

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The if & if/else Structure

• The if statement evaluates a logical expression and executes a group of statement when the expression is trueIf condition

StatementsEnd

• The if/else allows user to execute a series of statement if a condition is true and to skip to the else if the condition is false. Example:-

x=input('x=')if x>0 y=log(x)else disp('input must be positive')end

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The elseif Structure

• The elseif structure allows user to check multiple criteria while keeping the code easy to read.

• For example:-If age<11 disp(‘You cannot get any ID card’)elseif age<17 disp(‘You may have a children ID card’)else age>21 disp(‘You may have a adult ID card’)End

• In this example, the programme steps thru the structure until it find a true statement, execute & exit or until it encounters the else

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Example on Function with Logic Control% Calculates Area of a Triangle % Huron Formula :Input 3 sides% Usage: triangle_area(a,b,c)% area=triangle_area(a,b,c)% Example:- % triangle_area(3,4,5)% Area=triangle_area(6,8,10)function x=triangle_area(a,b,c)if a<0|b<0|c<0 error('Input a,b,c must be positive')elseif (a+b)<c|(a+c)<b|(b+c)<a warning('The sum of any two sides must be greater

than the third side')else s=1/2*(a+b+c); x=sqrt(s*(s-a)*(s-b)*(s-c));End% Save as triangle_area1.m and try (a,b,c) = (1,1,2.1)

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Array Indexing - Use an Array as an Index to an Array

• MATLAB supports a type of array indexing that uses one array as the index into another array.

• Example:- Array B indexes into elements 1, 3, 6, 7, and 10 of array A.A = 5:5:50A = 5 10 15 20 25 30 35 40 45 50

B = [1 3 6 7 10];

A(B) % syntax of Array Indexingans = 5 15 30 35 50

Hence, the numeric values of array B designate the intended elements of A.

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Array Indexing – Logical Indexing

A Simple Example on logic operations:->> q=1; r=2;>> q>r>> q<r

• We can use this logic operation in matrix for element selection. Logical indexing designates array elements of a matrix based on their position in an indexing array. This is a logical masking operation. True element in the indexing array is being used as a positional index.

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Example on Logical Indexing

• Example:- Eliminate elements for A>0.5. Creates logical array B that satisfies the condition A > 0.5,

and uses the positions of ones in B to index A. This is known as logical indexing:

Steps:-A = rand(3) B = A > 0.5 % set elements of B to 1 ifA(B) = 0

• The following is a short-hand logical indexing expression:-A(A > 0.5) = 0

• We can test if B is logical using islogic(B)

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Debugger

• Environment is created when functions are invoked and returned; variables are generated, modified and destroyed.

• We can check the programme state using a debugger.

• Debugger in MatLab available in two interfaces; command line interface (CLI) and graphical user interface (GUI)

• Using the debugger typically involved the following:- Set one or more breakpoints where the debugger will stop

execution• Breakpoint can be line number or a condition such as stop on

error, warning, etc.

Execute the programme and when the programme stops, you can examine the environment and troubleshoot your programme

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Example on the use of debugger

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Debugging

• When MATLAB reaches a breakpoint, it enters debug mode. The prompt changes to a K>> and, on the PC, the debugger window becomes active.

• All MATLAB commands are allowed at the prompt.

• To resume M-file function execution, use DBCONT or DBSTEP. To exit from the debugger, use DBQUIT.

• For example: to clear and set breakpoint at line 8 dbstop in ex_sumprimes at 8 dbclear in ex_sumprimes at 8

• Others: help debug

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Hints on Exercise 6.3

• Generate 4 spheres using sphere function from MatLab

• Cut the spheres

• Commands that you may needed:-

>> sphere

>> hold on

>> colormap(winter)

>> camlight

>> lighting phong

>> axis equal

220

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20 rzzyyxx

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Plottools, Property Editor & Inspector

>> a=randn(1000,2);hist(a)>> propedit % or from Desktop Menu>> inspect % bring up inspector>> propertyeditor % see desktop menu