matlab tutorial fundamental programming

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Prepared by: Khairul Anuar Ishak

Department of Electrical, Electronic & System Engineering Faculty of Engineering

Universiti Kebangsaan Malaysia

Produced with a Trial Version of PDF Annotator - www.PDFAnnotator.com

MATLAB tutorial of fundamental programming

i

Preface

This tutorial introduces the fundamental ideas for programming in MATLAB. The objective

is to help you at solving the kinds of mathematical problems that you will likely encounter as an

engineering student, as well as a researcher. It requires no prior knowledge of MATLAB or

programming experience but if you have a strong background in mathematics and computer

programming then you can quickly learn how MATLAB can help you with your course work

and design projects. However, for those of you who are just starting out learning MATLAB, then

this tutorial is for you.

Remember, it is assumed throughout all chapters that you are following along, using MATLAB

and entering all commands shown. The questions and answers of the exercises, will be given

during the workshop went off.

On completion of the workshop, participants should be able to:

• Use MATLAB to solve certain mathematical problems.

• Produce a simple MATLAB program files (m-files).

• Use MATLAB effectively and also being ready to explore more of MATLAB on your

own.

Enjoy the MATLAB! ;-)

Notes: You can e-mail me if you have any problems or corrections about these pieces of code, or

if you would like to add your own tips to those described in this document.

Khairul Anuar Ishak

e-mail: [email protected]

Produced with a Trial Version of PDF Annotator - www.PDFAnnotator.com

MATLAB tutorial of fundamental programming

ii

Contents

1 Introduction to MATLAB 1

What is MATLAB? 1

MATLAB System 2

The Advantages of MATLAB 2

Disadvantages of MATLAB 3

2 Getting Started 4

Starting MATLAB 4

Ending a Session 8

3 MATLAB Basics 9

Variables and Arrays 9

Arithmetic Operations 14

Common MATLAB Functions 16

4 Plotting and Visualization 17

Plotting in MATLAB 17

Images in MATLAB 24

5 Programming 25

Data Types 25

M-File Programming 27

Flow Control 30

CHAPTER 1: Introduction to MATLAB

1

What is MATLAB?

CHAPTER 1

Introduction to MATLAB

What is MATLAB?

MATLAB (short for MATrix LABoratory) is a special-purpose computer program optimized to perform engineering and scientific calculations. It is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation. Typical uses include:

Math and computation Algorithm development Modelling, simulation and prototyping Data analysis, exploration and visualization Scientific and engineering graphics Application development, including Graphical User Interface (GUI) building

MATLAB is an interactive system whose basic data element is an array that does not require dimensioning. This allows you to solve many technical computing problems, especially those with matrix and vector formulations, in a fraction of the time it would take to write a program in a scalar non-interactive language such as C, C++ or Fortran.

MATLAB has evolved over a period of years with input from many users. In university environments, it is the standard instructional tool for introductory and advanced courses in mathematics, engineering and science. In industry, MATLAB is the tool of choice for high-productivity research, development and analysis.

MATLAB features a family of application-specific solution called Toolboxes. Very important to most users of MATLAB, toolboxes allow you to learn and apply specialized technology. Toolboxes are comprehensive collections of MATLAB function (m-files) that extend the MATLAB environment to solve particular classes of problems. Areas in which toolboxes are available include signal processing, control systems, neural networks, fuzzy logic, wavelets, image processing, simulation and many others.


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MATLAB System

MATLAB System The MATLAB system consists of five main parts:

1. The MATLAB language. This is a high-level matrix/array language with control flow statements, functions, data structures, input/output, and object-oriented programming features. It allows both “programming in the small” to rapidly create quick and dirty throw-away programs, and “programming in the large” to create complete large and complex application programs.

2. The MATLAB working environment. This is the set of tools and facilities that you work with as the MATLAB user or programmer. It includes facilities for managing the variables in your workspace and importing and exporting data. It also includes tools for developing, managing, debugging, and profiling M-files, MATLAB’s applications.

3. Handle Graphics. This is the MATLAB graphics system. It includes high-level commands for two-dimensional and three-dimensional data visualization, image processing, animation, and presentation graphics. It also includes low-level commands that allow you to fully customize the appearance of graphics as well as to build complete Graphical User Interfaces on your MATLAB applications.

4. The MATLAB mathematical function library. This is a vast collection of computational algorithms ranging from elementary functions like sum, sine, cosine, and complex arithmetic, to more sophisticated functions like matrix inverse, matrix eigenvalues, Bessel functions, and fast Fourier transforms.

5. The MATLAB Application Program Interface (API). This is a library that allows you to write C and Fortran programs that interact with MATLAB. It include facilities for calling routines from MATLAB (dynamic linking), calling MATLAB as a computational engine, and for reading and writing MAT-files.

The Advantages of MATLAB

MATLAB has many advantages compared to conventional computer languages for technical problem solving. Among them are:

1. Ease of Use. MATLAB is an interpreted language. Program may be easily written and modified with the built-in integrated development environment and debugged with the MATLAB debugger. Because the language is so easy to use, it is ideal for the rapid prototyping of new programs.

2. Platform Independence. MATLAB is supported on many different computer systems, providing a large measure of platform independence. At the time of this writing, the language is supported on Windows NT/2000/XP, Linux, several versions of UNIX and the Macintosh.

3. Predefined Function. MATLAB comes complete with an extensive library of predefined functions that provide tested and pre-packaged solutions to many basic technical tasks. For examples, the arithmetic mean, standard deviation, median, etc. these and hundreds of other functions are built right into the MATLAB language, making your job much easier. In addition to the large library of function built into the basic MATLAB language,


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Disadvantages of MATLAB

there are many special-purpose toolboxes available to help solve complex problems in specific areas. There is also an extensive collection of free user-contributed MATLAB programs that are shared through the MATLAB Web site.

4. Device-Independent Plotting. Unlike most other computer languages, MATLAB has many integral plotting and imaging commands. The plots and images can be displayed on any graphical output device supported by the computer on which MATLAB is running.

5. Graphical User Interface. MATLAB includes tools that allow a programmer to interactively construct a graphical user interface, (GUI) for his or her program. With this capability, the programmer can design sophisticated data-analysis programs that can be operated by relatively inexperienced users.

6. MATLAB Compiler. MATLAB’s flexibility and platform independence is achieved by compiling MATLAB programs into a device-independent p-code, and then interpreting the p-code instructions at runtime. Unfortunately, the resulting programs can sometimes execute slowly because the MATLAB code is interpreted rather than compiled.

Disadvantages of MATLAB

MATLAB has two principal disadvantages. The first is that it is an interpreted language and therefore can execute more slowly than compiled languages. This problem can be mitigated by properly structuring the MATLAB program, and by the use of the MATLAB compiler to compile the final MATLAB program before distribution and general use.

The second disadvantage is cost: a full copy of MATLAB is five to ten times more expensive

than a conventional C or Fortran compiler. This relatively high cost is more than offset by then reduced time required for an engineer or scientist to create a working program, so MATLAB is cost-effective for businesses. However, it is too expensive for most individuals to consider purchasing. Fortunately, there is also an inexpensive Student Edition of MATLAB, which is a great tool for students wishing to learn the language. The Student Edition of MATLAB is essentially identical to the full edition.

CHAPTER 2: Getting Started

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Starting MATLAB

CHAPTER 2

Getting Started

Starting MATLAB

You can start MATLAB by double-clicking on the MATLAB icon or invoking the application from the Start menu of Windows. The main MATLAB window, called the MATLAB Desktop, will then pop-up and it will look like this:

Figure 2.1: The Default MATLAB desktop

When MATLAB executes, it can display several types of windows that accept commands or display information. It integrates many tools for managing files, variables and applications within the MATLAB environment. The major tools within or accessible from the MATLAB desktop are:

1. The Current Directory Browser 2. The Workspace Window 3. The Command Window 4. The Command History Window 5. The Start Button 6. The Help Window


5

Starting MATLAB

If desired, this arrangement can be modified by selecting an alternate choice from [View] [Desktop Layout]. By default, most MATLAB tools are “docked” to the desktop, so that they appear inside the desktop window. However, you can choose to “undock” any or all tools, making them appear in windows separate from the desktop. The Command Window

Figure 2.2: The Command Window

The Command Window is where the command line prompt for interactive commands is located. Once started, you will notice that inside the MATLAB command window is the text:

To get started, select “MATLAB Help” from the Help menu. >>

Click in the command window to make it active. When a window becomes active, its titlebar darkens. The “>>” is called the Command Prompt, and there will be a blinking cursor right after it waiting for you to type something. You can enter interactive commands at the command prompt (>>) and they will be executed on the spot.

As an example, let’s enter a simple MATLAB command, which is the date command. Click

the mouse where the blinking cursor is and then type date and press the ENTER key. MATLAB should then return something like this:

>> date ans = 01-Sep-2006

Where the current date should be returned to you instead of 01-Sep-2006. Congratulation!

You have just successfully executed your first MATLAB command!


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Starting MATLAB

The Command History Window

Figure 2.3: The Command History Window

The Command History Window, contains a log of commands that have been executed within the command window. This is a convenient feature for tracking when developing or debugging programs or to confirm that commands were executed in a particular sequence during a multi-step calculation from the command line. The Current Directory Browser

Figure 2.4: The Directory Browser

The Current Directory Browser displays a current directory with a listing of its contents. There is navigation capability for resetting the current directory to any directory among those set in the path. This window is useful for finding the location of particular files and scripts so that they can be edited, moved, renamed or deleted. The default directory is the Work subdirectory of the original MATLAB installation directory.


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Starting MATLAB

The Workspace Window

Figure 2.5: The Workspace Window The Workspace Window provides an inventory of all the items in the workspace that are

currently defined, either by assignment or calculation in the Command Window or by importing with a load or similar command from the MATLAB command line prompt. These items consist of the set of arrays whose elements are variables or constants and which have been constructed or loaded during the current MATLAB session and have remained stored in memory. Those which have been cleared and no longer are in memory will not be included. The Workspace Window shows the name of each variable, its value, its array size, its size in bytes, and the class. Values of a variable or constant can be edited in an Array Editor which is launched by double clicking its icon in the Workspace Window. The Help Window

Figure 2.6: The Help Window


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You can access the online help in one of several ways. Typing help at the command prompt will reveal a long list of topics on which help is available. Just to illustrate, try typing help general. Now you see a long list of “general purpose” MATLAB commands. In addition, you can also get help on the certain command. For example, date command. The output of help also refers to other functions that are related. In this example the help also tells you, See also NOW, CLOCK, DATENUM. You can now get help on these functions using the three different commands as well.

Ending a Session

>> help date DATE Current date as date string. S = DATE returns a string containing the date in dd-mmm-yyyy format. See also NOW, CLOCK, DATENUM.

There is a much more user-friendly way to access the online help, namely via the MATLAB

Help Browser. Separate from the main desktop layout is a Help desktop with its own layout. This utility can be launched by selecting [Help] [MATLAB Help] from the Help pull down menu. This Help desktop has a right side which contains links to help with functions, help with graphics, and tutorial type documentation. The Start Button

The Start Button (see figure 2.1) allows a user to access MATLAB tools, desktop tools, help files, etc. it works just like the Start button on a Windows desktop. To start a particular tool, just click on the Start Button and select the tool from the appropriate sub-menu.

Interrupting Calculations If MATLAB is hung up in a calculation, or is just taking too long to perform an operation,

you can usually abort it by typing [CTRL + C] (that is, hold down the key labeled CTRL, and press C).

Ending a Session One final note, when you are all done with your MATLAB session you need to exit

MATLAB. To exit MATLAB, simply type quit or exit at the prompt. You can also click on the special symbol that closes your windows (usually an × in the upper right-hand corner). Another way to exit is by selecting [File] [Exit MATLAB]. Before you exit MATLAB, you should be sure to save any variables, print any graphics or other files you need, and in general clean up after yourself.

CHAPTER 3: MATLAB Basics

9

Variables and Arrays

CHAPTER 3

MATLAB Basics


The fundamental unit of data in any MATLAB program is the array. An array is a collection of data values organized into rows and columns and known by a single name. Individual data values within an array are accessed by including the name of the array followed by subscripts in parentheses that identify the row and column of the particular value. Even scalars are treated as arrays by MATLAB – they are simply arrays with only one row and one column. There are three fundamental concepts in MATLAB, and in linear algebra, are scalars, vectors and matrices.

1. A scalar is simply just a fancy word for a number (a single value). 2. A vector is an ordered list of numbers (one-dimensional). In MATLAB they can be

represented as a row-vector or a column-vector. 3. A matrix is a rectangular array of numbers (multi-dimensional). In MATLAB, a two-

dimensional matrix is defined by its number of rows and columns.

This is a scalar, containing 1 element 10=a

[ ]4321=b

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

321

c

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

987654321

d

This is a 1×4 array containing 4 elements, known as a row vector

This is a 3×1 array containing 3 elements, known as a column vector

This is a 3×3 matrix, containing 9 elements

In MATLAB matricies are defined inside a pair of square braces ([]). Punctuation marks of a

comma (,), and semicolon (;) are used as a row separator and column separator, respectfully. You can also use a space as a row separator, and a carriage return (the ENTER key) as a column separator as well.


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UExamples 3.1 Below are examples of how a scalar, vector and matrix can be created in MATLAB. >> my_scalar = 3.1415 my_scalar = 3.1415

>> my_vector1 = [1, 5, 7] my_vector1 = 1 5 7

>> my_vector2 = [1; 5; 7] my_vector2 = 1 5 7

>> my_vector2 = [1 5 7] my_vector2 = 1 5 7

>> my_matrix = [8 12 19; 7 3 2; 12 4 23; 8 1 1] my_matrix = 8 12 19 7 3 2 12 4 23 8 1 1

>> my_vector1 = [1 5 7] my_vector1 = 1 5 7

Indexing into an Array Once a vector or a matrix is created you might needed to extract only a subset of the data, and this is done through indexing.

Row 1

Row 2

Col 1 Col 2 Col 3

A 2-by-3 Matrix

Figure 3.1: An array is a collection of data values organized into rows and columns


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Individual elements in an array are addressed by the array name followed by the row and column of the particular element. If the array is a row or column vector, then only one subscript is required. For example, according to the example 3.1:

o my_vector2(2) is 5 o my_matrix(3,2) is 4 or my_matrix(7) is 4

The Colon Operator

The colon (:) is one of MATLAB’s most important operators. It occurs in several different forms. UExamples 3.2

1. To create an incremental or a decrement vector

>> my_inc_vec1 = [1:7] my_inc_vec1 = [ 1 2 3 4 5 6 7]

>> my_inc_vec2 = [1:2:7] my_inc_vec2 = [ 1 3 5 7]

>> my_dec_vec = [5:-2:1] my_dec_vec = [ 5 3 1]

2. To refer portions of a matrix/vector >> my_matrix = [8 12 19; 7 3 2; 12 4 23; 8 1 1] my_matrix = 8 12 19 7 3 2 12 4 23 8 1 1 >> new_matrix1 = my_matrix(1:3,2:3) new_matrix1 = 12 19 3 2 4 23 >> new_matrix2 = my_matrix(2:4,:) new_matrix2 = 12 4 23 8 1 1

∗ NOTES: If the colon is used by itself within subscript, it refers to all the elements in a row or column of a matrix!


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Concatenating Matrices

Matrix concatenation is the process of joining one or more matrices to make a new matrix. The expression C = [A B] horizontally concatenates matrices A and B. The expression C = [A; B] vertically concatenates them. UExamples 3.3 Reshaping a Matrix

Here are a few examples to illustrate some of the ways you can reshape matrices. UExamples 3.4 Reshape 3-by-4 matrix A to have dimensions 2-by-6.

>> A = [8 19; 7 2]; >> B = [1 64; 4 5; 3 78]; >> C = [A; B] C = 8 19 7 2 1 64 4 5 3 78

>> A = [1 4 7 10; 2 5 8 11; 3 6 9 12] A = 1 4 7 10 2 5 8 11 3 6 9 12 >> B = reshape(A, 2, 6) B = 1 3 5 7 9 11 2 4 6 8 10 12


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UExamples 3.5 Transpose A so that the row elements become columns or vice versa. You can use either the transpose function or the transpose operator (’). To do this:

>> A = [1 4 7 10; 2 5 8 11; 3 6 9 12]; >> B = A’ B = 1 2 3 4 5 6 7 8 9 10 11 12

General Function for Matrix and Vector

There are many MATLAB features which cannot be included in these introductory notes. Listed below are some of the MATLAB functions regard to matrix and vector. Basic Vector Function

MATLAB includes a number of built-in functions that you can use to determine a number of characteristics of a vector. The following are the most commonly used such functions. size Returns the dimensions of a matrix length Returns the number of elements in a matrix min Returns the minimum value contained in a matrix max Returns the maximum value contained in a matrix sum Returns the sum of the elements in a matrix sort Returns the sorted elements in a matrix abs Returns the absolute value of the elements in a matrix UExamples 3.6 The following example demonstrates the use some of these functions. >> mnA = min(A)

mnA = 1 >> mxA = max(A) mxA = 4

>> sumA = sum(A) sumA = 10

>> stA = sort(A) stA = 1 2 3 4

>> A = [3 1 2 4]; >> szA = size(A) szA = 1 4

>> lenA = length(A) lenA = 4


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Arithmetic Operations

Functions to Create a Matrix This following section summarizes the principal functions used in creating and handling matrices. Most of these functions work on multi-dimensional arrays as well. diag Create a diagonal matrix from a vector cat Concatenate matrices along the specified dimension ones Create a matrix of all ones zeros Create a matrix of all zeros rand Create a matrix of uniformly distributed random numbers repmat Create a new matrix by replicating or tiling another UExamples 3.7 The following example demonstrates the use some of these functions.

Arithmetic Operations MATLAB can be used to evaluate simple and complex mathematical expressions. When we

move from scalars to vectors (and matrices), some confusion arises when performing arithmetic operations because we can perform some operations either on an element-by-element (array operation) or matrices as whole entities (matrix operation). Expressions use familiar arithmetic operators: Array Operators Operation MATLAB Form Comments Addition A + B Array addition is identical Subtraction A - B Array subtraction is identical Multiplication A .* B Element-by-element multiplication of A and B. Both

arrays must be the same shape, or one of them must be a scalar

Division A ./ B Element-by-element division of A and B. Both arrays must be the same shape, or one of them must be a scalar

>> C = rand(4,3) C = 0.9501 0.8913 0.8214 0.2311 0.7621 0.4447 0.6068 0.4565 0.6154 0.4860 0.0185 0.7919

>> A = zeros(2,4) A = 0 0 0 0

0 0 0 0 >> B = 7*ones(1,3) B = 7 7 7


15

Arithmetic Operations

Power A .^ B Element-by-element exponentiation of A and B. Both arrays must be the same shape, or one of them must be a scalar

UExamples 3.8 The following example demonstrates the use some of these operations. Matrix Operators Operation MATLAB Form Comments Addition A + B Array addition is identical Subtraction A - B Array subtraction is identical Multiplication A * B Matrix multiplication of A and B. The number of

columns in A must equal the number of rows in B. Division A / B Matrix division defined by A * inv(B), where

inv(B) is the inverse of matrix B. Power A ^ B Matrix exponentiation of A and B. The power is

computed by repeated squaring UExamples 3.9

>> A = [1 4 7 10; 2 5 8 11; 3 6 9 12] A = 1 4 7 10 2 5 8 11 3 6 9 12 >> B = [1 2 3 4; 5 6 7 8; 9 10 11 12] B = 1 2 3 4 5 6 7 8 9 10 11 12 >> C = A.*B C = 1 8 21 40 10 30 56 88 27 60 99 144

>> A = [1 2 3 4]; >> B = A.^2 B = 1 4 9 16

>> A = [ 2 4 ; 8 10] A = 2 4 8 10 >> B = [2 4; 2 5] B = 2 4 2 5 >> C = A./B C = 1 1 4 2

>> A = [ 2 4 ; 8 10]; >> B = [2 4; 2 5]; >> C = A*B C = 12 28 36 82

>> A = [ 2 4 ; 8 10]; >> B = [2 4; 2 5]; >> C = B*A C = 36 48

44 58


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Common MATLAB Functions

Built-in Variables

MATLAB uses a small number of names for built-in variables. An example is the ans variable, which is automatically created whenever a mathematical expression is not assigned to another variable. Table below lists the built-in variables and their meanings. Although you can reassign the values of these built-in variables, it is not a good idea to do so, because they are used by the built-in functions. Variable Meaning

ans Value of an expression when that expression is not assigned to a variable eps Floating-point precision i,j Unit imaginary number, i = j = 1− pi π , 3.14159265 …

realmax Largest positive floating-point number realmin Smallest positive floating-point number Inf

∞, a number larger than realmax, the result of evaluating 01

NaN Not a number, (e.g., the result of evaluating

00

UExamples 3.10

>> x = 0; >> 5/x Warning: Divide by zero ans = Inf

>> x = 0; >> x/x Warning: Divide by zero ans = NaN

Common MATLAB Functions A few of the most common and useful MATLAB functions are shown in table below. These

functions will be used in many times. It really helps you when one needs to manage variables and workspace and to perform an elementary mathematical operation. Managing Variables and Workspace

who List current variables whos List current variables, long form clear Clear variables and functions from memory disp Display matrix or text clc Clear command window demo Run demonstrations


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UExamples 3.11 Built-in Function of Elementary Math abs(x) Calculates x angle(x) Returns the phase angle of the complex value x, in radians exp(x) Calculates xemod(x) Remainder or modulo function log(x) Calculates the natural logarithm xelogsqrt(x) Calculates the square root of x sin(x) Calculates the sin(x), with x in radians cos(x) Calculates the cos(x), with x in radians tan(x) Calculates the tan(x), with x in radians ceil(x) Rounds x to the nearest integer towards positive infinity fix(x) Rounds x to the nearest integer towards zero floor(x) Rounds x to the nearest integer towards minus infinity round(x) Rounds x to the nearest integer

UExamples 3.12

>> whos Name Size Bytes Class ans 1x1 226 sym object y 1x1 8 char array v 4x5 200 double array x 1x3 500 double array

>> z = 2*sin(pi/2)+log(2) z = 2.6931 >> z = round(z) z = 3

Common MATLAB Functions

>> z = 2*sin(pi/2)+log(2) z = 2.6931 >> z = round(z) z = 3

>> str = [‘MATLAB Baguss..!’]; >> disp(str); MATLAB Baguss..!

CHAPTER 4: Plotting and Visualization

18

Plotting in MATLAB

CHAPTER 4

Plotting and Visualization

Plotting in MATLAB

MATLAB has extensive facilities for displaying vectors and matrices as graphs, as well as annotating and printing these graphs. This section describes a few of the most important graphics functions and provides examples of some typical applications. Creating a Plot

The plot function has different forms, depending on the input arguments. If y is a vector, plot(y) produces a piecewise linear graph of the elements of y versus the index of the elements of y. If you specify two vectors as arguments, plot(x,y) produces a graph of y versus x. For example, to plot the value of the sine function from zero to 2π, use: Creating Line Plots UExamples 4.1

>> x = 0:pi/100:2*pi; >> y = sin(x); >> plot(x,y);


19

Plotting in MATLAB

This is the basic command of plotting a graph. Besides that, MATLAB has commands which will let you add titles and labels and others in order to make your figures more readable. However, you need to keep the figure window open while executing these commands.

>> xlabel(‘Radian’); >> ylabel(‘Amplitude’); >> title(‘Plot of sin(x) vs x’); >> grid on;

The current limits of this plot can be determined from the basic axis function. So, in order to modify the x-axis within [0 2π], you need to run this function:

>> axis([0 2*pi -1 1]);


20

Plotting in MATLAB

Annotating Plots

You can adjust the axis tick-mark locations and the labels appearing at each tick mark. For example, this plot of the sine function relabels the x-axis with more meaningful values. UExample 4.2

>> x = 0:pi/100:2*pi; >> y = sin(x); >> plot(x,y); >> set(gca,’XTick’,-pi:pi/2:pi); >> set(gca,’XTickLabel’,{‘-pi’,’-pi/2’,’0’,’pi/2’,’pi’}); >> xlabel('-\pi \leq \Theta \leq \pi'); >> ylabel('sin(\Theta)'); >> title('Plot of sin(\Theta)');

Creating a Semilogarithmic Plot

Semilogarithmic plot is another type of figuring a graph by rescaling if the new data falls outside the range of the previous axis limits. UExample 4.3

>> x = linspace(0,3); >> y = 10*exp(-2*x); >> semilogy(x,y); >> grid on;


21

Plotting in MATLAB

Specifying the Color and Size of Lines You can control a number of line style characteristics by specifying values for line properties. LineWidth Width of the line in units of points MarkerEdgeColor Color of the marker or the edge color for filled markers MarkerFaceColor Color of the face of filled markers MarkerSize Size of the marker in units of points UExample 4.4

>> x = -pi:pi/10:pi; >> y = tan(sin(x)) - sin(tan(x)); >> plot(x,y,'--rs','LineWidth',2,... 'MarkerEdgeColor','k',... 'MarkerFaceColor','g','MarkerSize',10);

Multiple Plots

Often, it is desirable to place more than one plot in a single figure window. This is achieved by three ways: The subplot Function

The subplot Function breaks the figure window into an m-by-n matrix of small subplots and selects the ith subplot for the current plot. The plots are numbered along the top row of the figure window, then the second row, and so forth.


22

Plotting in MATLAB

UExample 4.5

>> x = linspace(0,2*pi); >> subplot(2,2,1); >> plot(x,sin(x)); >> >> subplot(2,2,2) >> plot(x,sin(2*x)); >> >> subplot(2,2,3) >> plot(x,sin(3*x)); >> >> subplot(2,2,4) >> plot(x,sin(4*x));

Multiple plots

You can assign different line styles to each data set by passing line style identifier strings to plot and placing a legend on the plot to identify curves drawn with different symbol and line types. UExample 4.6

>> x = linspace(0,2*pi); >> y1 = sin(x); >> y1 = cos(x); >> y1 = tan(x); >> plot(x,y1,x); >> axis([0 2*pi -1 1]);

The hold Function The hold command will add new plots on top of previously existing plots. UExample 4.6

>> x = -pi:pi/20:pi; >> y1 = sin(x); >> y2 = cos(x); >> plot(x,y1,'b-'); >> hold on; >> plot(x,y2,'g--'); >> hold off; >> legend('sin(x)','cos(x)');


23

Plotting in MATLAB

Line Plots in Three-Dimensions

Now, the three-dimension analog of the plot function is plot3. if x, y and z are three vectors of the same length, plot3(x,y,z) generates a line in 3-D through the points whose coordinates are the elements of x, y and z and then produces a 2-D projection of that line on the screen. UExample 4.7

>> Z = [0 : pi/50 : 10*pi]; >> X = exp(-.2.*Z).*cos(Z); >> Y = exp(-.2.*Z).*sin(Z); >> plot3(X,Y,Z,'LineWidth',2); >> grid on; >> xlabel('x-axis'); >> ylabel('y-axis'); >> zlabel('z-axis');

Three-Dimensional Surface Mesh Plots

The first step in displaying a function of two variables, z = f(x,y), is to generate X and Y matrices consisting of repeated rows and columns, respectively, over the domain of the function. Then use these matrices to evaluate and graph the function. Meshgrid function transforms the domain specified by two-vectors, x and y, into matrices X and Y. UExample 4.8

>> [X,Y] = meshgrid(-8:.5:8); >> R = sqrt(X.^2 + Y.^2); >> Z = sin(R)./R; >> mesh(X,Y,Z);


24

Images in MATLAB

Images in MATLAB

The basic data structure in MATLAB is the array, an ordered set of real or complex elements. Thus, MATLAB stores most images as two-dimensional arrays (i.e., matrices), in which each element of the matrix corresponds to a single pixel in the displayed image. For example, an image composed of 200 rows and 300 columns or different colored dots would be stored in MATLAB as a 200-by-300 matrix. Some images, such as RGB, require a three-dimensional array, where the first plane in the third dimension represents the red pixel intensities, the second plane represents the green pixel intensities, and the third plane represents the blue pixel intensities. This example reads an 8-bit RGB image into MATLAB and converts it to a grayscale image. UExample 4.9

>> rgb_img = imread('ngc6543a.jpg'); >> image(rgb_img); >> pause; >> graysc_img = rgb2gray(rgb_img); >> imshow(graysc_img);

CHAPTER 5: Programming

25

Data Types

CHAPTER 5

Programming

Data Types

There are many different types of data that you can work with in MATLAB. You can build matrices and arrays of floating point and integer data, characters and strings, logical true and false states, etc. you can also develop your own data types using MATLAB classes. Two of the MATLAB data types, structures and cell arrays, provide a way to store dissimilar types of data in the same array.

There are 15 fundamental data types (or classes) in MATLAB. Each of these data types is in

the form of an array. This array is a minimum of 0-by-0 in size and can grow to an n-dimensional array of any size. Two-dimensional versions of these arrays are called matrices. All of the fundamental data types are shown in lowercase text in the diagram below. Additional data types are user-defined, object-oriented user classes (a subclass of structure), and java classes, that you can use with the MATLAB interface to Java. Matrices of type double and logical may be either full or sparse. For matrices having a small number of nonzero elements, a sparse matrix requires a fraction of the storage space required for an equivalent full matrix. Sparse matrices invoke special methods especially tailored to solve sparse problems.

logical char CELL structure Java Classes

Function handle

int8, unit8, int16, uint16, int32, uint32, int64, uint64

single double

NUMERIC

ARRAY (full or sparse)


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The following table describes these data types in more detail. Data type Example Description int8, unit8, int16, uint16, int32, uint32, int64, uint64

int16(100)

Signed and unsigned integer arrays that are 8, 16, 32, and 64 bits in length. Enables you to manipulate integer quantities in a memory efficient manner. These data types cannot be used in mathematical operations.

char 'Hello' Character array (each character is 16 bits long). This array is also referred to as a string.

logical magic(4) > 10 Logical array. Must contain only logical 1 (true) and logical 0 (false) elements. (Any nonzero values converted to logical become logical 1.) Logical matrices (2-D only) may be sparse.

single 3*10^38 Single-precision numeric array. Single precision requires less storage than double precision, but has less precision and a smaller range. This data type cannot be used in mathematical operations.

double 3*10^300 5+6i

Double-precision numeric array. This is the most common MATLAB variable type. Double matrices (2-D only) may be sparse.

cell {17 'hello' eye(2)}

Cell array. Elements of cell arrays contain other arrays. Cell arrays collect related data and information of a dissimilar size together.

structure a.day = 12; a.color = 'Red'; a.mat = magic(3);

Structure array. Structure arrays have field names. The fields contain other arrays. Like cell arrays, structures collect related data and information together.

function handle

@humps Handle to a MATLAB function. A function handle can be passed in an argument list and evaluated using feval

user class inline('sin(x)') MATLAB class. This user-defined class is created using MATLAB functions.

java class java.awt.Frame Java class. You can use classes already defined in the Java API or by a third party, or create your own classes in the Java language.


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M-File Programming

MATLAB provides a full programming language that enables you to write a series of MATLAB statements into a file and then execute them with a single command. You write your program in an ordinary text file, giving the file a name of filename.m. The term you use for filename becomes the new command that MATLAB associates with the program. The file extension of .m makes this a MATLAB M-file. M-files can be scripts that simply execute a series of MATLAB statements, or they can be functions that also accept arguments and produce output. You create M-files using a text editor, then use them as you would any other MATLAB function or command. The process looks like this:

Kinds of M-files There are two kinds of M-files Script M-files Function M-files Do not accept input arguments or return output arguments

Can accept input arguments and return output arguments

Operate on data in the workspace Internal variables are local to the function by default

Useful for automating a series of steps you need to perform many times

Useful for extending the MATLAB language for you application


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Scripts

Scripts are the simplest kind of M-file because they have no input or output arguments. They're useful for automating series of MATLAB commands, such as computations that you have to perform repeatedly from the command line. Scripts operate on existing data in the workspace, or they can create new data on which to operate. Any variables that scripts create remain in the workspace after the script finishes so you can use them for further computations. UExample 5.1

% An M-file script to produce % Comment lines % "flower petal" plots theta = -pi:0.01:pi; % Computations rho(1,:) = 2*sin(5*theta).^2; rho(2,:) = cos(10*theta).^3; rho(3,:) = sin(theta).^2; for k = 1:3 polar(theta,rho(k,:)) % Graphics output pause end

Try entering these commands in an M-file called petals.m. This file is now a MATLAB script. Typing petals at the MATLAB command line executes the statements in the script.


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Functions

Functions are M-files that accept input arguments and return output arguments. They operate on variables within their own workspace. This is separate from the workspace you access at the MATLAB command prompt. UExample 5.2

If you would like, try entering these commands in an M-file called average.m. The average function accepts a single input argument and returns a single output argument. To call the average function, enter

function y = average(x) % AVERAGE Mean of vector elements. % AVERAGE(X), where X is a vector, is the mean of vector elements. % Nonvector input results in an error. [m,n] = size(x); if (~((m == 1) | (n == 1)) | (m == 1 & n == 1)) error('Input must be a vector') end y = sum(x)/length(x); % Actual computation

>> z = 1:99; >> average(z) ans = 50

The Function Definition Line

The function definition line informs MATLAB that the M-file contains a function, and specifies the argument calling sequence of the function. The function definition line for the average function is


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All MATLAB functions have a function definition line that follows this pattern. The Function Name - MATLAB function names have the same constraints as variable

names. The name must begin with a letter, which may be followed by any combination of letters, digits, and underscores. Making all letters in the name lowercase is recommended as it makes your M-files portable between platforms.

Flow Control MATLAB has several flow control constructs:

1. if 2. continue 3. break 4. switch and case 5. for 6. while

UIf

The if statement evaluates a logical expression and executes a group of statements when the expression is true. The optional elseif and else keywords provide for the execution of alternate groups of statements. An end keyword, which matches the if, terminates the last group of statements. The groups of statements are delineated by the four keywords--no braces or brackets are involved.

IF expression

statements ELSEIF expression

statements ELSE

statements END

UContinueU

The continue statement passes control to the next iteration of the for or while loop in

which it appears, skipping any remaining statements in the body of the loop. In nested loops, continue passes control to the next iteration of the for or while loop enclosing it. UBreakU

The break statement lets you exit early from a for or while loop. In nested loops, break exits from the innermost loop only.


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USwitch and Case

The switch statement executes groups of statements based on the value of a variable or expression. The keywords case and otherwise delineate the groups. Only the first matching case is executed. There must always be an end to match the switch.

SWITCH expression CASE expression

statements CASE expression

statements OTHERWISE

statements END

UFor

The for loop repeats a group of statements a fixed, predetermined number of times. A matching end delineates the statements. UWhile

The while loop repeats a group of statements an indefinite number of times under control of a logical condition. A matching end delineates the statements.

FOR variable = expression

Statements, ... Statements

END

WHILE expression Statements END

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