MATLAB Tutorial of Fundamental Programming

8/6/2019 MATLAB Tutorial of Fundamental Programming

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Prepared by:

Khairul Anuar IshakDepartment of Electrical, Electronic & System Engineering

Faculty of Engineering

Universiti Kebangsaan Malaysia


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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


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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 specializedtechnology. 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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CHAPTER 1: Introduction to MATLAB

3

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 hasmany 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 tointeractively 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. MATLABs flexibility and platform independence is achieved bycompiling 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.


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CHAPTER 2: Getting Started

4

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 Browser2. The Workspace Window3. The Command Window4. The Command History Window5. The Start Button6. The Help Window


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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 titlebardarkens. 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, lets 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 ENTERkey. 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 orexit at the prompt. You can also click on the

special symbol that closes your windows (usually an in the upper right-hand corner). Anotherway 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.


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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 threefundamental 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

=

3

2

1

c

=

987

654321

d

This is a 14 array containing 4 elements, known as a row vector

This is a 31 array containing 3 elements, known as a column vector

This is a 33 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 ENTERkey) as a column

separator as well.


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Examples 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 = [157]

my_vector2 =

1

5

7

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

my_matrix =

8 12 197 3 2

12 4 238 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 5o my_matrix(3,2) is 4 ormy_matrix(7) is 4

The Colon Operator

The colon (:) is one of MATLABs most important operators. It occurs in several different

forms.

Examples 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 orcolumn 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.

Examples 3.3

Reshaping a Matrix

Here are a few examples to illustrate some of the ways you can reshape matrices.

Examples 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 9 112 4 6 8 10 12


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Examples 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 8 910 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 matrixlength Returns the number of elements in a matrixmin Returns the minimum value contained in a matrixmax Returns the maximum value contained in a matrixsum Returns the sum of the elements in a matrixsort Returns the sorted elements in a matrixabs Returns the absolute value of the elements in a matrix

Examples 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 vectorcat Concatenate matrices along the specified dimensionones Create a matrix of all oneszeros Create a matrix of all zerosrand Create a matrix of uniformly distributed random numbersrepmat Create a new matrix by replicating or tiling another

Examples 3.7

The following example demonstrates the use some of these functions.


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 ofA and B. Both

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

be a scalar

Division A ./ B Element-by-element division ofA 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 00 0 0 0

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

B =

7 7 7


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Power A .^ B Element-by-element exponentiation ofA and B. Both

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

be a scalar

Examples 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.

DivisionA / B

Matrix division defined by A * inv(B), whereinv(B) is the inverse of matrix B.

Power A ^ B Matrix exponentiation of A and B. The power is

computed by repeated squaring

Examples 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 14 2

>> A = [ 2 4 ; 8 10];

>> B = [2 4; 2 5];

>> C = A*B

C =

12 2836 82

>> A = [ 2 4 ; 8 10];

>> B = [2 4; 2 5];

>> C = B*A

C =

36 4844 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 canreassign 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 Meaningans Value of an expression when that expression is not assigned to a variableeps Floating-point precisioni,j

Unit imaginary number, i = j = 1 pi , 3.14159265

realmax Largest positive floating-point numberrealmin Smallest positive floating-point numberInf

, a number larger than realmax, the result of evaluating0

1

NaN

Not a number, (e.g., the result of evaluating0

0

Examples 3.10

>> x = 0;

>> 5/x

Warning: Divide by zero

ans =Inf

>> x = 0;

>> x/x

Warning: Divide by zero

ans =

NaN


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 variableswhos List current variables, long formclear Clear variables and functions from memorydisp Display matrix or textclc Clear command windowdemo Run demonstrations


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Examples 3.11

Built-in Function of Elementary Math

abs(x) Calculates x

angle(x) Returns the phase angle of the complex value x, in radiansexp(x) Calculates xemod(x)

Remainder or modulo functionlog(x) Calculates the natural logarithm xelog

sqrt(x) Calculates the square root ofxsin(x) Calculates the sin(x), with x in radianscos(x) Calculates the cos(x), with x in radianstan(x) Calculates the tan(x), with x in radiansceil(x) Rounds x to the nearest integer towards positive infinityfix(x) Rounds x to the nearest integer towards zerofloor(x) Rounds x to the nearest integer towards minus infinityround(x) Rounds x to the nearest integer

Examples 3.12

>> whos

Name Size Bytes Class

ans 1x1 226 sym object

y 1x1 8 char array

v 4x5 200 double arrayx 1x3 500 double array

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

z =

2.6931

>> z = round(z)

z =

3


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

z =

2.6931

>> z = round(z)

z =

3

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

MATLAB Baguss..!


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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 ofy versus the index of the elements

ofy. If you specify two vectors as arguments, plot(x,y) produces a graph ofy versus x.

For example, to plot the value of the sine function from zero to 2, use:

Creating Line Plots

Examples 4.1

>> x = 0:pi/100:2*pi;

>> y = sin(x);

>>plot(x,y);


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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 2], you need to run this function:

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


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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.

Example 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.

Example 4.3

>> x = linspace(0,3);

>> y = 10*exp(-2*x);

>> semilogy(x,y);>> grid on;


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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 pointsMarkerEdgeColor Color of the marker or the edge color for filled markersMarkerFaceColor Color of the face of filled markersMarkerSize Size of the marker in units of points

Example 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.


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Plotting in MATLAB

Example 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.

Example 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.

Example 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)');


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Plotting in MATLAB

Line Plots in Three-Dimensions

Now, the three-dimension analog of the plot function is plot3. ifx,y andz 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 ofx,y andz and then produces a 2-D projection of that line on the screen.

Example 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 andy, into matricesXand Y.

Example 4.8

>> [X,Y] = meshgrid(-8:.5:8);

>> R = sqrt(X.^2 + Y.^2);

>> Z = sin(R)./R;>> mesh(X,Y,Z);


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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), inwhich 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.

Example 4.9

>> rgb_img = imread('ngc6543a.jpg');

>> image(rgb_img);

>> pause;

>> graysc_img = rgb2gray(rgb_img);>> imshow(graysc_img);


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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 JavaClasses

Functionhandle

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 Descriptionint8, 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 hasless precision and a smaller range. This data type

cannot be used in mathematical operations.double 3*10^300

5+6iDouble-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 informationtogether.

function

handle

@humps Handle to a MATLAB function. A function handle

can be passed in an argument list and evaluated

using fevaluser 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 offilename.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

argumentsOperate 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 theworkspace, 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.

Example 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

pauseend

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.

Example 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, andspecifies 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. if2. continue3.

break4. switch and case

5. for6. while

If

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 expressionstatements

ELSEIF expressionstatements

ELSEstatements

END

Continue

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 orwhile loop enclosing it.

Break

The break statement lets you exit early from a for orwhile loop. In nested loops, break exits

from the innermost loop only.


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Switch 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 expressionCASE expression

statementsCASE expression

statementsOTHERWISE

statementsEND

For

The for loop repeats a group of statements a fixed, predetermined number of times. A

matching end delineates the statements.

While

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, ...StatementsEND

WHILE expressionStatements

END

MATLAB Tutorial of Fundamental Programming

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