MATLAB Environment

When you run MATLAB, the programming frame is opened. The cursor awaits in the command window with the prompt > preceding it. If you run the student version, the prompt is EDU>.

Let us explore the console of MATLAB, which has a simple appearance. The default window will look like Figure 1-1.

The user might want to close any of these windows to reorganize the interface. You can also customize the appearance interface, such as the way it looks in terms of color, font, and so on. Click ENVIRONMENT and then Preferencesto open the menu shown in Figure 1-2.

Just by clicking on the items in the left frame shown in Figure 1-2, you can customize these settings based on your preferences.

When working with MATLAB, one of the most useful commands is the help command, which illustrates how a command works and how it is used in MATLAB. Once you type help and press Enter, you can click on any of the underlined subjects on the resulting screen to review them in detail.

Throughout the book, examples demonstrate the usage of MATLAB. Each example illustrates an important aspect of a feature of the subject in the relevant chapter.

In MATLAB, you can save your session from start to finish by saving your session with the save function. We can take a look at the following example of this.

Example 1-1. Type disp ('Hello World') at the prompt. Save your session in a file named my_session.

In this code, the command disp() displays whatever is typed between the single quotation marks next to it. If the expression to be displayed is a number, then there is no need to include the quotation marks. If the expression is a string or a letter, then we need to include the quotation marks before and after the text along with the disp() function.

Using MATLAB as a Calculator

MATLAB can be used as a calculator, as well. You can find the solution for any complex calculation. In the following example, we can see an illustration of this function.

Example 1-2. Find the result of .

As shown in the preceding code, π is represented by word pi in MATLAB. For the Euler’s number e, we need to type exp(2), and sqrt(7) should be used for finding the square root of 7. Because we did not assign a variable to the result, the result is shown as ans and it is printed on the screen, where it stands for answer.

Variables and Expressions

In programming languages such as C, C++, and Java, the type of the variable should be specified before the variable is used. However, in MATLAB, this is not the case. The variables are ready to use by just assigning their values. That makes MATLAB more practical for writing shorter and simpler code more quickly.

Some expressions, such as if, for, or end are reserved for the scripts of the language. These words are called keywords. To see a list of the keywords used in MATLAB, simply type iskeyword at the prompt.

we assign 3 to the variable named my_var. Any defined variable is stored as a double precision type in MATLAB by default, unless otherwise specified. Here, the variable my_var is a 1 x 1 matrix with type double. We examine data types later in this chapter.

To avoid confusion, any variable name to be assigned can be checked to see whether it is usable or not at the prompt using the isvarname command.

Another important point that programmers should keep in mind is that MATLAB is a case-sensitive language. In other words, there is a difference between a=5 and A=5 once they are defined in the workspace.

Example 1-3. Check whether it is permissible to use the following names as variable names in MATLAB: Howareyou, hi!, Hola+, Heidi, for, name1, Okay_5

Here, 0 or 1 values are assigned to the ans variable, the class type of which is logical.

As you can see, whenever new information is entered at the prompt, it is repeated. If you do not want the computer to repeat what you typed at the prompt, you can insert a semicolon at the end of the line before you press Enter.

Example 1-4. In the equation P*V = n*R*T, the variables are given as P=10, n=2, R=7, and T= ½. Find V according to the given formula.

As we can see, there are semicolons after each line except the last one. Because there is no semicolon to the right of the last line, we can see the result of that line after pressing Enter.

Formats

In MATLAB, there are line spacing formats and various numerical formats. Line spacing formats control the spacing between the lines in showing the results at the command window. Numerical formats shape the representation of the output.

Per the line spacing format, there are two options: compact and loose. The compact option keeps the lines tight and closer, whereas the loose option introduces additional spacing between the lines in the command window.

Example 1-5. Let A=22/7. Show A both in compact format and loose format in the command window.

We use the compact format throughout this book to save space.

Example 1-6. Let A=22/7. Show A in the formats of long scientific notation, short engineering notation, hexadecimal format, and fraction.

Vectors and Matrices

MATLAB’s foundation is based on matrices. In other words, the basic data type in MATLAB is a matrix. There exist close relations among arrays, vectors, and matrices. In this section, we explore arrays, vectors, matrices, and the colon operator used in MATLAB.

Arrays

An array is a group of objects having the same type, size, and attributes. An array that consists of one element is called a scalar. Arrays can be specified as vectors or matrices. A list of arrays arranged as a column or as a row is a one-dimensional matrix. We can think of a 4 × 5 matrix, having two dimensions as shown in Figure 1-3.

In Figure 1-3, the cell filled with yellow represents the array that constitutes the second row and the fourth column of the matrix. Therefore, we can think of arrays as elements of matrices.

Vectors

A one-dimensional matrix that represents a row or a column matrix is called a vector. In the example shown here, A is a row vector having four elements and B is a column vector having three elements.

To form a row vector, it is sufficient to leave a space between the cells. Also, a comma can be placed between the numbers as shown at the prompt here.

> A=[1,2,3,4]

A =

     1     2     3     4

> A=[1 2 3 4]

A =

     1     2     3     4

>

To create a column vector, we need to insert a semicolon between the numbers at the prompt as shown here.

> B=[1;2;3]

B =

     1

     2

     3

>

Using the size and length commands , you can check the size and length of the vectors A and B just specified.

> size(A)

ans =

     1     3

> size(B)

ans =

     3     1

> length(A)

ans =

     3

> length(B)

ans =

     3

>

linspace Command

The linspace command provides a very convenient way of forming a vector. Any vector can be created using this command when you want to use elements that are equally spaced.

For example, one could create a vector between 1 and 10 having 10 elements by just typing the following command at the prompt:

> Vec=linspace(1,10,10)

Vec =

     1     2     3     4     5     6     7     8     9    10

>

The same vector can be obtained in another way, as shown here:

>Vec=1:1:10

Vec =

     1     2     3     4     5     6     7     8     9    10

>

In this example, the vector starts with 1, and approaches 10 with an increment of 1. That is a very efficient way to create vectors in many problems.

Matrices

An array with more than one dimension is called a matrix. As shown here, A is a 3 × 2 matrix with two dimensions.

A(3,2) =6

Row #     Column #

When creating a matrix in MATLAB, we need to insert semicolons between rows as seen here.

> A=[1 2;3 4;5 6]

A =

     1     2

     3     4

     5     6

>

Special Matrices

There are a number of special matrices in MATLAB that are often used to make programmers’ jobs easier. These matrices can be used instead of needing to create them from scratch, thus saving time in programming. A list of the most useful ones is given in Table 1-3.

Table 1-3

Special Matrix Functions in MATLAB

Function	Explanation	Example
eye	Creates an identity matrix	eye(5)
ones	Creates a matrix where all the elements are ones	ones(5)
zeros	Creates a matrix where all the elements are zeros	zeros(5)
diag	Extracts or displays the diagonal part of a matrix	diag(A)
sparse	Creates a matrix where all the elements are zeros	sparse(5,5)
spdiags	Extracts all diagonals from the matrix	sparse(A)
speye	Creates an identity sparse matrix	speye(5,5)
rand	Creates a randomly generated matrix with values between 0 and 1	rand(5)
magic	Creates magic matrices	magic(3)

One of the special matrices from Table 1-3 is shown here.

> magic(3)

ans =

     8     1     6

     3     5     7

     4     9     2

>

Built-in Functions

MATLAB has numerous built-in, ready-to-use functions that make the programmer’s job much easier. Although it is hard to categorize these functions precisely, we can group the most frequently used ones into categories such as elementary math functions, trigonometric functions, complex numbers, random numbers, and basic plotting functions, although there are more than we can list here. Using the help command, you can easily review the descriptions of the functions and their example uses. For a list of all elementary math functions, simply type help elfun at the prompt in MATLAB. Most of the other built-in MATLAB functions are introduced and explained in subsequent chapters.

Data Types

In MATLAB, the default data type is double. This means that anything entered at the prompt is saved as double unless otherwise specified.

We can divide the data types into two major categories in MATLAB: homogeneous data types and heterogeneous data types (Figure 1-4). Homogeneous data types include the same type of data, whereas the heterogeneous data types have mixed or complex data types.

Homogeneous Data Types

Homogeneous data types have the same characteristics. These types may be characters, strings, integers, floating-point numbers, or logical data.

Characters and Strings

Characters are composed of strings. Letters, numbers, or symbols can be defined as characters in MATLAB. Characters can be defined by entering them between single quotation marks.

> Let="34"

Let =

34

> class(Let)

ans =

char

>

In this example, even though we define the variable Let as 34 having all numbers, due to the fact that these numbers are entered between the single quotation marks, MATLAB recognizes Let as a character. If the class command is used to display its class, we will see that it is of type character.

> H='How are you?'

H =

How are you?

> length(H)

ans =

    12

> class(H)

ans =

char

>

In the preceding example, the variable H is defined as a character of length 12. The variable is defined as a character by putting its name between the single quotation marks.

Example 1-11. Three variables are defined as ‘How are you?’, ‘the weather’, and ‘is it correct?’ for A, B, and C, respectively. We want to create a new character ‘How is the weather’ by using the given three variables alone. Write the code to achieve this task.

Solution 1-11. To this point, we have typed the commands in the command window. We can write the code in the editor and save it in the working directory of MATLAB. Then by just typing the name of the saved file, we can run the code. This code is written in editor and saved as CharEx.m. The following program can be used for this task.

CharEx.m

% Name of this file is CharEx.m

% This is Example 1-11

% This code gets some strings and puts them

% together for another string

A = 'How are you?';

B = 'the weather';

C = 'is it correct?';

NewOne = [A(1:4) C(1:3) B]

As shown, we extract the first four characters of A, the first three characters of C, and all of the B strings, and assign them into a new variable NewOne. If the percentage (%) symbol is put on a line, MATLAB ignores everything that comes after that % symbol, so this is used for commenting.

Once we run the code at the prompt, the following output will be obtained.

> CharEx

NewOne =

How is the weather

>

In MATLAB, there is a very useful command called char. Using this command, we can print all the characters defined by the American Standard Code for Information Interchange (ASCII) as shown in Figure 1-5.

From 32 to 127, these characters can be viewed as it is shown in the solution to Example 1-12.

Example 1-12. Write a program that prints out the lowercase and uppercase letters from the ASCII table.

Solution 1-12. The following code can be used to accomplish the given task.

Letters.m

% Name of this file is Letters.m

% This is Example 1-12

% This code prints alphabet letters

Small   = char(97:122);

Capital = char(65:90);

fprintf('Small letters are : %s ',Small);

fprintf('Big letters are : %s ',Capital);

Then in the command window, once we run the code at the prompt, we obtain the following output:

> Letters

Small letters are : abcdefghijklmnopqrstuvwxyz

Big letters are : ABCDEFGHIJKLMNOPQRSTUVWXYZ

>

In the code for Letters.m, the fprintf function prints purple characters up to the % symbol. After that, the letter s tells MATLAB that after that time, strings will be printed that are called Small and Capital. The part cuts the line and goes to the next line during printing.

Example 1-13. Bob wants to send the message “Start sending messages at 8:30” to Alice in a secret way as an encrypted message. Write a program that encrypts and decrypts Bob’s message. (Hint: Use the ASCII table)

Solution 1-13. The encryption and decryption parts can be given as follows.

HidingMessage.m

% Name of this file is HidingMessage.m

% This is Example 1-13

% This code encrypts and decrypts a message

%Encryption starts here

Message = 'Start sending message at 8:30';

Encryp = double(Message)+3;

fprintf('Encrypted Message : %s ',char(Encryp))

%Decryption starts here

Decryp = Encryp-3;

fprintf('Decrypted Message : %s ',char(Decryp))

In this solution, the message is converted to the corresponding numbers in the ASCII table using the command double. We then add 3 to the corresponding numbers of each letter for encryption. This shifts each letter by 3 to the right in the ASCII table. After the message is encrypted, it is decrypted back to its original version by subtracting 3 from the encrypted values. Once we run the code at the prompt, we obtain the following output:

> HidingMessage

Encrypted Message : Vwduw#vhqglqj#phvvdjh#dw#;=63

Decrypted Message : Start sending message at 8:30

>

MATLAB provides very useful functions for manipulating strings or characters. Some of the most commonly used functions are listed in Table 1-10.

Numerical Data

There exist two different kinds of numerical data types in MATLAB: integers and floating-point numbers. Integers are comprised of signed and unsigned types. There are eight types of integers in total, as shown in Table 1-11. The difference between these types is the storage space that they occupy in memory. If it is possible to do your calculations with low bit integers, you could save space in memory. When higher bit integers are preferred, more memory will be needed.

To find the maximum or minimum values of integers within the computer, you just need to type intmax('classname'). For example, if we type the following

> intmax('int8')

ans =

  127

> intmin('int64')

ans =

 -9223372036854775808

>

we see the values of the highest 8-bit integer and the lowest 64-bit integer. Also,

> intmin('uint64')

ans =

           0

> intmax('uint64')

ans =

 18446744073709551615

>

shows the lowest and highest unsigned 64-bit integers in the preceding code, using the intmin and intmax commands.

There are two types of floating-point numbers; namely, double-precision and single-precision numbers. Double-precision floating-point numbers are the default type for all entered variables. Single-precision floating-point numbers occupy 32 bits in memory, whereas double-precision floating-point numbers occupy 64 bits. We can check the highest and lowest values using the same commands we used for integers earlier.

> realmax('double')

ans =

  1.7977e+308

> realmin('single')

ans =

  1.1755e-38

>

Logical Data

In MATLAB, along with many other programming languages, 1 represents the logical true and 0 represents the logical false.

Example 1-14. Write a program that includes two variables as logical values. One should be true, and the other should be false. Compare these values using the logical and and logical or operators.

Solution 1-14. The following code can be used to accomplish the given task.

LogicalEx.m

% Name of this file is LogicalEx.m

% This is Example 1-14

% This code works with logical values

Logical1 = 3>2 % if it is true, it is 1

Logical2 = 5<4 % if it is false, it is 0

CombineWithAnd = Logical1 && Logical2 % and

CombineWithOr = Logical1 || Logical2  % or

If we run the code, we obtain the following result.

> LogicalEx

Logical1 =

     1

Logical2 =

     0

CombineWithAnd =

     0

CombineWithOr =

     1

> class(CombineWithOr)

ans =

logical

>

Once we check the class of the variable CombineWithOr after running the code, as just shown, it is logical data. Hence, the logical data values can be either 0 or 1.

Symbolic Data

Symbolic data are used to perform algebraic calculations using MATLAB’s symbolic toolbox. There are two ways of defining a symbolic variable. One is to type syms and the other way is to type sym as shown here.

> syms x

> class(x)

ans =

    'sym'

> y=sym('y')

y =

y

> class(y)

ans =

    'sym'

>

In either method, we can create symbolic data types, and then apply some algebraic operations such as taking the integral or derivative of them.

Plotting Graphics

MATLAB is a very powerful tool for graphics and plotting. A wide range of drawing tools are available for tasks such as plotting in polar coordinates, logarithmic graphics, animated 3-D plots, volume visualization plots, and so on. This section deals with the basic plotting of functions in two dimensions and plotting multiple functions on a single coordinate system or on a single figure.

Single Plotting

The basic command for drawing a function in MATLAB is the plot function. The simplest form of the plot command is plot(y), where y depends on its index. The most common use of the plot function is in the form of plot(x,y), which is the Cartesian plot of an (x,y) pair.

Example 1-18. Plot the function y = 2sinsin (x) through the interval of 0 ≤ x ≤ π.

Solution 1-18. If x is defined as a vector from 0 to pi using the linspace command, then we can draw the corresponding values of y versus x. In the following code, the distance from 0 to pi is divided into 100 points. If we pick a large number of points such as 1,000, the graph will become more precise.

> x=linspace(0,pi,100);

> y=2.*sin(x);

> plot(x,y)

>

The code just given produces the output shown in Figure 1-6.

Various features of graphics such as title, x label, y label, and grids are available in MATLAB. These features are shown in Table 1-15.

There are some other features available that allow programmers to work with line styles, colors, and sizes, as shown in Table 1-16.

To create a regular plot using the plot function , different options can be included in the drawing.

There is a remarkable number of special functions available to create two-dimensional and three-dimensional plots in MATLAB. In the command window, if you type >help specgraph and press Enter, you will see which special functions are available in your version.

Multiple Plots

It is possible to draw multiple plots on a single figure. That can be achieved in two ways.

We might have multiple plots on the same coordinate system besides having separate plots on one figure. If you want to draw different functions on the same axes, you can do it either by using one single plot function, or using the hold command and multiple plot commands.

Example 1-19. Plot the function y = 2 sinx with grids. Then, keep the first graph and plot a second function given by y = coscos (x) within the same interval. Insert the labels for each data set, as well.

Solution 1-19. The desired plot can be obtained using the following program and the results are shown in Figure 1-7.

> x=linspace(0,pi,100);

> y=2.*sin(x);

> plot(x,y)

> hold

Current plot held

> y2=cos(x);

> plot(x,y2)

> title('Title comes here')

> xlabel('This is x label')

> ylabel('This is y label')

> legend('2sin(x)','cos(x)')

> grid on

>

It is possible to draw multiple plots using different axes on the same figure via the subplot command as well.

Example 1-20. Plot the three functions given in Example 4-5 on different axes on the same figure using the subplot command.

Solution 1-20. The following program may be entered at the prompt to accomplish the given task.

> x=linspace(0,pi,200);

> subplot(3,1,1)

> plot(x,sin(x))

> subplot(312)

> plot(x,cos(x))

> subplot(3,1,3)

> plot(x,sin(x)+cos(x))

> grid on

>

As shown, subplot(312) is used instead of subplot(3,1,2). Both will produce the same result. Once the program is executed, the output shown in Figure 1-8 is obtained.

Problems

Write a program to list the elements of the array, and then display the content of the cell graphically.