Author: Saim Khalid

A matrix is a two-dimensional array of numbers.

In MATLAB, you create a matrix by entering elements in each row as comma or space delimited numbers and using semicolons to mark the end of each row.

For example, let us create a 4-by-5 matrix a −

a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]

MATLAB will execute the above statement and return the following result −

a =
  1     2     3     4     5
  2     3     4     5     6
  3     4     5     6     7
  4     5     6     7     8

Referencing the Elements of a Matrix

To reference an element in the m^th row and n^th column, of a matrix mx, we write −

mx(m, n);

For example, to refer to the element in the 2^nd row and 5^th column, of the matrix a, as created in the last section, we type −

a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(2,5)

MATLAB will execute the above statement and return the following result −

ans =  6

To reference all the elements in the m^th column we type A(:,m).

Let us create a column vector v, from the elements of the 4^th row of the matrix a −

a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
v = a(:,4)

MATLAB will execute the above statement and return the following result −

v =
  4
  5
  6
  7

You can also select the elements in the m^th through n^th columns, for this we write −

a(:,m:n)

Let us create a smaller matrix taking the elements from the second and third columns −

a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(:, 2:3)

MATLAB will execute the above statement and return the following result −

ans =
  2     3
  3     4
  4     5
  5     6

In the same way, you can create a sub-matrix taking a sub-part of a matrix.

a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(:, 2:3)

MATLAB will execute the above statement and return the following result −

ans =
  2     3
  3     4
  4     5
  5     6

In the same way, you can create a sub-matrix taking a sub-part of a matrix.

For example, let us create a sub-matrix sa taking the inner subpart of a −

3     4     5     
4     5     6     

To do this, write −

a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
sa = a(2:3,2:4)

MATLAB will execute the above statement and return the following result −

sa =
  3     4     5
  4     5     6

Deleting a Row or a Column in a Matrix

You can delete an entire row or column of a matrix by assigning an empty set of square braces [] to that row or column. Basically, [] denotes an empty array.

For example, let us delete the fourth row of a −

a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a( 4 , : ) = []

MATLAB will execute the above statement and return the following result −

a =
  1     2     3     4     5
  2     3     4     5     6
  3     4     5     6     7

Next, let us delete the fifth column of a −

a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(: , 5)=[]

MATLAB will execute the above statement and return the following result −

a =
  1     2     3     4
  2     3     4     5
  3     4     5     6
  4     5     6     7

Example

In this example, let us create a 3-by-3 matrix m, then we will copy the second and third rows of this matrix twice to create a 4-by-3 matrix.

Create a script file with the following code −

a = [ 1 2 3 ; 4 5 6; 7 8 9];
new_mat = a([2,3,2,3],:)

When you run the file, it displays the following result −

new_mat =
  4     5     6
  7     8     9
  4     5     6
  7     8     9

A vector is a one-dimensional array of numbers. MATLAB allows creating two types of vectors −

• Row vectors
• Column vectors

Row Vectors

Row vectors are created by enclosing the set of elements in square brackets, using space or comma to delimit the elements.

r = [7 8 9 10 11]

MATLAB will execute the above statement and return the following result −

r =

   7    8    9   10   11 

Column Vectors

Column vectors are created by enclosing the set of elements in square brackets, using semicolon to delimit the elements.

c = [7;  8;  9;  10; 11]

MATLAB will execute the above statement and return the following result −

c =
  7       
  8       
  9       
  10       
  11  
 

Referencing the Elements of a Vector

You can reference one or more of the elements of a vector in several ways. The i^th component of a vector v is referred as v(i). For example −

v = [ 1; 2; 3; 4; 5; 6];	% creating a column vector of 6 elements
v(3)

MATLAB will execute the above statement and return the following result −

ans =  3

When you reference a vector with a colon, such as v(:), all the components of the vector are listed.

v = [ 1; 2; 3; 4; 5; 6];	% creating a column vector of 6 elements
v(:)

MATLAB will execute the above statement and return the following result −

ans =
 1
 2
 3
 4
 5
 6

MATLAB allows you to select a range of elements from a vector.

For example, let us create a row vector rv of 9 elements, then we will reference the elements 3 to 7 by writing rv(3:7) and create a new vector named sub_rv.

rv = [1 2 3 4 5 6 7 8 9];
sub_rv = rv(3:7)

MATLAB will execute the above statement and return the following result −

sub_rv =

   3   4   5   6   7

There may be a situation when you need to execute a block of code several number of times. In general, statements are executed sequentially. The first statement in a function is executed first, followed by the second, and so on.

Programming languages provide various control structures that allow for more complicated execution paths.

A loop statement allows us to execute a statement or group of statements multiple times and following is the general form of a loop statement in most of the programming languages −

MATLAB provides following types of loops to handle looping requirements. Click the following links to check their detail −

Loop Control Statements

Loop control statements change execution from its normal sequence. When execution leaves a scope, all automatic objects that were created in that scope are destroyed.

MATLAB supports the following control statements. Click the following links to check their detail.

Decision making structures require that the programmer should specify one or more conditions to be evaluated or tested by the program, along with a statement or statements to be executed if the condition is determined to be true, and optionally, other statements to be executed if the condition is determined to be false.

Following is the general form of a typical decision making structure found in most of the programming languages −

MATLAB provides following types of decision making statements. Click the following links to check their detail −

An operator is a symbol that tells the compiler to perform specific mathematical or logical manipulations. MATLAB is designed to operate primarily on whole matrices and arrays. Therefore, operators in MATLAB work both on scalar and non-scalar data. MATLAB allows the following types of elementary operations −

• Arithmetic Operators
• Relational Operators
• Logical Operators
• Bitwise Operations
• Set Operations

Arithmetic Operators

MATLAB allows two different types of arithmetic operations −

• Matrix arithmetic operations
• Array arithmetic operations

Matrix arithmetic operations are same as defined in linear algebra. Array operations are executed element by element, both on one-dimensional and multidimensional array.

The matrix operators and array operators are differentiated by the period (.) symbol. However, as the addition and subtraction operation is same for matrices and arrays, the operator is same for both cases. The following table gives brief description of the operators −

Sr.No.	Operator & Description
1	+Addition or unary plus. A+B adds the values stored in variables A and B. A and B must have the same size, unless one is a scalar. A scalar can be added to a matrix of any size.
2	–Subtraction or unary minus. A-B subtracts the value of B from A. A and B must have the same size, unless one is a scalar. A scalar can be subtracted from a matrix of any size.
3	*Matrix multiplication. C = A*B is the linear algebraic product of the matrices A and B. More precisely,For non-scalar A and B, the number of columns of A must be equal to the number of rows of B. A scalar can multiply a matrix of any size.
4	.*Array multiplication. A.*B is the element-by-element product of the arrays A and B. A and B must have the same size, unless one of them is a scalar.
5	/Slash or matrix right division. B/A is roughly the same as B*inv(A). More precisely, B/A = (A’\B’)’.
6	./Array right division. A./B is the matrix with elements A(i,j)/B(i,j). A and B must have the same size, unless one of them is a scalar.
7	\Backslash or matrix left division. If A is a square matrix, A\B is roughly the same as inv(A)*B, except it is computed in a different way. If A is an n-by-n matrix and B is a column vector with n components, or a matrix with several such columns, then X = A\B is the solution to the equation AX = B. A warning message is displayed if A is badly scaled or nearly singular.
8	.\Array left division. A.\B is the matrix with elements B(i,j)/A(i,j). A and B must have the same size, unless one of them is a scalar.
9	^Matrix power. X^p is X to the power p, if p is a scalar. If p is an integer, the power is computed by repeated squaring. If the integer is negative, X is inverted first. For other values of p, the calculation involves eigenvalues and eigenvectors, such that if [V,D] = eig(X), then X^p = V*D.^p/V.
10	.^Array power. A.^B is the matrix with elements A(i,j) to the B(i,j) power. A and B must have the same size, unless one of them is a scalar.
11	‘Matrix transpose. A’ is the linear algebraic transpose of A. For complex matrices, this is the complex conjugate transpose.
12	.’Array transpose. A.’ is the array transpose of A. For complex matrices, this does not involve conjugation.

Relational Operators

Relational operators can also work on both scalar and non-scalar data. Relational operators for arrays perform element-by-element comparisons between two arrays and return a logical array of the same size, with elements set to logical 1 (true) where the relation is true and elements set to logical 0 (false) where it is not.

The following table shows the relational operators available in MATLAB −

Logical Operators

MATLAB offers two types of logical operators and functions −

• Element-wise − These operators operate on corresponding elements of logical arrays.
• Short-circuit − These operators operate on scalar and, logical expressions.

Element-wise logical operators operate element-by-element on logical arrays. The symbols &, |, and ~ are the logical array operators AND, OR, and NOT.

Short-circuit logical operators allow short-circuiting on logical operations. The symbols && and || are the logical short-circuit operators AND and OR.

Bitwise Operations

Bitwise operators work on bits and perform bit-by-bit operation. The truth tables for &, |, and ^ are as follows −

Assume if A = 60; and B = 13; Now in binary format they will be as follows −

A = 0011 1100

B = 0000 1101

—————–

A&B = 0000 1100

A|B = 0011 1101

A^B = 0011 0001

~A  = 1100 0011

MATLAB provides various functions for bit-wise operations like ‘bitwise and’, ‘bitwise or’ and ‘bitwise not’ operations, shift operation, etc.

The following table shows the commonly used bitwise operations −

Set Operations

MATLAB provides various functions for set operations, like union, intersection and testing for set membership, etc.

The following table shows some commonly used set operations −

MATLAB does not require any type declaration or dimension statements. Whenever MATLAB encounters a new variable name, it creates the variable and allocates appropriate memory space.

If the variable already exists, then MATLAB replaces the original content with new content and allocates new storage space, where necessary.

For example,

Total = 42

The above statement creates a 1-by-1 matrix named ‘Total’ and stores the value 42 in it.

Data Types Available in MATLAB

MATLAB provides 15 fundamental data types. Every data type stores data that is in the form of a matrix or array. The size of this matrix or array is a minimum of 0-by-0 and this can grow up to a matrix or array of any size.

The following table shows the most commonly used data types in MATLAB −

Example

Create a script file with the following code −

str = 'Hello World!'
n = 2345
d = double(n)
un = uint32(789.50)
rn = 5678.92347
c = int32(rn)

When the above code is compiled and executed, it produces the following result −

str = Hello World!
n =  2345
d =  2345
un = 790
rn = 5678.9
c =  5679

Data Type Conversion

MATLAB provides various functions for converting, a value from one data type to another. The following table shows the data type conversion functions −

Determination of Data Types

MATLAB provides various functions for identifying data type of a variable.

Following table provides the functions for determining the data type of a variable −

Example

Create a script file with the following code −

x = 3
isinteger(x)
isfloat(x)
isvector(x)
isscalar(x)
isnumeric(x)
 
x = 23.54
isinteger(x)
isfloat(x)
isvector(x)
isscalar(x)
isnumeric(x)
 
x = [1 2 3]
isinteger(x)
isfloat(x)
isvector(x)
isscalar(x)
 
x = 'Hello'
isinteger(x)
isfloat(x)
isvector(x)
isscalar(x)
isnumeric(x)

When you run the file, it produces the following result −

x = 3
ans = 0
ans = 1
ans = 1
ans = 1
ans = 1
x = 23.540
ans = 0
ans = 1
ans = 1
ans = 1
ans = 1
x =

      1          2          3
ans = 0
ans = 1
ans = 1
ans = 0
x = Hello
ans = 0
ans = 0
ans = 1
ans = 0
ans = 0

So far, we have used MATLAB environment as a calculator. However, MATLAB is also a powerful programming language, as well as an interactive computational environment.

In previous chapters, you have learned how to enter commands from the MATLAB command prompt. MATLAB also allows you to write series of commands into a file and execute the file as complete unit, like writing a function and calling it.

The M Files

MATLAB allows writing two kinds of program files −

• Scripts − script files are program files with .m extension. In these files, you write series of commands, which you want to execute together. Scripts do not accept inputs and do not return any outputs. They operate on data in the workspace.
• Functions − functions files are also program files with .m extension. Functions can accept inputs and return outputs. Internal variables are local to the function.

You can use the MATLAB editor or any other text editor to create your .mfiles. In this section, we will discuss the script files. A script file contains multiple sequential lines of MATLAB commands and function calls. You can run a script by typing its name at the command line.

Creating and Running Script File

To create scripts files, you need to use a text editor. You can open the MATLAB editor in two ways −

• Using the command prompt
• Using the IDE

If you are using the command prompt, type edit in the command prompt. This will open the editor. You can directly type edit and then the filename (with .m extension)

edit 
Or
edit <filename>

The above command will create the file in default MATLAB directory. If you want to store all program files in a specific folder, then you will have to provide the entire path.

Let us create a folder named progs. Type the following commands at the command prompt (>>) −

mkdir progs    % create directory progs under default directory
chdir progs    % changing the current directory to progs
edit  prog1.m  % creating an m file named prog1.m

If you are creating the file for first time, MATLAB prompts you to confirm it. Click Yes.

Alternatively, if you are using the IDE, choose NEW -> Script. This also opens the editor and creates a file named Untitled. You can name and save the file after typing the code.

Type the following code in the editor −

NoOfStudents = 6000;
TeachingStaff = 150;
NonTeachingStaff = 20;

Total = NoOfStudents + TeachingStaff ...
   + NonTeachingStaff;
disp(Total);

After creating and saving the file, you can run it in two ways −

• Clicking the Run button on the editor window or
• Just typing the filename (without extension) in the command prompt: >> prog1

The command window prompt displays the result −

6170

Example

Create a script file, and type the following code −

a = 5; b = 7;
c = a + b
d = c + sin(b)
e = 5 * d
f = exp(-d)

When the above code is compiled and executed, it produces the following result −

c =  12
d =  12.657
e =  63.285
f =    3.1852e-06

MATLAB is an interactive program for numerical computation and data visualization. You can enter a command by typing it at the MATLAB prompt ‘>>’ on the Command Window.

In this section, we will provide lists of commonly used general MATLAB commands.

Commands for Managing a Session

MATLAB provides various commands for managing a session. The following table provides all such commands −

Commands for Working with the System

MATLAB provides various useful commands for working with the system, like saving the current work in the workspace as a file and loading the file later.

It also provides various commands for other system-related activities like, displaying date, listing files in the directory, displaying current directory, etc.

The following table displays some commonly used system-related commands −

Input and Output Commands

MATLAB provides the following input and output related commands −

The fscanf and fprintf commands behave like C scanf and printf functions. They support the following format codes −

The format function has the following forms used for numeric display −

Vector, Matrix and Array Commands

The following table shows various commands used for working with arrays, matrices and vectors −

Plotting Commands

MATLAB provides numerous commands for plotting graphs. The following table shows some of the commonly used commands for plotting −