MATLAB : Introduction , Features , Display Windows, Syntax, Operators, Graph Plot

MATLAB
ANAMIKA KUMARI
ASSISTANT PROFESSOR
AMITY SCHOOL OF ENGINEERING & TECHNOLOGY

Introduction
to MATLAB
• MATLAB (MATrix LABoratory) is a fourth-generation
high-level programming language and interactive
environment for numerical computation, visualization
and programming.
• MATLAB is developed by MathWorks.
• It allows matrix manipulations; plotting of functions
and data; implementation of algorithms; creation of
user interfaces; interfacing with programs written in
other languages, including C, C++, Java, and
FORTRAN; analyze data; develop algorithms; and
create models and applications.
• It has numerous built-in commands and math
functions that help you in mathematical calculations,
generating plots, and performing numerical methods.

Uses of
MATLAB
MATLAB is widely used as a computational tool in
science and engineering encompassing the fields
of physics, chemistry, math and all engineering
streams. It is used in a range of applications
including:
• Signal processing and Communications
• Image and video Processing
• Control systems
• Test and measurement
• Computational finance
• Computational biology
• Algorithm development
• Data acquisition
• Modeling, simulation, and prototyping
• Data analysis, exploration, and visualization
• Scientific and engineering graphics
• Application development, including graphical user
interface building

Features of
MATLAB
• It is a high-level language for numerical
computation, visualization and application
development.
• It also provides an interactive environment for
iterative exploration, design and problem solving.
• It provides vast library of mathematical functions
for linear algebra, statistics, Fourier analysis,
filtering, optimization, numerical integration and
solving ordinary differential equations.
• It provides built-in graphics for visualizing data and
tools for creating custom plots.
• MATLAB's programming interface gives
development tools for improving code quality,
maintainability, and maximizing performance.

Understanding the
MATLAB Environment
• MATLAB development IDE can
be launched from the icon
created on the desktop.
• The main working window in
MATLAB is called the desktop.
When MATLAB is started, the
desktop appears in its default
layout:

Layout of
MATLAB R2013a
Command
Window
Workspace
Command
History
Current
Folder

MATLAB has four
windows
1. Command Window : All the commands are
entered in command window.
2. Workspace : Workspace contains all the
variable and details of same entered in
command window.
3. Command History : Command history shows
all the command entered in command
window.
4. Current folder : After saving the file
i.e., .m, .mat, .mex files are saved in current
folder. We can change the path of current
folder.

MATLAB has
three display
windows.
1. Command window
2. A graphics window which is used to display plots and
graphs.
3. An editor window which is used to create and modify M-
files.
M-files are files that contain a program or script of MATLAB
commands.
• If a semicolon (;) is typed at the end of a command the
output of the command is not displayed.
• When percent symbol (%) is typed in the beginning of a
line, the line is designated as a comment.

BASIC SYNTAX
• MATLAB environment behaves like a super-
complex calculator. You can enter commands at
the >> command prompt.
• MATLAB is an interpreted environment. In other
words, you give a command and MATLAB
executes it right away.

Hands on Practice
Example # 1
Type a valid expression, for example,
And press ENTER
When you click the Execute button, or type Ctrl+E, MATLAB executes it
immediately and the result returned is:
5+5
ans = 10

Example #2
Let us take up few more examples:
3 ^ 2 % 3 raised to the power of 2
ans = 9

Example #3
sin(pi /2) % sine of angle 90
ans = 1

Example #4
When you click the Execute button, or type Ctrl+E, MATLAB executes it immediately
and the result returned is:
(MATLAB provides some special expressions for some mathematical symbols, like pi for π, Inf
for ∞, i (and j) for √-1 etc. Nan stands for 'not a number’.)
7/0 % Divide by zero
ans = Inf
warning: division by zero

Use of Semicolon (;) in MATLAB
• Semicolon (;) indicates end of statement. However, if you want to
suppress and hide the MATLAB output for an expression, add a
semicolon after the expression.
For example,
x = 3;
y = x + 5
y = 8

Adding Comments
The percent symbol (%) is used for indicating a comment line.
For example,
• You can also write a block of comments using the block comment
operators % { and % }.
The MATLAB editor includes tools and context menu items to help you
add, remove, or change the format of comments.
x = 9 % assign the value 9 to x

Commonly used Operators and Special Characters
• MATLAB supports the following commonly used operators and special
characters:
Operator Purpose
+ Plus; addition operator.
- Minus; subtraction operator.
* Scalar and matrix multiplication operator.
.* Array multiplication operator.
^ Scalar and matrix exponentiation operator.
.^ Array exponentiation operator.
Left-division operator.
/ Right-division operator.

Commonly used Operators and Special Characters
(Cont.)
Operator Purpose
. Array left-division operator.
./ Array right-division operator.
: Colon; generates regularly spaced elements and represents
an entire row or column.
( ) Parentheses; encloses function arguments and array indices;
overrides precedence.
[ ] Brackets; enclosures array elements.
. Decimal point.
… Ellipsis; line-continuation operator
, Comma; separates statements and elements in a row
; Semicolon; separates columns and suppresses display.
% Percent sign; designates a comment and specifies
formatting.
= Assignment operator.

Naming
Variables
• Variable names consist of a letter followed by
any number of letters, digits or underscore.
• MATLAB is case-sensitive.
• Variable names can be of any length, however,
MATLAB uses only first N characters, where N is
given by the function namelengthmax.

Saving Your
Work
• The save command is used for saving all the
variables in the workspace, as a file with .mat
extension, in the current directory.
For example,
You can reload the file anytime later using the
load command.
save myfile
load myfile

On-line help
Command Description
Help Lists topic on which help is available
helpwin Opens the interactive help window
helpdesk Opens the web browser based help facility.
help topic Provides help on topic.
lookfor string Lists help topics containing string.
demo Runs the demo program.

Exercise
• Find the addition of two numbers in which one number is present in a
variable name a.
•

Experiment No. 1
Creating a One and Two- Dimensional Array (Row / Column Vector)
(Matrix of given size) then,
(A). Performing Arithmetic Operations -Addition, Subtraction,
Multiplication and Exponentiation.
(B). Performing Matrix operations -Inverse, Transpose, Rank with
PLOTS

MATRIX
Referencing the Element of Matrix

Creating Sub-Matrix
part of Matrix

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

Deleting a Row or a Column in a Matrix (cont)

Deleting a Row or a Column in a Matrix (cont.)

Matrix
Operations
The following basic and commonly used
matrix operations:
• Addition and Subtraction of Matrices
• Division of Matrices
• Scalar Operations of Matrices
• Transpose of a Matrix
• Concatenating Matrices
• Matrix Multiplication
• Determinant of a Matrix
• Inverse of a Matrix

Addition and Subtraction of Matrices

Division (Left,
Right) of Matrix
• You can divide two matrices using
left () or right (/) division
operators.
• Both the operand matrices must
have the same number of rows
and columns.

Scalar Operations of
Matrices
• When you add, subtract, multiply or divide a
matrix by a number, this is called the scalar
operation.
• Scalar operations produce a new matrix with
same number of rows and columns with each
element of the original matrix added to,
subtracted from, multiplied by or divided by
the number.

Transpose of a Matrix
• The transpose operation
switches the rows and columns
in a matrix. It is represented by a
single quote(').

Matrix Multiplication
• Consider two matrices A and B. If A is an m x n matrix and B is an n x p
matrix, they could be multiplied together to produce an m x n matrix
C. Matrix multiplication is possible only if the number of columns n in
A is equal to the number of rows n in B.
• In matrix multiplication, the elements of the rows in the first matrix
are multiplied with corresponding columns in the second matrix.
• Each element in the (i, j)th position, in the resulting matrix C, is the
summation of the products of elements in ith row of first matrix with
the corresponding element in the jth column of the second matrix.
• Matrix multiplication in MATLAB is performed by using the * operator.

Determinant
of a Matrix
• Determinant of a matrix
is calculated using the
det function of MATLAB.
Determinant of a matrix
A is given by det(A).

Rank of matrix
Syntax
• k = rank(A)
• Examples

Inverse of a Matrix
• The inverse of a matrix A is denoted by A−1 such that the following
relationship holds:
The inverse of a matrix does
not always exist. If the
determinant of the matrix is
zero, then the inverse does not
exist and the matrix is singular.
Inverse of a matrix in MATLAB
is calculated using the inv
function. Inverse of a matrix A
is given by inv(A).

PLOT: Create 2-D Graph and Customize Lines
This example shows how to create a simple
line graph.
• Use the linspace function to define x as a
vector of 100 linearly spaced values
between 0 and 2pi.
x = linspace(0,2*pi,100);
• Define y as the sine function evaluated at
the values in x.
y = sin(x);
• Plot y versus the corresponding values in x
figure
plot(x,y)

This example shows how to create a graph in a new figure window,
instead of plotting into the current figure.
• Define x and y.
• x = linspace(0,2*pi,25);
• y = sin(x);
• Create a stairstep plot of y
versus x. Open a new figure
window using the figure
command. If you do not open a
new figure window, then by
default, MATLAB® clears existing
graphs and plots into the
current figure.
• figure % new figure window
• stairs(x,y)

Colors, Line Styles, and Markers
• To change the line color, line style, and marker type, add a
line specification input argument to the x,y pair. For example,
'g:*' plots a green dotted line with star markers. You can omit
one or more options from the line specification, such as 'g:'
for a green dotted line with no markers. To change just the
line style, specify only a line style option, such as '--' for a
dashed line.
• For more information, see the LineSpec input argument for
plot.
• Specify Line Style
• Open Live Script
• This example shows how to create a plot using a dashed line.
Add the optional line specification, '--', to the x,y pair.
• y = sin(x);
• figure
• plot(x,y,'--')

Specify Line Style and Color
• This example shows how to specify the line
styles and line colors for a plot.
• Plot a sine wave with a green dashed line using
'--g'. Plot a second sine wave with a red dotted
line using ':r'. The elements of the line
specification can appear in any order.
• y1 = sin(x);
• y2 = sin(x-pi/4);
• figure
• plot(x,y1,'--g',x,y2,':r')

ARRAYS
• Arrays are Set of Elements having same data type or we can Say that Arrays are
Collection of Elements having same name and same data type.
• All variables of all data types in MATLAB are multidimensional arrays.
• A vector is a one-dimensional array and a matrix is a two-dimensional array.
• Two Dimensional Array or the Matrix
• The Two Dimensional array is used for representing the elements of the array in
the form of the rows and columns and these are used for representing the
Matrix A Two Dimensional Array uses the two subscripts for declaring the
elements of the Array
• “Like this int a[3][3]”
• This is the Example of the Two Dimensional Array In this first 3 represents the
total number of Rows and the Second Elements Represents the Total number of
Columns The Total Number of elements are judge by Multiplying the Numbers of
Rows * Number of Columns. In the above array the Total Number of elements

Special Arrays in MATLAB
• In this section, we will discuss some functions
that create some special arrays. For all these
functions, a single argument creates a square
array, double arguments create rectangular
array.
• The zeros() function creates an array of all
zeros:
• For example:

The ones() function creates an array of all
ones:

Multidimensional Arrays
• A multidimensional array in MATLAB® is an array with
more than two dimensions. In a matrix, the two
dimensions are represented by rows and columns.
• Each element is defined by two subscripts, the row
index and the column index. Multidimensional arrays
are an extension of 2-D matrices and use additional
subscripts for indexing. A 3-D array, for example, uses
three subscripts. The first two are just like a matrix, but
the third dimension represents pages or sheets of
elements.

Multidimensional Arrays
• An array having more than two dimensions is
called a multidimensional array in MATLAB.
Multidimensional arrays in MATLAB are an
extension of the normal two-dimensional matrix.
• Generally to generate a multidimensional array, we
first create a two-dimensional array and extend it.
• For example, let's create a two-dimensional array
a.

We can also use the cat()
function to build
multidimensional arrays.
It concatenates a list of
arrays along a specified
dimension:
Syntax for the cat() function is:
B = cat(3,A,[3 2 1; 0 9 8; 5 3 7])

Array Functions
. MATLAB provides the following functions to sort, rotate, permute, reshape, or shift array contents.
• Function Purpose
• length Length of vector or largest array dimension
• ndims Number of array dimensions
• numel Number of array elements
• size Array dimensions
• iscolumn Determines whether input is column vector
• isempty Determines whether array is empty
• ismatrix Determines whether input is matrix
• isrow Determines whether input is row vector
• isscalar Determines whether input is scalar
• isvector Determines whether input is vector
• blkdiag Constructs block diagonal matrix from input arguments
• circshift Shifts array circularly
• ctranspose Complex conjugate transpose

Examples
The following examples illustrate some of the functions mentioned above.
• Length, Dimension and Number
of elements:
• Create a script file and type the
following code into it:

Concatenating Matrice
• You can concatenate two matrices to create a larger matrix. The pair of
square brackets '[]' is the concatenation operator.
• MATLAB allows two types of concatenations:
• Horizontal concatenation
• Vertical concatenation
• When you concatenate two matrices by separating those using commas,
they are just appended horizontally. It is called horizontal concatenation.
• Alternatively, if you concatenate two matrices by separating those using
semicolons, they are appended vertically. It is called vertical
concatenation.

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

Sorting Arrays
• Create a script file and type the following code into it:

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

Reshape
• Reshape array collapse all in page
• Syntax
• B = reshape(A,sz)
• B = reshape(A,sz1,...,szN)
EXAMPLE
• h=[2 3 4 5;8 1 2 0;6 9 3 7]
• g=reshape(h,6,2)

Rotating of
Matrix
• SYNTAX :
• rot90 %Rotates matrix 90 degrees
• EXAMPLE:
• i=rot90(g)

Flipping a
Matrix
• SYNTAX :
• flipdim %Flips array along specified dimension
• Fliplr %Flips matrix from left to right
• flipud %Flips matrix up to down
• Example :
• j=fliplr(i)

Shifting the Matrix
• Circular Shifting of the Array Elements:
• Create a script file and type the following code into it:
• a = [1 2 3; 4 5 6; 7 8 9] % the original array a
• b = circshift(a,1) % circular shift first dimension values down by 1.
• c = circshift(a,[1 -1]) % circular shift first dimension values % down by 1
• % and second dimension values to the left % by 1.

It displays the
following result:

Relational Operators
• 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.

Relational Operators :
(EXAMPLE)

Relational Operators
: (EXAMPLE)

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.

Functions for Logical Operations
Function
• and(A, B)
• not(A)
• or(A, B)
• xor(A, B)
• all(A) %Determine if all array elements of array A are nonzero or true.

EXPERIMENT NO. 2
• AIM: Performing Matrix Manipulations - Concatenating,
Indexing, Sorting, Shifting, Reshaping, Resizing and Flipping
about a Vertical Axis / Horizontal Axis; Creating Arrays X & Y
of given size (1 x N) and Performing
(A). Relational Operations - >, <, ==, <=, >=, ~=
(B). Logical Operations - ~, &, |, XOR

ADDING VALUES IN A VECTOR
>> sum = 0;
for i = 1:5
sum = sum+i;
end
display(sum)
OUTPUT
sum =
15

CHECKING THE SUM
CHECK SUM:
>> A = [1 2 3 4 5]
OUTPUT
A =
1 2 3 4 5
>> B = sum(A)
OUTPUT
B =
15

RUNNING SUM
Program:
>> sum = 0;
>> for i = 1:5
sum = sum+i;
display(sum)
end
OUTPUT :
sum =
1
sum =
3
sum =
6
sum =
10
sum =
15

Cumulative sum
• Syntax –CUMSUM
• Find the cumulative sum of
the integers from 1 to 5. The
element B(2) is the sum of
A(1) and A(2), while B(5) is
the sum of elements A(1)
through A(5).
Eg:
>> A = [1 2 3 4 5]
A =
1 2 3 4 5
>> B = cumsum(A)
B =
1 3 6 10 15

Rand() Function: (Random)
• The rand() function creates an array of uniformly distributed random
numbers on (0,1):
• For example:
• MATLAB will execute the above statement and return the following
result:

Adding a Values in Vector:
>> sum = 0;
for i = 1:5
sum = sum+i;
end
display(sum)
OUTPUT
sum =
15

CHECK SUM:
• >> A = [1 2 3 4 5]
OUTPUT
A = 1 2 3 4 5
>> B = sum(A)
OUTPUT
B = 15

CHECK RUNNING SUM:
>> sum = 0;
>> for i = 1:5
sum = sum+i;
display(sum)
end
OUTPUT
sum =
1
sum =
3
sum =
6
sum =
10
sum =
15

CHECK CUMSUM:
• >> A = [1 2 3 4 5]
OUTPUT
A =
1 2 3 4 5
>> B = cumsum(A)
OUTPUT
B =
1 3 6 10 15

RANDOM:
• >> B = rand(3)
• OUTPUT
• B =
0.4447 0.9218 0.4057
0.6154 0.7382 0.9355
0.7919 0.1763 0.9169
>> plot(B)

Cont.
• >> B = randn(3)
• OUTPUT
B =
0.1746 -0.5883 0.1139
-0.1867 2.1832 1.0668
0.7258 -0.1364 0.0593
>> plot(B)

Rounding to the nearest integer value using
Round, Floor, Ceil and Fix functions
• round(A) : Round to nearest integer
• ceil(A) : Round toward positive infinity; rounds the elements of A to
the nearest integers greater than or equal to A.
• fix(A) : Round toward nearest zero
• floor(A) : Round toward negative infinity; rounds the elements of A to
the nearest integers less than or equal to A.

Examples with syntax (Rounding Functions)
• 1. ROUND
>>round(3.67)
• OUTPUT
ans = 4
• 2. FLOOR
>>floor(3.67)
• OUTPUT
ans = 3
• 3. CEIL
>>ceil(3.67)
• OUTPUT
ans = 4
• 4. FIX
>>a = [1.88 2.05 9.54 8.5]
• OUTPUT
• a = 1.8800 2.0500 9.5400 8.5000
>>fix(a)
• ans = 1 2 9 8

Derivatives of Exponential, Logarithmic, and
Trigonometric Functions

TRIGONOMETRIC FUNCTIONS
• 1. sin(t)
>> x=(0:0.01:2*pi);
>> y=sin(x);
>>plot(x,y);
2. cos(t)
>> x=(0:0.01:2*pi);
>> y=cos(x);
>>plot(x,y);

3. cosec(t)
>> x=(0:0.01:2*pi);
>> y=csc(x);
>>plot(x,y);
• 4. sec(t)
• >> x=(0:0.01:2*pi);
• >> y=sec (x);
• >>plot(x,y);

• 5. tan(t)
>> x=(0:0.01:2*pi);
>> y=sin(x);
>>plot(x,y);
• 6. cot(t)
>> x=(0:0.01:2*pi);
>> y=cot(x);
>>plot(x,y);

LOGARITHMIC FUNCTIONS
• 1. log(t)
>> x=(0:0.01:20)
>> plot(log(x))
Warning: Log of zero
2. log10(t)
>> x=(0.01:0.01:20)
>> plot(log(x))

Exponential function
• Exponential function is an elementary function that operates
element-wise on arrays.
• Its domain also includes complex numbers
• Y = exp(X) returns the exponential for each element of X.

Example : (Exp. #5)
• Creating a vector X with elements, Xn = (-1)^n+1/(2n-1) and Adding
up 100 elements of the vector, X;
• And, plotting the functions; over the interval 0 < x < 4 (by choosing
appropriate mesh values for x to obtain smooth curves), on a
Rectangular Plot
1. x,
2. x^3,
3. exp,
4. exp(x^2)

Solution:
• Adding up to 100 elements
>> n = 1:100;
x = ( (-1).^(n+1) ) ./ (2*n - 1);
y = sum(x)
• x
plot(x(1,1:4))

Cont.
• x3
• a=x.^3;
• plot(a(1,1:4))
• Exp(x)
• b=exp(x)
• plot(b(1,1:4))
• Exp(n2)
• c=exp(x.^2);
• plot(c(1,1:4))

Plotting with Graphical Enhancements

MATLAB PROGRAM:- (Generating a Sinusoidal Signal )
Generating a Sinusoidal Signal of a given frequency with Titling, Labeling, Adding Text, Adding Legends, Printing
Text in Greek Letters, Plotting as Multiple and Subplot. Time scale the generated signal for different values.
t=-0.25:0.0001:0.25;
f1=3;
y1=sin(2*pi*f1*t);
y2=sin(2*pi*f1*2*t);
y3=sin(2*pi*f1*4*t);
y4=sin(2*pi*f1*0.25*t);
y5=sin(2*pi*f1*0.625*t);
plot(t,y1,'k',t,y2,'g',t,y3,'b',t,y4,'m',t,y5,'r')
xlabel('Time(-0.2 < x < 0)')
ylabel(' Amplitude (sine values)')
title('Graph of sine waves having different time value')
legend('y1','y2','y3','y4','y5')

Graph Editing : (with help of figure properties)

First, Second and third Order Ordinary Differential
Equation using Built-in Functions and plot.
Syntax:
dsolve
(Ordinary differential equation and system
solver )

Procedure Of Solving Diff. Equations
• STEP 1: Before using dsolve, create the symbolic function for which
you want to solve an ordinary differential equation. Use sym or syms
to create a symbolic function. For example, create a function y(x):
• syms y(x)
• STEP 2: specify initial or boundary conditions, use additional
equations. (If you do not specify initial or boundary conditions, the solutions
will contain integration constants, such as C1, C2, and so on. )

First Order Diff. Equation
• >> y = dsolve('Dy = y*x','x’); -----------------Equation
• >> y = dsolve('Dy = y*x','y(1) = 1','x’);
• >> x = linspace(0,1,20);
• >> z = eval(vectorize(y));
• >> plot(x,z);
Equation Initialization
With Respect to X

Second Order Diff. Equation
• >> eq1 = 'D2y + 8*Dy + 2*y = cos(x)’; -----------------Equation
• >> inits2 = 'y(0)=0, Dy(0)=1'; -----------------Intialization
• >> y = dsolve(eq1,inits2,'x');
• >> x = linspace(0,1,20);
• >> plot(x,z);
Equation Initialization
With Respect to X
SYNTAX

Third Order Diff. Equation
• >> eq1 = 'D3y + 3*D2y + Dy = cos(x)';
• >> inits2 = 'y(0)=0, Dy(0)=1,D2y(0)=3';
• >> y = dsolve(eq1,inits2,'x');
• >> x = linspace(0,1,20);
• >> plot(x,z);

Script with a request for input
• Input Funtion:
• x = input (prompt) displays the text in prompt and waits for the user to input a value and
press the Return key. The user can enter expressions, like pi/4 or rand(3), and can use
variables in the workspace.
• • If the user presses the Return key without entering anything, then input returns an
empty matrix.
• • If the user enters an invalid expression at the prompt, then MATLAB® displays the
relevant error message, and then redisplays the prompt.
• Example:
• str = input(prompt,'s') returns the entered text as a string, without evaluating the input
as an expression.

If, Else, Else If Statements:
• if expression, statements, end evaluates
an expression, and executes a group of
statements when the expression is true.
An expression is true when its result is
nonempty and contains only nonzero
elements (logical or real numeric).
Otherwise, the expression is false.
• The elseif and else blocks are optional.
The statements execute only if previous
expressions in the if...end block are
false. An if block can include multiple
elseif blocks.
Syntax
if expression
statements
elseif expression
statements
else
statements
end

MATLAB PROGRAM:-
• %Writing brief Scripts starting each Script with a request for
input(using input) to Evaluate the function h(T) using if-else
statement, where, h(T) = (T – 10) for 0 < T < 100 = (0.45 T + 900) for T
> 100. Exercise: Testing the Scripts written using A). T = 5, h = -5 and
B). T = 110, h =949.5%

Program:
T=input('enter the value:')
if(T>0 & T<100)
h=(T-10)
elseif(T>100)
h=(0.45*T+900)
else
disp('Enter a number greater than 0');
end
• COMMAND WINDOW RESULT:-
>>enter the value:5
T =
5
h =
-5
>> enter the value:110
T =
110
h =
949.5000

t=0:0.1:10;
y=sin(t);
z = sin(t) + sin(3*t)/3 + sin(5*t)/5 + sin(7*t)/7 + sin(9*t)/9;
plot(t,y,t,z);
legend('Sine wave','Square wave')
title('Generating square wave from sum of sine waves')
xlabel('Time period')
ylabel('Amplitude')
%Generating a Square Wave from sum of Sine Waves of certain
Amplitude and Frequencies.%

Basic 2D and 3D plots
Contour Plots
A contour plot displays isolines of matrix Z. Label the contour lines using clabel.
contour(X,Y,Z), contour(X,Y,Z,n), and contour(X,Y,Z,v) draw contour plots of Z using X and Y to determine the x and y values.
• If X and Y are vectors, then length(X) must equal size(Z,2) and length(Y) must equal size(Z,1). The vectors must be strictly increasing or
strictly decreasing and cannot contain any repeated values.
• If X and Y are matrices, then their sizes must equal the size of Z. Typically, you should set X and Y so that the columns are strictly
increasing or strictly decreasing and the rows are uniform (or the rows are strictly increasing or strictly decreasing and the columns are
uniform).
If X or Y is irregularly spaced, then contour calculates contours using a regularly spaced contour grid, and then transforms the data to X or
Y.
contour3 creates a 3-D contour plot of a surface defined on a rectangular grid.
contour3(X,Y,Z), contour3(X,Y,Z,n), and contour3(X,Y,Z,v) draw contour plots of Z using X and Y to determine the x and y values.
• If X and Y are vectors, then length(X) must equal size(Z,2) and length(Y) must equal size(Z,1). The vectors must be strictly increasing or
strictly decreasing and cannot contain any repeated values.
• If X and Y are matrices, then their sizes must equal the size of Z. Typically, you should set X and Y so that the columns are strictly
increasing or strictly decreasing and the rows are uniform (or the rows are strictly increasing or strictly decreasing and the columns are
uniform).
If X or Y is irregularly spaced, then contour3 calculates contours using a regularly spaced contour grid, and then transforms the data to X or
Y.

Bar Graph Plot
bar(y) creates a bar graph with one bar for each element in y. If y is a
matrix, then bar groups the bars according to the rows in y.
bar3 draws a three-dimensional bar graph.
bar3(Y) draws a three-dimensional bar chart, where each element in Y
corresponds to one bar. When Y is a vector, the x-axis scale ranges from
1 to length(Y). When Y is a matrix, the x-axis scale ranges from 1 to
size(Y,1) and the elements in each row are grouped together.

• Pie Chart Plot
• pie(X) draws a pie chart using the data in X. Each slice of the pie chart represents an element in X.
• • If sum(X) ≤ 1, then the values in X directly specify the areas of the pie slices. pie draws only a partial pie
if sum(X) < 1.
• • If sum(X) > 1, then pie normalizes the values by X/sum(X) to determine the area of each slice of the pie.
• • If X is of data type categorical, the slices correspond to categories. The area of each slice is the number
of elements in the category divided by the number of elements in X.
• pie3(X) draws a three-dimensional pie chart using the data in X. Each element in X is represented as a slice
in the pie chart.
• • If sum(X) ≤ 1, then the values in X directly specify the area of the pie slices. pie3 draws only a partial pie
ifsum(X) < 1.
• • If the sum of the elements in X is greater than one, then pie3 normalizes the values by X/sum(X) to
determine the area of each slice of the pie.

• Sphere Plot
• The sphere function generates the x-, y-, and z-coordinates of a unit
sphere for use with surf and mesh.
• sphere generates a sphere consisting of 20-by-20 faces.
• sphere(n) draws a surf plot of an n-by-n sphere in the current figure.
• [X,Y,Z] = sphere(n) returns the coordinates of a sphere in three
matrices that are (n+1)-by-(n+1) in size. You draw the sphere with
surf(X,Y,Z) or mesh(X,Y,Z).

• Line Plots
• The plot3 function displays a three-dimensional plot of a set of data
points.
• plot3(X1,Y1,Z1,...), where X1, Y1, Z1 are vectors or matrices, plots one
or more lines in three-dimensional space through the points whose
coordinates are the elements of X1, Y1, and Z1.

• Polygon Plots
• The fill function creates colored polygons.
• fill(X,Y,C) creates filled polygons from the data in X and Y with vertex color specified
by C. C is a vector or matrix used as an index into the colormap. If C is a row vector,
length(C) must equal size(X,2) and size(Y,2); if C is a column vector, length(C) must
equal size(X,1) and size(Y,1). If necessary, fill closes the polygon by connecting the
last vertex to the first.
• The fill3 function creates flat-shaded and Gouraud-shaded polygons.
• fill3(X,Y,Z,C) fills three-dimensional polygons. X, Y, and Z triplets specify the polygon
vertices. If X, Y, or Z is a matrix, fill3 creates n polygons, where n is the number of
columns in the matrix. fill3 closes the polygons by connecting the last vertex to the
first when necessary.

• Cylinder Plot
• cylinder generates x-, y-, and z-coordinates of a unit cylinder. You can
draw the cylindrical object using surf ormesh, or draw it immediately
by not providing output arguments.
• [X,Y,Z] = cylinder returns the x-, y-, and z-coordinates of a cylinder with
a radius equal to 1. The cylinder has 20 equally spaced points around
its circumference.

Parametric Space Curves
• >> t = 0:pi/50:10*pi;
• >> st = sin(t);
• >> ct = cos(t);
• >> plot3(st,ct,t);
Output:

3-D Contour Lines
• >>x = -2:0.25:2;
• >>[X,Y] = meshgrid(x);
• >>Z = X.*exp(-X.^2-Y.^2);
• >>contour3(X,Y,Z,30)
• Output:

Pie Chart & Bar Chart
• >> x = [1,2,3,4,5,6,7,8];
• >> pie(x);
• Output:
• >> z = magic(5);
• >> b = bar3(z);
• Output:

MATLAB : Introduction , Features , Display Windows, Syntax, Operators, Graph Plot

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