Introduction to MATLAB
What is MATLAB
High level language for technical computing
Stands for MATrix LABoratory
Everything is a matrix - easy to do linear algebra
The MATLAB System
Development Environment
Mathematical Function Library
MATLAB language
Application Programming Language
Matlab Screen
Command Window
type commands
Current Directory
View folders and m-files
Workspace
View program variables
Double click on a variable
to see it in the Array Editor
Command History
view past commands
save a whole session
using diary
Variables
No need for types. i.e.,
int a;
double b;
float c;
All variables are created with double precision unless
specified and they are matrices.
Example:
>>x=5;
>>x1=2;
After these statements, the variables are 1x1 matrices
with double precision
Matrices & Vectors
All (almost) entities in MATLAB are matrices
Easy to define:
Use ‘,’ or ‘ ’ to separate row elements -- use ‘;’ to separate rows
>> A = [16 3; 5 10]
A = 16 3
5 10
Matrices & Vectors - II
Order of Matrix - m n
m=no. of rows, n=no. of columns
Vectors - special case
n=1 column vector
m=1 row vector
Creating Vectors and Matrices
Define >> A = [16 3; 5 10]
A = 16 3
5 10
>> B = [3 4 5
6 7 8]
Transpose B = 3 4 5
6 7 8
Matrix:
Vector : >> A=[1 2; 3 4];
>> a=[1 2 3]; >> A'
>> a' ans =
1 1 3
2 2 4
3
Creating Vectors
Create vector with equally spaced intervals
>> x=0:0.5:pi
x =
0 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000
Create vector with n equally spaced intervals
>> x=linspace(0, pi, 7)
x =
0 0.5236 1.0472 1.5708 2.0944 2.6180 3.1416
Equal spaced intervals in logarithm space
>> x=logspace(1,2,7)
x =
10.0000 14.6780 21.5443 … 68.1292 100.0000
Note: MATLAB uses pi to represent , uses i or j to represent imaginary
unit
Variables — Scalars, Vectors,
and Matrices
Real scalar >> x = 5
Complex scalar >> x = 5+10j (or >> x = 5+10i)
Row vector >> x = [1 2 3] (or x = [1, 2, 3])
Column vector >> x = [1; 2; 3]
3 × 3matrix >> x = [1 2 3; 4 5 6; 7 8 9]
Caution (Complex elements of a matrix should not be typed
with spaces, i.e., ‘-1+2j’ is fine as a matrix element, ‘-1 + 2j’
is not. Also, ‘-1+2j’ is interpreted correctly whereas ‘-1+j2’ is
not)
Complex scalar >> x = 3+4j
Real part of x >> real(x) ⇒ 3
Imaginary part of x >> imag(x) ⇒ 4
Magnitude of x >> abs(x) ⇒ 5
Angle of x >> angle(x) ⇒ 0.9273
Complex conjugate of x >> conj(x) ⇒ 3 - 4i
Creating Matrices
zeros(m, n): matrix with all zeros
ones(m, n): matrix with all ones.
eye(m, n): the identity matrix
rand(m, n): uniformly distributed
random
randn(m, n): normally distributed
random
magic(m): square matrix whose
elements have the same sum, along
the row, column and diagonal.
Concatenation of Matrices
x = [1 2], y = [4 5], z=[ 0 0]
A = [ x y]
1 2 4 5
B = [x ; y]
1 2
4 5
Matrix operations
^: exponentiation
*: multiplication
/: division
\: left division. The operation A\B is
effectively the same as INV(A)*B,
although left division is calculated
differently and is much quicker.
+: addition
-: subtraction
Array Operations
Evaluated element by element
.' : array transpose (non-conjugated transpose)
.^ : array power
.* : array multiplication
./ : array division
Very different from Matrix operations
>> A=[1 2;3 4]; But:
>> B=[5 6;7 8]; >> A.*B
>> A*B 5 12
19 22 21 32
43 50
Some Built-in functions
mean(A):mean value of a vector
max(A), min (A): maximum and minimum.
sum(A): summation.
sort(A): sorted vector
median(A): median value
std(A): standard deviation.
det(A) : determinant of a square matrix
dot(a,b): dot product of two vectors
Cross(a,b): cross product of two vectors
Inv(A): Inverse of a matrix A
Adding Elements to a Vector or a Matrix
>> A=1:3 >> C=[1 2; 3 4]
A= C=
1 2 3 1 2
>> A(4:6)=5:2:9 3 4
A= >> C(3,:)=[5 6];
1 2 3 5 7 9 C=
1 2
>> B=1:2 3 4
B= 5 6
1 2
>> B(5)=7; >> D=linspace(4,12,3);
B= >> E=[C D’]
1 2 0 0 7 E=
1 2 4
3 4 8
5 6 12
Operators (relational, logical)
== Equal to
~= Not equal to
< Strictly smaller
> Strictly greater
<= Smaller than or equal to
>= Greater than equal to
& And operator
| Or operator
Flow Control
if
for
while
break
….
Graphics - 2D Plots
plot(xdata, ydata,
‘marker_style’);
For example: Gives:
>> x=-5:0.1:5;
>> sqr=x.^2;
>> pl1=plot(x, sqr, 'r:s');
Graphics - Overlay Plots
Use hold on for overlaying graphs
So the following: Gives:
>> hold on;
>> cub=x.^3;
>> pl2=plot(x, cub,'b:o')
Graphics - Annotation
Use title, xlabel, ylabel and legend
for annotation
>> title('Demo plot');
>> xlabel('X Axis');
>> ylabel('Y Axis');
>> legend([pl1, pl2], 'x^2', 'x^3');
Graphics - Annotation
Graphics-Stem()
stem()is to plot discrete sequence data
The usage of stem() is very similar to plot()
cos(n/4)
1
>> n=-10:10;
>> f=stem(n,cos(n*pi/4)) 0.5
>> title('cos(n\pi/4)')
>> xlabel('n') 0
-0.5
-1
-10 -5 0 5 10
n
subplots
Use subplots to divide a plotting window into several panes.
Cosine Sine
1 1
>> x=0:0.1:10; 0.8 0.8
>> f=figure; 0.6 0.6
>> f1=subplot(1,2,1); 0.4 0.4
>> plot(x,cos(x),'r'); 0.2 0.2
>> grid on; 0 0
>> title('Cosine')
-0.2 -0.2
>> f2=subplot(1,2,2);
>> plot(x,sin(x),'d'); -0.4 -0.4
>> grid on; -0.6 -0.6
>> title('Sine'); -0.8 -0.8
-1 -1
0 5 10 0 5 10
Save plots
Use saveas(h,'filename.ext')
to save a figure to a file.
Useful extension types:
bmp: Windows bitmap
>> f=figure;
emf: Enhanced metafile
>> x=-5:0.1:5;
eps: EPS Level 1
>> h=plot(x,cos(2*x+pi/3));
fig: MATLAB figure
>> title('Figure 1');
jpg: JPEG image
>> xlabel('x');
m: MATLAB M-file
>> saveas(h,'figure1.fig')
tif: TIFF image, compressed
>> saveas(h,'figure1.eps')
Sine Wave in Matlab
t = [ 0 : 1 : 40 ]; % Time Samples
f = 500; % Input Signal Frequency
fs = 8000; % Sampling Frequency
x = sin(2*pi*f/fs*t); % Generate Sine
Wave
figure(1);
stem(t,x,'r'); % View the samples
figure(2);
stem(t*1/fs*1000,x,'r'); % View the
samples
hold on;
plot(t*1/fs*1000,x); % Plot Sine Wave
Practice Problems
Plot the following signals in linear scale
x(t ) sin( 3t ) 5 t 5
y(t ) e 2t 3 0t 5
Plot the following signals, use log scale for y-axis
x(t ) et 2 (2t 1) 0 t 10
Plot the real part and imaginary part of the following signal
x(t ) e0.5t j (t / 3) 0 t 10
For the signal in previous question, plot its phase and magnitude
How to download MATLAB
Pls follow the below link to register and download the official
version of MATLAB.
Portal Link:
http://www.mathworks.com/academia/tah-portal/indian-institute-
of-information-and-technology-allahabad-40677782
Pls Register with email-id provided by Institute and login on the
portal for downloading the setup during installation use the
same registration details for automatic licensing with the
installation.
Concerned Email-ids for Sec-A
(for lab related help)
Dr. Sudharsan Parthasarathy sudharsan.p@iiita.ac.in
Mr. Anup Shrivastava rse2017002@iiita.ac.in
Mr. Neelesh Gupta rse2017003@iiita.ac.in
Mr. Abhishek Kumar Srivastava mec2018013@iiita.ac.in
Mr. Kumar SIDDHANT mec2018005@iiita.ac.in
Mr. Vanteddu Saikiran Reddy mec2019027@iiita.ac.in
Ms. Sandhya S mec2019014@iiita.ac.in
Mr. Ravi R mec2019013@iiita.ac.in
Ms. Khushbu K mec2019003@iiita.ac.in
Concerned Email-ids for Sec-B
(for lab related help)
Dr. Hemant Kumar hemant@iiita.ac.in
Ms. Neha Jaiswal rse2018501@iiita.ac.in
Mr. Ashutosh Kumar Yadav rse2019003@iiita.ac.in
Mr. Ajmire Shreerang Satish imm2015001@iiita.ac.in
Mr. Shubham Saurav imm2015007@iiita.ac.in
Ms. Pitranshi Sonkar mec2019005@iiita.ac.in
Mr. Anuj Chauhan mec2019011@iiita.ac.in
Mr. MOHD AMIR UMAR mec2019028@iiita.ac.in
Concerned Email-ids for Sec-C
(for lab related help)
Dr. Hemant Kumar hemant@iiita.ac.in
Mr. Akhilesh Panchal rse2016505@iiita.ac.in
Mr. Ajmire Shreerang Satish imm2015001@iiita.ac.in
Mr. Jadhav Chaitanya Dnyaneshwar mec2018012@iiita.ac.in
Ms. Babli Kumari mec2018009@iiita.ac.in
Mr. A Krishnadev mec2019004@iiita.ac.in
Mr. Ramaniwas Pandey mec2019026@iiita.ac.in
Mr. Mohd Amir Umar mec2019028@iiita.ac.in
