Introduction to matlab

Introduction to MATLAB
and Simulink
BY
Ms.S.R.VIDHYA
ASSISTANT PROFESSOR OF
MATHEMATICS

• “The Language of Technical Computing”
• Numerical Programming Environment
• MATLAB - MATrix LABoratory
• High-Level Interpreted Language
• Uses:
• Analyze Data
• DevelopAlgorithms
• Create Models andApplications.
• MultidisciplinaryApplications
Introduction to MATLAB and Simulink

• Acquire and Analyze Data from different sources
• Data from Measuring and Sensing Instruments
• Recorded Data (Spreadsheets, text files, images, audio files, etc)
• Analyze Data using different tools
• Develop Functions andAlgorithms
• Visualize Data in terms of graphs, plots, etc
• Simulink is used to Develop Models andApplications
• Deploy Code as StandaloneApplications

• MATLAB is a Multi-discipinary Tool
• Can be used in any Numerical ComputationApplication
• 90+ Toolboxes in multiple fields
• Mathematics(Symbolic Math, Statistics, Curve fitting, Optimization)
• Communications & Signal Processing (RF, LTE, DSP, Wavelets)
• Machine Vision (Image Processing, Computer Vision)
• Control Systems (Fuzzy Logic, Predictive Control, Neural Networks)
• Parallel Computing and Distributed Computing
• Statistics and Curve Fitting
• Computational Finance ( Financial, Econometrics, Trading, etc)
• Instrument Control, Vehicle Networks (CAN) , Aerospace

• Simulink is a Block Diagram Environment for Multidomain
simulation and Model-Based Design.
• Build, Simulate and Analyze models using Blocks.
• Connect to External Hardware (FPGA, DSP Processors,
Microprocessor, Microcontroller, etc) and run the models there
directly.
• Simscape (Physical Systems – Mechanical, Electrical, Hydraulic, etc)
• SimMechanics ( Robotics, Vehicle Suspensions, HIL system support)
• SimDriveline (1-D Driveline System Simulation)
• SimHydraulics (Hydraulic Components)
• SimRF (RF Systems)
• SimPowerSystems (Electrical Power Systems)
• SimElectronics (Motors, Drives, Sensors, Actuators, etc)

• MATLAB has optimized mathematical algorithms which
perform mathematical operations very efficiently.
• High speed of computation.
• Easy to learn and write MATLAB code.
• Tons of built-in code and freely available User-submitted code.
• Simulink uses Block approach with Drag-And-Drop.
• Easy to use and implement models.
• No hassle deployment of same model to multiple devices

• 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 ArrayEditor
• Command History
• View Past Commands
• Save a whole
session using
Diary

• MATLAB works primarily (almost exclusively) with matrices.
• MATLAB functions are optimized to handle matrix operations.
• MATLAB can handle upto 13-dimensional matrices.
• Loops can be vectorized for faster operations.

• Matrix is a one- or multi-dimensional array of elements.
• Elements can be numerical, variables or string elements.
• By default, MATLAB stores numbers as double precision.
• ALL data in MATLAB are viewed as matrices.
• Matrices can be:
• Created Manually by User
• Generated by MATLAB Functions
• Imported from stored databases or files

• Unlike C, MATLAB is an interpreted language. So, there is no
need for Type Declaration.
• A single variable is interpreted as 1x1 matrix.
>> a = 5
a =
5
• Arrays are represented as a series of numbers (or characters)
within square brackets, with or without a comma separating the
values.
>> b = [1 2 3 4 5] % Percentage Symbol indicates Comment
b =
1 2 3 4 5

• 2-D or Multidimensional Arrays are represented withinsquare
brackets, with the ; (semicolon) operator indicating end of a
row.
>> c = [1 2 3 ; 4 5 6 ; 7 8 9 ; 10 11 12]
c =
1 2 3
4 5 6
7 8 9
10 11 12
• c is now a 2-D array with 4 rows and 3 columns
Note : Variable names are case sensitive and can be upto 31 characters long, and have
to start with an alphabet.

• Character strings are treated as arrays too.
>> name = 'Ravi’
is the same as
>> name = [‘R’ ‘a’ ‘v’ ‘i’]
And gives the output:
name =
Ravi
• Strings and Characters are both declared within SINGLE
quotes (‘ ’)

1 2 3
4 5 6
• Unlike in case of C, MATLAB array indices start from 1.
>> d = [1 2 3 ; 4 5 6]
d =
• Addressing an element of the array is done by invoking the
element’s row and column number.
• In order to fetch the value of an element in the 2nd row and 3rd
column, we use:
>> e = d(2,3)
e =
6

• Rather than addressing single elements, we can also use
commands to address multiple elements in an array.
• The ‘:’ (colon) operator is used to address all elements in arow
or column.
• The ‘:’ operator basically tells the interpreter to addressALL
elements.
• The ‘:’ operator can also be used to indicate a range ofindices.

• Consider the earlier example: d = [1 2 3; 4 56]
•>> f = d(1, :) % Address All elements of 1st Row
f =
% Address All elements in 2nd Column
1 2 3
• >> g = d(:,2)
g =
2
5
%Address Rows from 1 to 2 and Columns from 1 to 2
>> h = d(1:2,1:2)
h =
1 2
4 5

• In some cases, we need to generate large matrices, which is difficult
to generate manually.
• There are plenty of built-in commands for this purpose!
• >> i = 0:10 % Generate numbers from 0 to 10 (Integers)
i =
0 1 2 3 4 5 6 7 8 9 10
• >> j = 0:0.2:1 % Generate numbers from 0 to 1, in steps of 0.2
j =
0 0.2000 0.4000 0.6000 0.8000 1.0000
• >> k = [1:3; 4:6;7:9] % Generate a 3x3 matrix of numbers 1 through 9
k =
1 2 3
4 5 6
7 8 9

• >> l = ones(3,2) %Generate a 3x2 matrix populated with 1s
l =
1 1
1 1
1 1
• >> m = zeros(2,4) %Generate a 2x4 matrix of 0s
m =
0 0 0 0
0 0 0 0
% Generate a 3x4 matrix of random numbers (Between 0 and 1)• >> n = rand(3,4)
n =
0.8147 0.9134 0.2785 0.9649
0.9058 0.6324 0.5469 0.1576
0.1270 0.0975 0.9575 0.9706

• x = linspace(a,b,n) % Generates n linearly-spaced values between a and b
(inclusive)
>> x = linspace(0,1,7)
x =
0 0.1667 0.3333 0.5000 0.6667 0.8333 1.0000
• x = logspace(a,b,n) % Generates n values between 10a and 10b in logarithm
space
>> x = logspace(0,1,7)
x =
1.0000 1.4678 2.1544 3.1623 4.6416 6.8129 10.0000

• Operations upon Matrices can be of two types:
• Element-wise Operation
• Matrix-wise Operation
• Common Arithmetic Operations:
• Addition (+)
• Subtraction (-)
• Multiplication (*)
• Division (/)
• Exponentiation (^)
• Matrix Inverse (inv)
• Left Division () [AB is equivalent to INV(A)*B]
• Complex Conjugate Transpose (’)

• By default, the Operators perform Matrix-wise operations.
• During Matrix-wise operations, care must be taken to avoid
dimension mismatch, specially with exponentiation, division
and multiplication.
• In case of scalar + matrix operations, matrix-wise operations are
equivalent to element-wise operations.
• ie.
Scalar + Matrix = [Scalar + Matrix(i,j)]
Scalar * Matrix = [Scalar * Matrix(i,j)]
• A dot operator(.) preceding the operator indicatesElement-wise
operations.

• Let a = [2 5; 8 1];
b = [1 2 3; 4 5 6];
c = [1 3; 5 2; 46];
% 2 x 2 Matrix
% 2 x 3 Matrix
% 3 x 2 Matrix
2 5 8
6 9 12
• Matrix Addition (or Subtraction):
>> y = b+c' % b and c have different dimensions.
y =
• Complement:
>> d = c' % d is now a 2x3 matrix
d =
1 5 4
3 2 6

• Matrix Multiplication (Or Division):
>> x = b*c % b(2x3) * c(3x2) = y (2x2). No dimension mismatch
x =
23 25
53 58
• In case of element-wise multiplication, the corresponding
elements get multiplied (Matrix Dimensions must agree)
% b(2x3)*c(2x3). No dimension mismatch)>> y = b .* d
y =
1 10 12
12 10 36

• Element-wise Exponentiation is NOT the same as Matrix-wide
exponentiation.
• Matrix Exponentiation needs square matrix as input.
>> a^2 % Matrix Exponentiation: ans = a * a
ans =
44 20
32 44
>> a.^2 % Element-wise Exponentiation: ans = a .* a
ans =
4 25
64 4

1 2 3 1 5 4
4 5 6 3 2 6
• Matrices can be concatenated just like elements in a matrix.
• Row-wise concatenation ( separated by space or commas)
 >> f = [b d]
 f =
• Column-wise concatenation (separated by semicolon)
>> g = [b ; d]
g = 1 2 3
4 5 6
1 5 4
3 2 6

% Generates a (n x n) Normally Distributed Random Matrix
% Generates a (n x n) Identity Matrix
% (n x n) Magic Matrix (Same Sum along Row, Column and Diagonal)
• >> randn(n)
• >> eye(n)
• >> magic(n)
• >> diag(A) % Extracts the elements along the primary diagonal of Matrix A
• >> blockdiag(A,B,C,..) % Generates a block diagonal matrix, with A, B, C, .. As
diagonal elements.
• >> length(x) % Calculates length of a vector x
• >> [m,n] = size(x) % Gives the [Rows,Columns] size of vectorx
• >> floor (x)
• >> ceil (x)
• >> clc
• >> clear
• >> close
• >>a = []
% Round x towards negative infinity (Floor)
% Round x towards positive infinity (Ceiling)
% Clears Command Window
% Clears the Workspace Variables
% Close Figure Windows
%Generates an Empty Matrix

Function Description
Max(x) Return largest element in a vector (each column)
Min(x) Return smallest element in a vector (each column)
Mean(x) Returns mean value of elements in vector (each column)
Std(x) Returns standard deviation of elements in vector (each column)
Median(x) Returns median of elements in vector (each column)
Sum(x) Returns sum of all values in vector (each column)
Prod(x) Returns product of elements in vector (each column)
Sort(x) Sorts values in vector in ascending order
Corr(x) Returns Pair-wise correlation coefficient
Hist(x) Plots histogram of vector x

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