Fundamentals of matlab

MATLAB orientation course:MATLAB orientation course: Organized byOrganized by FOCUS – R&DFOCUS – R&D
Fundamentals of MATLABFundamentals of MATLAB
Delivered byDelivered by
Dr. Suman ChakrabortyDr. Suman Chakraborty
ProfessorProfessor
Department of Mechanical EngineeringDepartment of Mechanical Engineering
IIT KharagpurIIT Kharagpur

OutlineOutline
• Introduction – Using MATLAB
• Basics of Programming
• Introduction to 2D and 3D plot
• Statistical Analysis
• Numerical Analysis
• Symbolic Mathematics
• Conclusion

What is MATLABWhat is MATLAB
• “matrix laboratory”
• Was originally written to provide easy
access to matrix software developed by
the LINPACK and EISPACK projects that
together presented the state-of-the-art
software for matrix manipulation
• Standard instructional tool for industrial
optimization and advance computations in
mathematics, engineering, and science

More about MATLABMore about MATLAB
• High-performance language for technical
computing
• Integrates computation, visualization, and
programming in an easy-to-use user
environment

Uses of MATLABUses of MATLAB
• Math and computation
• Algorithm development
• Application development, including
graphical user interface (GUI) building
• Data analysis, exploration, and
visualization
• Modeling, simulation, and prototyping
• Scientific and engineering graphics

Components of MATLABComponents of MATLAB
• Basic Window
• Extensive Help
• GUI
• Toolboxes
• SIMULINK

ToolboxesToolboxes
Control System Communications
Financial Fuzzy Logic
Image Processing Neural Network
PDE Signal Processing
Statistics Symbolic Math
And Many More …

SimulinkSimulink
• Simulink Extensions
– Simulink Accelerator
– Real-Time Workshop
– Stateflow
• Blocksets
– DSP
– Nonlinear Control Design
– Communications
– Fixed-Point

Documentation SetDocumentation Set
• MATLAB incorporates an exclusive set of online
help and function references containing following
divisions –
– MATLAB Installation Guide
– Getting Started with MATLAB
– Using MATLAB
– Using MATLAB Graphics
– The MATLAB Application Program Interface
Guide
– New features guide

Basic WindowBasic Window
Command line
Result
Visualization
File
Management
Working
Variables
Command
History
Menu
Working Directory

Help and DemoHelp and Demo
Access Matlab Help Menu
Or
Type help in Command Window
Type help subtopic
Access Matlab Demo Menu
Or
Type demo in Command Window

Basics of ProgrammingBasics of Programming

File TypesFile Types
• .m files
Script (executable program)
Function (user written function)
• .fig files Plot visualization and
manipulation
• .dat or
.mat files
Working with Formatted
Data

Script and Function FilesScript and Function Files
Script Files Function Files
Parameter
Assignment
Statement
Evaluation
Function Declaration on top
Syntax: function [output parameters] = function name (input parameters)
Save the file in – function name.m

VariablesVariables
MATLAB variables are created when they
appear on the left of an equal sign. The
general statement
>> variable = expression
creates the “variable” and assigns to it the value
of the expression on the right hand side
||Types of variables||
Scalar Variables
Vector Variables
Matrices
Strings

Creating and Operating withCreating and Operating with
VariablesVariables
Scalar Vector
Strings
# variable with one row
and one column
>> x = 2;
>> y = 3;
>> z = x + y;
>> w = y – x;
>> u = y*x;
# variable with many rows
and columns
>> x = zeros(4,2);
>> y = ones(6,8);
>> x(1,3) = 1729;
>> x(:,1) = [0 0 0 0]
Colon Notation
>> sFirst = ‘Hello’
>> sSecond = ‘All’
>> sTotal = [sFirst, ‘ ’, sSecond]

Handling MatricesHandling Matrices
Initialization Transpose
Multiplication
Inverse
Determinant Eigenvalues

OperatorsOperators
Arithmetic operators
Plus +
Minus -
Matrix multiply *
Array multiply .*
Matrix power ^
Array power .^
Backslash or left matrix divide
Slash or right matrix divide /
Left array divide .
Right array divide ./
Kronecker tensor product kron
Relational operators
Equal ==
Not equal ~=
Less than <
Greater than >
Less than or equal <=
Greater than or equal >=
Logical operators
Short-circuit logical AND &&
Short-circuit logical OR ||
Element-wise logical AND &
Element-wise logical OR |
Logical NOT ~
Logical EXCLUSIVE OR xor

CONTROL FLOW STATEMENTSCONTROL FLOW STATEMENTS
“for” Loop
for n=1:3 % Starting value=1, end=3, increment=1
for m=3:-1:1 % Starting value=3, end=3, increment= -1
a(n,m) = n.^2 + m.^2;
end % End of the “for” loop of “m”
end % End of the “for” loop of “n”
Output
2 5 10
a = 5 8 13
10 13 18

“while” Loop
n = 0; eps = 1;
while (1+eps) > 1
eps = eps/2;
n = n + 1; % “n” indicates how many times the loop is
executed
end
OUTPUT
n = 53
WHILE STATEMENTSWHILE STATEMENTS

“if-else” Statement
rt = 1:4; pp=0; qq=0;
for i=1:4
if (rt(i) < 2)
pp = pp + 1; % Indicates how many times “if” executed
else
qq = qq + 1; % Indicates how many times “else” executed
end % End of “if-else” statement
end % End of “for” Loop
OUTPUT
pp = 1
qq = 3
IF-ELSE STATEMENTSIF-ELSE STATEMENTS

Debugging MATLABDebugging MATLAB
• Syntax Error
– e.g. a function has been misspelled or a parenthesis
has been omitted
– Display error message and line number
– “??? Error: File: D:MATLAB6p5workDNA melting langevinHeteroSeq1.m
Line: 17 Column: 16
Assignment statements do not produce results. (Use == to test for
equality.)”
• Run-time Error
– e.g. insertion of a wrong variable or a calculation has
been performed wrongly such as “divided by zero” or
“NaN”

Introduction to 2D and 3D plotIntroduction to 2D and 3D plot

Plots Using MATLABPlots Using MATLAB
• 2-D Graphics
• 3-D Graphics

Example: Plot y = sin x in 0 ≤ x ≤ 2π
2-D Graphics2-D Graphics

Command Line PlottingCommand Line Plotting

Editing FiguresEditing Figures
Edit Button
Legend
Text
Axis Label
Line or Point Type

Command Line EditingCommand Line Editing

Plot in Polar Co-ordinatePlot in Polar Co-ordinate

Fitting PolynomialsFitting Polynomials

Data StatisticsData Statistics

Plotting polynomialsPlotting polynomials
y = x3
+ 4x2
- 7x – 10 in 1 ≤ x ≤ 3

Specialized Plots using MATLABSpecialized Plots using MATLAB
• Bar and Area Graphs
• Pie Charts
• Histograms
• Discrete Data Graphs

Bar and Area PlotsBar and Area Plots

Pie ChartsPie Charts

HistogramsHistograms

Discrete Data GraphsDiscrete Data Graphs

3-D Graphics3-D Graphics
Use “plot3” in place of “plot” : Simple Enough !!!!

Use of “Mesh”, “Surf”, “Contour”Use of “Mesh”, “Surf”, “Contour”

Statistical AnalysisStatistical Analysis

Data Import in MATLABData Import in MATLAB
• Data as explicit list of elements
– e.g. [1 3 -5 5 7 10 5]
• Create Data in M-file
– Data editor can be utilized, more effective
than the first one
• Load data from ASCII file
– e.g. g = load(‘mydata.dat’)
• Read data using fopen, fread and
MATLAB file I/O functions

Other methods of ImportOther methods of Import
• Specialized file reader function
– dlmread Read ASCII data file
– imread Read image from graphics file
– wk1read Read spreadsheet (WK1) file
– auread Read Sun (.au) sound file
– wavread Read Microsoft WAVE (.wav) sound file
– readsnd Read SND resources and files (Macintosh)
• MEX-file to read the data
• Develop an associated Fortran or C
program

Exporting Data from MATLABExporting Data from MATLAB
• Diary Command
– creates a diary of present MATLAB session in
a disk file (excluding graphics)
– View and edit with any word processor
– e.g. diary mysession.out
diary off
• Save data in ASCII format
• Write data in .mat file

Specialized Write FunctionsSpecialized Write Functions
• dlmwrite Write ASCII data file
• wk1write Write spreadsheet (WK1) file
• imwrite Write image to graphics file
• auwrite Write Sun (.au) sound file
• wavwrite Write Microsoft WAVE (.wav) sound file
• writesnd Write SND resources and files (Macintosh)

Data StatisticsData Statistics
• Basic functions for data statistics:
– max Largest component
– min Smallest component
– mean Average or mean value
– median Median value
– std Standard deviation
– sort Sort in ascending order
– sortrows Sort rows in ascending order
– sum Sum of elements

More Statistical FunctionsMore Statistical Functions
– prod Product of elements.
– diff Difference function and
approximate derivative
– trapz Trapezoidal numerical
integration
– cumsum Cumulative sum of elements
– cumprod Cumulative product of elements
– cumtrapz Cumulative trapezoidal numerical
integration

Covariance and CorrelationCovariance and Correlation
• Function cov evaluates
– Variance of a vector i.e. measure of spread or
dispersion of sample variable
– Covariance of a matrix i.e. measure of
strength of linear relationships between
variables
• Function corrcoef evaluates
– correlation coefficient i.e. normalized
measure of linear relationship strength
between variables

Minimizing FunctionsMinimizing Functions
• Minimizing Functions with one variable
– fmin (function name, range)
• Minimizing Functions with several
variables
– fmins (function name, starting vector)
Example:
>> a = fmin (‘humps’,0.4,0.9)
>> a = 0.6370

Plotting Mathematical FunctionsPlotting Mathematical Functions
fplot('humps',[-3,3])

Numerical AnalysisNumerical Analysis

Functions for Finite DifferencesFunctions for Finite Differences
• diff Difference between
successive elements of a
vector
Numerical partial derivatives
of a vector
• gradient Numerical partial derivatives
a matrix
• del2 Discrete Laplacian of a
matrix

Functions for Fourier AnalysisFunctions for Fourier Analysis
• fft Discrete Fourier transform
• fft2 Two-dimensional discrete Fourier
transform
• fftn N-dimensional discrete Fourier transform.
• ifft Inverse discrete Fourier transform
• ifft2 Two-dimensional inverse discrete Fourier
transform
• ifftn N-dimensional inverse discrete Fourier
transform
• abs Magnitude
• angle Phase angle

Solving Linear EquationsSolving Linear Equations
• Solution by Square System
• Overdetermined System
• Undetermined System
General situation involves a square coefficient
matrix A and a single right-hand side column
vector b.
e.g. Ax = b then solution: x = bA
System is solved by ‘backslash’ operator

Overdetermined EquationOverdetermined Equation
With a, b dataset fitting equation is predicted as
a
eccab −
+= 21)(
MATLAB finds C1 = 0.4763 and C2 = 0.3400

Undetermined EquationUndetermined Equation
• More unknowns than equations
• Solution is not unique
• MATLAB finds a basic solution even it is
not unique
• Associated constraints can not be coupled
to MATLAB

Ordinary Differential EquationsOrdinary Differential Equations
• Nonstiff solvers
– ode23: an explicit Runge-Kutta (2,3) formula i.e.
Bogacki-Shampine pair
– ode45: an explicit Runge-Kutta (4,5) formula i.e.
Dormand-Prince pair
– ode113: Adams-Bashforth-Moulton PECE solver
• Stiff solvers
– ode15s, ode23s, ode23t and ode23tb

Generic Syntax for ODE SolverGeneric Syntax for ODE Solver
>> [T,Y] = solver (‘Func’, tspan, y0);
'Func' String containing the name of the file
that contains the system of ODEs
tspan Vector specifying the interval of integration.
For a two-element vector tspan = [t0 tfinal], the
solver integrates from t0 to tfinal.
y0 Vector of initial conditions for the problem.
Output:
T Column vector of time points
Y Solution array. Each row in Y corresponds to
the solution at a time returned in the
corresponding row of T

Numerical IntegrationNumerical Integration
The area under a section of a function F(x)
can be evaluated by numerically
integrating F(x), a process known as
quadrature. The in-built MATLAB functions
for 1D quadrature are:
• quad - Adaptive Simpson’s Rule
• quad8 - Adaptive Newton Cotes 8
panel rule

Numerical Integration - Example
>> Q = quad (‘sin’,0,2*pi)
>> Q = 0

Performing Double IntegralPerforming Double Integral
% function declaration
>> function integrnd_out = integrnd (x,y)
>> integrnd_out = x*sin(x) + y*cos(y);
% Double Integral Evaluation
>> x_min = pi;
>> x_max = 2*pi;
>> y_min = 0;
>> y_max = pi;
>>
>> intg_result = dblquad (‘integrnd’, x_min, x_max, y_min, y_max)
>> intg_result = -9.8698

Symbolic MathematicsSymbolic Mathematics

Symbolic MathematicsSymbolic Mathematics
• The Symbolic Math Toolboxes include
symbolic computation into MATLAB’s
numeric environment
• Facilities Available with Symbolic Math
Toolboxes contain – Calculus, Linear
Algebra, Simplification, Solution of
Equations, Variable-Precision Arithmetic,
Transforms and Special Applied Functions

DemonstrationsDemonstrations
Command Line Demonstrations are available
with Symbolic Math Toolboxes

Example: DifferentiationExample: Differentiation
>> syms a x
>> fx = sin (a*x)
>> dfx = diff(fx)
>> dfx = cos (a*x)*a
% with respect to a
>> dfa = diff(fx, a)
>> dfa = cos (a*x)*x

In Summary - Why MATLAB !In Summary - Why MATLAB !
• Interpreted language for numerical computation
• Perform numerical calculations and visualize the
results without complicated and time exhaustive
programming
• Good accuracy in numerical computing
• Specially in-built with commands and
subroutines that are commonly used by
mathematicians
• Toolboxes to make advance scientific
computations easy to implement

Thank YouThank You

Fundamentals of matlab

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