Matlab-fundamentals of matlab-1

MATLAB orientation course: MATLAB orientation course: Organized byOrganized by FOCUS – R&D FOCUS – R&D

Fundamentals of MATLABFundamentals of MATLABDelivered byDelivered by

Dr. Suman ChakrabortyDr. Suman ChakrabortyProfessorProfessor

Department of Mechanical EngineeringDepartment of Mechanical EngineeringIIT KharagpurIIT Kharagpur

http://www.iitkgp.ernet.in/


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

ResultVisualization

File Management

WorkingVariables

CommandHistory

MenuWorking Directory



Help and DemoHelp and DemoAccess Matlab Help Menu

OrType 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 filesScript (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 FilesScript Files Function Files

ParameterAssignment

StatementEvaluation

Function Declaration on topSyntax: function [output parameters] = function name (input parameters)

Save the file in – function name.m



VariablesVariablesMATLAB 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 VariablesVector Variables

MatricesStrings



Creating and Operating with Creating 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 MatricesInitialization Transpose

Multiplication

Inverse

Determinant Eigenvalues



OperatorsOperators

Arithmetic operatorsPlus + 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” Loopfor 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:\MATLAB6p5\work\DNA melting langevin\HeteroSeq1.m

Line: 17 Column: 16Assignment 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 polynomialsy = 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 GraphicsUse “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 = b\ASystem is solved by ‘backslash’ operator



Overdetermined EquationOverdetermined Equation

With a, b dataset fitting equation is predicted asaeccab 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 pointsY 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



DemonstrationsDemonstrationsCommand 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
