Cece Matlab Intro1

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MATLABCECE ACADEMIC TEAM

Prepared by: Sameh Attia



Course Contents

Introduction to MatlabMatlab ProgrammingMath (Symbolic)GUIIntro to Simulink

19/7/2011Matlab CECE Academic Team



Introduction to Matlab




Contents

What‟s MATLAB?Important CommandsMatlab As a CalculatorM-File

VectorsMatricesFind & operatorsElementary operationsPlotting & Finding MaximumObtaining zero Crossing (roots)Integration & DifferentiationObtaining Peaks






What‟s MATLAB?

UsesAcademic

Solving Equations

Integration & DifferentiationData Exploration ,Analyzing &Visualization

ApplicationsSignals ProcessingCommunicationsImage ProcessingMilitary (Air Defense)




What‟s MATLAB?

Differences from CYou don‟t have to define a variable in MATLAB beforeusing it.

It is easier in Mathematical operations like Matrices &Complex.No need to Compile in Matlab.




What‟s MATLAB?




Important Commands


clc Clear command window.clear Clear variables and functions from memory.help Display help text in Command Window.

doc Display HTML documentation in the Help browser.who,whos List current variables.Save

save FILENAME saves all workspace variables to the binary "MAT-file“.save FILENAME X Y Z saves X, Y, and Z.Save FILENAME.dat –ascii save workspace in readable format.

load Load workspace variables from disk.



Matlab As a Calculator


x=9; y=8;z=sin(2*x)+exp(-y)+sqrt(x+y)+log(x*y)+x^2+ye3

Note log(x) means Ln xye3 y*10^3asin(x) sin inverse of xsind(x) x in degrees

Complex z=3+5iabs(z) - angle(z) - imag(z) - real(z) - conj(z)





Useful constantspi π

i,j Imaginary unit

eps Floating-point relative accuracyrealmin Smallest floating-point numberrealmax Largest floating-point number

Inf InfinityNaN Not-a-number





Display FormatsFormat short: four decimals ( the default)

π = 3.141 6

Format long:15 decimalsπ = 3.141592653589793



M-File


The best way to write a big program.M-Files can be used to write Scripts & Functions

Functions

need input & output argumentsVariables are local

ScriptsVariables are global

Can be called by writing its name in the command windowTo open a new M- file, click on „new‟ icon or write„edit‟ in the command window



M-File


Test Programclc,clearx=3;

y=6;z=x+sin(y)/6

Save it (Don‟t use reserved words), Run it „F5‟

To make comments in M-file, use %



M-File


The input FunctionPrompt for user input

x = input(„enter the value of x „)

To allow the user to enter a Stringy = input(„enter your name ‟, ‟s‟)

The disp Functiondisp(x) If x is a string, the text is displayed.



M-File


ExerciseWrite a program to encourage the user to enter hisname & age, then display

user_name is user_age years old

Solutionclc,clearx=input(„your name? „ , „s‟);

y=input(„ your age? „ );

Disp([x „is‟ num2str(x) „years old‟])



Vectors


A Matrix of one row or one coloumn.To enter a vector

x=[ 3 5 2 5 3];To define an interval

y=start:step:stop;z=linspace(start, stop,no. of elements)



Vectors


Operations on vectorsx=[ 2 4 8 -6 10 ];

x(1) 2x(end) 10x(3:end) [ 8 -6 10 ]x(2:2:end) [ 4 -6 ]

X‟ TransposeSum(x) 2+4+8+-6+10Prod(x) 2*4*8*-6*10Mean(x) averageLength (x) 5Max(x) 10



Matrices


Operations on MatricesTo write A Matrix

a=[ 4 6 -1 ; 9 7 2 ; 11 1 8 ];

a(2,3) 2a(2:end, 2:end) [ 7 2 ; 1 8 ]

a( : , 1) [ 4 ; 9 ; 11 ]a(4) 6



Matrices


Operations on Matricesa=[ 4 6 -1 ; 9 7 2 ; 11 1 8 ];

a‟ TransposeSize(a) 3x3det(a) determinantinv(a) inverserank(a) 3Sum(a) vector with the sum over each column[m,n]=eig (a) m eigenvectors , n eigenvalues



Matrices


Special Matriceszeros(3,4)I=eye(4)

p=ones(2,3)d=diag([-3 4 2])r=rand(4)

r=randint(4,4)r=randint(4,4,[2,10])m=magic(3)



Matrices


Matrix Concatenationa= b=

To make c= c=[ a ; b]

To make c= c=[ a b‟ ]



Find & Operators


The Find FunctionFind indices of nonzero elements.I=find(EXPR)

Evaluates the logical expression EXPR and returns theindices of those elements of the resulting matrix thatare equal to the logical TRUE state.

x=[ 2 4 8 -6 10 ]i=find(x==8)

then i=3



Find & Operators


Relational operatorsEqual ==Not equal ~=Greater than >Less than or equal <=Greater than or equal >=

Logical Operatorsand Element-wise logical AND &or Element-wise logical OR |

not Logical NOT ~xor Logical EXCLUSIVE ORany True if any element of vector is nonzeroall True if all elements of vector are nonzero





Finding Maximum


ExerciseWrite a program to find the maximum of

y = -x^2 + 3x + 2

Plot the Function indicating the maximum point



Finding Maximum


Solutionx=-6:.1:6;y=-x.^2+3*x+2;

plot(x,y), hold on, gridi=find(y==max(y));plot(x(i),y(i),'ro')

hold off



Obtaining zero Crossing (roots)


ExerciseWrite a program to obtain the zero crossing (roots) ofthe function y=cos x*e^-.3x ,Plot it indicating the zeros



Obtaining zero Crossing (roots)


Solutionx=linspace(0,10,1000);

y=cos(x).*exp(-.3*x);

plot(x,y), hold on ,gridys=[y(1) y(1:end-1)];ym=ys.*y;

iz=find(ym<=0);plot(x(iz),y(iz),'ro')

Note If the Function is polynomial, use roots()



Integration & Differentiation


IntegrationZ = TRAPZ(X,Y) computes the integral of Y with respectto X using the trapezoidal method.

To ComputeX=0:0.01:10;Y=sin(x);I=trapz(x,y)



Integration & Differentiation


DifferentiationTo Compute

x=linspace(1,10,200);

y=sin(x).*exp(-.3*x);plot(x,y), grid, hold alldydx=diff(y)./diff(x);

dydx=[dydx dydx(end)];plot(x,dydx)



Obtaining Peaks


ExerciseWrite a program to obtain the peaks of y=sin x*e^-.3xPlot it indicating the peaks points.



Obtaining Peaks


Solutionx=0:0.05:10;y=sin(x).*exp(-.3*x);

plot(x,y), grid,hold ondydx=diff(y)./diff(x);dydxs=[dydx(1) dydx(1:end-1)];

dydxm=dydx.*dydxs;iz=find(dydxm<=0);plot(x(iz),y(iz),'ro')



References

[1] “Using Matlab version 6” , Mathworks[2] “Introduction to Matlab 7 for engineers”, William J

[2] David F. Griffiths , „‟An Introduction to Matlab‟‟.

[3] Matlab Help.




THANK YOU!Prepared by: Sameh Attia

E il S h tti 91@ il

Cece Matlab Intro1

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