Dr. Munaf Salim › lmsdatapool... · Dr. Munaf Salim 16 diary ex4_1.dat % program computes the nodal voltages % given the admittance matrix Y and current vector I % Y is the admittance

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COMPUTER LAB

CPEG415Dr. Munaf Salim

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Unit OneUnit OneUnit OneUnit OneBasics of MatLab

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Use Matlab as a calculator

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>> 1.2 + 2.3

>> e

>> pi

>> (3+i) + (2+i*4)

• But most importantly it's great with matrices

• Row vector

>> r = [1 2 3 4]

• Column vector

>> c = [1+i; 2+3*i; 3+2*i; 4+5*i]

• >> a = r*c

• >> m = c*r


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• Multiply a matrix by a scalar:

>> m = 10*m

>> m = a*m

>> m = c*r;

>> m

>> m2 = [1 2; 3 4]

>> c'

>> c.'

>> v = [1:1:100];

>> v = [2:2:100];

>> v = [4:5:39]

>> v = [4:5:40]

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• Concatenating matrices:

>> c = [2; 4]

>> d = [1; 3]

>> z = [c d]

OR

>> z = [c; d]

• Notice the size of the matrices matters

>> e = [1 2 3; 4 5 6; 7 8 9]

• Try

>> z =[c e]


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• So start with a matrix >> A = [1 3 5 7; 2 4 6 8; 11 13 15 17];

• Get the element from row 2, column 3 >> A(2,3)

• Get the entire 2nd row >> A(2,:)

• Get the entire 3rd column >> A(:,3)

• How about this: >> A(1:3, 2:3)

• Or you can assign number to those locations:

>> A(2,3) = 100

>> A(2,:) = [100 100 100 100]

>> A(:,3) = [100; 100; 100]

>> A(1:3, 2:3) = [200 200; 200 200; 200 200]

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>> ones(1,4)

>> A(2,:) = 400.*ones(1,4)

>> A(:,3) = 400.*ones(3,1)

Find the size of a matrix >> size(A)

• Produce a matrix of zeros with the same dimensions >> zeros(size(A))

• The identity matrix is useful >> eye(3)

>> A = rand(3,3)

• Adding the elements of a matrix >> sum(A)

>> sum(sum(A))

• Finding the maximum / minimum elements

>> max(A)

>> max(max(A))


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• [x, k] = min(A)

• Square every element of A >> A.^2

• Cube every element of A >> A.^3

• Find the square root of every element of A >> sqrt(A)

• Define an array Y of 100 values between -5 and +6, inclusive.

>> Y = linspace(-5,6,100)

• Define an array F of 100 values evenly spaced on a logarithmic scale from 1E-5 to 1E6.

>> Y = logspace(-5,6,100)

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• Just a preview of how useful Matlab can be:

• >> x = 0:0.01:pi;

• >> y = sin(x)

• >> z = cos(x)

• >> plot(x, y)

• >> hold on

• >> plot(x, z, ′r′)

• If you want to delete the figure, try

• >> clf


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• Some more useful commands

• >> who

• >> doc

• >> help

• >> lookfor >> lookfor inverse

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• Many functions are available in Matlab:

• exp, sqrt, log, log10 , abs, angle, conj ,imag, real , ceil, floor, fix, round, sign, cos, sin, csc, sec, cot, tan, acos, asin, acsc, asec, acot, atan, atan2(y,x) , cosh, sinh, csch, sech, coth, tanh , acosh, asinh, acsch, asech, acoth, atanh,

• You can use the functions as follows:

• >> abs(-2)

• >> abs(1+i)

• >> abs(1+i)

• >> A = [1 2 3]

• >> B = [1 1 1]

• >> dot(A,B)

• >> cross(A,B)

Matlab Program Files

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• Script Files : Script files are just lists of commands. When you run the script file, they are executed as if they were typed into the computer. The script file can use any variable defined in your workspace (in Matlab) and all variables that it defines are now available from your workspace.

• Functions: Functions are script files with data encapsulation, that is, there is a list of inputs to the function file and a list of output. Any variable that you define in the function that is not in the list of outputs is not available in your workspace.

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• Script Files : Script files are just lists of commands. When you run the script file, they are executed as if they were typed into the computer. The script file can use any variable defined in your workspace (in Matlab) and all variables that it defines are now available from your workspace.

• Functions: Functions are script files with data encapsulation, that is, there is a list of inputs to the function file and a list of output. Any variable that you define in the function that is not in the list of outputs is not available in your workspace.

function y=myfunction(x)

y = x.^2;

• >> y = myfunction(3)

• y = myfunction([1 2 3])

NODAL ANALYSIS

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NODAL ANALYSIS

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NODAL ANALYSIS

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diary ex4_1.dat

% program computes the nodal voltages

% given the admittance matrix Y and current vector I % Y is the admittance matrix and I is the current vector % initialize matrix y and vector I using YV=I form

Y = [ 0.15 -0.1 -0.05; -0.1 0.145 -0.025; -0.05 -0.025 0.075];

I = [5; 0; 2];

% solve for the voltage

fprintf('Nodal voltages V1, V2 and V3 are \n')

v = inv(Y)*I

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NODAL ANALYSIS

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function [V] = testcircuit(Y,I )

%UNTITLED this function provides the general solution of

% set of algebraic equations

V=Y/I;

>> Y=[0.15 -0.1 -0.05; -0.1 0.145 -0.025; -0.05 -0.025 0.075];

>> I = [5; 0; 2];

>> V=testcircuit(Y,I)

NODAL ANALYSIS

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>> Y = [0.75 -0.2 0 -0.5; -5 1 -1 5; -0.2 0.45 0.166666667 -0.0666666667; 0 0 0 1];

>> I = [5 0 0 10]';

>> V=testcircuit(Y,I)

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NODAL ANALYSIS

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>> Z = [40 -10 -30; -10 30 -5; -30 -5 65];

>> V = [10 0 0]';

>> I=testcircuit(Z,V)


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• You can have functions with multiple input parameters

function f = myfunction2(x,c)

f= x(1)^2 + c*x(2)^2;

• Or

function [f, g] = myfunction2(x,c)

f = x(1)^2 + c*x(2)^2;

g = x(1)+x(2);

>> [a b] = myfunction2([3 2],4)

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• Input/Output

>> disp('The speed is')

>> disp(speed)

Type the following into a file, save, then run the script.

x = input('Input the value for the variable x')

s = input('Input the expression for the string s', 's')

k = menu('Choose a data marker', 'o', '*', '+', 'x');

x = 0:0.1:pi;

f = sin(x);

type = ['o', '*', '+', 'x'];

plot(x, f, type(k))


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• Relational Operations

>> x = [3 2 1]

>> y = [2 4 1]

>> z = (x < y)

>> z = (x > y)

>> z = (x == y)

>> z = (x ~= y)

>> z = (x <= y)

>> z = (x >= y)

>> z = (x >= 2)

>> z = y(x)

>> nz = ~z

>> x(nz)

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• More on conditionals:

• any(x) returns a scalar =1 if any element in the vector x is nonzero and 0 otherwise.

• any(A) returns a row vector with same number of columns as A with ones and zeros depending on whether the corresponding column has any nonzero elements

• all(x) returns a scalar =1 if all elements in the vector x are nonzero and 0 otherwise.

• all(A) returns a row vector with same number of columns as A with ones and zeros depending on whether the corresponding column has all nonzero elements.

• find(A) returns an array of indices of the nonzero elements of A


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>> any([1 2 3])

>> any([0 0 0])

• Does y have any zero elements? (0 if yes, 1 if no)

>> all([1 2 3])

>> all([1 0 3])

for matrices:

>> A = [1 2 3; 0 2 1; 4 5 6]

>> any(A)

>> all(A)

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• Logical Operators


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• Logical Operators

>> A = [1 1 0 0];

>> B = [1 0 1 0];

>> ~A

>> A&B

>> A|B

>> xor(A,B)

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• The “find” Command

• The find command is a powerful command that can be used to locate elements in a vector that satisfy a certain criterion.

• >>x=[-3 0 7 5 -8 -9 0 4 5];

• >>index=find(x<0)

• >>x(index)

• >>index2=find(x==0)

• >>x=(index2)

• >>index3=find(abs(x)<4)

• >>x(index3)


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• Conditional statements:

if expression

commands

elseif expression

commands

elseif expression

commands

OPTIONAL

elseif expression

commands

else

commands

end

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The switchThe switchThe switchThe switch----case constructcase constructcase constructcase construct

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% Four-function calculator

num1=input(‘Enter a number: ‘);

num2=input(‘Enter a number: ‘);

op=input(‘Enter the operation: ‘)

switch op

case ‘+’

x=num1+num2

case’-‘

x=num1-num2

case’*’

x=num1*num2

otherwise

x=num1/num2

end

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Loop Constructs

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• for Loop:

for index= start : step : end

Command statements

end

n=1;

m=0;

x(1)=0;

for k=1:3:100

m=m+k;

x(n+1)=x(n)+m/k;

n=n+1;

end

• x

• Here is another example with matrices:

A=[1,2,5;7,9,0];

for v=A

disp(v)

end

• Here is a demonstration of a “while” loop

• k=1;

• n=1;

• m=0;

• x(1)=0;

• while k<=100

• m=m+k;

• x(n+1)=x(n)+m/k;

• n=n+1;

• k=k+3;

• end

• x

Loop Constructs

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• for Loop:

for index= start : step : end

Command statements

end

n=1;

m=0;

x(1)=0;

for k=1:3:100

m=m+k;

x(n+1)=x(n)+m/k;

n=n+1;

end

• x

A=[1,2,5;7,9,0];

for v=A

disp(v)

end

for k=1:10

for m=1:4

x=0.005*k;

y=30*m;

z(k,m)=10*exp(-y*x)*cos(120*pi*x);

end

end

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Loop Constructs

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• Find the sum of the following series s=1+3+5+7+…+99

>>s=0.0;

>>for k=1:2:99

s=s+k;

end

>>s

Loop Constructs

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• while loop

>>while condition

Command statements

end

>>

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Loop Constructs

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• while loop

>>while condition

Command statements

end

>>

Loop Constructs

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• while loop

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PolynomialsPolynomialsPolynomialsPolynomials

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• P(s) = 2s2 + 4s + 5 can be expressed as a vector by entering the statement P=[2 4 5],

• The “roots” Command


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• The “poly” & “polyval” Commands

• The poly command is used to recover a polynomial from its roots. If r is a vector containing the roots of a polynomial, poly(r) return a row vector whose elements are the coefficients of the polynomial.

• The polyval command evaluates a polynomial at a specified value. If p is a row vector containing the coefficients of a polynomial, polyval(p,s) return the value of the polynomial at the specified value s.

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Polynomial multiplicationPolynomial multiplicationPolynomial multiplicationPolynomial multiplication

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• The product of two polynomial p(x) and q(x) is found by taking the convolution of their coefficients. MATLAB makes use of the conv function to obtain the coefficients of the required polynomial product. The coefficients should be in the order of decreasing power. Multiplication of more than two polynomials requires repeated use of conv.

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Polynomial multiplicationPolynomial multiplicationPolynomial multiplicationPolynomial multiplication

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Introduction to PlottingIntroduction to PlottingIntroduction to PlottingIntroduction to Plotting

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• >>plot (x,y, ‘linestyle_mark_color’);

• Plot a polynomial function:

>> a=[1,4,-15,9,1];

>> x=[-2:0.01:2];

>> f=polyval(a,x);

>> plot(x,f,'+-r'),xlabel('x'),ylabel('f(x)'),axis([-2,2,-9,9]),grid

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• Symbol of Lines, Marks & Colors


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• for more than one plot when plot(x,y,x,z,x,w) will not work

>> f=logspace(-1,3,200);

>> hf=1./((j*2*pi*f).^2-0.1*( j*2*pi*f)+10^2);

>> plot(f,abs(hf))

>> semilogx(f,abs(hf));

>> loglog(f,abs(hf));

>> semilogx(f,angle(hf));

>> semilogx(f,atan2(imag(hf),real(hf))*180/pi);

>> loglog(x,y)

>> semilogx(x,y)

>> semilogy(x,y)


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• polar(theta,f)

• stairs(x,y)

• bar(x,y)

• stem(x,y)

• plotyy(x,y,u,v,’function’,’function’)

• plotyy(x,y,u,v,’plot’,’stem’)

• plotyy(log10(f),(abs(hf)),log10(f),angle(hf),'semilogy','plot')

• figure(n)

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• Polyfit

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Documents

Dr. Munaf Salim › lmsdatapool... · Dr. Munaf Salim 16 diary ex4_1.dat % program computes the nodal voltages % given the admittance matrix Y and current vector I % Y is the admittance