Matlab PPTworkshop1

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MATLABWorkshopLecture 1

MATLAB WorkshopMATLAB Basics

Mohamed Taha

Communication Engineering DepartmentPrincess Sumaya University

[email protected]

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1 MATLAB Basics

What is MATLAB

It is an abbreviation to MATrix LABoratory Front end for a matrix library It is an interpreted language It contains huge amount of built in functions and

accept user defined functions

Compatible with almost all programming languages(C++, JAVA, .net applications), etc.

Memory allocations and de-allocations are done au-tomatically

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MATLAB data structures and data types

Basic data structure is matrix MATLAB calls matrices arrays Basic data type is double

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MATLAB Layout

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Interactive computing with MATLAB

Using MATLAB as a calculator ans is a default variable used if a variable is not

specified to hold the result

At the command prompt

>> 2+6-4*sin(4)ans = 11.0272

If we assign the variable x the last statement

>> x = 2+6-4*sin(4)x = 11.0272

ans disappeared

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% sign is used to write a comment% This is my first command

The last statement is totaly ignored by MATLAB

; is used to suppress the result, useful when theresult is a huge matrix (image)>>a=1;

To display the result>> a or disp(a)

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MATLAB vectors

Row vector A = [1 0 1] is entered in MATLABas A=[1 0 -1]

spaces are used between the elements

commas can be used as well

>> A=[1 0 -1]A = 1 0 -1

The size and data structure can be checked bytyping >> whose A

Name Size Bytes Class

A 1x3 24 double

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Column vector A =

1

0

1

>> A=[1;0;-1]A = 1

0-1

To convert a row vector to a column vector, usetranspose operator

A = 10

-1>> B=AB = 1 0 -1

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Matrices

Matrices are collection of column or row vectors m n matrix, contains m rows and n columns

The matrix A =

[1 12 0

1 j 2

]is entered as

>> A=[1 1/2 0;-1 j 2]A =

1.0000 0.5000 0-1.0000 0 + 1.0000i 2.0000

Size of the matrix or vector can be returned as>> [m,n]=size(A)m = 2n = 3

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Accessing the elements of a matrix/vector

For a vector (column or row), elements can be ac-cessed by specifying the number of the element

First element is a number 1 and not 0 in the arrayA = [1 0 -1]>> A(1)ans = 1

>> A(2)ans = 0

>> A(3)ans = -1

>> A(end)ans = -1

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For matrix, elements are accessed by specifying theirlocations in the row and column

A =

1 1 5j 0 2 + 3 j1 2 7/2

>> A=[1 -1 5 ; -j 0 2+3*j ; 1 2 -7/2];

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Elements of A are accessed as

Colon operator : is used to specify range ofcolumns and rows

1:3, produces [1 2 3]

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Creating vectors automatically

It is much efficient to create matrices and vectors auto-matically

Functions used to create matrices can be used to createvectors, opposite is not always possible.

For vectors:

x = linspace(StartVal , EndVal, N); Creates a row vector of N linearly spaced numbersbetween StartVal and EndVal

Increment = difference between any two consec-utive numbers = EndV alStartV alN1 Creates 10 elements between 1 and 5>> x=linspace(-1,5,10);

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The increment can be checked by subtracting anytwo consecutive numbers in x

>> x(2)-x(1)>> ans = 0.667

Exactly equals to 5(1)101 = 0.667

x = StartVal : Increment : EndVal

Exactly the same as linspace

x=-1:0.667:5

Produces the same x produced previously bylinspace

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Creating matrices automatically

Several functionsFunction Operation

eye(m,n) m n identity matrixzeros(m,n) m n matrix of zerosones(m,n) m n matrix of onesdiag(m) mm diagonal matrixdiag(m) extract diagonalsrand(m,n) m n randomly generated matrixrandn(m,n) m n randomly generated matrixhilb(m) mm Hilbert matrixmagic(m) mm magic square

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Matrix algebra

AB, A and B are vectors or matrices of the samesize

>> A=[1 0 -1; 1/2 j -3];>> B=ones(2,3);>> C=A-B;

AB, columns {A} = rows {B}

>> A=[1 0 -1; 1/2 j -3];>> B=ones(2,3);>> C=A*B;

A. B, multiply the corresponding elements of Aand B, A and B must be of the same size

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>> A=[1 0 -1; 1/2 j -3];>> B=ones(2,3);>> C=A.*BC =

1.0000 0 -1.00000.5000 0 + 1.0000i -3.0000

A./B, divide the corresponding elements in A andB, A and B must be of the same size

>> A=[1 0 -1; 1/2 j -3];>> B=ones(2,3);>> C=A./BC =

1.0000 0 -1.00000.5000 0 + 1.0000i -3.0000

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Inverse of a matrix A, A is a square, full rank matrix>> A=randn(3);>> B=inv(A)B =

0.1749 -0.6997 -0.7158-0.2860 0.1538 1.05680.9737 -0.2917 -0.5160

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Matrix functions

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MATLAB built in variables

MATLAB has several built in variables

These variables name should not be used for user definedvariables

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User defined variables

Should starts with characters a-z or A-Z Can have any remaining characters Maximum length 31 Should not have the name of a built in vari-

able/function or a user defined function

A is different from a, case sensitive

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Polynomials

Most engineering problems based on polynomial manip-ulations

Some functions

The polynomial f(x) = x2 + 2x + 1 is entered asf=[1 2 1];

The polynomial g(x) = x2 + 1 is entered as

g=[1 0 1];

The value of g(0.5)polyval(g,-0.5)

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c(x) = f(x)g(x) is computed as

>> f=[1 2 1];>> g=[1 0 1];>> c=conv(f,g)

c =

1 2 2 2 1

The result is interpreted from right to left as

c(x) = 1 + 2x + 2x2 + 2x3 + x4

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Vectorization

Transforming any problem to matrix-vector manipula-tion

Useful in engineering problems

In this case loops are avoided.

Consider the C-loop

pi=3.14;N=5;

for (i=0; i < N ; i++){

x[i]=pi*i/4;}

MATLAB version x=0:pi/4:pi

Uses 15 of the time required for the C-loop

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2 Plotting

Plotting (x,y) dataTwo dimensional plots are created with the plotfunction.

plot(x,y)plot(xdata,ydata,symbol)plot(x1,y1,x2,y2,...)plot(x1,y1,symbol1,x2,y2,symbol2,...)

x and y must have the same size, x1 and y1 musthave the same size, x2 and y2 must have the samesize, etc.

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Different axis scaling

Name Axis scaling

loglog log10(y) versus log10(x)plot linear y versus xsemilogx linear y versus log10(x)semilogy log10(y) versus linear x

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Linear Scale

>>x=-10:0.1:10;>>y=x.2;>>plot(x,y)>>grid

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Log Scale

>>x=linspace(0,1,10);>>y=exp(2*x);>>semilogy(x,y)

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Practice

1. Use colon operator to create a 100 elements vectorbetween 3 and 10 with uniform spacing betweenelements.

2. For the vector created in (1), square all elements.

3. Create 4 4 normal random matrix, A. Find a newmatrix, B such that its columns are the diagonal ofthe matrix A.

Ans. diag(A)*ones(1,4)

4. Create a 3 3 uniform random matrix, X. Findthe eigen value decomposition of the matrix, X =V V 1.

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5. Create 1 100 random vector with zero mean andunity variance. Check the values of the mean andthe variance using MATLAB commands.

6. You need to use the randn, mean, var functions.To find help about these functions, at the commandprompt, type, help FunctionName.

7. Create the matrix1 3 0

2 9 18 0.5 7

Write MATLAB commands to:

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Extract the elements of the second row Interchange column 3 and column 1 Subtract row 1 from row 2 and store the result

in the second row

Multiply all elements in row 1 and all elementsin column 2 and store the result in row 1

8. Given the vectors x =[

1 3 7],

y =[

2 4 2], A =

[3 1 6

5 2 7

], and

B =

1 4

7 8

2 2

.Determine which of the following statements willcorrectly execute (and if not, state why). For thecorrectly executed statements give the final result

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using MATLAB.

1. x + y 2.[x; y] 3.B A 4.B./x5.x + A 6.[x; y] 7.B A 8.B./x9.A [x, y] 10.ones(1, 3) A 11.[x; y] + A

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