Matlab Tutorial_General Use

8/10/2019 Matlab Tutorial_General Use

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AUC_MENG 375 Prof. Dr. Maki K. Habib

Introduction MATLAB stands for Matrix Laboratory

The window below appears when MATLAB starts

exit MATLAB with the command exit or quit


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Matrices can be introduced into MATLAB

in several different ways:

Entered by an explicit list of elements,

Generated by built-in statements and functions, Created in M-files, Loaded from external data files.


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(1)Math functions and matrix

operations:We deal with data in MATLAB as matrices.

For example, An array of data X= 1, 0, 9, 11, 5 is a 1x5 matrix, A scalar number 9 is an 1x1 matrix.


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Basic operations : How to define a row matrix (1xn):

>>X=[1 0 9 11 5] % define row Matrix 1x5% each element can be separated by spaces as shown or by%commas , .

% Here is The MATLAB echoX =

1 0 9 11 5NOTES :

(1) The MATLAB will treat all entries after the% sign as a comment.

(2) To stop the echo add ";"at the end of the line>> X=[1 0 9 11 5];


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How to define a column Matrix:

>>Y=[1; 3; 5; 7; 8] %define column Matrix 5x1

%Here is the Matlab echo:Y = 1

357

8


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How to define a 2 dimensional Matrix

Y =1 2 33 6 7

11 4 7

>>Y= [1 2 3; 3 6 7; 11 4 7]

%define 3x3 matrix where each row is separated%by semicolon%Here is the Matlab echo


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How to get the size of a Matrix:

Note: ans means answer

>> Y=[1; 3; 5; 7; 8];% Define column Matrix 5x1

>> size(Y)% get the size of the Matrix

% Here is the Matlab echo

ans=5 1

% 5 1 => means 5 rows and 1 column


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This table summarizes most Matricesoperations:

ExampleDescriptionOperation

Addition

+

Subtract

-

Multiply

*

Note:Matrix multiplication review is shown in the nextslide


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Review on matrix multiplication

Note: To multiply two matrices the number of columns ofthe first matrix must be equal to number of rows in theother matrix


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ExampleDescriptionOperation

Element by

elementmultiplication

.*

Matrixtranspose

>>C = A.*BC= 2 8 18

0 15 4263 64 0

>>C = AC= 1 4 7

2 5 83 6 0


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Element-by-

elementdivision

./

Element

-by-elementpower

.^


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>>a=[1 3 7 2 0]a = 1 3 7 2 0

>>b=[0 3 7 7 8]b = 0 3 7 7 8

% we initialized two matrices a and b>>c=a.*b % element by element multiplication

c = 0 9 49 14 0>>d=b' % d is a matrix contains the transpose of b

d = 0

3778

>>e=a*d % multiply a[1x5] d[5x1] to give e[1x1]e= 72

1Example


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How to get the roots of a Polynomial :EXAMPLE 2:

>> c=[1 2 3 4 5];% we write the coefficients of the polynomial

% the row matrix c = [1 2 3 4 5] represents the%polynomial x4 + 2 x3 + 3 x2 + 4 x + 5=0

>> roots(c)ans= 0.2878 + 1.4161i

0.2878 - 1.4161i-1.2878 + 0.8579i-1.2878 - 0.8579i

We want to get the roots of the polynomial x4 + 2 x3 + 3 x2 + 4 x + 5=0 The command roots computes the roots of thepolynomial.


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EXAMPLE 3:

>> a=[-1 1] %The row matrix represents the rootsa = -1 1

>> poly(a) %The command poly(a) computes the%polynomial (x-1)(x+1)=0

ans = 1 0 -1%the output is the coefficient of the polynomial x^2-1%the coefficient of x^2 is 1, coefficient of x is 0 ,%and the constant is -1

We want to get the polynomial x^2-1 from its roots-1 , 1

We use the command poly that computes thepolynomial (x-1)(x+1)=0

How to get a Polynomials from its roots:


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Example function:

num = [ 1 8 16 9 6]

den = [ 1 6 11 6][ r , p, k] = r esi due( num, den)

r =-6.0000-4.0000

3.0000

p =-3.0000-2.0000-1.0000

k =1 2

4 3 2

3 2

( ) 8 16 9 6( ) 6 11 6

6 4 323 2 1

B s s s s s

A s s s s

ss s s

+ + + +=

+ + +

= + + + +

+ + +Constants

Roots

Residue

Partial-fraction expansion function


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(2) 2d Plotting and 3d Plotting:FunctionMATLAB

Command

Syntax: start : step size : endEx: 0 : 0.1 : 5So this defines the array0,0.1,0.2,0.3..,4.8,4.9,5Note: this is used in plotting to specify

the domain ( independent variable )

Definingarray of

numbers

Note: for the function y = f(x)The domain: the values of the independent variable xThe range: values of y


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FunctionMATLABCommand

Syntax: Plot (variable1,variable2,marker);plot variable1 versus variable2

Note: Markers are optionalNote: Markers table is shown next

Plot

The plot command can be used to plot twosuperimposed plots on the same graph

Syntax:Plot (variable1,variable2,variable3,variable4)plot variable1 versus variable2 and variable3versus 4 on the same graph


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Syntax: Xlabel (name)Labels x-axis with the name in betweenthe quotesNote: name is a string defined between

the quotes

Xlabel

Syntax: Ylabel (name)Labels y-axis with the name in between

the quotes

Ylabel

Syntax: title (name)Labels the graph with the name inbetween the quotes

Title


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Syntax: gridAdds grid to the graphNote: grid command has no arguments

grid

Syntax: gtext (name)Labels the graph line with the name inbetween the quotes

gtext


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EXAMPLE 4:To plot the function:

>> t=0:0.1:5;% The range of t from 0 to 5 with an increment of 0.1

>> y=1./(t-exp(t)).^3+sin(t);% defining function y>> plot(t,y);% plot t on the horizontal axis versus y on the vertical axis

>> title( Plot of Example); %adds title to the graph>> xlabel(t); ylabel(y) ; grid;>> gtext(1/(t-exp(t)^3+sin(t))


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output:5Example


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EXAMPLE 5:

Two or more plots can be shown on thesame graph as shown in this example.

In this example, an additional function"y2 is to be shown with function y1

plotted on the same graph.


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>>x=0:0.01:1; %array starting from 0 to 1 with step 0.01>>y1=x; % y1 is equal to x, a straight line with slope 45>>y2=x.^2;>>plot(x,y1,bo',x,y2,gx')>>grid;>>xlabel('x')>>ylabel('y1,y2')>>title(Example4)

Note:Markers are used in the "plot" function for the

purpose of identification.


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Syntax: plot3 (x,y,z)Plot 3d graphs

It plots x versus y and z

plot3

Syntax: view ([1 0 0])

To show the graph from another viewEx:view([1 0 0])=>Show view parallel tox axis, ie: perpendicular to y-z plane

view

Commands used for 3d plotting:


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Different uses of view command:view ([0 0 1])

view ([1 0 0])

view ([0 1 0])


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3D plotting using plot3 command:

A 3-D plot is shown in the following example,where two functions sin(4t) , cos(4t) are plottedas parameter t increases from 0 to 5 at anincrement of 0.01.

>>t=0:0.01:5; % array from 0 to 5 with step 0.01>>plot3(t,sin(4*t),cos(4*t));

% plot command plot x versus y versus z>>xlabel('t');>>ylabel('sin(4*t)');>>zlabel('cos(4*t)');

>>grid;

:6EXAMPLE


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Example 6 output:

Note: we can get different views using the viewcommand as illustrated below


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Add the following line to previous program:>>view([1 0 0])

>>view([0 1 0])

C d d f 3d l i


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Syntax: [x,y]= meshgrid (array ofnumber1,array of number2)meshgrid function is used to transformthe domain for plotting using the surfcommand.

meshgrid

Syntax: surf (f)Where f is function to be plottedsurf

Commands used for 3d plotting:


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Meshgrid and surf commands:At each intersection point between array X and array Y the

function Z is being plotted


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3d plotting using surf command :

To generate a 3-D plot using surf command, youfirst need to establish the domains of the "x andy using meshgrid command.

Note:The meshgrid function is used to transform thedomain for plotting using the surf command.

EXAMPLE 7:

In this example, we want to plot the function: z=3sin(y) * cos(x)


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output:7Example


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AUC_MENG 375 Prof. Dr. Maki K. HabibMENG 476 and MENG 375

(3)How to write in an M-file:

We use m-file to:

save set of commands to be executed in a singlestep, and

write and save MATLAB functions.

Note :We can use any text editor program and save the fileas .m extension


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Restrictions when saving the m-file:

We can give any name to the m-file

But:No spaces are allowed

No dashes or commas or : or


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Steps:

(1) click on the new m-file icon as shown:

=> The window below will appear:


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Note :

You can specify the current working directory wherethe file is saved:

(2) Write the required lines then save and run

the program


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Here is a simple program written in an m-file

EXAMPLE 8:A = [1 2; 3 4] %define 2x2 matrixC=A.*A %perform element by elementmultiplication

Save and run the programHeres the output:

A =1 23 4

C =1 49 16

Note:the output appears in the command window.


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EXAMPLE 9:An m-file function named add_sub that has 2 inputsx, y and 1 output r, this function performs addition,Subtraction as follows..

function r=add_sub(x,y)r(1)=x+y;r(2)=x-y;

Calling the function will directly give the output>> add_sub(10,5)ans =

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