Matlab Seminar 2010

8/8/2019 Matlab Seminar 2010

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What is MATLAB ?

MATrix LABoratory

Developed by The Mathworks, Inc (http://www.mathworks.com)

Interactive, integrated, environment

± for numerical computations

± for symbolic computations

± for scientific visualizations

It is a high-level programming language



Characteristics of MATLAB

Programming language based (principally) on matrices .

± Slow - an interpreted language ,i.e .not pre-compiled.Avoid for loops; instead use vector form whenever

possible .

± Automatic memory management, i.e., you don't haveto declare arrays in advance .

± Intuitive, easy to use .

± Shorter program development time than traditional programming languages such as Fortran and C .

± Can be converted into C code via MATLAB compiler for better efficiency .

Many application-specific toolboxes available .



Start menu Matlab MATLAB

³>>´ ±

>> date



Getting Help

>> help date

>> helpwin date

helpwin gives you the same information as help, but in a different window.



Getting Help

>> doc date

>> lookfor date % search for keywords that best describe the function

>>Ctrl+C% stop Matlab from running

>> clc % clear screen



Special characters

>> % default command prompt

% % comment - MATLAB simply ignores anything to the

right of this sign (till the end of the line).

>> % my comment

; % semicolon at the end of the line will prevent MATLAB

from echoing the information you type on the screen.

>> a=20

>> B=20;



Creating Variables

Matlab as a calculator:

>>2+5

>>7*10+8

>>5^2

µans¶ - "answer", used in MATLAB as the default variable.



Defining Your Own Variables

When Matlab comes across a new variable name - it

automatically creates it.

Begins with a LETTER, e.g., A2z.

Can be a mix of letters, digits, and underscores (e.g., vector_A,

but not vector-A)

Not longer than 31 characters.

No spaces

Different mixes of capital and small letters = different

variables.

For example: "A_VaRIAbLe", "a_variable", "A_VARIABLE",

and "A_variablE

>> String=µthis is a string¶



Listing & Clearing Variables

>> whos

>> clear, clear all %clear variables from memory

>> a=10

>> b = 20

>> the_average = (a + b ) / 2



Creating vectors

Row separator:

space/coma (,)

Creating sequences:

From : jump: till

linespec(X1, X2, N)

generates N points between

X1 and X2.

Coulmn separator:

Semicolon (;)



Creating Matrices

Matrices must be rectangular.

Creating random matrices:

2-by-4 random matrix

(2 rows and 4 columns).



Creating Matrices

You can combine existing vectors as matrix elements:

You can combine existing matrices as matrix elements:



Indexing Into a Matrix

>> B=A(3,1);

>>A(:,end)=[1;7;3;8;4];

The row number is first, followed by the column number.



Linear Algebra Operations



Matrix Multiplication

Inner dimensions must be equal

Dimension of resulting matrix = outermost

dimensions of multiplied matrices

Resulting e

lements = dot product of the rows of

the 1st matrix with the columns of the 2nd matrix



Type the following:

>>a=[2 3]

>>b=[3 2]

>>a*b

>>a.*b

>>a.*b¶

>>a*b¶

Vector Multiplication



String Arrays

Created using single quote delimiter (')

Indexing is the same as for numeric arrays



String Array Concatenation



Working with String Arrays



Example: Solving Equations

Solve this set of simultaneous equations: Ax=B, x=?



Cr eating Scr ipts with MATLABCr eating Scr ipts with MATLAB

Editor/Debugger Editor/Debugger

Automatically saves files as ASCII text files for you.

Scripts in MATLAB has the ".m" suffix.

They are also called "M-files".

Open Matlab Editor:

File New M-file OR:

>> editRun



Add path Add path

>> addpath C:\EMEM899\Somedirectory

Set path



Scr ipt M Scr ipt M--files files

Standard ASCII text files Contain a series of MATLAB expressions

A script does not define a new workspace

% Comments start with "%" character

pause % Suspend execution - hit any key to continue.

keyboard % Pause & return control to command line.

% Type "return" to continue.

break % Terminate execution of current loop/file.

return % Exit current function% Return to invoking function/command line.

Continue % go to next iteration

Input % Prompt for user input



A Simple Scr ipt A Simple Scr ipt

% a simple MATLAB m-file to calculate the

% square root of an input numbers.

my_num=input('insert a number');% now calculate the square root of the number and print

it out:

square_root = sqrt(my_num)

Write a program which receives a number from the user,

calculates it¶s square root (use µsqrt¶ command) and displays

the result.

save the script as "square_root_script.m" in your own folder



Running Scr ipts Running Scr ipts

>> square_root_script

The header - comments you place at the beginning of your scripts will bereturned to users when they get help for your script.

>> help square_root_script

Note: The variables defined in the script remain in the workspace even

after the script finishes running. Creating comments: ctrl+r, or right click on the mouse, or

%{

coment

coment%}



Find and Replace ± ctrl+F

Key words

Wrong use of key words

Indenting: Ctrl+I

Running Scr ipts ( Running Scr ipts (22) )



F low C ont r ol C onst r ucts F low C ont r ol C onst r ucts

Logic Control:

± IF / ELSEIF / ELSE

± SWITCH / CASE / OTHERWISE

Iterative Loops:

± FOR

± WHILE



The if, elseif and else statementsThe if, elseif and else statements

if I == J

A(I,J) = 2;

elseif abs(I-J) == 1

A(I,J) = -1;

else

A(I,J) = 0;

end

Works on Conditional statements

Logic condition is µtrue¶ if its different then 0.

ELSEIF does not need a matching END, while ELSE IFdoes.

if I == J

A(I,J) = 2;

else if abs(I-J) == 1

A(I,J) = -1;

else

A(I,J) = 0;

end %else if

end %if



Boolean Operators & Indexing



Switch, C ase, and Other wiseSwitch, C ase, and Other wise

switch input_num

case -1input_str = 'minus one';

case 0

input_str = 'zero';

case 1

input_str = 'plus one';

case {-10,10}

input_str = '+/- ten';

otherwise

input_str = 'other value';

end

More efficient than elseif statements

Only the first matching case is executed



P r oblem P r oblem

Build a program which receives a variable x and its units

(mm, cm, inch, meter) and calculates Y- it¶s value in

centimeters units. Use switch case.

1 Inch = 2.54 cm

Write a comment for error case.

Save the file under units.m



SolutionSolution

x = 3.0;

units = 'mm';

switch units

case {'in','inch'}

y = 2.54*x % converts to centimeters

case {'m','meter'}y = x*100 % converts to centimeters

case { 'millimeter','mm'}y = x/10;

disp ([num2str(x) ' in ' units ' convertedto cm is :' num2str(y)])

case {'cm','centimeter'}y = x

otherwise

disp (['unknown units:' units])y = nan;

end



Similar to other programming languages

Repeats loop a set number of times (based on index)

Can be nested

Each loop is closed with end.

The for loopThe for loop

N=10;

for I = 1:2:N

for J = 1:N A(I,J) = 1/(I+J-1);

end

end



The while loopThe while loop

I=1; N=10;

while I<=N

J =1;

while J<=N

A(I,J)=1/(I+J-1);J =J+1;

end

I=I+1;

end

Similar to other programming languages

Repeats loop until logical condition returns FALSE.

Can be nested.

Stopping infinity loop:

Ctrl+C

Ctrl+break



Array Operations



Line Plots in Two Dimensions

Plot (x,y)

makes a two-dimensional line plot for each point in X and its

corresponding point in Y: (X(1),Y(1)), (X(2),Y(2)), (X(3),Y(3)), etc.,

and then connect all these points together with line.

E

xample:

>> x=1:1:5;

>>Y=[2 7 0 -8 6];

>> plot (x,y);

>> xlabel (µlabel for x-axis¶)

>> ylabel (µlabel for y-axis¶) >> title (µtitle¶)



C

heck the foll

owing: x_points = [-10 : .05 : 10];

plot(x_points, exp(x_points)); % plot in Blue (default)

grid on

hold on

plot(x_points, exp(.95 .* x_points),'m'); % plot in Magenta plot(x_points, exp(.85 .* x_points), 'g'); % plot in Green

plot(x_points, exp(.75 .* x_points), ' p'); % plot a star

hold off

xlabel('x-axis'); ylabel('y-axis');

title('Comparing Exponential Functions

');

legend ('1', '2', '3', '4')

Multiple Plots

- 10 -5 0 5 10 0

0. 5

1

1. 5

2

2. 5 x 10

4

x-axis

y - a x i s

Comp aring E xponential Func tions

1

2

3

4



Subplots

multiple plots in the same window, each with their own

axes.

Subplot (M,N,P)

M ± rows N - columns

P ± number of subplot

in the figure

Subplot (2,2,1)



More about figures

Figure % Open a new figure without closing old figures

Figure (i) % Open the i-th figure

Close all % close all open figures axis ([xmin xmax ymin ymax]) % sets scaling for the x-

and y-axes on the current plot.



Special Graph Annotations (TeX)



Plot Editor Toolbar



Exercise

x = (1, 1.05, 1.1, 1.15« 5)

Y=sin(x)

Z=log(x)

Put your name in the title

Hint: check the doc on function ³LineSpec .́

Create the following:

1 1.5 2 2 .5 3 3 .5 4 4 .5 5 -1

-0.5

0

0 .5

1

1 .5

2Merav's graph

x

y

sin(x)

log(x)



Solution

x=1:0.05:5;

y=sin(x);

z=log(x);

hold on plot (x,y,'-.r*')

plot (x,z,'-.go')

hold off

title ('Merav''s graph');

xlabel ('x')

ylabel ('y')

legend ('sin(x)', 'log(x)');



More exercise

Make a 3 three-dimensional graph of (x,y,z) ± use Matlab help.

Make two separate 2-D graphs, with separate axis, in the same window:

y vs. x, and z vs. x.

Use the same x,y,z as defined in the previous exercise

1

2

3

4

5

-1

-0.5

0

0. 5

10

0. 5

1

1. 5

2

x

3D graph

y

z

1 2 3 4 5 -1

-0.8

-0.6

-0.4

-0.2

0

0. 2

0. 4

0. 6

0. 8

1s in(x)

x

y =

s i n ( x )

1 2 3 4 5 0

0. 2

0. 4

0. 6

0. 8

1

1. 2

1. 4

1. 6

1. 8

x

log(x)

z



Solution

3-D graph:

>> plot3(x,y,z)

>> grid

>> xlabel ('x')

>> ylabel('y')

>> zlabel('z')

>> title ('3D graph')

Subplots

>> subplot (1,2,1);

>> plot(x,y);

>> title ('sin(x)');>> xlabel('x');

>> ylabel('y=sin(x)');

>> grid;

>> subplot (1,2,2);

>> plot(x,z);>> xlabel('x');

>> title ('log(x)');

>> grid;

>> ylabel ('

z'

);

Matlab Seminar 2010

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