introduction to matlab zongqiang liao research computing group unc-chapel hill

Introduction to MATLABIntroduction to MATLAB

Zongqiang LiaoResearch Computing Group

UNC-Chapel Hill

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Course outlineCourse outline

Introduction

Getting started

Mathematical functions

Matrix generation

Matrix and array operations

Reading and writing data files

Basic plotting

Basic programming

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IntroductionIntroduction

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IntroductionIntroduction

The name MATLAB stands for MATrix LABoratoryIt is good at dealing with matrices

Vendor’s website: http//:www.mathworks.com

Advantages of MATLABEasiness of use

Powerful build-in routines and toolboxes

Good visualization of results

Disadvantage of MATLABCan be slow

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Getting startedGetting started

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MATLAB desktopThe Command Window

The Command History

The Workspace

The Current Directory

The Help Browser

The Start Button

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Keeping track of your work sessiondiary command

>> diary

or

>> diary FileName

Stop the recording

>> diary off

Start the recording again

>>diary on

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Using MATLAB as a calculator>> 1+2*3

ans =

7

You may assign the value to a output variable

>> x=1+2*3

x=

7

x can be used in the some calculation later

>> 4*x

ans =

28

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Suppressing outputYou can suppress the numerical output by putting a

semicolon (;) at the end of the line

>> t=-13;

We can place several statements on one line, separated by commas (,) or semicolons(;)

>> t=-13; u=5*t, v=t^2+u

u=

-65

v=

104

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Managing the workspaceThe results of one problem may have an effect on

the next one

Issue a clear command at the start of each new independent calculation

>> clear

or

>> clear all

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Miscellaneous commandsTo clear the Command Window

>> clc

To abort a MATLAB computation

ctrl-C

To continue a line

…

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Getting helpUse help to request info on a specific function

>> help sqrt

Use doc function to open the on-line version of the help menu

>> doc plot

Use lookfor to find function by keywords

>> lookfor functionkeyword

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Mathematical functionsMathematical functions

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Lists of build-in mathematical functionsElementary functions

>> help elfun

Special functions

>> help specfun

Such as

sin(x), cos(x), tan(x), ex, ln(x)

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Example 1

Calculate z=e-asin(x)+10 for a=5, x=2, y=8

>> a=5; x=2; y=8;

>> z=exp(-a)*sin(x)+10*sqrt(y)

z=

28.2904

y

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Example 2

Calculate the roots of a equation

ax2+bx+c=0, for a=2, b=1, and c=-4

>> a=2; b=1; c=-4;

>> x1=(-b+sqrt(b^2-4*a*c))/(2*a)

x1=

1.1861

>> x2=(-b-sqrt(b^2-4*a*c))/(2*a)

x2=

-1.1861

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Example 3

>> log(142)

ans=

4.9558

>> log10(142)

ans=

2.1523

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Example 4

Calculate sin( /4)

>> sin(pi/4)

ans =

0.7071

Calculate e10

>> exp(10)

ans =

2.2026e+004

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Matrix generationMatrix generation

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The name MATLAB is taken from ”MATrix LABoratory.” It is good at dealing with matrices.

Actually all variables in MATLAB are matrices. Scalars are 1-by-1 matrices

vectors are N-by-1 (or 1-by-N) matrices.

You can see this by executing

>> size(x)

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Entering a matrix

Begin with a square bracket, [

Separate elements in a row with spaces or commas (,)

Use a semicolon (;) to separate rows

End the matrix with another square bracket, ]

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• Entering a matrix: A typical example

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

>> A=

1 2 3

4 5 6

7 8 9

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Matrix indexing

View a particular element in a matrix

For example, A(1,3) is an element of first row and third column

>>A(1,3)

>>ans =

3

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Colon operator in a matrix

Colon operator is very useful in the usage of MATLAB

For example, A(m:n,k:l) specifies portions of a matrix A: rows m to n and column k to l.

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Example 1

Rows 2 and 3 and columns 2 and 3 of matrix A

>>A(2:3, 2:3)

ans =

5 6

8 9

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Example 2

Second row element of matrix A

>>A(2, :)

ans =

4 5 6

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Example 3

Last two columns of matrix A

>>A(:, 2:3)

ans =

2 3

5 6

8 9

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Example 4

Last rows of matrix A

>>A(2:end, :)

ans =

4 5 6

7 8 9

The end here denotes the last index in the specified dimension

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Transposing a matrix

The transposing operation is a single quote (’)

>>A’

ans =

1 4 7

2 5 8

3 6 9

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Concatenating matrices

Matrices can be made up of sub-matrices

>>B= [A 10*A; -A [1 0 0; 0 1 0; 0 0 1]]

B =

1 2 3 10 20 30

4 5 6 40 50 60

7 8 9 70 80 90

-1 -2 -3 1 0 0

-4 -5 -6 0 1 0

-7 -8 -9 0 0 1

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Generating vectors: colon operator

Suppose we want to enter a vector x consisting of points (0, 0.1, 0.2, 0.3,…,5)

>>x=0:0.1:5;

All the elements in between 0 and 5 increase by one-tenth

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Generating vectors: linear spacing

Suppose we want to have direct control over the number of points.

>>y=linspace(a, b, n)

For example,

>>theta=linspace(0, 2*pi, 101)

Creates a vector of 101 elements in the interval

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Elementary matrix generatorseye(m,n)

eye(n)

zeros(m,n)

ones(m,n)

diag(A)

rand(m,n)

randn(m,n)

logspace(a,b,n)

For a complete list of elementary matrices

>>help elmat

>>doc elmat

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Matrix arithmetic operationMatrix arithmetic operation

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Matrix arithmetic operation


Arithmetic operations

A+B or B+A

A*B

A^2 or A*A

a*A or A*a

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Matrix functions

det

diag

eig

inv

norm

rank

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Matrix functionsFor example

>> A=[1 2 3; 4 5 6; 7 8 0];

>>inv(A)

ans =

-1.7778 0.8889 -0.1111

1.5556 -0.7778 0.2222

-0.1111 0.2222 -0.1111

>>det(A)

ans =

27

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More matrix operations

Calculate the sum of elements in the second row of matrix A

>> sum(A(2,:))

Calculates the sum of the last column of A

>>sum(A(:,end))

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Array arithmetic operationArray arithmetic operation

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Array arithmetic operation


Array operations

Array operations are done element-by-element

The period character (.) is used in array operations

The matrix and array operations are the same for addition (+) and subtraction (-)

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Array operations

If A and B are two matrices of the same size with elements A=[aij] and B=[bij]

C=A.*B produces a matrix C of the same size with elements cij = aijbij

C=A./B produces a matrix C of the same size with elements cij = aij/bij

C=A.^2 produces a matrix C of the same size with elements cij = aij

2

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Array operationsExample 1

A= B=

>>C=A.*B

C=

10 40 90

160 250 360

490 640 810

987

654

321

908070

605040

302010

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Array operations

Example 2

>>C=A.^2

C=

1 4 9

16 25 36

49 64 81

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Save and load data file

Use command save to save the variable in the workspace

For example, use command save:

>> x = [1 3 -4];

>> y = [2 -1 7];

>> z = [3 2 3];

>> save Filename.mat

The command saves all variables in the workspace

into a binary file Filename.mat

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Save only certain variables by specifying the variable names after the file name

>> save Filename.mat x y

Save variables into ASCII data file

>> save Filename.dat x y –ascii

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The data can be read back with the load command

>> load Filename.mat

Load only some of the variables into memory

>> load Filename.mat x

Load the ASCII data file back into memory

>> load Filename.dat -ascii

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The textread function

The load command assumes all of data is of a single type

The textread function is more flexible, it is designed to read ASCII files where each column can be of a different type

The command is:

>> [A,B,C,...] = textread(filename, format, n);

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The textread function

For example, if a text file “mydata.dat” contains the following lines:

tommy 32 male 78.8

sandy 3 female 88.2

alex 27 male 44.4

saul 11 male 99.6

The command is:>> [name,age,gender,score] = textread(‘mydata.dat’, ‘%s %d %s %f’, 4);

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C style read/write

MATLAB allows C style file access. It is crucially important that a correct data format is used.

The steps are:

Open a file for reading or writing. A unique file identifier is assigned.

Read the data to a vector

Close the file with file identifier

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C style read/write: formatted files

In order to read results in formatted data files, the data format of the files must be know

For example, the numeric data is store in a file ‘sound.dat’. The commands reading data are:

>> fid = fopen(‘sound.dat’,‘r’);

>> data = fscanf(fid, ‘%f’);

>> fclose(fid);

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C style read/write: unformatted/binary files

In order to read results in unformatted data files, the data precision of the files must be specified

For example, the numeric data is store as floating point numbers using 32 memory bits in a file ‘vib.dat’. The commands reading data are:

>> fid1 = fopen(‘vib.dat’,‘rb’);

>> data = fread(fid1, ‘float32’);

>> fclose(fid);

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Basic plottingBasic plotting

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Plotting elementary functions

To plot the function y=sin(x) on the interval

[0, 2 ]

First create a vector of x values ranging from 0 to 2

Compute the sine of these values

Plot the result

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>>x=0:pi/100:2*pi;

>>y=sin(x);

>>plot(x,y)

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Adding titles, axis labels

>>xlabel (‘x=0:2\pi’);

>>ylabel (‘Sine of x’);

>>title (‘Plot of the Sine function’);

The character \pi creates the symbol

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Multiple data sets in one plot

Several graphs may be drawn on the same figure

For example, plot three related function of x: y1=2cos(x), y2=cos(x), and y3=0.5cos(x), on the interval [0, 2 ]

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>> x = 0:pi/100:2*pi;

>> y1 = 2*cos(x);

>> y2 = cos(x);

>> y3 = 0.5*cos(x);

>> plot(x,y1,‘--’,x,y2,‘-’,x,y3,‘:’)

>> xlabel(‘0 \leq x \leq 2\pi’)

>> ylabel(‘Cosine functions’)

>> legend(‘2*cos(x)’,‘cos(x)’,‘0.5*cos(x)’)

>> title(‘Typical example of multiple plots’)

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Subplot

The graphic window can be split into an m*n array of small windows.

The windows are counted 1 to mn row-wise, starting from the top left

For example, plot three related function of x: y1=sin(3 x), y2=cos(3 x), y3=sin(6 x), y4=cos(6 x), on the interval [0, 1]

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Subplot>> x = 0:1/100:1;

>> y1 = sin(3*pi*x);

>> y2 = cos(3*pi*x);

>> y3 = sin(6*pi*x);

>> y4 = cos(6*pi*x);

>> title(‘Typical example of subplots’)

>> subplot(2,2,1), plot(x,y1)

>> xlabel(‘0 \leq x \leq 1’), ylabel(‘sin(3 \pi x)’)


>> xlabel(‘0 \leq x \leq 1’), ylabel(‘cos(3 \pi x)’)


>> xlabel(‘0 \leq x \leq 1’), ylabel(‘sin(6 \pi x)’)


>> xlabel(‘0 \leq x \leq 1’), ylabel(‘cos(6 \pi x)’)

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Subplot

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Programming in MATLABProgramming in MATLAB

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Programming in MATLAB


M-File scripts

In order to repeat any calculation and/or make any adjustments, it is create a file with a list of commands.

“File New M-file”

For example, put the commands for calculating the roots of a quadratic equation into a file called quat.m

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M-File scripts

Enter the following statements in the filea = 2;

b = 1;

c = -4;

x1=(-b+sqrt(b^2-4*a*c))/(2*a)

x2=(-b-sqrt(b^2-4*a*c))/(2*a)

Save and name the file, quat.m

Note: the first character of the filename must be a letter

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M-File scripts

Run the file

>> quat

x1=

1.1861

x2=

-1.1861

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M-File scripts

It is possible to modify the file so that it prompts you for inputting values of a, b, and c each time it runs.

a = input(‘Enter a: ’);

b = input(‘Enter b: ’);

c = input(‘Enter c: ’);

x1=(-b+sqrt(b^2-4*a*c))/(2*a)

x2=(-b-sqrt(b^2-4*a*c))/(2*a)

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M-File scriptsRe-run this file, you may type in the values for a, b

and c

>> quat

Enter a: 3

Enter b: 4

Enter c: 5

x1 =

-0.6667 + 1.1055i

x2 =

-0.6667 - 1.1055i

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M-File scriptsMATLAB treats anything that appears after the % on

a line as comments and these line will be ignored when the file runs

% -------------------------------------------------------

% quat.m is to solve quadratic equation ax^2 + bx + c =0

% -------------------------------------------------------




x1=(-b+sqrt(b^2-4*a*c))/(2*a)

x2=(-b-sqrt(b^2-4*a*c))/(2*a)

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M-File scripts

You can display the first block of comment lines in any .m file by issuing the help command

>>help quat

% -------------------------------------------------------

% quat.m is to solve quadratic equation ax^2 + bx + c =0

% -------------------------------------------------------

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M-File functionsFunctions are routines that are general and applicable

to many problems.

To define a MATLAB function:Decide a name for the function, making sure that it

does not conflict a name that is already used by MATLAB.

Document the function

The first command line of the file must have this format:

Function[list of outputs]=functionname(list of inputs)

…….

Save the function as a M-file

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M-File scriptsIn the previous example, it is convenient to have a

separate file which calculate the roots of a quadratic equation

% -------------------------------------------------------

% quatsolv.m is to compute the roots of quadratic

% equation ax^2 + bx + c =0

% -------------------------------------------------------

function [x1, x2] = quatsolv(a, b, c)

x1=(-b+sqrt(b^2-4*a*c))/(2*a)

x2=(-b-sqrt(b^2-4*a*c))/(2*a)

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M-File scriptsTo evaluate this function, a main program is needed. This

main program provides input argumentss (a, b, and c)

% -------------------------------------------------------

% main.m is to solve quadratic equation ax^2 + bx + c =0

% it calls the external function quatsolv.m

% -------------------------------------------------------




[x1, x2] = quatsolv(a, b, c);

x1

x2

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M-File scripts

Example 2:

A new quatsolv2.m file is defined as the following:

% ----------------------------------------------------------

% quatsolv2.m is to compute the values of

% quadratic equation ax^2 + bx + c

% ----------------------------------------------------------

function y = quatsolv2(x)

global a b c

y = a*x^2 + b*x + c;

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M-File scriptsExample 2:

A new main file% -------------------------------------------------------

% main2.m is to plot quadratic equation ax^2 + bx + c for

% some range.

% it calls the external function quatsolv2.m

% -------------------------------------------------------

global a b c

a = 1;

b = 0;

c = -2;

fplot(‘quatsolv2’,[-4, 4])

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M-File scripts If run main2.m

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Questions and comments?Questions and comments?

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Questions and comments?

Questions and comments?

For assistance with MATLAB, please contact the Research Computing Group:

Email: [email protected]

Phone: 919-962-HELP

Submit help ticket at http://help.unc.edu

introduction to matlab zongqiang liao research computing group unc-chapel hill

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