A Quick Start on MATLAB

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AA =

1 2 3

4 5 6

7 8 9

Be careful! MATLAB is case-sensitive, so A and a, are different beasts from

MATLABs point of view!

Operations on matricesNow that you have introduced a matrix to MATLAB you can do whatever you

want with it! For example you can transpose it. How?! Very easy just type: A

ans =

1 4 7

2 5 8

3 6 9

Or you can find sum of the elements in each column: sum(A)

ans =

12 15 18

Note: ifA is a vector (row vector or column vector), sum(A) returns the sum over all its

elements.Question: How do you get summation of elements in each row?

Question: How do you get summation of over all the elements?

All the following operators work with the same as sum(.):

mean(A) : Returns average of elements in a vector (row vectorcontaining average of each column, for matrices)

var(A) : Returns variance of elements in a vector (row vector

containing variance of each column, for matrices)

For standard deviation use std(A).

median(A) : Returns average of elements in a vector (row vector

containing average of each column, for matrices)

max(A) : Returns maximum element in a vector (row vector containing

maximum element in each column, for matrices)

min(A) : Returns minimum element in a vector (row vector containing

minimum element in each column, for matrices)

In many cases you need to know the position of the maximum or minimum element. You

can use the following command: [m,i]=max(A)

m =

7 8 9

i =

3 3 3

Where, m contains the maximum elements of each column, and i contains the position of

the maximum element in each column.


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Access to a matrixs elements (Subscripts):Accessing to a elements of a matrix is very easy, for example if you want to show

the element in 3rd row and 1st column:

A(3,1)

ans =

7

and if you want to show the whole 3rd column, just use colon: A(:,3)

ans =

3

6

9

Some other useful operators on matrices* In order to find dimensions of a matrix, use size: size(A)

ans =

3 3

For vectors, you can also use length.

*From linear algebra, we know that all the useful information about a matrix is stored in

its eigenvalues and eigenvectors. Use function eig: eig(A)

ans =

16.1168

-1.1168

-0.0000

What appears on screen is a vector containing eigenvalues ofA. In order to get

eigenvectors use: [V,D]=eig(A)

V =

0.2320 0.7858 0.4082

0.5253 0.0868 -0.8165

0.8187 -0.6123 0.4082

D =

16.1168 0 0

0 -1.1168 0

0 0 -0.0000

V contains eigenvectors ofA and diagonals ofD are eigenvalues.

*To get diagonal elements of a matrix use:


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diag(A)

ans =

1

5

9

* To find determinant of a matrix, just type1: det(A)

ans =

0

*To find inverse of a matrix, just type2: inv(A)

Warning: Matrix is close to singular or badly scaled.

Results may be inaccurate. RCOND = 2.055969e-018.

ans =

1.0e+016 *

-0.4504 0.9007 -0.4504

0.9007 -1.8014 0.9007

-0.4504 0.9007 -0.4504

Special matricesMany times, in your programs you need to have a matrix of zeros, ones, identity

matrix or random matrices of arbitrary size.

zeros(m,n) : mn matrix of zero elements

ones(m,n) : mn matrix of ones

eye(m,n) : mn matrix with ones on principal diagonal and zero

elsewhere

rand(m,n) : mn matrix with uniform(0,1) random elementsrandn(m,n) : mn matrix with normal(0,1) random elements

For more matrix functions type help elmat on MATLAB command window.

Matrices as argument of a mathematical functionAll the mathematical functions operate on each element of a matrix. For example

function log(A), returns logarithm of each of the elements in A: log(A)

ans =

0 0.6931 1.09861.3863 1.6094 1.7918

1 The determinant is not exactly zero, but MATLAB round up the numbers that it shows on the screen. Sovery small numbers appear as zero, be careful! Many of the 0s that you see on the screen might not be

zero!2 Good! Now you are exposed to MATLABs warnings. They are not errors (they dont stop the flow of

your computation), but sometimes they are extremely helpful for tracking mistakes in your program.

Fortunately, MATLAB is very generous in producing them; youre going to see a lot of these warnings if

you are thinking of being a MATLAB expert!


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1.9459 2.0794 2.1972

For more help on mathematical functions type help elfun on MATLAB command

window.

Summation, subtraction, multiplication and division

You can perform all the basic operations, as long as you dont violate thedimensions requirements. MATLAB also lets you perform multiplications and divisions

element by element. Look at the following example (Look at the dot,.): a=[12 34 5];

b=[2 17 1];

a./b

ans =

6 2 5

a.*b

ans =

24 578 5

For square matrices you cab calculate a number to the power of a matrix: 2^A

ans =

1.0e+004 *

0.7962 0.9782 1.1603

1.8029 2.2154 2.6276

2.8097 3.4523 4.0950

You can also perform this, element by element (Look at the dot, .):

2.^A

ans =

2 4 8

16 32 64

128 256 512

For more information on operators type help ops in MATLAB command window.

Flow ControlMATLAB has five flow control constructs:

if statements

switch statements for loops

while loops

break statements

ifThe if statement evaluates a logical expression and executes a group of statements whenthe expression is true. The optional elseif and else keywords provide for the execution of


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R =

12 34 5

144 1156 25

1728 39304 125

Note: The increments in the first line need not be 1, in fact you can have the counter

counts at any pace, e.g.: for t=-21:.9:12,

In fact the above command can be used to generate a vector of equally spaced numbers. t=1:.5:4;

t

t =

1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000

whileThe while loop repeats a group of statements an indefinite number of times under control

of a logical condition. A matching end delineates the statements.Here is a complete program, illustrating while, if, else, and end, that uses interval

bisection to find a zero of a polynomial. a = 0; fa = -Inf;

b = 3; fb = Inf;

while b-a > eps*b

x = (a+b)/2;

fx = x^3-2*x-5;

if sign(fx) == sign(fa)

a = x; fa = fx;

else

b = x; fb = fx;

end

endx

The result is a root of the polynomialx3 - 2x - 5, namelyx =

2.0946

breakThe break statement lets you exit early from a for or while loop. In nested loops, break

exits from the innermost loop only.Here is an improvement on the example from the previous section. a = 0; fa = -Inf;

b = 3; fb = Inf;

while b-a > eps*b

x = (a+b)/2;

fx = x^3-2*x-5;

if fx == 0

break

elseif sign(fx) == sign(fa)

a = x; fa = fx;

else

b = x; fb = fx;


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end

end

x

x =

2.0946

Question: Why is the use of break a good idea?

GraphsOne of easiest things to do with MATLAB is drawing a graph, It is also where

you have the most fun with MATLAB! Look at the following example: t=1:.1:50;

x=exp(-t/10).*sin(t/2);

plot(t,x)

And the following graph appears in a new graph window.

Get more information by typing help plot on command window. Also some other

useful graphical functions are subplot, hold, grid and hist. Make sure to take a

look at MATLAB help on these commands, they are very useful.

Help and Online Documentation4

There are several different ways to access online information about MATLAB functions.

The help command

The help window

The MATLAB Help Desk

Online reference pages

Link to The MathWorks, Inc.

The help CommandThe help command is the most basic way to determine the syntax and behavior of a

particular function. Information is displayed directly in the command window. For

example help fliplr

Shows

FLIPLR Flip matrix in left/right direction.

4 The followings are adapted exactly from MATLAB helpdesk since I do not know whether it is accessible

on our system or not.


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FLIPLR(X) returns X with row preserved and columns flipped

in the left/right direction.

X = 1 2 3 becomes 3 2 1

4 5 6 6 5 4

See also FLIPUD, ROT90, FLIPDIM.

Note: MATLAB online help entries use uppercase characters for the function andvariable names to make them stand out from the rest of the text. When typing function

names, however, always use the corresponding lowercase characters because MATLAB

is case sensitive and all function names are actually in lowercase.All the MATLAB functions are organized into logical groups, and MATLAB's directory

structure is based on this grouping. For example, all the linear algebra functions reside in

the matfun directory. To list the names of all the functions in that directory, with a briefdescription of each: help matfun

Matrix functions - numerical linear algebra.

Matrix analysis.

norm - Matrix or vector norm.

normest - Estimate the matrix 2-norm

...

The commandhelp

by itself lists all the directories, with a description of the function category eachrepresents:matlab/general

matlab/ops

...

The Help WindowThe MATLAB help window is available on PCs by selecting the HelpWindow optionunder the Help menu, or by clicking the question mark on the menu bar. It is also

available on all computers by typinghelpwin

To use the help window on a particular topic, typehelpwin topic

The help window gives you access to the same information as the help command, but the

window interface provides convenient links to other topics.

The lookfor CommandThe lookfor command allows you to search for functions based on a keyword. It

searches through the first line of help text, which is known as the H1 line, for eachMATLAB function, and returns the H1 lines containing a specified keyword. Forexample, MATLAB does not have a function named inverse. So the response fromhelp inverse

isinverse.m not found.

Butlookfor inverse


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finds over a dozen matches. Depending on which toolboxes you have installed, you will

find entries likeINVHILB Inverse Hilbert matrix.

ACOSH Inverse hyperbolic cosine.

ERFINV Inverse of the error function.

INV Matrix inverse.

PINV Pseudoinverse.IFFT Inverse discrete Fourier transform.

IFFT2 Two-dimensional inverse discrete Fourier transform.

ICCEPS Inverse complex cepstrum.

IDCT Inverse discrete cosine transform.

Adding -all to the lookfor command, as inlookfor -all

searches the entire help entry, not just the H1 line.

The Help DeskThe MATLAB Help Desk provides access to a wide range of help and reference

information stored on a disk or CD-ROM in your local system. Many of the underlying

documents use HyperText Markup Language (HTML) and are accessed with an InternetWeb browser such as Netscape or Microsoft Explorer. The Help Desk process can be

started on PCs by selecting the Help Desk option under the Help menu, or, on all

computers, by typinghelpdesk

All of MATLAB's operators and functions have online reference pages in HTML format,

which you can reach from the Help Desk. These pages provide more details and

examples than the basic help entries. HTML versions of other documents, including this

manual, are also available. A search engine, running on your own machine, can query allthe online reference material.

The doc CommandIf you know the name of a specific function, you can view its reference page directly. Forexample, to get the reference page for the eval function, typedoc eval

The doc command starts your Web browser, if it is not already running.

Printing Online Reference PagesVersions of the online reference pages, as well as the rest of the MATLAB

documentation set, are also available in Portable Document Format (PDF) through theHelp Desk. These pages are processed by Adobe's Acrobat reader. They reproduce the

look and feel of the printed page, complete with fonts, graphics, formatting, and images.

This is the best way to get printed copies of reference material.

Link to the MathWorksIf your computer is connected to the Internet, the Help Desk provides a connection to The

MathWorks, the home of MATLAB. You can use electronic mail to ask questions, makesuggestions, and report possible bugs. You can also use the Solution Search Engine at

The MathWorks Web site to query an up-to-date data base of technical support

information.


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Learning MoreTo see more MATLAB examples, select Examples and Demos under the menu, or typedemo

at the MATLAB prompt. From the menu displayed, run the demos that interest you, andfollow the instructions on the screen.

For a more detailed explanation of any of the topics covered in this book, see

The MATLAB Installation Guide describes how to install MATLAB on your

platform.

Using MATLAB provides in depth material on the MATLAB language, working

environment, and mathematical topics.

Using MATLAB Graphics describes how to use MATLAB's graphics andvisualization tools.

The MATLAB Application Program Interface Guide explains how to write C or

Fortran programs that interact with MATLAB.

MATLAB Product Family New Features provides information on what is new in

this release and information that is useful in making the transition from previous

releases of MATLAB to this release.For the very latest information about MATLAB and other MathWorks products, point

your Web browser to:

http://www.mathworks.comand use your Internet News reader to access the newsgroupcomp.soft-sys.matlab

Welcome to the world of MATLAB!
http://www.mathworks.com/http://www.mathworks.com/

A Quick Start on MATLAB

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