Arab Open University

Faculty of Computer Studies

M133: Numerical Analysis

Chapter 1

Introduction to MATLAB

MATLAB

This introduction will give

• Some basic ideas

• Main advantages and drawbacks compared

to other languages

MATLAB

What Is MATLAB?

MATLAB (MATrix LABoratory)

• High-performance language for technical computing

• Computation, visualization, and programming in an

easy-to-use environment

Typical uses include:

• Math and computation

• Algorithm development

• Modelling, simulation and prototyping

• Data analysis, exploration and visualization

• Scientific and engineering graphics

• Application development, including Graphical User

Interface building

MATLAB

MATLAB is an INTERPRETED language

…with all the advantages and drawbacks !

…there is a MATLAB Compiler, but it‟s not worth too

much in terms of speed

MATLAB takes care of the usual programming

overhead, e.g. memory allocation, data type

conversion, parameters by value/reference

… with all the advantages and drawbacks !

MATLAB is NOT object oriented, although there are

some attempts to extend it

MATLAB

MATLAB is able to cooperate with other

languages, e.g.

• C, C++

• JAVA

• Fortran

Why MATLAB

A good choice for vision program development

because:

• Easy to do very rapid prototyping

• Easy to learn, well documented

• A good library of image processing functions

• Excellent display capabilities

• Widely used for teaching and research in

universities and industry

• Another language to impress your boss with !

Why not MATLAB

Has some drawbacks:

• Slow for some kinds of processes

• Not geared to the web

• Not designed for large-scale system

development

MATLAB Components

MATLAB consists of:

• The MATLAB language

a high-level matrix/array language with control flow statements,

functions, data structures, input/output, and object-oriented

programming features.

• The MATLAB working environment

the set of tools and facilities that you work with as the MATLAB

user or programmer, including tools for developing, managing,

debugging, and profiling

• Handle Graphics

the MATLAB graphics system. It includes high-level commands

for two-dimensional and three-dimensional data visualization,

image processing, animation, and presentation graphics.

• …(cont‟d)

MATLAB Components

…

• The MATLAB function library

a vast collection of computational algorithms ranging from

elementary functions like sum, sine, cosine, and complex

arithmetic, to more sophisticated functions like matrix inverse,

matrix eigenvalues, Bessel functions, and fast Fourier

transforms as well as special image processing related

functions

• The MATLAB Application Program Interface (API)

a library that allows you to write C and Fortran programs that

interact with MATLAB. It include facilities for calling routines

from MATLAB (dynamic linking), calling MATLAB as a

computational engine, and for reading and writing MAT-files.

MATLAB

Some facts for a first impression

• Everything in MATLAB is a MATRIX !

• Again: MATLAB is an interpreted language, no

compilation needed (but possible)

• Again: MATLAB does not need any variable

declarations, no dimension statements, has no

packaging, no storage allocation, no pointers

• Programs can be run step by step, with full access to

all variables, functions etc.

What does MATLAB code look like?

What‟s the output ?

A simple example:

a = 1

while length(a) < 10

a = [0 a] + [a 0]

end

What does MATLAB code look like?

A simple example:

a = 1

while length(a) < 10

a = [0 a] + [a 0]

end

which prints out Pascal‟s triangle:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

(with “a=” before each line).

What does MATLAB code look like?

Another simple example:

t = 0:pi/100:2*pi;

y = sin(t);

plot(t,y)

What does MATLAB code look like?

Another simple example:

t = 0:pi/100:2*pi;

y = sin(t);

plot(t,y)

Remember:

EVERYTHING IN MATLAB

IS A MATRIX !

creates 1 x 200 Matrix

Argument and result: 1 x 200 Matrix

Matrices

!

Matrices

• Rows and columns are always numbered

starting at 1

• MATLAB matrices are of various types to

hold different kinds of data (usually floats or

integers)

• A single number is really a 1 x 1 matrix in

MATLAB!

• MATLAB variables are not given a type,

and do not need to be declared

• Any matrix can be assigned to any variable

Matrices

Building matrices with [ ]:

A = [2 7 4]

B = [2; 7; 4] Or B = A′

C = [2 7 4; 3 8 9]

D = [ C C ]

2 7 4

2

7

4

2 7 4

3 8 9

?

Matrices

Building matrices with [ ]:

A = [2 7 4]

B = [2; 7; 4] Or B = A′

C = [2 7 4; 3 8 9]

D = [ C C ]

2 7 4

2

7

4

2 7 4

3 8 9

2 7 4

3 8 9

2 7 4

3 8 9

Polynomials as Row Matrices

>> p1 = [1 -10 35 -50 24] % specify the coefficients of p1(x)

p1 =

1 -10 35 -50 24

>> roots_p1 = roots(p1) % Find the roots of p1

roots_p1 =

4.0000

3.0000

2.0000

1.0000

Roots of the polynomial:

Consider

p1(x) = x4 – 10x3 + 35x2 – 50x + 24

Polynomials as Row Matrices

>> r = [1 2 3 4] % specify the roots of the polynomial

r =

1 2 3 4

>> p1 = poly(r) % Find the polynomial coefficients

p1 =

1 -10 35 -50 24

>> a = polyval(p1,1) % Evaluate p1 at x = 1

a =

0

Polynomial construction from known roots

Polynomials as Row Matrices

>> p1 = [1 -3 0 5 7 9];

>> p2 = [2 0 -8 0 4 10 12];

>> p1p2 = conv(p1,p2) % Product of p1(x) and p2(x)

p1p2 =

2 -6 -8 34 18 -24 -74 -88 78 166 174 108

>> p3 = polyder(p2) % Compute the derivative of p2(x)

p3 =

12 0 -32 0 8 10

Product of the polynomials:

p1(x) = x5 – 3x4 + 5x2 + 7x + 9

p2(x) = 2x6 – 8x4 + 4x2 + 10x + 12

Polynomials as Row Matrices

>> p1 = [1 0 -3 0 5 0 7 9];

>> p2 = [2 -8 0 0 4 10 12];

>> [q1,r1] = deconv(p1,p2) % Divide p1(x) by p2(x) to find the

quotient q1(x) and the remainder r1(x)

q1 =

0.5000

r1 =

4 -3 0 3 2 3

Division of the polynomials:

Matrices

Matrices

Some operators must be handled with care:

A = [1 2 ; 4 5]

B = A * A prints 9 12

24 33

B = A .* A prints 1 4

16 25

Element by element multiplication

Submatrices

A matrix can be indexed using another matrix, to

produce a subset of its elements:

a = [100 200 300 400 500 600 700] b = [3 5 6]

c = a(b):

300 500 600

Submatrices

To get a subsection of a matrix, we can produce the

index matrix with the colon operator:

a(2:5)

prints

ans = 200 300 400 500

• This works in 2-D as well, e.g. c(2:3, 1:2) produces a

2 x 2 submatrix.

• The rows and columns of the submatrix are

renumbered.

loops

„for‟ loops in MATLAB iterate over matrix elements:

b = 0

for i = [ 3 9 17]

b = b + i;

end

Result: 29

Note:

THIS IS NOT THE WAY YOU SHOULD

PROGRAM A SUM, SINCE LOOPS ARE SLOW

IN MATLAB !

loops

„for‟ loops in MATLAB iterate over matrix elements:

b = 0

for i = [ 3 9 17]

b = b + i;

end

Result: 29

The MATLAB way to write that program would have been:

b = sum([ 3 9 17]);

Avoid loops if possible !

% Example for runtime difference of loops and built in functions

a=rand(10000,1000); % Matrix with 10000000 (1e7) elements

tic

theSum=0;

for i=1:size(a,1)

for j=1:size(a,2)

theSum = theSum + a(i,j);

end

end

toc

fprintf('result of loop: %f\n',theSum);

tic

theSum=sum(a(:));

toc

fprintf('result of loop: %f\n',theSum);

-----------------------------------------------

Elapsed time is 0.203000 seconds.

result of loop: 4999093.175950

Elapsed time is 0.078000 seconds.

result of loop: 4999093.175950

loops

Here: Speed up factor 2.6

loops

The typical „for‟ loop looks like:

for i = 1:6

…

end

Which is the same as:

for i = [1 2 3 4 5 6]

…

end

loops

Or a bit more sophisticated:

for i = 1:2:7

…

End

Which is the same as:

for i = [1 3 5 7]

…

end

loops

Once again:

AVOID LOOPS

Avoiding loops

How to avoid loops:

Task:

count the elements being greater than 5 in the

following matrix M:

2 7 4

3 8 9

2 7 4

3 8 9

The non-MATLAB way:

counter=0

For rows=1:2

For columns=1:6

if M(rows,columns) > 5

inc counter

end

end

Avoiding loops

The MATLAB way:

T = M > 5;

Count = sum (T(:));

Or shorter:

Count = sum(M(:) > 5);

Avoiding loops

Another example, showing the mighty

INDEXING possibilities:

Task: eliminate the whitespaces in the following

vector M

Avoiding loops

A B C D A B C D

i = find (M ~= „ „); % result: i = [1 3 4 6]

M = M(i);

Or shorter:

M = M(find(M ~= „ „));

Avoiding loops

A B C D A B C D

survivingSubSegs = pointDensity >= minDensity;

diffSubSegs = diff([0 survivingSubSegs 0]);

startSeg = find(diffSubSegs == 1);

endSeg = find(diffSubSegs == -1) - 1;

Avoiding loops

An example how to work without loops,

taken from the EMSF algorithm for line detection

What’s the purpose ?

Images

So why MATLAB and IMAGE

PROCESSING ?

Images

Images can be treated as

matrices !

Images

Loading an image:

a = imread(„picture.jpg‟);

imshow(a);

Images

Image (=matrix) size:

size(a): 384 512 3

R G B

384

512

Images

Color image:

3D Matrix of RGB planes

Images

Show RED plane:

a(:,:,2:3) = 0;

imshow(a);

Images

Show GREEN plane:

a(:,:,[1 3]) = 0;

imshow(a);

Images

Show BLUE plane:

a(:,:,1:2) = 0;

imshow(a);

Images

Advanced: Shuffling columns

rn = rand(1,512);

[rn1,i] = sort(rn);

b = a(:,i,:);

imshow(b);

Images

By the way…

MATLAB can also handle

• Movies

• 3D objects

• …

Conclusion

• MATLAB is a mighty tool to manipulate

matrices

• Images can be treated as matrices

• MATLAB is a mighty tool to manipulate

images

In my opinion…

• MATLAB should be used to code software

prototypes

• Research is mostly about prototypes, not

runtime-optimized software

• MATLAB should be used in research

In my opinion…

• MATLAB prototypes must be re-coded (e.g. in

C++) if there‟s need for speed

• Algorithm development time is drastically

shorter in MATLAB

Conclusion

CONCLUSION:

Use MATLAB

How to go on

MATLAB is exceptionally well documented:

Opening

help/MATLAB help/Getting started

help/MATLAB help/Using MATLAB

Offers help to the environment, programming

concepts, function libraries etc.

How to go on

The „help <functionname>‟ command shows the

first comment-lines of the function given by the

m-file <functionname>.

„Doc‟ does the same, but nicer (html-style,

graphics, examples)

How to go on

The TAB key automatically extends commands

given. This is sometimes helpful if the function

name should be obvious:

• Task: sort the rows of the matrix A

• Idea: there could be a function named „sortXXXX‟

• Type: „sort + TAB‟

• Result: sort, sortcellchar, sorted, sortiv, sortrows, sortrowsc

How to go on

Result: sort, sortcellchar, sorted, sortiv, sortrows, sortrowsc

This looks promising !

„help sortrows‟ will exclude doubt:

SORTROWS Sort rows in ascending order.Y = SORTROWS(X) sorts the rows of the matrix X in ascending

order as a group. X is a 2-D numeric or char matrix. For a char

matrix containing strings … (+usage, examples etc.)

How to go on

Another helpful command is „lookfor‟:

„lookfor <topic>‟ looks for the string <topic> in all

first comments lines (the ones shown by the

„help‟ command) of ALL functions, returning

functions with a hit.

e.g. „lookfor sort‟:

How to go on

e.g. „lookfor sort‟:

bestof.m: %BESTOF(index,names,M,n,<show>) returns the sorted comparison

values of polygon(index) + filenames

CPLXPAIR Sort numbers into complex conjugate pairs.

ISSORTED True for sorted vector.

SORT Sort in ascending order.

SORTROWS Sort rows in ascending order.

RTMDLSORTFLDS is a RTW support function.

DSORT Sort complex discrete eigenvalues in descending order.

ESORT Sort complex continuous eigenvalues in descending order.

DSPBLKSORT DSP Blockset sort block helper function.

UISORTDATA GUI for sorting matrices by row

XREGLVSORTER Function to sort items in listview

sortiv.m: % function [out,err] = sortiv(in,sortflg,nored,epp)

EIGFUN Function to return sorted eigenvalues (used in GOALDEMO).

V2SORT Sorts two vectors and then removes missing elements.…

…

How to go on

Note:

…a creative search using the right topics with

„lookfor‟ can save a lot of time. MATLAB comes

with mostly all basic things you can think of.

Search before you program !

… a Google search „MATLAB +topic‟ is

sometimed an unbelievably satisfying source of

time-saving program collections.

How to go on

Now:

• Browse the documentation !

• Read sample codes !

• Simply browse the list of functions (doc)

• Try and type some lines, use the graphics !

Some Tips

http://mathworks.com/academia/student_center/tut

orials/launchpad.html

http://courses.csail.mit.edu/6.869/resources.html

http://www.math.siu.edu/matlab/tutorials.html