Introduction andMATLAB Basics

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Lecture

MATLAB

Further information in the tutorial: http://www.cv.tu-berlin.de/lehre/cv/dbv/matlab.pdf

!Use the MATLAB Help System!

● MATLAB: Matrix Laboratory, designed for matrix manipulation● Pro:

➔ Syntax similar to C/C++/Java➔ Automated memory management➔ Dynamic data types➔ Single instructions manipulate entire vectors and matrices➔ A wide range of libraries for signal processing, visualisation, machine learning...➔ Platform independent, inclusion of C/C++/Java/... modules possible

● Con:➔ Costs money➔ Uses lots of memory➔ Can be slow for certain types of problems

VariablesScalars

>> a = 5

a =

5>>

>> a = 5;>> a

a =

5>>

(Semicolon suppresses output)

Matrices

>> a = [1,2,3]

a =

1 2 3>>

Elements of a row are separated by commas >> a = [1,2,3;

4,5,6]

a =

1 2 3 4 5 6>>

Rows are separated by semicolons

Basic Datatypes● double: Floating point number, the most common datatype in MATLAB

➔ Other numeric datatypes: float, int32, uint8, ... rather uncommon

● Complex numbers

● Strings

>> a = complex(1,-2)a = 1.0000 - 2.0000i

>> a = 1-2*ia = 1.0000 - 2.0000i

Warning: i can be redefined

(overwritten)!

>> a = 1; whos('a'); Name Size Bytes Class a 1x1 8 double arrayGrand total is 1 element using 8 bytes

>> a = ['test123', '456']a =test123456

Advanced Datatypes

>> a = {[1,2,3], 'test123'}a = [1x3 double] 'test123'

>> a.b = 2; a.c = [2,3,4];>> aa = b: 2 c: [2 3 4]

● Cell Arrays: Generalised matrix➔ Elements can have differing datatypes➔ Elements can have different sizes

● Structures➔ Combine various data in a 'field/value' type structure➔ Fields and associated datatypes do not have to be declared (and can

change at run-time)

Arithmetic Operators 1

● Addition and subtraction

>> a = 5; b=6;>> a + b

ans =

11>>

>> a = [1,2,3; 4,5,6]; b = [0,1,2; 3,4,5];>> a - b

ans =

1 1 1 1 1 1>>

>> a = [1,2; 3,4]; b = [1;2;3];>> a + b??? Error using ==> plusMatrix dimensions must agree.

>> a = [1,2; 3,4];>> a + 5

ans =

6 7 8 9>>

● Matrices must have the same size to be added or subtracted➔ Exception: Scalars can be added to matrices

Arithmetic Operators 2

● The * operator is used for matrix multiplication

>> a = 5; b = 6;>> a * b

ans =

30>>

>> a = [0,1; 1,0]; b = [1;2];>> a * b

ans =

2 1>>

>> a = [1,2; 3,4];>> a * 2

ans =

2 4 6 8>>

>> a = [1; 2]; b = [2; 1];>> a .* b

ans =

2 2>>

● The .* operator multiplies corresponding elements of the operands

Arithmetic Operators 3

>> a = 2; b = 3;>> a / b

ans =

0.6667>>

>> a = 2; b = [1,2; 3,4];>> a ./ b

ans =

2.0000 1.0000 0.6667 0.5000>>

>> a = [1,2; 3,4]; b = [2,1; 1,2];>> a ./ b

ans =

0.5000 2.0000 3.0000 2.0000>>

● Division with / has the expected effect for scalars

● In the case of matrices, the ./ operator causes element-wise division

● Matrices can also be divided using the / operator. This operation solves the system of linear equations associated with the matrices involved

Arithmetic Operators 4

● Scalars and matrices can be raised to a power using ^ and .^ respectively

● For matrices, the ^ operator is equivalent to repeated matrix multiplication

>> a = 5;>> a ^ 2

ans =

25>>

>> a = [1,2; 3,4];>> a .^ 2

ans =

1 4 9 16>>

>> a = [1,2; 3,4];>> a ^ 3ans =

37 54 81 118>>

>> a = [1,2; 3,4];>> a * a * aans =

37 54 81 118>>

Logical Operators● In MATLAB, True and False are represented by 1 and 0, repectively● The operators {==, ~=} test the operands for equality

● The operators{>, <, >=, <=} compare the magnitudes of operands

● All logical operators can be applied to matrices, where they act on each element

>> a = 5; a < 3ans =

0>>

>> a = 5; a >= 5ans =

1>>

>> a = [1,2; 3,4];>> a == 3ans =

0 0 1 0>>

>> a = [1,2; 3,4]; b = [1,0; 3,0];>> a > bans =

0 1 0 1>>

>> a = 3; a == 0ans =

0>>

>> a = 3; a ~= 0ans =

1>>

Working with Matrices 1● Matrices do not have to be created by explicitly listing their contents

● ones(rows, columns) initialises a matrix of ones

● zeros(rows, columns) initialises a matrix of zeros

● zeros and ones can also be used to create higher dimensional (3D,4D etc.) matrices

● a:b initialises a vector [a, a+1, a+2, ... , b]

● a:c:b initialises a vector [a, a+c, a+2*c, ... , b]

>> ones(2,3)

ans =

1 1 1 1 1 1>>

>> 1:5

ans =

1 2 3 4 5>>

>> 2:-0.5:1

ans =

2.0000 1.5000 1.0000>>

>> zeros(2,3)

ans =

0 0 0 0 0 0>>

Working with Matrices 2● MATLAB indices start at 1

● a(y,x) is the value of a in row y and column x

● Several matrix locations can be accessed simultaneously using lists of indices● The special index “:” accesses an entire dimension of a matrix

● Elements in a matrix can be addressed using only a single index (see “Linear Indexing” in

the MATLAB Help system)

>> a = [1,2; 3,4];>> a(2,1)

ans =

3>>

>> a = [1,2; 3,4];>> a([1,2],2)

ans =

2 4>>

>> a = [1,2; 3,4];>> a(1:2,2)

ans =

2 4>>

>> a = [1,2; 3,4];>> a(:,2)

ans =

2 4>>

Working with Matrices 3● The ' operator transposes a matrix and (complex) conjugates each element

● The size function determines the size of a matrix

● Other important functions include:● min, max: Find the minimal/maximal value in a vector● sum: Sum the elements of a vector● mean, std: Mean and standard deviation in a vector● find: Find the indices of elements that satisfy a certain condition● abs: Compute the absolute value

>> a = [1,2; 3,4];>> a'

ans =

1 3 2 4>>

>> a = [1,2; 3,4];>> a

a =

1 2 3 4>>

>> a = ones(10,100); size(a)

ans =

10 100>>

Flow Control 1

if Syntax

if logical-valueInstruction 1Instruction 2...

elseInstruction 3Instruction 4...

end

If Example

>> a = 1;>> if (a >= 0)

disp('a ist > 0!'); enda ist > 0!>>

● Conditional statements use if

● The else part of an if statement is optional

● A sequence of if statements can often be replaced by a single switch statement (see

MATLAB Help!)

Flow Control 2

for Syntax

for Variable = ListInstruction 1Instruction 2...

end

for Example 1

>> for i=[2,4,6]disp(i);

end

2 4 6>>

for Example 2

>> for i=1:3disp(2*i);

end

2 4 6>>

for Loops

while Loops

whlie Syntax

while ConditionInstruction 1Instruction 2...

end

while Example

>> a = 6;>> while (a > 0)

disp(a);a = a-4;

end

6 2>>

Writing Functions 1

Important● MATLAB will only find your .m file if the directory containing it is

either● set as the “Current Directory” in the main window● or is permanently added to the search path using File ->

Set Path...

● New (user defined) functions are defined in .m files

● The file name has to correspond to the function name

➔ E.g. the function myFunc is defined in myFunc.m

● New .m Files can be created using the menu item File -> New -> M-File

● Several functions can be defined in a single .m file, however only the main program is visible to the outside

Writing Functions 2

● A function begins with a declaration that contains the function name and lists inputs (parameters) and outputs:

● output1, output2 ...: The outputs, or results, of the function● input1, input2 ...: The input parameters to the function● Name: The name of the function

● A very simple MATLAB function could be the following:

● Comments in MATLAB Programms begin with %, as shown above

function [output1, output2, output3, ... ]=Name(input1, input2, ... )

% Function test1:% Computes the sum of in1 and in2

function [out]=test1(in1, in2)out = in1 + in2;

end

Writing Functions 3

>> summe = test2(5,6); >> [summe, diff] = test2(5,6);

>> total = test1(5,6);>> totalans =

11>>

% Function test2:% Computes the sum and the difference of in1 und in2

function [out1, out2]=test2(in1, in2)out1 = in1 + in2;out2 = in1 - in2;

end

● Functions can be executed in the MATLAB main window

● Several outputs are possible by simply assigning values to all output variables:

● Not all outputs of a function have to be used (assigned) by the caller

Graphics

● The figure command opens a new window for graphical output

● The close command closes the currently active figure

>> figure>>

plot

>> plot([-5:5].^2)>> title('Parabola')>> xlabel('X')>> ylabel('Y')>> legend('x^2')

>> x = cos(0:0.1:2*pi)>> y = sin(0:0.1:2*pi)>> plot(x,y)

imshow

>> imshow(diag(0:200),[ ])>> colorbar>>

● imshow displays matrices as images

● The empty square braces indicate that intensities are automatically scaled (minimum and maximum become black and white, respectively)

● The example above displays a matrix with the values [0:200] on the diagonal

● imshow can also display colour images

imread & subplot

>> rgb = imread('img/desert.jpg');>> grau = rgb2gray(rgb);>> subplot(2,1,1)>> imshow(rgb)>> subplot(2,1,2)>> imshow(grau)>>

●imread reads an image from a file

●In the case of colour images, the result is a 3D matrix with RGB values

●rgb2gray converts colour images to grayscale

●subplot is used to display several graphics outputs in a single window

>> rgb = imread('img/desert.jpg');>> grau = double(rgb2gray(rgb));

For image processing and analysis, it is almost always necessary to cast grayscale values to the 'double'

datatype:

Breakpoints

>> test1([1,2], ones(2))??? Error using ==> plusMatrix dimensions must agree.

Error in ==> test1 at 5out = in1 + in2;

>> test1([1,2], ones(2))5 out = in1 + in2;K>> in1, in2in1 = 1 2

in2 = 1 1 1 1

● The execution of a function can be halted at arbitrary points using breakpoints➔ The contents of variables at the breakpoint in the function can be viewed and changed➔ This is often usefull when debugging functions

Breakpoints are enabled by clicking onthe '-' marker at the beginning of a line

Automatically Switching to Debug Mode

(The Debug menu in the main window)

(Enable the debug mode automatically incase of an error)

● MATLAB can be configured to switch to debug mode automatically, as soon as an error occurs➔ Usefull when there are several potential sources of errors

Exercises

● MATLAB is optimised for the manipulation of matrices

● Loops in which elements of a matrix are processed individually are very slow

● Good MATLAB programs therefore avoid loops all together

● Surprisingly many problems can be solved by manipulating entire matrices without explicit iteration, even when the solution is sometimes more memory intensive

● The aim of this exercise is, therefore, to solve a number of simple and not so simple tasks without using explicit loops over matrices (i.e. no for or while loops allowed!)

● The following slides describe the prototypes of the functions to be implemented

function splitShow(imgA,imgB)

>> imgA = imread('img/desert.jpg');>> imgA = double(rgb2gray(imgA));>> imgB = edge(imgA,'canny');>> splitShow(imgA,imgB)>>

● A processed image (imgB) is to be compared with the original (imgA)

● Both images are cut in half and concatenated to make their comparison easy● Both intensities in both images need to be scaled such that their gray values lie in the same range

before the two image halves are concatenated

function [n]=matchCount(A,num)

● Function matchCount counts how often a given number num occurs in matrix A

>> A = [1,2; 2,3]

A =

1 2 2 3>> matchCount(A,1)

ans =

1>>

>> A = [1,2; 2,3]

A =

1 2 2 3>> matchCount(A,2)

ans =

2>>

function [A]=replicate(vect, num)

● The vector vect is repeated num times to produce matrix A

● vect can be a row-vector or a column-vector

● Do not use the MATLAB repmat function!

>> a = [1,2,3,4]

a =

1 2 3 4>> replicate(a,5)

ans =

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4>>

>> a = [1;2;3;4]

a =

1 2 3 4>> replicate(a,5)

ans =

1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4>>

function [circ]=circle(radius)

>> imshow(circle(100),[])>>

>> circle(4)

ans =

0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0

>>

1.4142 1.0000 1.41421.0000 0 1.00001.4142 1.0000 1.4142

ExampleDistances for radius = 1

● circle computes a quadratic matrix circ with (2*radius+1) rows and columns

● circ contains a region of 1s in the shape of a circle (of radius radius)

● Hint: Begin by computing a matrix of distances to the centre element of the matrix

➔ The replicate function could come in handy