Matlab workshop

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Introduction to MATLAB

Lecture Series by CEPSTRUM

Presented byPresented byPratik Kotkar & Akash BaidPratik Kotkar & Akash Baid

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Topics..

What is MATLAB ?? Basic Matrix Operations Script Files and M-files Some more Operations and Functions

APPLICATIONS: Plotting functions .. Image Processing Basics .. Robotics Applications .. GUI Design and Programming

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MATLAB

MATLAB is a program for doing numerical computation. It was originally designed for solving linear algebra type problems using matrices. It’s name is derived from MATrix LABoratory.

MATLAB has since been expanded and now has built-in functions for solving problems requiring data analysis, signal processing, optimization, and several other types of scientific computations. It also contains functions for 2-D and 3-D graphics and animation.

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MATLAB

Everything in MATLAB is a matrix !

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MATLAB

The MATLAB environment is command oriented somewhat like UNIX. A prompt appears on the screen and a MATLAB statement can be entered. When the <ENTER> key is pressed, the statement is executed, and another prompt appears.

If a statement is terminated with a semicolon ( ; ), no results will be displayed. Otherwise results will appear before the next prompt.

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The MATLAB User Interface

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MATLAB

To get started, type one of these commands: helpwin, helpdesk, or demo

» a=5;» b=a/2

b =

2.5000

»

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MATLAB Variable Names

Variable names ARE case sensitive

Variable names can contain up to 63 characters (as of MATLAB 6.5 and newer)

Variable names must start with a letter followed by letters, digits, and underscores.

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MATLAB Special Variables

ans Default variable name for results

pi Value of eps Smallest incremental number

inf InfinityNaN Not a number e.g. 0/0i and j i = j = square root of -1realmin The smallest usable positive real numberrealmax The largest usable positive real number

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Math & Assignment Operators

Power ^ or .^ a^b or a.^b

Multiplication * or .* a*b or a.*b

Division / or ./ a/b or a./b

or \ or .\ b\a or b.\a

NOTE: 56/8 = 8\56

- (unary) + (unary)Addition + a + bSubtraction- a - bAssignment= a = b (assign b to a)

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Other MATLAB symbols

>> prompt

. . . continue statement on next line, separate statements and data% start comment which ends at end of line; (1) suppress output

(2) used as a row separator in a matrix

: specify range

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MATLAB Relational Operators

MATLAB supports six relational operators.

Less Than <Less Than or Equal <=Greater Than >Greater Than or Equal >=Equal To ==Not Equal To ~=

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MATLAB Logical Operators

MATLAB supports three logical operators.

not ~ % highest precedenceand & % equal precedence with oror | % equal precedence with and

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MATLAB Matrices

MATLAB treats all variables as matrices. For our purposes a matrix can be thought of as an array, in fact, that is how it is stored.

Vectors are special forms of matrices and contain only one row OR one column.

Scalars are matrices with only one row AND one column

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MATLAB Matrices

A matrix with only one row AND one column is a scalar. A scalar can be created in MATLAB as follows:

» a_value=23

a_value =

23

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MATLAB Matrices

A matrix with only one row is called a row vector. A row vector can be created in MATLAB as follows (note the commas):

» rowvec = [12 , 14 , 63]

rowvec =

12 14 63

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MATLAB Matrices

A matrix with only one column is called a column vector. A column vector can be created in MATLAB as follows (note the semicolons):

» colvec = [13 ; 45 ; -2]

colvec =

13 45 -2

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MATLAB Matrices

A matrix can be created in MATLAB as follows (note the commas AND semicolons):

» matrix = [1 , 2 , 3 ; 4 , 5 ,6 ; 7 , 8 , 9]

matrix =

1 2 3 4 5 6 7 8 9

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Extracting a Sub-Matrix

A portion of a matrix can be extracted and stored in a smaller matrix by specifying the names of both matrices and the rows and columns to extract. The syntax is:

sub_matrix = matrix ( r1 : r2 , c1 : c2 ) ;

where r1 and r2 specify the beginning and ending rows and c1 and c2 specify the beginning and ending columns to be extracted to make the new matrix.

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MATLAB Matrices

A column vector can be extracted from a matrix. As an example we create a matrix below:

» matrix=[1,2,3;4,5,6;7,8,9]

matrix = 1 2 3 4 5 6 7 8 9

Here we extract column 2 of the matrix and make a column vector:

» col_two=matrix( : , 2)

col_two =

2 5 8

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MATLAB Matrices

A row vector can be extracted from a matrix. As an example we create a matrix below:

» matrix=[1,2,3;4,5,6;7,8,9]

matrix =

1 2 3 4 5 6 7 8 9

Here we extract row 2 of the matrix and make a row vector. Note that the 2:2 specifies the second row and the 1:3 specifies which columns of the row.

» rowvec=matrix(2 : 2 , 1 : 3)

rowvec =

4 5 6

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Use of M-File

There are two kinds of M-files: Scripts, which do not accept input

arguments or return output arguments. They operate on data in the workspace.

Functions, which can accept input

arguments and return output arguments. Internal variables are local to the function.

Click to create a new M-File

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M-File as script file

Save file as filename.m

Type what you want to do, eg. Create matrices

If you include “;” at the end of each statement,result will not be shown immediately

Run the file by typing the filename in the command window

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Reading Data from files

MATLAB supports reading an entire file and creating a matrix of the data with one statement.

>> load mydata.dat; % loads file into matrix.% The matrix may be a scalar, a vector, or a % matrix with multiple rows and columns. The% matrix will be named mydata.>> size (mydata) % size will return the

number% of rows and number of% columns in the matrix

>> length (myvector) % length will return the total

% no. of elements in myvector

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Some Useful MATLAB commands

who List known variables whos List known variables plus their size help >> help sqrt Help on using sqrt lookfor >> lookfor sqrt Search for

keyword sqrt in m-files what >> what a: List MATLAB files in a: clear Clear all variables from work space clear x y Clear variables x and y from work

space clc Clear the command window

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Some Useful MATLAB commands

what List all m-files in current directory dir List all files in current directory ls Same as dir type test Display test.m in command

window delete test Delete test.m cd a: Change directory to a: chdir a: Same as cd pwd Show current directory which test Display directory path to ‘closest’

test.m

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MATLAB Logical Functions

MATLAB also supports some logical functions.xor (exclusive or) Ex: xor (a, b) Where a and b are logical expressions. The xor

operator evaluates to true if and only if one expression is true and the other is false. True is returned as 1, false as 0.

any (x) returns 1 if any element of x is nonzeroall (x) returns 1 if all elements of x are

nonzeroisnan (x) returns 1 at each NaN in xisinf (x) returns 1 at each infinity in xfinite (x) returns 1 at each finite value in x

32Matlab Selection Structures

An if - elseif - else structure in MATLAB. Note that elseif is one word.

if expression1 % is true% execute these commands

elseif expression2 % is true% execute these commands

else % the default% execute these commands

end

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MATLAB Repetition Structures

A for loop in MATLAB for x = array for ind = 1:100

b(ind)=sin(ind/10) end

while loop in MATLAB while expression while x <= 10

% execute these commands end

x=0.1:0.1:10; b=sin(x); - Most of the loops can be avoided!!!

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Scalar - Matrix Addition

» a=3;» b=[1, 2, 3;4, 5, 6]b = 1 2 3 4 5 6» c= b+a % Add a to each element of bc = 4 5 6 7 8 9

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Scalar - Matrix Subtraction

» a=3;» b=[1, 2, 3;4, 5, 6]b = 1 2 3 4 5 6» c = b - a %Subtract a from each element of bc = -2 -1 0 1 2 3

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Scalar - Matrix Multiplication

» a=3;» b=[1, 2, 3; 4, 5, 6]b = 1 2 3 4 5 6» c = a * b % Multiply each element of b by ac = 3 6 9 12 15 18

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Scalar - Matrix Division

» a=3;» b=[1, 2, 3; 4, 5, 6]b = 1 2 3 4 5 6» c = b / a % Divide each element of b by ac = 0.3333 0.6667 1.0000 1.3333 1.6667 2.0000

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The use of “.” – “Element” Operation

Given A:

Divide each element of A by 2

Multiply each element of A by 3

Square each element of A

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MATLAB Toolboxes

MATLAB has a number of add-on software modules, called toolbox , that perform more specialized computations.

Signal Processing Image Processing Communications System Identification Wavelet Filter Design Control System Fuzzy Logic Robust Control µ-Analysis and Synthesis LMI Control Model Predictive Control …

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MATLAB Demo

Demonstrations are invaluable since they give an indication of the MATLAB capabilities.

A comprehensive set are available by typing the command >>demodemo in MATLAB prompt.

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An Interesting, MATLAB command

why

In case you ever needed a reason

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Plot

PLOT Linear plot. PLOT(X,Y) plots vector Y

versus vector X PLOT(Y) plots the columns

of Y versus their index PLOT(X,Y,S) with plot

symbols and colors See also SEMILOGX,

SEMILOGY, TITLE, XLABEL, YLABEL, AXIS, AXES, HOLD, COLORDEF, LEGEND, SUBPLOT...

x = [-3 -2 -1 0 1 2 3];y1 = (x.^2) -1;plot(x, y1,'bo-.');

Example

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Plot Properties

XLABEL X-axis label.

XLABEL('text') adds text beside the X-axis on the current axis.

YLABEL Y-axis label.

YLABEL('text') adds text beside the Y-axis on the current axis.

...xlabel('x values');ylabel('y values');

Example

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Hold

HOLD Hold current graph.

HOLD ON holds the current plot and all axis properties so that subsequent graphing commands add to the existing graph.

HOLD OFF returns to the default mode

HOLD, by itself, toggles the hold state.

...hold on;y2 = x + 2;plot(x, y2, 'g+:');

Example

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Subplot

SUBPLOT Create axes in tiled positions.

SUBPLOT(m,n,p), or SUBPLOT(mnp), breaks the Figure window into an m-by-n matrix of small axes

x = [-3 -2 -1 0 1 2 3];y1 = (x.^2) -1;% Plot y1 on the topsubplot(2,1,1);plot(x, y1,'bo-.');xlabel('x values');ylabel('y values');% Plot y2 on the bottomsubplot(2,1,2);y2 = x + 2;plot(x, y2, 'g+:');

Example

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Figure

FIGURE Create figure window.

FIGURE, by itself, creates a new figure window, and returns its handle.

x = [-3 -2 -1 0 1 2 3];y1 = (x.^2) -1;% Plot y1 in the 1st Figureplot(x, y1,'bo-.');xlabel('x values');ylabel('y values');% Plot y2 in the 2nd Figurefigurey2 = x + 2;plot(x, y2, 'g+:');

Example

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Surface Plot

x = 0:0.1:2;y = 0:0.1:2;[xx, yy] = meshgrid(x,y);zz=sin(xx.^2+yy.^2);surf(xx,yy,zz)xlabel('X axes')ylabel('Y axes')

x = 0:0.1:2;y = 0:0.1:2;[xx, yy] = meshgrid(x,y);zz=sin(xx.^2+yy.^2);surf(xx,yy,zz)xlabel('X axes')ylabel('Y axes')

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contourf-colorbar-plot3-waterfall-contour3-mesh-surf

3 D Surface Plot

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Convolution

The behavior of a linear, continuous-time, time-invariant system with input signal x(t) and output signal y(t) is described by the convolution integral

- h(t), assumed known, the response of the system to a unit impulse input

For example,x = [1 1 1 1 1]; [1 1 1 1 1]h = [0 1 2 3]; [3 2 1 0]conv(x,h)

yields y = [0 1 3 6 6 6 5 3] stem(y);

ylabel(‘Conv');xlabel(‘sample number’);

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Image Processing Toolbox

The Image Processing Toolbox is a collection of functions that extend the capability of the MATLAB ® numeric computing environment. The toolbox supports a wide range of image processing operations, including: Geometric operations Neighborhood and block operations Linear filtering and filter design Transforms Image analysis and enhancement Binary image operations Region of interest operations

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MATLAB Image Types

Indexed images : m-by-3 color map

Intensity images : [0,1] or uint8Binary images : {0,1}RGB images : m-by-n-by-3

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Indexed Images

» [x,map] = imread('trees.tif');» imshow(x,map);

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Intensity Images

» image = ind2gray(x,map);» imshow(image);

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Binary Images

» imshow(edge(image));

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RGB Images

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Image Display

image - create and display image objectimagesc - scale and display as imageimshow - display imagecolorbar - display colorbargetimage- get image data from axestruesize - adjust display size of imagezoom - zoom in and zoom out of 2D plot

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Image Conversion

Gray2ind - intensity image to index imageim2bw - image to binaryIm2double - image to double precisionIm2uint8 - image to 8-bit unsigned integersIm2uint16 - image to 16-bit unsigned integersInd2gray - indexed image to intensity imagemat2gray - matrix to intensity imagergb2gray - RGB image to grayscalergb2ind - RGB image to indexed image

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GEOMETRIC OPERATIONS

“imcrop” crops an image to a specified rectangle. imcrop displays the input image and waits for you to specify the crop rectangle with the mouse.

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IMAGE ENHANCEMENT

Adjust intensity imadjust histeq

Noise removal linear filtering median filtering adaptive filtering

>>im2 = histeq(im);>>imshow(im2)

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TRANSFORMS

Fourier Transform-fft2, fftshift, ifft2

Discrete Cosine Transform (DCT)-dct2, idct2, dctmtx, dctdemo

Radon Transform-radon, iradon, phantom

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Robotics Application

Lez Concorrenza - The Automation-Robotics Event, Techniche 2005

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Concepttake imagefilter using medfilt2take the subarray of ball region, find cluster

of max area ,find its centroidtake the subarray of robot region , find

cluster of max area, find its centroidinterpolate the ball using the ball's current

and previous coordinate , give output

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MATLAB Code

parport=digitalio('parallel','LPT1');addline(parport,0:7,'out');ball_x_prev = 1;ball_y_prev = 1;

while (1) % code for acquiring image

filtered_image=medfilt2(bw,[3 3]); % filter the image region_ball = filtered_image[20:460,10:575]; % ball region region_bot = filtered_image[20:460,575:630]; % robot region

label = bwlabel(region_ball,4); %label the clusters in the region data = regionprops(label,'basic'); % data ontains properties of clusters in the region object = find([data.Area]==max([data.Area])) % object conatains the label of the cluster

with max area

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ball_x = data(object).Centroid(1); %x coordinates of the ball ball_y = data(object).Centroid(2);

label = bwlabel(region_bot,4); %label the clusters in the region data = regionprops(label,'basic'); % data ontains properties of clusters in the

region object =find([data.Area]==max([data.Area])) % object conatains the label of the

cluster with max area

robot_x = data(object).Centroid(1); %x coordinates of the bot robot_y = data(object).Centroid(2);

% Algorithm for movement of robot if (ball_x > ball_x_prev) % the ball is returning to the bot

% Do something if (robot_y > y_proj)

% Do something elseEtc.

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Graphical User Interface

What is GUI: A graphical user interface (GUI) is a user interface built with graphical objects such as

ButtonsText fieldsSlidersMenus

If the GUI is designed well-designed, it should be intuitively obvious to the user how its components function.

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Push ButtonsRadio Buttons

Frames

Checkbox Slider

Edit text

static textAxes

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Graphical User Interface

Guide Editor

Property InspectorResult Figure

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GUI: Spectrum Analyzer

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Thanks

Questions ??

Matlab workshop

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