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Introduction to Matlab
Introduction to Matlab
Instructions ................................................................................................................................................... 4 Requirements ................................................................................................................................... Instructions ...................................................................................................................................... Preparations ............................................................................................................................................ 11 Installation of Matlab ......................................................................................................................... 12 Downloading the necessary materials ............................................................................................... 13 Configuration of Matlab .................................................................................................................... 14 Lesson 1: Matlab Basics ............................................................................................................................ 17 What Can You Use Matlab For? ........................................................................................................... 18 Examples in Command Line Mode ................................................................................................... 20 Demonstration Examples by Matlab ................................................................................................. 23 Example From Psychological Research ............................................................................................ 24 The User Interface ................................................................................................................................. 26 Desktop Display Options ................................................................................................................... 27 The «Command Window» ................................................................................................................. 29 The «Workspace» .............................................................................................................................. 30 The «Current Directory» Browser ..................................................................................................... 32 The «Command History» .................................................................................................................. 33 Using the Help System ...................................................................................................................... 34 Summary ............................................................................................................................................ 36 Numbers and Variables in Matlab ......................................................................................................... 37 Representation of Numbers ............................................................................................................... 38 Variables ............................................................................................................................................. 39 Summary ............................................................................................................................................ 40 Data Representation 1: Scalars, Vectors, and Matrices ......................................................................... 41 Scalars ................................................................................................................................................ 42 Vectors ............................................................................................................................................... 43 Matrices .............................................................................................................................................. 44 Summary ............................................................................................................................................ 46 Matrix Manipulation .............................................................................................................................. 47 Matrix Concatenation ......................................................................................................................... 48 Matrix Duplication ............................................................................................................................. 49 Creation of Special Matrices ............................................................................................................. 50 Matrix Transformation ....................................................................................................................... 51 Exercise 1: Create a Complex Data Matrix ...................................................................................... 52 Summary ............................................................................................................................................ 54 Mathematical Operators and Functions ................................................................................................. 55 Operators ............................................................................................................................................ 56 Functions ............................................................................................................................................ 57 Exercise 2: Implementing a Mathematical Formula .......................................................................... 58 Exercise 3: Validation of a Magic Square ........................................................................................ 59 Summary ............................................................................................................................................ 60
http://www.edulap.ch/static/matlab/ - Version from: 11.2.2010
................................. 81 Exercise 5: Gaussian function for a vector ............................. 99 Lesson 3: Working with External Files ................................. 118 Summary ................................................................... 105 Summary ............................................................................................................ch/static/matlab/ .................................................... 87 Comparison Operators and Logical Operations ............................................................................................................................. 63 Lesson 2: Programming in Matlab ........................................................................................................................................................................................................................................................................ 103 Example: Data Import from an External File ............................................................................................................. 72 Special Cases .................................... 93 String creation and concatenation ............................................................................................................................................................................................... 65 The Editor/Debugger ................................. 101 Interactive Data Import ..............................................................Introduction to Matlab Self-test Questions ............................................................................................................................................................................ 109 Data Representation 3: Cell Arrays ............................................................................................................................................................................................. 116 Data Representation in Structure Arrays ..................... 91 Summary ...................................................................................................................................................................................Version from: 11.......................................................................................................................................................................................................................................... 117 Application example ......................................................................................................................................... 86 The switch-case structure .......................................................................................................................edulap....................... 114 Summary ........................................................... 89 Exercise 6: Standardisation Function ...................................................................................................................................................................................................................................................................................................................................................................................................... 111 Create and Reference Cell Arrays ................................................................................................................................................................................................................................................... 110 Data Representation as Cell Arrays ............. 75 Summary ................................. 83 Summary .............................................................................................................................. 85 The branching structure if-elseif-else ........................................ 82 Vectorisation of Loops ................................................................................................... 68 Exercise 4: Programming a Script .................................................................... 61 Glossary ...................................................................2010 2 ..................................... 112 Second example on data import from external files ................................................... 102 Data Input from External Files: Programmed ........................................................................ 96 Summary ........................................................................................... 100 Data Import ................................................................................................................... 64 M-Files: Scripts and Functions ............................ 115 Data Representation 4: Structure Arrays ..... 120 http://www.. 70 Function Programming ...................................................................................................................................................................................................................................................................................................................... 92 Data Representation 2: Character Strings ............................................................................................................................ 84 Program Control Structures: Conditional Branching ............................................................................................................................................................................................................................................................. 78 The For Loop ........ 80 Exit Loops with the break Statement .................................................. 94 Examine and Compare Strings ........................... 97 Self-test Questions .....2............ 98 Glossary .................................................................................................................................................................................................................................. 77 Program Control Structures: Loops ................................................................................................................................ 79 The While Loop .......................................................... 119 Your Data Processing Project ................................... 66 Script Programming ..................................................................................
...................................................................................................................................................................................................................... Basic Statistical Functions ......................................................... Summary .............................................................................................. Selection of Files and Directories ........................................................ Summary ........................................................................................................................................................................................................edulap........... Brief Demonstration of Other Functions ............................. Bar Graphs ............................................................................................................................. Logical Indexing ..................Data Processing ........................................................................................................................... Data Selection: Logical Indexing and the «find» Function ...................................................................................................................................................................................................................................... Creation and Manipulation of Figures ............................................................................... Exercise P2: User Inputs .................................................................................................................................................................... Summary ....................... Random Data with Defined Distributions ............. Exercise P1: Data Import ....................................................................................................................Version from: 11..................................................... Summary ................. Figure Properties ..... Exercise P4: Project Task ....................................................................................................................... Graphics Tools ........................ A Helpful Function: subM ............................ Writing Data to External Files .............................................................................................................................................................................................................. Axes .............................................. Summary ......................................................................................................................... Sample Code: Select All Files in a Directory ...................................... Lesson 4: Data Processing and Graphical Presentation ............. Correlation and Covariance .................................................................................................................................................................................................Graphical Data Display .................................................... Annotate and Extend Graphics .............................................................................................................................................................................................................................................................................. User Interaction ....................2010 3 .................................... 121 122 123 124 127 128 132 134 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 152 153 155 156 157 158 160 161 162 163 164 165 169 171 172 177 179 180 http://www............................................................................ Graphics Basics: Figures and Axes ....................................................................................................................................................................................................................................................2............................................................................................................................................................................................................................. Summary ......................................................................................... The find Function .................................................................. Other User Input Features ........................................................................................................................................................................................................................................................................................................................................................................................................... Data Base: EyeData Processing ....................................................................................Introduction to Matlab Data Base ............................. Descriptive Statistics .......................................................................................................... The Plot function ...................................................... Multiple Axes ....................... Exercise P5: Project Task .......................................................................................................ch/static/matlab/ ..................................................... Basic Functions to Write to External Files .................................................... Basic Structure .............................................................. Exercise P3: Save Data ................................................................................................................................................................................. Final Remarks ............................... Glossary ................................................
Introduction to Matlab
What is covered by this tutorial?
This introductory course is intended to provide a practical introduction to working with the program Matlab® by The MathWorks, particularly focussing on aspects being relevant for data processing in psychological research. Matlab is often used in experiments applying psychophysical methods such as electroencephalography (EEG), eye tracking, or registration of galvanic skin response (GSR). Put more generally, Matlab is very useful for the evaluation of large data sets that are often acquired automatically, as it is the case in logfile analysis or internet experiments as well. Why Matlab? Matlab is a programming language often used in psychological research. It is especially suitable for data analysis but can be applied for programming computer-controlled experiments as well. In contrast to other programming languages, a particular advantage of Matlab is that is works as an «interpreter»: commands that are typed in are processed immediately without having to compile the program beforehand; skipping this step leads to a faster development cycle. In that way, you can try out the syntax of a command in an uncomplicated manner and see whether they lead to the intended effect. Then the tested commands can be pasted into the final program file. The scope of this course Matlab is a very comprehensive software package, and most users only use a small part of it. Thanks to a very good integrated documentation and help system, it is relatively easy to learn additional commands once one has understood the basics. In this sense, this course is confined to the basic functionality of Matlab, i.e. matrix-based data processing and visualisation.
http://www.edulap.ch/static/matlab/ - Version from: 11.2.2010
Introduction to Matlab
The functionality of SimuLink (simulation program) will not be covered. Likewise, the functions of specialised tool boxes (neural network toolbox, wavelet toolbox etc.) cannot be covered; these are only rarely put to use in the course of psychological research. Rather, a solid basis should be established, starting from which it should be possible to autonomously acquire further knowledge and skills if needed. If you would like to support our initiative to build this course, which is an open educational resource, and are a native speaker of English: The course is in need of proofreading, as it was translated by a nonnative speaker of English (as you sure have noticed). If you are willing to proofread a part (however small) of this course, please contact me. Thank you very much! Overview over the contents • • • • • • • • • What can Matlab be used for? How to work with the user interface The basics: numbers, data types, operators, functions, etc. Programming of scripts and functions Program control structures: looping and branching Reading data from file, processing them, and writing them back to file Interaction with the user Statistical functions Graphics functions
All lesson contents can be practiced and applied in short practice assignments. In addition, self-test questions are available in order to assist the learning process by evaluating what you have learned. Moreover, in the course of this tutorial, you will be able to develop a somewhat larger program project that is typical for applications in psychological research: importing and aggregation of data from several data sets, doing calculations with these data, saving the results in a format suitable for further processing (e.g. with SPSS or Statistica), and visualisation of the results. Authoring
This learning resource was realised as a sub-project of the edulap project.
http://www.edulap.ch/static/matlab/ - Version from: 11.2.2010
Introduction to Matlab
Roman von Wartburg, Ph.D. Contents, didactical concept, implementation, translation, start page animation
Sarah Steinbacher, dipl. designer FH Graphic design
Radka Wittmer, M.Ed. Didactics counsel
Stephanie Schütze, Dipl. psych. Usability evaluation
Joël Fisler Implementation of graphic design Support This project was supported by several institutions:
http://www.edulap.ch/static/matlab/ - Version from: 11.2.2010
Introduction to Matlab «Introduction to Matlab» by Roman von Wartburg/Distance Learning University Foundation Switzerland is licensed under a Creative Commons «Attribution/Non-Commercial/Share Alike» 2. you may not use it for commercial purposes. you may distribute the resulting work only under the same or similar license to this one. The complete eLML source code is contained in the content packages that are available from various learning resource repositories such as SWITCHcollection. or build upon it. That is. distribute. transform. Content package in IMS/CP format This version is intended for uploading to a learning management system such as OLAT.ch/static/matlab/ . and adapt the work. you can unpack this archive to your hard disk and open locally with your web browser. or ILIAS. The content packages can be downloaded here: ZIP archive of the HTML version If you do not have permanent web access. Moodle. if you alter. transmit. you are free to copy.2010 7 .2.edulap. http://www.5 Switzerland License. Further information Implementation and distribution This course was implemented with eLML. The conditions are: You must attribute the work by naming the original author.Version from: 11.
Bachelor level methodological and statistical basic knowledge in the field of psychology (or other social sciences) will help understand the practical examples. University of Bern) make Matlab available for free to staff and students. you should be able to go through this course without significant difficulties. please consult the system requirements at the Mathworks website. Matlab is a commercial software and a license has to be purchased. it is indispensable to have the Matlab software package installed on the same computer. to be realistic. • If you are experienced with other modern programming languages and thus know the way of thinking and the basic concepts of programming. you will have to correct the preference settings of your internet browser accordingly. If you are in doubt. or E-Prime.edulap. Most current computers that are not older than 5 to 8 years will have enough power to run Matlab. The basic concepts and structures of Matlab do not substantially differ from those of other modern (procedural) languages. a license is offered by Mathworks for $99. the objectives and the level of demand will differ between these two groups. you should be able to write Matlab routines from scratch. We suppose that.Version from: 11. and write simple routines based on the examples in the course. For people with no or only rudimentary knowledge in programming. Microsoft Excel. For students. Windows.g. you should not experience serious problems to acquire the basics of Matlab as they are taught in this course. Please contact the IT support of your institution. • Hardware and software requirements As this course encompasses practical exercises as a constitutive part. but not imperative. previously known as SunOS). After that. Certain academic institutions (e. For a quick test click here. http://www.2. Matlab is available for Macintosh. after having studied this course. various Linux distributions and Solaris (UNIX operating system. Experience in computer programming is very helpful. If you don't see a new window popping up after that. this group of learners will be able to understand and modify existing Matlab programs. • • Objectives We tried to design this course in a way that experienced programmers as well as beginners can profit.ch/static/matlab/ . If you are used to working with software packages such as SPSS. Mathematical knowledge exceeding this is not necessary. make sure that your internet browser does not block pop-up windows for the website or learning management system on which this course runs. previous knowledge as listed below will be helpful: • Basic experience in working with computers is indispensable.Introduction to Matlab Requirements Previous knowledge To profit from this Matlab course. the course will be relatively demanding. Web browser requirements In this course. Therefore. certain contents will be displayed in pop-up windows. You will find installation instructions in the paragraph Installation. However.2010 8 .
Version from: 11.2.ch/static/matlab/ .5 * pi pi is an internally predefined value Important information. key points and summaries are displayed in such a box and are marked with the corresponding icon. All commands that have to be entered in Matlab's «command window» are displayed as shown below (the prompt >> must not be typed): >> a = sin(2) Explanations are printed in italics and are not to be entered: >> 23.2010 9 . and other parts of the program code are highlighted with the following text style: matlab_code Calls to Matlab's menu functions are formatted like this: Desktop > Desktop Layout > Default This. All text areas suggesting concrete activity in Matlab are set in a green box and labelled with this icon. Pop-up: If links labelled with this icon are clicked. We think that this is the way how knowledge of this kind is acquired the most efficiently. Special notations Matlab expressions such as commands. Further icons Specific text areas are labelled with other icons to point out their relevance: Notes: This icon indicates additional. functions. for example.Introduction to Matlab Instructions This tutorial is designed as a «hands-on» course: Everything that is being taught can and should be tried out immediately in the Matlab program running in parallel. Help: Points to additional information in Matlab's help system.edulap. indicates the operation: http://www. a box or a new window open to display the information in. complementary information.
2. You can read this document even when you do not have internet access.Introduction to Matlab Further features In this course. Command list: This list contains all commands used in the course. • • PDF print version: You can downnload the complete course as a PDF document. You can access them via the additional menu items below the main navigation of this tutorial (for the HTML version) or via the footer (content package version running in a learning management system such as OLAT). narrow window which you can conveniently place beside your other open windows for better visibility. two more functions are available to assist in your learning process. or print parts of it.ch/static/matlab/ .edulap. http://www.Version from: 11. The list will open in a new.2010 10 .
and sample solutions Configuration of Matlab http://www.edulap.Version from: 11.Introduction to Matlab Preparations This section describes the preparatory steps necessary for doing this course: • • • Installation of Matlab on your computer Downloading and saving of the necessary materials such as example programs. data files.ch/static/matlab/ .2.2010 11 .
do it now.ch/static/matlab/ .Introduction to Matlab Installation of Matlab Which version of Matlab do I need? Version 7. as the documentation is an indispensable resource for working with this complex program package. A student license is available from Mathworks for $99. certain details of the user interface may be different.g. or both. especially due to useful extensions of the editor's functionality and improved help functions. University of Bern) make Matlab available for free to staff and students.edulap. however. http://www. Please contact the IT support of your institution. a license has to be obtained.2. Certain academic institutions (e. It is possible to use older versions. For Matlab. Select both. Follow the instructions provided by the installation program. Important: Some versions of Matlab ask you to decide what exactly you want to install: the main application.2010 12 . Basically. If Matlab has not been installed on your computer yet.2 / R2006a or newer is recommended.Version from: 11. the documentation. working with Matlab is substantially more pleasant with the newer versions.
Version from: 11.edulap.zip. e. Please download the data files now.zip. e.2. Extract these files to another location. or data files to test the programs you have written.ch/static/matlab/ . It is useful to memorise or write down the name of this folder. My Documents\matlab-course\data\.Introduction to Matlab Downloading the necessary materials To do this course. because we will have to configure it in Matlab right away (cf. My Documents\matlab-course\m\ or d:\m\. http://www. as described below: Examples and sample solutions You will find these program files in the ZIP archive file examples.g. Important: This folder will be your working folder for the programs you write. you are asked to download these files to your computer now. Thus. sample solutions. you need several data files such as code examples. Data Some of the examples and exercise assignments need data files.2010 13 . here). Please extract the contents to a new folder (= directory). You can download them as ZIP archive data.g.
In our case. All paths for internal functions and toolboxes provided with the Matlab package have already been configured. Confirm by hitting OK Click Save and Close http://www. Afterwards you are ready to go! Please check/configure the following settings: Search path setting Matlab has to be told where to look for programs. Please proceed as indicated below: • • • • Select menu item File > Set Path Click the button Add Folder.edulap.. here). look for the target folder and select it.2. Please follow these steps according to the instructions below. In the file browser.Introduction to Matlab Configuration of Matlab Several settings are necessary or helpful to make Matlab «operational»: • • • setting the search path for your new programs configuration of the proxy server for internet access (if necessary) The tabulator size of the editor can be customised to suit one's taste. this is the location where you have extracted the code examples and sample solutions from the downloaded ZIP archive (see section «Materials»..Version from: 11.ch/static/matlab/ . but you have to let Matlab know the storage location of the programs you write yourself (the so-called «M-files»).2010 14 .
In case your computer is connected to a local area network using a so-called «proxy server».ch/static/matlab/ .unibe. or you don't know its address. contact your IT support. the address and port number of your institution's proxy server have to be entered.. (see illustration below).. If you don't know whether a proxy server is in use at all. Matlab has to be informed of its address. Otherwise.edulap. internet access is required. If there is no proxy server.2.ch / 80». http://www. you find this configuration option under the menu item File > Preferences. In Matlab. uncheck «Use a proxy server to connect to the Internet».Version from: 11.2010 15 . Instead of «proxy.Introduction to Matlab Dialog box to configure the search path for M-files Proxy server for internet access For some functions of the help system. Hint: It is the same address as the one configured in your internet browser as proxy server. configure its address as shown below.
Lesson 2. You can configure the tab setting like this: Select the menu item File > Preferences. it is advisable to set the same value for «Tab size» and «Indent size».Version from: 11. and leads to a more or less compact and clearly arranged representation.edulap. and then set the tab size according to the illustration below...Introduction to Matlab Proxy server settings for internet access Tab setting for the editor This option influences the display of program code in the editor.ch/static/matlab/ . but it's a matter of taste (cf..2. Tabulator settings for the editor http://www.2010 16 . section M-Files -> Editor/Debugger) . A value of 2 has proven optimal for most users.
2. vectors. http://www. and you learn how to interact with Matlab by means of the user interface.Version from: 11.edulap. matrices) You can manipulate these data types and apply mathematical functions and operations to them.Introduction to Matlab Lesson 1: Matlab Basics In this lesson you'll get to know the features and possibilities provided by Matlab. Moreover.2010 17 . basic facts of data representation and manipulation are introduced.ch/static/matlab/ . Learning Objectives • • • • • • You get an overview of what you can do with Matlab You know the different parts of the user interface You can adapt the user interface to your needs You know how to perform calculations in command line mode You get to know Matlab's basic methods to represents data (scalars.
In what cases is it advantageous to use Matlab? Small amounts of data that are acquired and evaluated only once can easily and efficiently be processed with spreadsheed software such as MS Excel or OpenOffice Calc. in particular). fMRI 3. galvanic skin resistance measurements and the like). And to execute a program. you can skip these sections and continue with The user interface. or Java. A particular advantage of Matlab is that. or only in limited and unflexible implementations. Matlab is short for Matrix laboratory. Examples are psychophysical experiments (EEG 2. scalar. eye tracking. an overview of the possibilities of Matlab is given. In these applications. 1 The most important way to represent data in Matlab.2010 18 . Usually. C+ +. Thus.2. In the field of mathematics. automating this process by means of a Matlab program will be profitable. vector). http://www. you can write data evaluation programs in other programming languages such as Visual Basic. or log file analyses. internet questionnaires. The thus verified commands can then transferred by «copy-and-paste» to your program files. Afterwards they can be statistically analysed in statistics packages such as Statistica or SPSS. Moreover. Matlab is a programming language and environment that makes use of specialised data types (matrices 1. you can quickly test how the syntax of the command has to be to yield the desired result. Thus. It is seldom worthwile to use Matlab for such tasks.ch/static/matlab/ . Moreover. Matlab allows for the programming of user-friendly interfaces for data evaluation programs that are repeatedly used. dedicated statistics functions and other interesting features which are not available in other software packages. it is even possible to compile Matlab programs and run them «stand alone». In case you already know the potential of Matlab. it can be used as an «interpreter»: you can enter single commands and have them executed immediately. Re-calculating the whole data set with the changed procedure is then done in a snap. • • • Certainly. evaluating and graphical displaying of numerical data. showing which steps are often realised with Matlab. Matlab offers a plethora of graphics functions.or higher-dimensional matrices (cf.Introduction to Matlab What Can You Use Matlab For? Below. a matrix is a table of numbers or other values. complicated data evaluation procedures can also be performed by collaborators who are less skilled with the computer. in this way. but Matlab is a language designed especially for processing. you do not need to pre-process (compile) it beforehand. the expression «matrix» refers to two. Matrices differ from ordinary tables in that they can be used for calculations. the application of programmed data evaluation routines is a more efficient way if the evaluation procedure has to be changed over and over again to 'fine-tune' it. Matlab programs are executed almost as fast as program code written in compiling languages such as C++ or Pascal. The use of Matlab is more appropriate in the following cases: • If you have to evaluate large amounts of data that are acquired automatically by means of computers and other technical appliances.edulap. contrary to most other languages.Version from: 11. Typical data processing workflow Below you see the schematic diagram of a typical project. it is way too laborious to manually preprocess every single data set with a spreadsheet software and export it to a statistics software package. Note to programmers: In spite of this user-friendly interface.
Introduction to Matlab Exemplary data processing workflow http://www.2010 19 .edulap.Version from: 11.2.ch/static/matlab/ .
i. Example 1: The use of Matlab as a (somewhat oversized) «pocket calculator» >> 27*5 >> 2^10 >> diameter=14.01:pi >> y = sin(x) >> plot(x. If no variable name such as diameter is noted.e. enter the commands listed in the examples below in the «command window» right behind the command prompt >>.z. the result will be saved in the default variable ans (answer). you don't have to understand every command in detail. the cosine values are calculated and plotted in red into the same graph. Start Matlab.'r') Explanations: First.2010 20 . Additionally. Then. Now you can try out some of Matlab's features yourself.01 is generated.edulap. and see what happens. a sequence of values between -pi and pi with intervals of 0. i.y) >> hold on >> z = cos(x) >> plot(x. For now. http://www.e. pi is an internally predefined variable that can be used at any time. the sine values of these data are calculated.ch/static/matlab/ . they will be explained later on in this course. as opposed to programmed mode. and repeatedly executed later on (more on that subject see Lesson 2). the results are plotted by means of the plot function. just after the command prompt >>.Version from: 11. Matlab will then execute them immediately. Subsequently. Example 2: Plotting a graph in command line mode >> x = -pi:.6 >> circumference=diameter*pi >> area=diameter^2*pi/4 >> ans Explanations: Simple calculations can be executed in the command line mode.2. hold on «fixates» the graph so that it will not be deleted by the subsequent plot command. a program is written first.Introduction to Matlab Examples in Command Line Mode Command line mode means that commands are directly entered in the «command window» on the «command line».
edulap. As you can see now. http://www.ch/static/matlab/ . mean and std calculate the mean and standard deviation values. these raw data are visualised in a new graphics window.2. 1000). 1000 normally distributed random values are generated by means of the randn function (the semicolon at the end of the line suppresses the display of the generated values in the command window).Introduction to Matlab Afterwards. >> plot(data) >> hist(data) >> mean(data) >> std(data) Explanations: First. randn generates values with a mean of 0 and a standard deviation of 1.2010 21 . or by entering close on the command line. hist draws a histogram showing the normal distribution shape of the data (you might have to get the graphics window to the foreground to see the result). Example 3: Some basic statistics functions demonstrated >> data = randn(1. close the graphics window: Either in the usual way windows are closed. By means of plot.Version from: 11.
edulap.ch/static/matlab/ .Version from: 11.2.Introduction to Matlab http://www.2010 22 .
http://www. the Help system is opened. you will have to click Run in the Command Window in the top right corner (and then repeatedly click Next or Run this demo to continue).g. numerous impressive demos are availabe. Two ways to start the demos Now. In the left window panel called help browser. You can run some of them in order to get a better picture of the power of Matlab.ch/static/matlab/ . e. open the directory structure «MATLAB» (click the «+» symbol). Recommended: • • • • 2-D Plots 3-D Plots Vibrating Logo Earth's Topography After selecting a demo.Version from: 11. in «Graphics».edulap. Select the demos via Matlab's Start Button or via the Help menu.2010 23 .Introduction to Matlab Demonstration Examples by Matlab In Matlab's documentation.2. Now you can view some of the demos.
Scanpath plot: Program with graphical user interface Density plot of fixations: 2D density plot Density plot of fixations: 3D density plot Plots of saccade amplitude and frequency per direction http://www.Introduction to Matlab Example From Psychological Research The following graphs exhibit some of the possibilities how to visualise eye movement data by means of Matlab programs (source: Perception and Eye Movement Laboratory. To enlarge click on the images.ch/static/matlab/ . University Hospital Bern).2010 24 .2.edulap. Neurology.Version from: 11.
Introduction to Matlab Only pictures can be viewed in the PDF version! For Flash etc. see online version.2010 25 .2. Only screenshots of animations will be displayed.edulap.ch/static/matlab/ .Version from: 11. [link] Animated scanpath display http://www.
Version from: 11. or «desktop». it is important to know what information is available through Matlab's help system. To know their functions is essential to be able to work with Matlab efficiently.2010 26 . is partitioned into different sub-windows.edulap. Matlab's user interface (desktop) http://www.ch/static/matlab/ .Introduction to Matlab The User Interface Overview Matlab's user interface.2. The most important parts of the user interface will thus be explained in this section: • • • • the command window the workspace the current directory browser the command history In addition.
2010 27 .edulap.ch/static/matlab/ . the size and position of window parts can be changed.Introduction to Matlab Desktop Display Options The desktop is made up of different areas. sub-windows can be shown independently or docked to other parts. For these functions. use the buttons in the top right corner of a sub-window and the various options in the desktop menu.2. Further user interface areas can be added or removed by means of the menu item Desktop. The image below shows the default settings. http://www. Default settings of the desktop The latest Matlab versions (approx. or you can shift the dividing lines between sub-windows etc. it is no mistake if your screen does not look exactly the same as shown in the figure. Thus. The available areas can be arranged in various ways. since version 2008a) have a somewhat different default layout.Version from: 11.
please restore the default now by selecting Desktop > Desktop Layout > Default http://www. If your Matlab desktop does not correspond to the default layout.2.Version from: 11.2010 28 .edulap. you can find out in the help system. The figure below shows how to find information on the desktop. Open it via the menu Help > Product Help.ch/static/matlab/ .Introduction to Matlab Example of a different desktop arrangement If you want to know in more detail what options are available.
You have already used it to enter the first examples.ch/static/matlab/ . error messages and the like also appear here. Previously typed commands can be re-displayed by means of the <arrow up> und <arrow down> keys.g. without clearing the contents of the command window completely clears the command window (clear command window) Explanations: The command format changes the display of values in the command window in manyfold ways.edulap. and the programs can output results and messages to this window. by typing docsearch format in the command window). format compact disables the output of superfluous empty lines.Version from: 11. For further options please refer to the information in the help system (e.2010 29 . Warnings. Matlab's «Command Window» Some command window settings The following commands influence the way how data are shown in the command window: >> pi >> format compact >> pi >> home >> clc display PI set the output format 'compact' now it is more compact indeed go to the top left position. It is used to enter commands and call programs. in order to maybe change and re-run them. http://www.Introduction to Matlab The «Command Window» The «Command Window» area is the communication channel between you and Matlab.2.
Introduction to Matlab The «Workspace» The workspace can be seen as Matlab's working memory.Version from: 11. and programs can access them directly. The ones used most often are Open and the various graphics tools.2.ch/static/matlab/ . all used variables are stored. In the figure below you can see that the variables used in the demo examples are now displayed in the workspace. Here.edulap. http://www. and have a look at the tools available in the toolbar of the workspace.2010 30 . Here you can access the variables directly to display their values or to change them. Matlab's "Workspace" Tools in the Workspace Select a variable in the workspace with the mouse.
ch/static/matlab/ .Version from: 11.2010 31 .edulap.Introduction to Matlab http://www.2.
cf. Please do not confuse this with the «search path». Alternatively.Introduction to Matlab The «Current Directory» Browser This area is placed in the same sub-window as the workspace and can be accessed by means of the current directory tab. by which Matlab has to be informed of where program files are stored.ch/static/matlab/ .edulap. It is used to browse the computer's file system and thus select the current directory for data loading and saving operations as well as to select the root directory of the editor.2. The latter is indicated in the input field named «Current Directory» in the top right corner of the desktop. section Configuration of Matlab. Matlab's «Current Directory» window http://www.Version from: 11.2010 32 . it is possible to select the current directory there.
This list can be searched. Matlab's "Command History" How to re-run previously entered commands Find and select the commands highlighted in the figure above (e.2. http://www.edulap. These commands should still be listed there as you have entered them in the first examples of this lesson. single commands can be re-run. the History of your work with Matlab is listed. if you have not done this.g.e. or you can build a program (script) from several commands you have selected in the command history.2010 33 . the commands you have recently entered in the command window.Introduction to Matlab The «Command History» In this sub-window. i. select some other commands listed there. by using shift-click or ctrl-click).ch/static/matlab/ . The selected commands are executed again. Then select the menu item «Evaluate Selection» via the context menu (right mouse click on the selected items) or simply press F9.Version from: 11.
docsearch operators • • • Finding help contents Matlab offers three ways how to find help for specific questions. 1. The most important ones are listed below (please try them out immediately in Matlab): • • Via Help > Product Help. the Help Navigator. In this way. the Help Browser/Help Navigator is opened (see figure below) By means of the F1 key. Similarly.ch/static/matlab/ . 2. It is not only indispensable for beginners when learning Matlab. the first found entry is also shown in the main window of the help system. Help for specific functions: doc function name. it contains (as you have seen before) a wealth of examples. but also for advanced users to assist in the daily work. http://www. the help system entry for this function is immediately displayed.edulap. In the bottom left corner you can find the link «Open Help Browser» allowing for switching to the full display. and hyperlinks to online resources provided by Mathworks.g. you can enter the help system's search function by direct command. If you don't know exactly what entry you are looking for. How to call the Help System The help system can be called in different ways. If you do this from within the Command Window.Introduction to Matlab Using the Help System Matlab's help system is extremely well equipped and supersedes any printed manual. Contents: The help items are shown as a logically structured table of contents. In so doing. a reduced version will be opened. you can select a command typed in the command window before and call help for it by means of the context menu (right click) Help on Selection (or by pressing F1).2. doc sin. Index: alphabetically ordered index of help topics Search function: In the field Search for: you can search for specific key words.Version from: 11. e.g. some introductory tutorials.2010 34 . 3. e. Apart from the documentation of the Matlab main program and additional tool boxes. They are available in the left part of the help system window. The results are then displayed in Search Results. similar to other sub-windows of the desktop.
Introduction to Matlab Matlab's help system Furthermore. In the command window. several options are offered in the main window: Searching by categories. • • • • • Type plot3 in the Help Navigator and click Go (alternatively: enter doc plot3 on the command line) scroll down and select the four program code lines after «Examples: Plot a three-dimensional helix» Select Edit > Copy or press Ctrl-C Switch to the command window..Version from: 11. and select Edit > Paste or press CTRL-V Press the Enter key to execute the commands. store favourites. in the main window you can navigate back and forth. search.2. you can then test the example. alphabetical list. WOW! http://www.. Similar to web browser functionnality.2010 35 . and hyperlinks to printable versions of the documentation (pdf) and external resources at the Mathworks homepage. immediately after starting the help system. How to copy example code from the help system Code examples as listed in certain help topics can simply be transferred to the command window (or a selfwritten program) by means of standard copy-and-paste procedures. and. or print.ch/static/matlab/ . searching for object properties.edulap.
2010 36 . In the Command Window. you can select the current directory for data storage as well as the root directory for the editor. Matlab's help system is an indispensable aid for beginners as well as experienced users.2. The «Workspace» is the working memory of Matlab. It stores the used variables on which programs operate. • The «Command Window» area is the communication channel between the user and the Matlab program.Version from: 11. In the window «Command History» you find the commands you have entered throughout the current session in the command window. • • • • • http://www. Warnings. There. commands can be entered. and programs can output results and messages.edulap.Introduction to Matlab Summary The most important contents of the section «The User Interface» are summarised below.ch/static/matlab/ . The «Current Directory» browser is used to access the computer's file system. error messages and the like are also shown here. previously entered commands can be repeated with the keys <arrow up> and <arrow down>. Here. and then changed and re-executed. It makes a printed manual unnecessary.
In the next sections you can learn the basics that are necessary to work in the command line mode: • • • • • How are numbers represented in Matlab? What are variables? The most important data type: the matrix How to work with matrices What operators and functions can be used for calculations? These points not only pertain to the command line mode. can be performed in a simple way in the command line mode. calculations.Version from: 11. as you will learn in Lesson 2: Programming in Matlab Using the command line mode allows for testing commands before including them in a program.2010 37 . i.e.Introduction to Matlab Numbers and Variables in Matlab As you have seen in section Why Matlab?. which is useful in case you are not sure of their syntax or function. by directly typing commands in the Command Window.ch/static/matlab/ . http://www.2.edulap. graphical displays etc. but also to self-written programs.
736 >> 784.400 >> pi activate compact display correctly entered number this is interpreted as TWO numbers. Please enter the commands listed below in the Command Window and try to understand what Matlab does with your inputs. numbers with decimal places are written with a period. the letter e is used to separate the exponent (to the base of 10). Matlab has representations for two special values: infinite (inf) and «not a number» (NaN). The comma is used to separate consecutive commands on the same line. The result of an operation (below it will only be entering a number) is assigned to the predefined variable ans (answer). that can be used at any time for 1.Introduction to Matlab Representation of Numbers As usual in English.Version from: 11.2. Please try out the following commands that illustrate this. Examples: >> 1. separated by the comma i.2010 38 . These values can be the result of calculations. such as division by zero. >> format compact >> 23.746 x 105 of course. you must not write large integer numbers with commas pi is a pre-defined constant.746e5 >> 584e-11 Contrary to other programming languages. unless it is explicitely assigned to a specific variable. >> 2/0 >> -5/0 >> 0/0 >> inf/inf >> 0*inf division by 0 yields inf minus infinite is also possible 0 devided by 0 results in NaN http://www.ch/static/matlab/ . and can as such also be assigned to a variable.edulap. negative exponents are allowed as well For numbers in scientific notation.e.
matrices. >> Speed = 63 >> g65_fubar = 3 >> Speed >> speed >> 6test = 2 >> _foo = 1 >> hi$there >> pi = 11 >> sin = 0 the equal sign assigns a value to a variable another valid name recall the value this does not work when spelt lowercase a name not starting with a letter is invalid ditto the only special character allowed is the underscore _ It is even possible to redefine pre-defined constants such as pi or function names (here.edulap. http://www.e. structured data etc.Introduction to Matlab Variables Data are stored in Matlab's working memory (i.Version from: 11. that is when they are assigned a value for the first time.2010 39 . Variable naming conventions A variable is identified by a unique name. Variable names are case-sensitive. to reserve the necessary memory space for them). In the examples below you can see what variable names are allowed. A variable is a reserved «place» in computer memory that can be referenced with a unique name. but has to be used with care (or better not at all).. This fact is expressed by saying that a variable is of a certain data type (or just «type»). the workspace) as variables. Matlab will automatically reserve the memory space at the time of their first usage. The name has to begin with a letter. and how these values can be recalled again.e. A variable can contain various kinds of data. or the «underscore» _.. numbers.ch/static/matlab/ .mat now the variable Speed is no longer in the Workspace deletes all variables (note the Workspace window) loads back the variables from the file (see the Workspace window) Saving and loading workspace variables can also be done by means of the menu buttons of the Workspace window. Single variables can be removed from the Workspace with the clear command. The contents of the Workspace can be saved to the hard disk with save (to the folder that is selected in the Current Directory Browser window) and loaded back from the hard disk by using load. how variables can be filled with values. variables do not have to be pre-defined (i. In the examples below we only use simple numbers. Single variables can directly be deleted in the Workspace (select the variable and hit the 'delete' key or use context menu > delete). Examples for data types are simple numbers. Contrary to many other programming langauges. character sequences (strings). Loading and saving variables in the Workspace Alle variables that have been used are visible in the Workspace.2. i. Please try it out again by yourself: >> save data >> clear Speed >> clear >> load data saves all variables to the file data. capitalising is relevant.e. You will get to know further data types later on in this course. after that it can contain further letters. the sine function sin).
that are not allowed in other programming languages or applications.7e6 for 2. A variable is referenced by a unique name. for instance 2. In Matlab. • • • Decimal places of a number are separated by a period. • • http://www.2. Scientific notation is spelt with e. It has to begin with a letter and can contain more letters. numbers or the «underscore» _.Introduction to Matlab Summary In the following.ch/static/matlab/ .edulap. Variable names are case-sensitive. operations such as division by zero.2010 40 .7 x 10 6.Version from: 11. you find a brief summary of the most important points of the section «Numbers and Variables». result in defined values such as inf for infinite or NaN für «not a number».
and Matrices Matlab knows various ways to represente data. Vectors. 2 for male) in the third. Example: A simple data set. The most common form of a matrix is the two-dimensional matrix. sex (e. A matrix is well suited to store data in a similar way as it is usually done when building a table . to quickly create a new data set.2. only one element Vector: one-dimensional matrix Matrix: matrix with two or more dimensions.g. they are also called arrays. some special cases of matrices in terms of their number of dimensions are referred to as: • • • Scalar: «null-dimensional» matrix.2010 41 . comparable to a table. Matrices can only contain numerical values (exception: character strings.edulap.e. thus the name Matlab (Matrix Laboratory).ch/static/matlab/ . see section Data Representation 1: Character Strings in the next lesson. A simple matrix with data from five subjects According to the terminology used in linear algebra. http://www. containing the subject number in the first column. or to hold data that have been acquired by a technical system.e. and the measured values of two dependent variables in the forth and fifth column. You will learn more about these data types in the following sections. Sometimes. 1 for female.g.Introduction to Matlab Data Representation 1: Scalars.Version from: 11. his/her age in the second. The most important one is the representation as Matrix. i.
ch/static/matlab/ . including scalars and vectors! (with one exception. column 1 determines whether sc is a scalar (1 = yes.1) >> isscalar(sc) This is a scalar. see section Programming of Functions. The notation with square brackets [ ] always designates a matrix.Introduction to Matlab Scalars A scalar is a matrix with one row and one column. more general notation as 1x1 matrix is identical to sc .2010 42 . Example 3). 0 = no) http://www.2. Thus.edulap. Please try this out yourself: >> sc = 93 >> sc2 = [13] >> sc(1.the element in row 1.Version from: 11. the square brackets are not mandatory here. and thus only contains a single numerical value.
8] >> rvect(2) >> rvect(0) >> cvect = [12. Dependent on whether the elements are arranged vertically or horizontally.Introduction to Matlab Vectors A vector contains more than one numerical element. they are referred to as: • • column vectors (one column. The semicolon separates the rows returns the first to the second element of the vector generates a vector with numbers in equal distance if the middle value is omitted.Version from: 11. inf] >> cvect(1:2) >> seq = 0:2:10 >> seq2 = 20:30 >> seq3 = pi:-. Try to understand the examples below: >> rvect = [1 4 8] >> rvect = [1. there is no 0th element! a column vector. here: Converstion of a row into a column vector is this a vector? determines the length of a vector http://www.2.ch/static/matlab/ .1:-pi >> seq2' >> isvector(seq2) >> length(seq3) a row vector with three elements the elements can be separated by spaces or commas read back the second element of the vector Important: contrary to other languages.4. any number of rows) row vectors (one row.edulap. 55. these elements are arranged side by side «in single file». any number of columns) In other words. the distance (increment) is 1 negative or fractional increments are allowed as well The apostrophe transposes a matrix.2010 43 . a vector is a matrix with only a single row or a single column.
The most common kind of matrix is the twodimensional one (m rows. 3) >> M4 = [1:4.ch/static/matlab/ .Introduction to Matlab Matrices In the field of mathematics. colormap(map) >> m4 = magic(4) loads a pre-defined data set into the workspace (variable X) shows it as an image loads the correct colour palette. 4) >> M4(3. [1 3 2 4]) >> M4(1. and accessing the elements of a matrix is also possible in numerous ways. Matlab also supports matrices with more than two dimensions.edulap.3 5 8. 6:2:12] >> M4(1. Demonstration example: The matrix in Dürer's «Melancholia» >> load durer >> image(X) >> colormap(map) >> load detail >> image(X). 2:3) = -1 >> mag = magic(4) >> mag = mag(:. as you can see in the examples below.3 2 1] >> M3(2. 6) = [] a 3x3 matrix access single elements (row. 2:end) >> M4(3. 4) = 55 >> M5 = M4(1:2. too (find the difference!) Matrices can be built in various ways. col) the entire 3rd column.e. the : designates all elements the notation for number sequences is possible.2010 44 . 3) >> M3(:.2.Version from: 11. >> M3=[12 13 10. you can remove a row from a matrix the same to delete a column http://www. too end designates the last element lies «beyond» the matrix Matlab will automatically enlarge the matrix and fill with zeroes assign a part of the matrix to a new variable assign a value to only part of the matrix the magic square again convert it into Dürer's square by swapping column 2 and 3 i. a matrix is a table of numbers. indexing with a vector expand matrix M4 to a three-dimensional one yields the size of the matrix (as a vector!) ask for the number of rows only (2 would be the columns) number of dimensions number of elements create an empty matrix ask whether the matrix is indeed empty generate yet another matrix (Pascal's triangle) in this way. >> isempty(emptymatrix) >> isempty(mag) >> p = pascal(8) >> p(3. Building matrices and accessing their contents and properties. Can you see the matrix? an other data set containing the image detail a magic square! Matlab can do this. n columns). 1. :) = [] >> p(:. 2:3) >> M4(1:2. 1) >> ndims(M4) >> numel(M4) >> emptymatrix = []. 3) = 100 >> matrixsize = size(M4) >> size(M4. very similar to a table as you know it from applications such as MS Excel (but only containing numerical values).
4) is thus identical with data(17).2. the element data(2. Instead of addressing them by row and column index. containing the value 14. you can address the x'th element of a matrix.Introduction to Matlab Linear indexing Linear indexing allows for a different way of accessing the elements of a matrix.2010 45 .see figure). In the pictured matrix.ch/static/matlab/ . with a single argument. then in rows . http://www. In that way.edulap.Version from: 11. a matrix can be thought of as being serially numbered (first in columns.
2010 46 . the elements have to be enclosed in square brackets [ ]. the second one is the column. Additionally. When indexing elements of a matrix.ch/static/matlab/ .2. Number sequences (= vectors) can be produced with the : . but only column 12 of the matrix. The indices always run from 1 to n. isvector: check whether a variable is a scalar or a vector. you again find the most important points in a brief summary. e. respectively length determines the length of a vector ndims returns the dimensionality (number of dimensions) of a matrix numel calculates the total number of elements of a matrix size returns the size of a matrix isempty determines whether a matrix is empty http://www. the indices are enclosed in round brackets ( ). Matlab also allows for higher-dimensional matrices. data(:. 10:2:50 for all even numbers from 10 to 50.g. The elements of matrices and vectors that belong to the same row are separated with a space or comma. When defining matrices and vectors.notation.Introduction to Matlab Summary Below. Points to remember • • • • • • • • • • • A scalar is a matrix with one row and one column. a matrix can be seen as being serially numbered. n columns). The semicolon separates rows.g. A vector is a matrix with a single row (row vector) or a single column (column vector).Version from: 11.edulap. 12) for all rows. Linear indexing: Instead of addressing elements by row and column index. Commands • • • • • • isscalar. relevant Matlab commands are listed. n columns and p planes. that is with only a single numerical value. the brackets are optional. thus you can address the x'th element of a matrix with a single argument. e. the first index is the row. the index 0 (the «zeroth» element) does not exist in Matlab.g. For scalars. In two-dimensional matrices. e. A solitary colon designates all elements of a row or column. with m rows. The most common matrix is the two-dimensional matrix (m rows.
http://www. you learn various possibilities to manipulate Matrices: • • • • matrix concatenation matrix duplication creating special matrices matrix transformation This section will be concluded with a first practical exercise.Version from: 11.edulap.2010 47 .2.ch/static/matlab/ .Introduction to Matlab Matrix Manipulation In this section.
more than two matrices are possible An overview of the basic matrix manipulation commands can be found in the help system. 5 rows.g. b. >> b = randn(5. Matlab provides dedicated functions for matrix concatenation. by entering doc elmat (elementary matrices and matrix manipulation. b] >> b = randn(5. 3 columns horizontal concatenation vertical concatenation: does not work this way because the number of columns is inequal thus. a] the semicolon prevents the output of a in the Command Window random numbers. b] >> e = [a. e. >> c = [a b] >> d = [a. b) >> vertcat(a.2.Version from: 11.2010 48 . Please try to comprehend this by following the examples below: >> a = magic(5).3). d. we convert b into a 5x5 matrix now it works you can also concatenate more than two matrices at once The above examples clarify how the semicolon after a statement is used to suppress the output of generated values to the command window. Besides the above demonstrated possibilities.) http://www.edulap. This is again demonstrated by means of some examples: >> horzcat(a. >> d = [a.5).Introduction to Matlab Matrix Concatenation Matrices can be concatenated with the normal [ ] -notation.ch/static/matlab/ . a) horizontal concatenation vertical concatenation.
2010 49 .2. a. 2 = horizontally. b) matrix duplication.2. >> m = magic(3). a. duplicate twice vertically and three times horizontally general function: concatenate along dimension n (1st argument) 1 = vertically.Version from: 11.edulap.3) >> cat(1. Here. Please study the usage of these two commands by doing the manipulations below. >> n = repmat(m. b) >> cat(2.ch/static/matlab/ . 3 = in «planes» Illustration of the cat function http://www. The variables a and b should still be in your workspace. as you have used them in the previous examples.Introduction to Matlab Matrix Duplication The two most important matrix duplication functions are called repmat (repetition of matrices) and cat (concatenation).
ch/static/matlab/ . a thing more for mathematicians magic squares http://www. 3) >> allones = ones(4) >> a(1:5. >> zeros(7.Version from: 11. you can see the most important ones of these functions. for linear algebra Pascal's triangle matrix.5 >> b = ones(7. This can sometimes be helpful to test statistical functions or generate test data sets. In the examples below. 3) * 81 >> rand(1. Pascal's triangle etc.Introduction to Matlab Creation of Special Matrices Certain special matrices are needed again and again. 1:10) = 3. a square matrix results To create a matrix with other values.2010 50 .edulap. Also see Random Numbers in Lesson 4 Particular matrices for linear algebra: identity matrix. there are several ways. random numbers between 0 and 1 normally distributed random numbers with a mean of 0 and a standard deviation of 1 so-called identity matrix (only square matrix is possible). Some examples: • • • Matrices filled with zeroes or ones Matrices with random numbers with different distributions. 8) >> randn(2. thus Matlab provides commands to create such matrices.2. 6) >> eye(5) >> pascal(7) >> magic(8) Matrix with zeroes Matrix with ones. If only one argument is given.
edulap.2. 0 1 2 3 4.2010 51 .Introduction to Matlab Matrix Transformation The most important transformations are: • • • Mirroring (horizontally or vertically) Rotation Transposition (swap rows and columns) Examples to try out: >> a = [1 2 4 8 16.Version from: 11.ch/static/matlab/ . >> fliplr(a) >> flipud(a) >> rot90(a) >> rot90(a. 3) >> a' flip left-right: mirror aling the vertical axis flip up-down: mirror along the horizontal axis counter-clockwise rotation by 90 degress (default: once) rotate by 90 degrees three times transpose matrix (exchange rows and columns) http://www. -1 -6 0 1 6].
Try to accomplish this with as few commands as possible. Four values are labelled as "missing data" by the value NaN. and try first to use the help system if necessary.Introduction to Matlab Exercise 1: Create a Complex Data Matrix You have now learned the basics of how to create matrices with various contents and how to manipulate them. randn Sample solution >> testdata = (27:36)' % subject numbers upper half >> testdata = [testdata ones(1. it is helpful to be able to create a test data set to test a data evaluation program before you have acquired «real» data. At the end of the exercise you will find a link to the sample solution that you can consult in case you need help. Please do not fall back on the sample solution too early.Version from: 11. Tips for functions that can be used: eye.ch/static/matlab/ .edulap. containing hypothetical test data as pictured below. Explanation of the data: Column 1: subject number Column 2: 1st or 2nd run of the experiment Columns 3-12: mark several experimental conditions Column 13: normally distributed random numbers (they do not have to be identical with the pictures values). it is important to realise that there is more than one possible solution.2010 52 . by solving an example on your own. repmat. For learning success it is central that you now try to use this knowledge yourself. 10)' eye(10)] % group numbers of group 1 and diagonal http://www.2. However. Create the matrix testdata in the workspace. Task description Sometimes. Try to do this now in the following exercise.
edulap. Everything after the % sign are comments and are not interpreted by Matlab.Version from: 11. 11:13]. 2) = 2 % group numbers of group 2 >> testdata(:.2. 13) = NaN % add missing values You can copy/paste all code lines to the Command Window.ch/static/matlab/ .Introduction to Matlab >> testdata = repmat(testdata.2010 53 . 13) = randn(20. 1) % random data >> testdata([4. 2. 1) % duplicate the whole matrix vertically >> testdata(11:20. http://www.
flipud: mirrors a matrix left/right or up/down rot90: rotation by 90 degrees data': transposition of matrix data. complete matrices are used.edulap.ch/static/matlab/ . columns.2010 54 . repmat: duplicate a matrix zeros. e. vertcat: horizontal or vertical concatenation of matrices cat: general command to concatenate matrices in rows. d = [a. The to-beconcatenated matrices need to have the same dimensions. swapping rows and columns http://www. planes. Matrices can be concatenated horizontally and vertically by means of the normal [ ]-notation.g. randn generate matrices containing random numbers with equal or normal distribution. that is the equal number of rows when concatenating horizontally. fliplr. ones create a matrix with zeroes or ones rand. etc.Introduction to Matlab Summary Points to remember • • A semicolon after a command suppresses the output of the created values in the Command Window.Version from: 11. and equal number of columns when concatenating vertically. b]. i. Instead of single numerical values. Commands • • • • • • • • horzcat.e.2.
Version from: 11. etc. Call this by entering elementary math in the search field of the Help System. mathematical operators and functions are explained. • • • • trigonometrical functions: sine. etc.g. sum. Other mathematical manipulations are realised as functions. and many more. descriptive functions such as minimum. The Help System provides more information on all available functions.2010 55 .ch/static/matlab/ . cosine.. sign. maximum. The range of functions provided by Matlab is enormous. etc. mean values and the like basic mathematical functions such as: square root.. Later on. rounding. http://www.2. the question of priorities of operations and the bracket rules are important as well. two exercises will be provided so that you can practise the use of functions and operators.Introduction to Matlab Mathematical Operators and Functions In this section. tangent. multiplication * and division / exponential functions such as square ^2 In this context.edulap. subtraction -. e. Mathematical operators are mathematical operation symbols such as: • • • • addition +. thus only the most important ones can be introduced in this course. logarithm.
* magic(3) >> magic(3) * 5 Addition is always performed element by element. If you are unsure about the function of an operator. element-by-element product) To multiply each element of a matrix with 5. you can just test it in command line mode before inserting the statement into your program.edulap. However. To perform element-by-element multiplication. usually not important for applications in our field). >> a * magic(3) >> a . i. The sequence of how different operators are evaluated follows the general precedence mathematical rules (e. you can just multiply it with a scalar (5 in this case). When performing calculations.2010 56 . The two matrices have to be of the same size. you can use the operator . you can either enter arithmetic operators in the Help Navigator. You can find help on this topic by using the key word operator precedence in the Help System.e. certain peculiarities of Matlab become relevant. or you can type docsearch 'arithmetic operators' in the Command Window (the inverted commas are necessary because the search term includes a space).2. operations with matrices (and vectors 9) follow other rules in some cases (linear algebra). that is only one row or one column http://www. 7 9 «null-dimensional» matrix. as usual. everything works as you would expect from a pocket calculator. As long as you exclusively work with scalars 7. To display this information.ch/static/matlab/ . Please try to understand the following examples: >> magic(3) + ones(3) >> a(1:3. brackets are used if a different sequence is necessary.Introduction to Matlab Operators The Help System provides a good overview over the mathematical operators and how to spell them.Version from: 11. only one element one-dimensional matrix.* (array multiplication. Multiplication of two matrices is NOT performed element by element (linear algebra. 1:3) = 5. This method is called «scalar expansion». multiplication/division before addidion/subtraction ).g.
.Version from: 11. square root.edulap. mean. sine. http://www.2010 57 .Introduction to Matlab Functions Matlab provides a plethora of pre-defined mathematical functions (e. you find the relevant information in Contents under Function reference > Mathematics > Elementary math Examples for mathematical functions: >> data = magic(10).ch/static/matlab/ .g.) In the Help System. two sum statements can be nested minimum and maximum per column standard deviation in columns functions such as the sine separately calculate the results for each element rounding function another «function»: answer on all possible questions.2. etc.. >> sum(data) >> sum(sum(data)) >> min(data) >> max(data) >> std(data) >> sin(data) >> round(pi) >> why calculates the sum in columns for the overall sum.
s = 5.Version from: 11.2. in Matlab to be executed with exp. >> y = . x = 2. >> y = 1/(s*sqrt(2*pi))*exp(-1/2*((x-m)/s)^2) definition of input values How is the formula to be written correctly? The result should be 0. s = 5. x = 2.0782 10 density function of normally distributed data http://www..ch/static/matlab/ .Introduction to Matlab Exercise 2: Implementing a Mathematical Formula Try to implement the formula of the Gaussian bell shape 10. Sample solution >> m = 3.2010 58 . m is the mean value or the expected (peak) value Erwartungswert (peak of the curve) s is the standard deviation ("width" of the shape) x is the independent value e is the exponential function.edulap.. The square root function is called sqrt >> m = 3.
and the two diagonals have to be equal. >> m = magic(7).ch/static/matlab/ .Introduction to Matlab Exercise 3: Validation of a Magic Square Check the correctness of a 7x7 magic square: The sum of all rows.. >> sum(m) % sum of columns >> sum(m') % transpose m to obtain row sums >> sum(diag(m)) % calculate the sum of the main diagonal >> sum(diag(fliplr(m))) % the other diagonal http://www. >> . columns. Sample solution >> m = magic(7).edulap.2.2010 59 ..Version from: 11.
Otherwise. the sequence of how they are performed follows the general mathematical rules (e. which are different (and which are seldom relevant for applications in psychology). multiplication/division before addition/subtraction). max: minimum and maximum std: standard deviation sin. Help System: You find the function overview in «Contents» Function reference > Mathematics > Elementary math.2. tan etc.edulap.2010 60 . As usual. • Commands • • • • • sum: calculates the sum min. cos.Introduction to Matlab Summary Points to remember • When evaluating consecutive mathematical operations. You can find an overview of all operators by typing docsearch 'arithmetic • • • operators' Addition and subtraction of whole matrices is performed element-by-element.ch/static/matlab/ ./ b.* b and a .g.Version from: 11. Element-by-element mulitplication and division of whole matrices requires a special syntax: a . brackets are needed if a different sequence is necessary.: trigonometric functions round: rounding http://www. Matlab will perform a matrix multiplication or division according to the rules of linear algebra.
8 3. 1. Matrices Which statement will generate the matrix a shown below? r r r r a a a a = = = = [ [ ( [ 1 1 1 1 5 5 5 6 8 3. try to find the answer to the following question: The function to draw a three-dimensional scatter plot is ___________ . User interface Which command is used to clear the command window? r clear r clc r r home clrcmd What is NOT possible to do in the Workspace window? r Remove variables from the Workspace r Change the contents of variables r r Read data from external sources perform calculations How can you select the folders in which Matlab searches for functions (M-files)? r In the Current Directory browser r with cd (change directory) r By using the menu item File > Set Path Help System In the Help System. 6 7 1. b=a'. 3 1 8 ] Which command sequence leads to the pictured matrix being printed in the Command Window? r a=[0 8 3. 6 7 1. 8 3. please try to answer the questions below.Introduction to Matlab Self-test Questions To test your understanding. 5 6 6 6 6 6 7 1.2010 . b(1. [a b] 61 http://www.ch/static/matlab/ . 8 7 0 1 0 8] 0 1 0 8] 0 1 0 8) 0.2.:)=NaN.edulap.Version from: 11.3 5 5]. 0.
3 5 5]. [a b] a=[0 8 3. b=a'. b=a'.Version from: 11. b=b(2:3.:)=[]. b(1. b(1.ch/static/matlab/ .3 5 5]. b=transpose(a).2.:).:)=[].Introduction to Matlab r r r a=[0 8 3. [a b] a=[0 8 3. b] Mathematical operations Which code represents the shown formula? r r r r y y y y = = = = 2*exp(-t/tau)/sqrt(x+1*x-1) 2*exp(-t/tau)/sqrt((x+1)*(x-1)) 2(exp(-t/tau)/sqrt((x+1)*(x-1))) 2*e^(-t/tau)/sqrt((x+1)*(x-1)) http://www.2010 62 . [a.3 5 5].edulap.
Introduction to Matlab
EEG: Electro-encephalography: registration of the electrical activity of the brain fMRI: functional magnetic resonance imaging Gaussian bell shape: density function of normally distributed data matrix: The most important way to represent data in Matlab. In the field of mathematics, a matrix is a table of numbers or other values. Matrices differ from ordinary tables in that they can be used for calculations. Usually, the expression «matrix» refers to two- or higher-dimensional matrices (cf. scalar, vector). scalar: «null-dimensional» matrix, i.e. only one element vector: one-dimensional matrix, that is only one row or one column
http://www.edulap.ch/static/matlab/ - Version from: 11.2.2010
Introduction to Matlab
Lesson 2: Programming in Matlab
Basically, a program is a sequence of statements that will be executed when running the program. The succession of executed statements is determined by program control structures such as loops or conditional branchings. This sequence of statements is stored in a file and can thus be called again at any time.
Learning Objectives
• • • • •
You know the most important functions of the Editor. You understand the difference between scripts and functions. You can write simple scripts and functions. You know the most important loop and branching structures. You know how to use character strings.
http://www.edulap.ch/static/matlab/ - Version from: 11.2.2010
Introduction to Matlab
M-Files: Scripts and Functions
All programs written in Matlab are stored as so-called M-files with the file name extension .m. This is also true for most functions that are included in Matlab's basic function library as well as additional toolboxes. In the following sections, you will learn how to write and execute such programs. There are two kinds of program or M-files: scripts and functions. Scripts A script contains a sequence of statements that works in the same way as if you entered these statements one after the other in the Command Window. Accordingly, scripts can access all variables in the Workspace, and variables created by scripts are stored in the Workspace. Functions A function is characterised by the fact that (in most cases) values are passed to it to be processed, and the function returns the calculated results to the «caller» (i.e. to the statement entered in the Command Window, or another script or function). Thus, this is the same as - for instance - with standard functions, e.g. computation of a mean value with a = mean(b). The data to be processed are passed to the function in matrix b, and the calculated mean value is returned in variable a. The Editor/Debugger As a prerequisite for being able to write scripts and functions, you have to get to know the proper tool, that is the Editor. It is designed to edit M-files. This will be explained in the next section. At the same time, this program serves as the so-called «Debugger», that is the aid to find errors (bugs) in a program and fix them (referred to as debugging). This will be introduced later in Lesson 3, Section Applications: External Files.
http://www.edulap.ch/static/matlab/ - Version from: 11.2.2010
http://www.edulap. surfc(X.Z] = peaks(30). a Matlab program file with the file name extension .2.m.e.Version from: 11.. or ctrl-click on a Mac with single-button mouse) or by doing the same in the Directory Browser. now the program is executed.ch/static/matlab/ . Demonstration of the editor: Please perform the steps described below to see how programs are written in the editor.. You should save it to the location you have defined earlier as the path for your M-files (see Configuration of Matlab).Y. the built-in Editor is used. the editor creates an empty M-file. the tool to support tracking down errors.m) in the Windows file manager. • • Start the editor by typing edit in the Command Window. In the Command Window.Z) colormap hsv axis([-3 3 -3 3 -10 5]) • • Save the program by selecting File > Save as. The Editor also serves as Debugger.2010 66 . [X. name it editordemo. the Matlab Editor is activated as well.Y. if you double click an M-file (that is. While opening. Please note: In some older Matlab versions. The editor can be called in different ways: • • • By typing edit or edit function name (or script name) by selecting a function or script name in the Command Window and choosing open via the context menu (right mouse click. i. The Debugger will be demonstrated in Lesson 3 in the Example: Data Import. type editordemo.Introduction to Matlab The Editor/Debugger To write programs. but without the Debugging features.. Copy-and-paste the following statements to the Editor window.
2.2010 67 .Version from: 11.edulap.Introduction to Matlab That's how your screen should look like after this example http://www.ch/static/matlab/ .
it is possible to write more than one statement on a line.Introduction to Matlab Script Programming A script is a file containing a sequence of statements. These lines (up to the first empty line) are printed if you call the help information for this script by typing help script name in the Command Window. • • • Writing scripts As demonstrated above. only one statement is written on a single program line.m) in the Command Window. or by a semicolon which separates the statements and prevents output to the Command Window at the same time. in the same way as if you had «manually» entered these statements one after the other in the Command Window. Writing the statements in the Editor window Saving the script as an M-file with a new name Executing a script A script is executed by typing the script name (i.e. Empty lines: Any number of empty lines can be inserted in order to visually structure the program.Version from: 11.ch/static/matlab/ . When the script is called.edulap. They will not influence the function of the program at all. a well-formed script begins with some comment lines describing the function of the script. However. Comments are marked by a percent sign %. A semicolon after the statement prevents that the calculated values are printed to the Command Window. or by calling it from within another script or a function. In this case. for better readability. http://www.2010 68 . Header lines/Help text: As shown in the figure below. the statements are separated by a comma. Structure of a Script • • Program lines: Usually. Matlab executes these statements sequentially. writing a script subsumes several steps: • • • Starting the Editor: an empty file is opened. Scripts can access all variables in the workspace. the file name without the extension . Everything on a line that follows this sign will not be interpreted by Matlab. and accordingly. the variables generated by scripts are stored in the workspace.2.
ch/static/matlab/ .Introduction to Matlab A simple script.2010 69 . http://www. you can see the output when calling the script.2. In the Command Window.edulap. and its help information.Version from: 11.
m. http://www. Write a script that creates the data matrix from Exercise 1 (but without the NaN values). Data matrix to be created Save the script. and prints these values to the Command Window. for instance with the name exercise4. These statements are processed in the same way as if they had been entered in the Command Window.ch/static/matlab/ . For the creation of the data matrix. or copy the code from the box below.2010 70 . This script can then be executed repeatedly. You have seen how this is done in the section above.2. calculates the mean and standard deviation of the data in column 13 per group. Column 1: subject number Column 2: 1st or 2nd run of the experiment Column 3-12: mark the different experimental conditions Column 13: normally distributed random data (they do not need to be identical with the values in the figure). 1 A script is a sequence of statements that is stored in a file (M-file). you can either re-use your solution of Exercise 1.edulap. in your working directory (the one directory you created in Section Preparations/Materials).Introduction to Matlab Exercise 4: Programming a Script The goal of this exercise is to write a script 1 containing the statments you used in Exercise 1.Version from: 11.
std % Exercise 4: This script creates the data matrix from exercise 1. testdata = [testdata ones(1..edulap. Other necessary functions: mean.2010 71 . Sample solution (opens in a new window) The solution can also be found in the M-file exercise4_sol. 2) = 2. omit the semicolon after a calculation statement. testdata(:. you can just write the variable name as a statement (as in Command Line mode). 2.2. 10)' eye(10)].1).ch/static/matlab/ . http://www. and % outputs these values to the command window.13) = randn(20. testdata = repmat(testdata..m (from the file examples. % generate the matrix testdata = (27:36)'. % calculates the mean and standard deviation per group.zip you downloaded before). 1). % calculations and output .Introduction to Matlab Hints: To output data to the Command Window. or you can use the function disp(variable name).Version from: 11. testdata(11:20.
the input parameters: They specify what values can be passed to the function. That is. It contains the so-called function definition. As to their access to data (variables). The main advantage of a function is its reusability. containing a sequence of Matlab statements.m A simple function with one input and one output parameter. The Workspace as you know it is «invisible» to the function. If there are changes.e. and that the function returns the results to the «caller» (i.Version from: 11. the M-file name). Example 1: M-file gauss1. http://www.edulap. It can represent a script or a function. they can only access those variables that have been passed to them in the function call.e. or another script or function). the Command Window. with a fixed mean value % and standard deviation % another comment (will NOT be displayed when typing help gauss1) s = 5.2.ch/static/matlab/ . When the function has finished. private Workspace containing the variables passed and to be returned. functions allow for more efficient programming. this temporary Workspace is deleted. the output (or return) parameters: They specify the values in which the function returns the results. they are called with their name (the file name of the M-file) and the necessary arguments. Tasks that have to be done in different applications only need to be written once. 2 A file with the extension . and the change becomes relevant for all calling programs at once.m. This definition specifies: • • • the function name. a function only differs from a script in its first line.Introduction to Matlab Function Programming Function M-files 2 you have written yourself are applied in the same way as the functions provided by Matlab.e. the sine function sin. it obtains a temporary. % sigma m = 3. they only have to be made once in the code of the function. While a function is being executed. and originates from the file examples. and the programs themselves become more compact and thus better readable and easier to maintain.zip. functions are «encapsulated».2010 72 . % mean value y = 1/(s*sqrt(2*pi))*exp(-1/2*((x-m)/s)^2). i. It should be available in your directory for M-files. e. Please open this function in the Editor. function y = gauss1(x) % Calculates the value of the gaussian bell shape. Thus.g. for example y = sin(x) A function is characterised by the fact that (in the majority of cases) values to be processed are passed to them. as well as temporary variables created by the function itself to perform the internal calculations. Structure of a function Formally. It has to be identical with the file name under which the function is saved (i.
maximal value function [meanval. This is the only case in which the square brackets [ ] are not used to describe a matrix. m and s are variable as well. s) % Calculates the value of the gaussian bell shape with variable mean value % and standard deviation y = 1/(s*sqrt(2*pi))*exp(-1/2*((x-m)/s)^2). minimum = min(M_in). function y = gauss2(x. meanval = mean(M_in).edulap.2.m A function with several input parameters. minimum. 3. m.Version from: 11. Using the function: >> result = gauss2(2.2010 73 . 5) Example 3: M-file stats.Introduction to Matlab Explanations • • For more information on the gaussian bell shape see Exercise 2 in Lesson 1. Line 2 and 3 contain a short function description as comments. % Calculates statistical values for a row vector % % INPUT : M_in . They are specified in square brackets. • Using the function: >> result = gauss1(2) Example 2: M-file gauss2. the function is defined with its input and output paramters.m A function with more than one output parameter. in order to make sure that you know what the function does when looking at it half a year later. gauss1 is the function name and has to be identical to the M-file name. stddef = std(M_in). but also be written % after the help text lines. maximum] = stats(M_in) % Remark: The function definition can be in the first line. Explanations: Now.input vector containing the data % OUTPUT: meanval . stddev. Line 1: Here. and have to be passed to the function during the call. y is the variable that is used to return the calculated result to the caller.mean value % stddev . but just a list of output parameters. x stands for the value that is passed to the function.ch/static/matlab/ . and that somebody else has a better chance to understand it.minimal value % maximum . http://www.standard deviation % minimum . All comments up to the first blank line are displayed when help gauss1 is typed in the Command Window. It is strongly advised to add descriptions and explanations to all functions.
the variables are filled "from front to back".2010 74 .2.ch/static/matlab/ .Introduction to Matlab maximum = max(M_in).edulap.Version from: 11. mnm. s2. 300)*100+100 >> [m. http://www. s3] = stats(Min) create a row vector with random numbers get back all 4 output parameters But it is also possible not to fetch all 4 return parameters in this case. mxm] = stats(M_in) >> stats(M_in) >> a = stats(M_in) >> [s1. Using the function: >> M_in = randn(1. s.
for instance). if nbarg == 0 return end for arg_i = 1:nbarg substr = varargin{arg_i}(:)'. A vector or a matrix whose elements are interpreted as ASCII coded characters.ch/static/matlab/ .Introduction to Matlab Special Cases Special case 1: Function without parameters If a function is to be written that does not need any input values (e. the 3 4 In every field of a Cell Array.g. a loop is executed nbarg times. nbarg = length(varargin). end Explanations: First. Then. e. You will learn more about cell arrays 3 in Lesson 4.2010 75 . the function strxcat (also mentioned here) is presented: function string = strxcat(varargin) % A variable number of strings or numbers are concatenated into the output string.Version from: 11. As an example for a function with a variable number of input parameters. different data types can be stored. once for each input string. In the loop. the function definitions look like this: >> function numbers = randomx() No input parameters: just leave the brackets empty >> function [] = No output parameters: two possibilities draw_graph(M_in) >> function draw_graph(M_in) Special case 2: Variable number of parameters Occasionally. string = [string num2str(substr)]. Character string. or does not return any results (but creates a graphical output. % % INPUT : n strings or numbers % OUTPUT: string string = []. chapter Cell Arrays.g. matrices of different size.edulap. it is necessary to have a function that does not strictly specify how many input or output parameters are used. function string = strxcat(varargin) variable number of input paramters varargout = readsomenumbers(fid) variable number of return parameters The variables varargin (variable number of arguments IN) and varargout (variable number of arguments OUT) are Cell arrays. a function that generates special random numbers).2. http://www. the number of strings 4 passed as input is determined with the length function and stored as nbarg. a special data type that can contain various kinds of data.
converted from number into string if necessary. and concatenated with the previous strings.2.2010 76 .Introduction to Matlab arg_i-th element is extracted.edulap.Version from: 11. http://www.ch/static/matlab/ .
A semicolon at the end of a code line prevents the output of calculated or created values in the Command Window. i. Scripts can access all variables in the Workspace. During execution.e. functions are «encapsulated» with regard to data access. A function differes from a script in that (in most cases) values are passed to the function to be processed.2010 77 . • Commands • function [return parameters] = function name(variables for input parameters) definition of a function with input and return parameters disp(): output of values to the Command Window • http://www.2. containig the variables passed as input and return parameters as well as variables defined within the function itself. Contrary to scripts. In the same way. a script can be called from within another script or function.edulap. they cannot access the variables in the general Workspace. and the variables created in the script are stored in the Workspace. private Workspace. A script can be called from the Command Window by typing its file name (without .Version from: 11.Introduction to Matlab Summary Points to remember • • • • • A script contains a sequence of statements that are processed in the same way as if they had been entered one after the other in the Command Window.m).ch/static/matlab/ . a function obtains a temporary. and the results can be passed back to the «caller». but only those variables that have been passed in the function call.
There are two kinds of loops: • • the for-loop: It is used if it is pre-determined how many times the statements have to be repeated. http://www.edulap.ch/static/matlab/ .Version from: 11. This is achieved by using loops.2.2010 78 . the while-loop: It allows for making the number of repetitions dependent on a comparison within the loop.Introduction to Matlab Program Control Structures: Loops It is often necessary to repeat a sequence of statements.
i.the so-called loop index. It can be used like any other variable within the loop. >> for i = magic(7). i. it is set to the next value of range. That is.row vector or matrix. all notations of vectors are allowed: >> for i = pi:-.3:-pi. the loop is executed as many times as there are columns in the matrix. i. end http://www. With every pass through the loop. for the loop index. >> disp(facts) >> sumvalue = sum(facts). Any valid variable name is allowed. Simple for loop: >> for index = 1:30 >> facts = factor(index).Version from: 11. the loop index obtains a whole column of range at each pass. statement n end indexvar . end If a matrix is given as range. range .2010 79 .edulap.10) * 20. >> end Matlab does not do anything until it hits end calculate the prime factors of the loop index display them further statements with this. For loop examples Please try to understand the way how for loops work by studying the examples below. but only row vectors Basically.. and will be executed any sequence of numbers enumeration vector created by a function. end >> for i = [1 4 7 11 13 17 3 5].ch/static/matlab/ . This is the schematic syntax of the for loop: for indexvar = range statement 1 . the for loop is applied. It defines which values are assigned to indexvar.2. the loop is closed.Introduction to Matlab The For Loop If the number of necessary repetitions is known before the loop is started.. end >> for i = rand(1. i.
Version from: 11. >> end execute the loop as long as index is smaller as or equal to 30 print prime factors increment index http://www. statement n end The loop is executed as long as the condition results in true (i. usually at the begin of the loop.. the corresponding end statement).2. You will find detailed information on how to specify comparisons in the section Comparison Operators and Logical Operations. The syntax of the while loop in pseudo code: while condition statement 1 .e.Introduction to Matlab The While Loop The while loop is applied when the number of passes is dependent on a comparison made each time the loop is executed.2010 80 . The first time the condition evaluates as false (value = 0). Program execution then continues with the first statement after the loop (i. a value > 0).e. the loop is left.. >> while index <= 30 >> disp(factor(index)) >> index = index + 1.ch/static/matlab/ . A simple while loop: >> index = 1.edulap. The condition is always evaluated at the begin of the loop.
end >> end already leave the loop when the index is 20 Example 2: while loop with break index = 1.2010 81 . for instance. With this statement. That is.Version from: 11.2. while true disp(factor(index)) if index > 30 break end index = index + 1.edulap. in this example: ALWAYS (counterpart: false or 0). break. Or you can terminate a for loop before the loop index has reached its last value. even if it has not «finished». the break statement causes the program execution to continue after the end statement that closes the loop. Example 1: for loop with premature exit >> for index = 1:30 >> disp(sum(factor(index))) >> if index == 20. end Explanations true (or the value 1) in the while statement means: the comparison result is true.Introduction to Matlab Exit Loops with the break Statement It is possible to prematurely exit for. a while loop can be written whose exit comparison is done at the end or anywhere within the loop instead of at the beginning.and while loops by means of the break statement. http://www.ch/static/matlab/ .
m) by means of a loop in order to enable it to calculate the values for a row vector and return the results as a vector.m). Save the function as gauss3.edulap. Start out with these lines: function Moutput = gauss3(Minput. Afterwards call the function with values from -5 to 5 (with intervals of 0.2010 82 .Version from: 11. m.m http://www.ch/static/matlab/ . s) % Calculates the values of the gaussian bell shape for the row vector % Minput.. with the mean value m and standard deviation s .1) and graphically display the values by means of plot Sample solution (opens in a new window) The solution can also be found in the M-file gauss3_sol..2.Introduction to Matlab Exercise 5: Gaussian function for a vector Rewrite the Gaussian function version 2 (M-file gauss2.
one possibility to solve this task is: >> i = 0. Using the means you know up to now. >> y(i) = sin(t).Introduction to Matlab Vectorisation of Loops Thanks to the data representation method as matrices.01:10.2. >> for t = 0:. >> y = sin(t). it is often possible to process complete data sets much more efficiently than as it would be feasible with loops.01:10 >> i = i + 1. Or in an even more compact form: >> y = sin(0:.ch/static/matlab/ .edulap.01:10). Please have a look at the following example: The task is to compute the sine of 1001 values from 0 to 10 and store it in row vector y.2010 83 . http://www.Version from: 11. >> end The «vectorised» version is simpler and executes faster: >> t = 0:.
2010 84 . any vector can be used. Commands • for index=1:n (some statements) end Repetition loop.2. while (condition) (some statements) end Loop with conditional exit. i.Introduction to Matlab Summary Points to remember • • The for loop is used whenever it is predetermined how many times a sequence of statements has to be executed. Instead of 1:n. The while loop is applied when the number of reiterations has to be dependent on a condition. The comparison is always evaluated at the beginning of the loop. The statements are executed as long as the condition is fulfilled. results in true (value > 0). break: allows to exit for and while loops at any time.Version from: 11.e.ch/static/matlab/ .edulap. • • http://www.
edulap.Version from: 11. http://www.2010 85 .Introduction to Matlab Program Control Structures: Conditional Branching In almost every program it is necessary to process some statements only under certain conditions. and the switch-case structure. Matlab offers two constructs to achieve this: • • the if-elseif-else structure. To realise this.ch/static/matlab/ .2. so-called conditional branchings are used.
it is possible to realise any number of subsequent elseif comparisons.Introduction to Matlab The branching structure if-elseif-else You can see how this structure works in the examples below. You can execute the script by hitting the F5 key in the Editor window. http://www. The function num2str will be explained later (see here).edulap. Example 2: if-else structure with more than two cases Again. % generate random numbers for i = 1:length(a) if a(i) < 0 disp([num2str(a(i)) ': number is below zero']) else disp([num2str(a(i)) ': number is above zero']) end end Explanations: The composed statement after disp displays the current entsprechende number together with the text.2.ch/static/matlab/ .20. you can load the appropriate M-file example_if_elseif. % Example 1 for if-else a = rand(20) * 100 . % Example 2 for if-elseif-else a = rand(20) * 100 . or by typing example_if in the Command window. for i = 1:length(a) if a(i) < 0 disp([num2str(a(i)) ': number is below zero']) elseif a(i) >= 0 && a(i) <= 20 % is the value >= 0 AND <= 20? disp([num2str(a(i)) ': small number']) else disp([num2str(a(i)) ': large number']) end end Explanations: Obviously.2010 86 .m into the Editor.Version from: 11.20. Example 1: if-else structure with two cases Load the M-file example_if.m into the Editor.
. case {'fix'... elseif strcmp(designator.edulap. a great number of single comparisons with the same variable have to be done. . expr3. in the course of a if-elseif-else structure.'endtrial') % statements. Example: Replacing a multiple if comparison by a switch-case structure Please study the following implementation of a multiple comparison with if-elseif-else (the function strcmp compares two strings): if strcmp(designator...'blink') % statements... statement end indicator is the variable that contains the value on which the conditional branching is based. After otherwise. elseif strcmp(designator. Single values as well as Cell Arrays with several values can be used.Introduction to Matlab The switch-case structure If. the switch-case structure is the better solution: The schematic syntax is: switch indicator case expr statement. 'blink'} http://www. else % all remaining cases end The following implementation is more elegant and easier to understand: switch designator case date % statements.ch/static/matlab/ .'date') % statements. the program is continued after the end statement. expr2.... the following statements within the case block are executed.2010 87 .'start') % statements. those statements follow that have to be executed in case none of the previous conditions have been met..'fix') || strcmp(designator.2.. statement otherwise statement.. case 'starttrial' % statements.... It can be a scalar or a string.. .Version from: 11. 'sacc'. case 'endtrial' % statements.... Afterwards.'sacc') || strcmp(designator. ..} statement. expr contains the comparison values (scalars or strings).. The case statement compares the indicator with expr. .. elseif strcmp(designator.. If they are the same.. statement case {expr1.
.ch/static/matlab/ .edulap.Introduction to Matlab % statements.. otherwise % all remaining cases end http://www.Version from: 11.2010 88 .2.
zero).edulap.Version from: 11. The tilde symbol ~ always means a logical inversion. thus not brackets are necessary v now contains the truth value 'false' or 0 the ~ «inverts» the truth value (NOT function) Comparisons of vectors and matrices are evaluated element-by-element! This only works if both are of the same size. To achieve this.: if (x < y || y ~= 0) . as shown in the previous section.2010 89 . Examples: >> true >> false >> x = 77. two logical operators are available: • • && as AND operation: The expression is only true if condition 1 and condition 2 are true. http://www.. >> x < y >> x ~= y >> x <= 77 && y > 0 >> v = x == y >> ~v >> a=1:4. that is. >> if (x < y || y ~= 0) && (v == true || numel(a) == 4) >> disp('that is true') >> else >> disp('that is wrong') >> end By the way: If a program line becomes very long so that it does not fit into the editor window any more and thus becomes confusing. you have already seen various comparison operators such as «smaller than» oder «larger than or equal as». comparison operation either return the value true (internally pre-defined as 1. Comparison Operators Below. the basic comparisons are shown: A A A A == B ~= B < B or A > B <= B or A >= B test for equality: double equal sign! not to be mixed up with =.. >> length(a)==4 || ~isempty(b) >> a == b Such comparisons mostly appear after an if statement. see the Help System with the key word 'relational operators'. Concatenation of Comparisons It is possible to combine more than one comparison. it can be split by using . || as OR operation: Contrary to common language use. it means "A or B or both"! the pre-defined values is x smaller than y? is x not equal to y? && and || are always evaluated last. but any value > 0 is interpreted as "true") oder false (internally represented as 0. For an overview. NOT test for «smaller» or «larger» test for «smaller or equal» or «larger or equal» As the result..ch/static/matlab/ .Introduction to Matlab Comparison Operators and Logical Operations In the two examples above.2.. y = 12. that would be a value assignment test for inequality. b=[1 3 5 7].
2010 90 .ch/static/matlab/ .2.edulap.Version from: 11.Introduction to Matlab && (v == true || numel(a) == 4) http://www.
e. Before the calculation. If the matrix has more than two dimensions. that z-standardises a maximally two-dimensional matrix of data (that is.edulap. isempty. it also correctly evaluates vectors.m as well.Introduction to Matlab Exercise 6: Standardisation Function Write a function named standardize. i.ch/static/matlab/ . std. The formula to be used is: The function is expected to return the transformed values in a matrix with the same size as the input matrix. the calculated mean value and the standard deviation (which will then be 0 or NaN). error.Version from: 11.2. without loops. • Tips for useful functions (you might have to look them up in the Help System): mean.m http://www. numel. but no scalars. Use several for. as at least two data points are necessary for these calculations). ndims. would be realised). reshape. as well as returning the mean value and the standard deviation.2010 91 . the «vectorised» solution is called standardize_vect.or while loops to implement this (you might also try to figure out how a «vectorised» solution. the function has to return an empty matrix [ ]. the function has to exit and print an appropriate error message. size. the matrix passed to the function has to be checked for validity: • If it is empty or only contains only one element. return Sample solution (opens in a new window) You can find the solution in the M-file standardize_sol. disp. as well as a warning text printed to the Command Window.
2.ch/static/matlab/ . value 3. value 4..2010 92 .Version from: 11.edulap..Introduction to Matlab Summary • Branching structure with multiple comparisons: if (condition 1) (statements) elseif (condition 2) (statements) else (statements) end Branching structure with case differentiation on a single variable: switch indicator case (value 1) (statements) case {value 2.} (statements) otherwise (statements) end • http://www. .
Matlab offers the option to store text information in matrices a well. every number in a matrix is interpreted as character coded in ASCII.Introduction to Matlab Data Representation 2: Character Strings Up to now. or if you wish to output results or usage hints for the user in clear text. However. However.2010 93 . or short. tab-separated data). http://www.2. if you want to import and process data from an ASCII 7 files (e. In this case. This way to work with text information is often applied. Lesson 3: Cell Arrays). «strings».edulap. the most common norm to represent alphanumerical characters. it is introduced first for didactical reasons. as it is relatively easy to understand (cf. for example. To this end.Version from: 11. This will be the case.ch/static/matlab/ . we have only worked with matrices containing numbers.g. but it is not the best and not the only way to do this. you will often have to process text information. 7 American Standard Code for Information Interchange. that is «character strings».
Version from: 11. Please try to follow the examples below to find out how this is done.2.' >> n = num2str(23.2010 94 . >> t1 = 'The quick brown fox jumps ' >> t2 = 'over the lazy dog.Introduction to Matlab String creation and concatenation First you need to know how character strings (or briefly «strings») are created.28) >> ischar(t1) >> m = str2num('3. Often. it is also necessary to convert numerical results into a string and chain it with another string. t2) fixed texts are entered in inverted commas conversion of a number into a string yields trueif the matrix contains characters conversion of a number that is stored in a string into a scalar concatenation of text as with 'normal' vectors http://www.edulap.ch/static/matlab/ .1415926') >> t3 = [t1 t2] >> t4 = strcat(t1.
'nine'. strcat = string concatenation If you want to store several strings in a matrix (that is. you can use a little function specifically written for that purpose (it is not included in the standard Matlab functions. 3000)))/100 >> output = strxcat('The final amount is: '. you can find it with the downloaded examples).'seven'] >> z=strvcat('four'. The function strxcat is defined as: function string = strxcat(varargin) It concatenates any number of strings and numbers into a single string. To avoid this. length(z2) This works fine as all words have four characters This does not. all rows of a matrix have to contain the same number of elements.ch/static/matlab/ .'five'.'seven') >> z1 = z(1. sumvalue. as 'seven' is longer correct statement address the first row however.Version from: 11.'five'. Thus. you can have a closer look at it in the editor: edit strxcat http://www.'nine'] >> z=['four'.Introduction to Matlab another way. :) >> length(z1) >> z2 = deblank(z1). Section Special Cases). ' Dollars') strxcat is a simple example for a function with a variable number of input parameters (cf. Matlab will fill up rows with shorter texts with blank characters (the function to vertically concatenate strings is called strvcat = string vertical concatenation)! >> z=['four'. this quickly leads to complicated and confusing code. If you are interested in how this is done. Example: >> sumvalue = fix(sum(rand(1. a space character has been added deblank removes spaces at the end of a string A helpful function: strxcat If you want to concatenate several strings and numerical results.'five'. in rows).2.2010 95 . it is five characters long.'nine'.edulap. there is a complication: As you know.
The variables from the preceding examples of this lesson should still be in the workspace. please try out the following lines. strfind finds a pattern (the second argument) in a string (first argument). The basic function is strcmp (string comparison). >> strcmp(z2. ' ') Finds a string in an other one.ch/static/matlab/ . or ignoring uppercase/lowercase differences To see these functions in action. E) >> strncmp(t2. use strcmpi (i stands for case-insensitive) only compares the first n characters (this is also possible case-insensitive .Version from: 11.strncmpi) http://www. 'over it'.2010 96 . String comparison To find out whether two strings are identical. 4) comparison wrong. because the comparison is case-sensitive if this is not wanted. strncmp. that not only allow for a simple equality or inequality test. strncmpi. The variables from the preceding examples of this lesson should still linger in the workspace.edulap. they are best demonstrated with examples. 'one') >> E = 'One'. dependent on the content of a string. result: starting position(s) of the found matches position of all space characters in pos Explanations: findstr compares two strings and checks whether the shorter one is contained in the longer one. E) >> strcmpi(z2. you cannot simply use the comparison operators == or ~= you already know.Introduction to Matlab Examine and Compare Strings Find specific contents in strings Often you will have to process data in differing ways. You may want to look up these differences in the Help System. 'fox') >> findstr(t3. >> strcmp(z2.2. >> findstr(t3. Thus you need operations that allow for the examination of string contents. This function exists in several variants strcmpi. you have to use specific functions to that end. Two easily confused functions are available: strfind and findstr Again. but also for testing only a restricted number of characters. 'cat') >> pos = strfind(t3.
with i: case-insensitive http://www. In contrast to variable names. Thus. strcmpi: compare strings.Introduction to Matlab Summary Points to remember • • (Character) Strings are matrices whose elements are interpreted as ASCII-coded characters.edulap.2010 97 . with i: case-insensitive strncmp.Version from: 11. Commands • • • • • • • • • • length: Determines the length of a string (same as with vectors) str2num: Transformation of a number stored in a string into a scalar num2str: Conversion of a number into a string ischar: returns true if the argument is a matrix containing characters strcat: string concatenation strvcat: vertical string concatenation deblank: removal of blank characters from the end of a string findstr. strfind: finds a string in another one strcmp. literal texts are written in inverted commas: a = 'Hello'. but a literal text. strncmpi: compare the first n characters of strings.ch/static/matlab/ . Hello is not a variable.2.
end. if i>20. while true. i^2). end i=6. t function hello() t t t function (ciphers. q = ___________ (m(11:15). end Which is the result of the statement: 4 >= sqrt(9) && ~false r r r r 3 0 false 1 Which statement has to be inserted to get the result 1 (= true) in variable q? m = 'To err is human. i^2). end for i = 7:28.'.2010 98 . break. Programming Which of the function definition(s) is/are correct? Multiple answers are possible. break. name. age] = getsubject(1. 'Human') http://www.2. i=i+1. i^2). end.while i <22.Version from: 11. disp(i. disp(i. but to really foul things up requires a computer. number) = generate(value.edulap. end t t t i=7. disp(i. please try to answer the questions below.Introduction to Matlab Self-test Questions To test your understanding. 6) function [] = startprocess(grunt) Which code lines fulfil the following goal: Output of the numbers 7 to 21 and their squared values in the Command Window? Several answers can be correct.ch/static/matlab/ . t for i = 7:21. modus) function [subj. disp(i^2). if i==21.
String: Character string. It can represent a script or a function.Version from: 11. These statements are processed in the same way as if they had been entered in the Command Window.ch/static/matlab/ . containing a sequence of Matlab statements. and the function returns results. e. A vector or a matrix whose elements are interpreted as ASCII coded characters. M-file: A file with the extension . different data types can be stored.edulap. matrices of different size.g. However. similar to a script. http://www. Script: A script is a sequence of statements that is stored in a file (M-file). Functions cannot access the variables in the common Workspace. Function: A sequence of statements that is stored in a file (M-file). Cell array: In every field of a Cell Array.Introduction to Matlab Glossary ASCII: American Standard Code for Information Interchange. values can be passed to a function. the most common norm to represent alphanumerical characters.2010 99 .m.2.
calculus. the data have to be stored externally in a format that can be processed by other applications such as Excel. SPSS or Statistica. you have the possibility to implement a larger exercise project that is subdivided into several phases. you can learn to practically realise these steps. You can save the processed data to an external file. statistics. To this end. http://www. so that they can easily be processed afterwards (summarising. These data have to be stored in a suitable way in Matlab.Introduction to Matlab Lesson 3: Working with External Files In this lesson you will learn important functions which are indispensable in psychological research applications. plotting etc. In this and the following lesson.ch/static/matlab/ .edulap.2. You understand how these steps are integrated in an exemplary application. Presentation) or technical systems (MRI. aggregation. You know the most important ways how a program can interact with the user. eye trackers etc. transformation. Again. Finally. first the raw data files as they are created by other programs (E-Prime. • • • • Typically.) are read into Matlab. You get to know further data types.2010 100 . the schematic procedure of a typical project is shown: Learning Objectives • • • • • You are able to import data into Matlab in various ways. EEG.) Often.Version from: 11. the user can influence data processing by direct interaction with the program.
Nowadays.2010 101 .Introduction to Matlab Data Import If you want to process and visualise data. you first have to «get them into the program». Matlab is very well equipped to import such data. Basically. This option is useful to explore a single data set and graphically display the contents.2.that is.ch/static/matlab/ . the typical application in research. there are two ways to do that: • • Comfortable features that can be used to import data «manually» from various standard applications. most systems that are used to acquire psychophysical and behavioural data allow to store the data in simple text files.edulap. This method is chosen if new sets of data in the same format have to be processed again and again . http://www.Version from: 11. Importing data by a Matlab program.
the Import Wizard creates two data sets: a matrix with the numerical data..the «Import Wizard» Import the file exp1. and a «cell array» (see here) containing the text data.2010 102 . by selecting it in the Directory Browser..Introduction to Matlab Interactive Data Import To quickly have a look at a data set.e. As you can see. You can also call the Import Wizard from within a program: uiimport (also see import) The keyword to find information on that topic in the Help System is import wizard.. and transfer the data from applications such as Excel. xml. or Lotus files without having to write a program for that purpose. They let you import data from the system clipboard or from text. SPSS or similar by means of copy-and-paste 1 or Edit > Copy and Edit > Paste). Matlab provides comfortable features. Import from files . or via File > Import Data. Import by means of copy-and-paste This is the most simple. open this matrix in the «Variable Editor» (double click on the variable name in the Workspace).Version from: 11.2. data that has been saved beforehand from another application by copying it to the clipboard.ch/static/matlab/ .xls (it is contained in the zip file data. • • • by using Edit > Paste to Workspace.edulap. On Mac OS: cmd-C and cmd-V http://www. they also call the Import Wizard. and select Clipboard at the item Select Data Source 1 On PC/Windows: CTRL-C and CTRL-V. Afterwards. the data can be processed and/or visualised. but not the most versatile method: Create a matrix of appropriate size in the workspace. type uiimport -pastespecial in the Command Window or simply type uiimport. Excel..zip and should be found in your working directory). Import from the system clipboard You can import data from the system clipboard. i. The following options are available. and choosing «Import data» via the context menu (right click).
2. mode) Opens a file. the file is looked for in the current directory. it advances accordingly. 2. mode is the operation mode. or *. and ends with an end-offile marker (EOF). data can be read or written: functions fgetl. When the pointer hits the EOF mark. 3. Basic functions for reading from external files We assume that we want to work with ASCII data (e.txt. the procedure is terminated.please refer to the Help System. that starts with the first character. d:\daten\jan08\data. A file can be seen as a serial sequence of data elements (single alphanumerial characters in the case of data in the ASCII 2 format). Alternatively. 2 4 American Standard Code for Information Interchange.g. a «reading pointer» is moved forward through the file . If the «reading pointer» is already in the middle of the line.with every reading operation. e. tab-separated or comma-separated text files such as *. If the file cannot be opened. We first use the most basic commands . A vector or a matrix whose elements are interpreted as ASCII coded characters.ch/static/matlab/ . fprintf etc.g. the file has to be «closed» again: function fclose. fscanf. that is up to the next line break (CR. the most common norm to represent alphanumerical characters. *. but usually this is neither necessary nor useful. For dealing with binary data there are dedicated commands (fread). Subsequently. a complete path can be given. Finally. it first has to be «opened»: function fopen.tab.Introduction to Matlab Data Input from External Files: Programmed How does a file work? Basically in quite a simple way. The necessary functions to work with files are best explained by means of an example. only the rest of the line is read. to get a basic understanding of the procedure.csv). Character string. fid = fopen(filename. fid obtains the value -1. The pointer could be moved backward as well. the most important options are 'r' (read .open the file for writing or creation). It has to be stated in all subsequent operations accessing this file. however. the basic commands seem more suitable. LF).2010 103 . Most of the described commands have more parameters than shown here .txt fid is the «identification number» of the opened files. When reading the file.open the file for reading only) and 'w' (write . To prepare a file for reading or writing. data = fgetl(fid) Reads a complete line.edulap. to make sure that the to-be-accessed file is unequivocally referenced in the case of several open files. Schematic depiction of seqential access to the elements of a file Schematic procedure of file operations 1. If only a file name is given in parameter filename.Version from: 11.parts of the task could also be solved with more complex statements. http://www. The result of the operation is a String 4 (vector 5 with characters).
Introduction to Matlab data = fscanf(fid.edulap. other application can fully access it. For the format specifications and all other options see the following example and the information in the Help System. otherwise false. that is only one row or one column http://www.Version from: 11.2. n) Reads n data elements in a specified format which is given in format. Only then. feof(fid) Checks whether the end of the file has been reached (eof = end of file).ch/static/matlab/ . 5 one-dimensional matrix. returns true if this is the case. fclose(fid) Closes the file.2010 104 . format.
2010 105 . At the same time. you can see how the most important functions of the Debugger 6 are used. http://www.2.Version from: 11.edulap.dat): The function is defined as: function [Mdata.ch/static/matlab/ .Introduction to Matlab Example: Data Import from an External File This example represents a typical function as it is used to import data from a text file. Mfamilyname] = load_data1('exp1. Mfirstname and Mfamilyname: 6 Editor function to assist in finding and correcting errors in a program. The data file to be imported looks like this (also see file exp1.dat') The data are returned by the function in the three variables Mdata. Mfirstname.
Version from: 11.Introduction to Matlab Exploring the function in the Debugger Please watch the screencast below that demonstrates how you can examine a program in the Debugger and free it from errors. Afterwards. http://www.ch/static/matlab/ .2.2010 106 .edulap. you can try this out yourself in Matlab.
Version from: 11. The table header is skipped. • • • • Now. Try to set a so-called «break point» on line 17 by clicking on the dash after the line number. Open the function load_data1. afterwards the data lines are read until the end of the file is reached. http://www.2. you can query the value of variables in the Command Window or in the Workspace.m in the Editor. Mfamilyname] = load_data1('exp1. Only screenshots of animations will be displayed. Please try to do this yourself now. that is the first three lines. Lines 53-60: Read a complete data line.2010 107 .ch/static/matlab/ . First names and surnames are extracted into two separate string matrices. the break point symbol has changed its colour to red (in most Matlab versions). set a break point further down in the program and continue with Debug > Continue (or F5). and packed into another matrix. program execution is already stopped on line 17. Lines 35-40: Read the 2nd line and decode the date. [link] Preview of the block structure of load_data1: The function first reads the information in the «file header». fid indicates this with the value -1. If not. Lines 22-33: Read the 1st line. Later Matlab versions will point out even earlier that there seems to be an error on that line. Matlab will now inform you that you cannot set a break point because the program contains a syntax error (line 39). before executing this line. or you can continue program execution up to the current cursor location by Debug > Go Until Cursor.edulap. Alternatively. • Explanations of the program's function • • • • • • Lines 17-20: Load the file and return an error message in case it is not found. Try to correct it and save the function afterwards. the other data columns are converted to numerical values if necessary. From now on. Solution A closing bracket at the end of line 39 is missing: datestring = rdata(pos(1) + 1:length(rdata) ). Line 52: Start of the main loop that runs until EOF (end of file) is reached. decode the file name and check that there is no conflict with the actual file name.dat') Due to the break point. Call the function from the Command Window: >> [Mdata. that is. That means that it is now active. you will find additional hints on how the program works in detail.Introduction to Matlab Only pictures can be viewed in the PDF version! For Flash etc. In this process. you can continue the program step-wise by selecting Debug > Step (or hit the F10 key). see online version. Mfirstname. You can examine the value of a variable by placing the mouse pointer over a variable name in the code. • • • • Make sure that your directory containing the example data is selected as the «current directory». Lines 42-43: "Over-reads" (skips) the recording system info and the table header line. set it again.
Remember that. or type its name in the Command Window).ch/static/matlab/ . and 11) are converted into numerical data so that they can be stored in a single numerical matrix afterwards. has five data values arranged vertically. • To investigate the error in more detail. when horizontally concatenating matrices. we make use of error breakpoints. we activate Always stop if error and run the function again.Introduction to Matlab • • Lines 62-81: The three data values registered as alphanumerical text (columns 3. however. that is.Version from: 11. and you can examine the involved variables (place the mouse pointer over the variable in the Editor. program execution will be stopped because Matlab found the following error: ??? Error using ==> horzcat CAT arguments dimensions are not consistent. Now the program will stop at the error. it should work correctly and return the imported values. If you place the mouse pointer on the different variables in the square brackets of the vertcat statement. http://www.2010 108 . We can correct this by transposing data. data.2.edulap. the number of rows of the matrices have to be identical. Can you find the error? How can you correct it? Solution The problem lies on line 86: • Mdata = vertcat(Mdata. double click it in the Workspace.. Via Debug > Stop if Errors/ Warnings. [gendern age condn data calibn]). • On line 86. that is by correcting this into data'. that is they only contain one row..this cannot work. Lines 84-86: The three return variables are filled with the data. you will se that all except data are scalars. We want to have the data values side by side on the same line. • When you re-run the function now. five rows . 5.
edulap.Introduction to Matlab Summary • • • • • fid = fopen(filename.2010 109 . n): Reads n data units in a certain format.Version from: 11.ch/static/matlab/ . format. specified in format fclose(fid): closes a file feof(fid): checks whether the end of the file has been reached (eof = end of file) http://www.2. mode): Opens a file data = fgetl(fid): reads one line data = fscanf(fid.
Version from: 11. especially matrices of different size.with certain restrictions . a cell array allows for storing differing data types in every one of its data fields (= cells).strings as their contents.edulap.ch/static/matlab/ . http://www. While matrices only accept numbers and .Introduction to Matlab Data Representation 3: Cell Arrays In this chapter you will get to know a different.2.2010 110 . comfortable way to represent data in Matlab: in so-called cell arrays.
3) structure arrays 12 (they are not depicted here and will be explained in section Data Representation 4: Structure Arrays). scalars 8.Version from: 11.edulap. i. or n-dimensional matrices 10 of any size (cell 1.ch/static/matlab/ .1 / cell 2. vectors.2) matrices with strings (cell 1.1 / cell 1.Introduction to Matlab Data Representation as Cell Arrays As you can see in the figure below.3 / cell 2. Schematic depiction of a cell array http://www. Each cell can contain different data entries: • • • • numerical matrices.2) further cell arrays (cell 2.2010 111 .2. a cell array consists of several cells that are arranged in a matrix-like fashion.e.
1 this is indeed a string visualisation of the structure any matrix convert a matrix into a cell array. the cells are filled with contents: >> A{1.1} = 3+7i.50). To do this.Introduction to Matlab Create and Reference Cell Arrays Cell arrays can be recognised by the fact that their indices are not stated in round brackets as for matrices. each string is stored in a separate cell.[25 25]) >> c{2. Please try to understand the function of these statements.2010 112 .[20 40].2} = 'Anne Smith'.ch/static/matlab/ . >> A{1. -pi:pi/4:pi}. It is possible (but less clear) to define it all in one statement: A = {[1 4 3. empty cells are added as necessary.edulap. http://www.1} = [1 4 3.1} >> A{1. 0 5 8. 0 5 8. but in curly brackets { }. >> b = num2cell(m). >> c = mat2cell(m. Now. >> A{2. the cell array will be dynamically extended in the same way as matrices. The following examples show how cell arrays can be applied: Creation of a cell array: Below you can see how the cell array shown above can be built. a cell array always has to be «rectangular».3) >> ischar(A{1. >> A = cell(2. 7 2 9]. Referencing and transforming >> A >> A{1.2}) >> cellplot(A) >> m = randn(60. 2) This statement pre-defines an empty cell array wiht m x n cells. This is optional.1} >> d = cell2mat(c) recall the complete cell array select cell 1. If you do not do that. 'Anne Smith'. As a matrix. >> A{2. 3+7i.1}(2.1 reference a single element of the matrix in cell 1. as soon as additional cells are adjoined. This method is supported by many Matlab functions.2} = -pi:pi/4:pi. one element per cell split matrix into sub-matrices per cell convert the cell array back into a matrix Example for strings in cell arrays Cell arrays are often used to store strings of different length without having to care for the problem of differing lengths.2.Version from: 11. 7 2 9].
'The quick brown fox'.edulap.ch/static/matlab/ .Version from: 11. 'jumps over the lazy dog'} >> texts{4} >> length(texts{3}) http://www.Introduction to Matlab An example: >> texts = {'Hello world'.2010 113 . num2str(pi).2.
ch/static/matlab/ . http://www. which also returns the data in a cell aray. The function can be called by [Mdata. • • Open the function load_data2. Cfirstname.Introduction to Matlab Second example on data import from external files The previous example will now be changed in a way that (1) the name information is returned as a cell array. this function is intentionally left incomplete) on the lines 59-61.edulap. (regarding data processing. Cdata = textscan(fid. but with a single call of the function textscan.dat'). The format of the data is defined in a format string (%s are strings. Cfamilyname] = load_data2('exp1.Version from: 11. Mdata = [Cdata{4} Cdata{6:10}].m by following the steps described below. Cdata{x} will then contain all data from column x. the data are re-configured according to the needs: • • Cfirstname = Cdata{1}. Alphanumerical data are stored as a cell array in a cell. Please have a look at the function load_data2.2010 114 . '%s %s %s %f %s %f %f %f %f %f %s'). Cfamilyname = Cdata{2}. and (2) the data are not read in a loop by using fscanf. This statement reads data into a cell array until the end of the file has been reached.m in the Editor On line 47 you see how textscan is applied. the numerical data as matrices.2. %f are floating point numbers).
Version from: 11. one element per cell mat2cell: divide matrix into sub-matrices per cell cell2mat: convert a cell array into a matrix textscan: read data from a file into a cell array http://www. Cell arrays can be recognised by the fact that their indices are enclosed by curly brackets { }. furthre cell arrays or structure arrays. not round brackets as in matrices. Commands • • • • • cellplot: visualisation of the structure of a cell array num2cell: convert a matrix into a cell array. strings.Introduction to Matlab Summary Points to remember • • A cell array consists of several cells that are arranged in a matrix-like way.ch/static/matlab/ .2. Every cell can contain various kinds of data such as complete matrices.2010 115 .edulap.
Version from: 11.edulap.2. Every cell can contain various kinds of data such as complete matrices.Introduction to Matlab Data Representation 4: Structure Arrays Another useful way to represent data are the so-called structure arrays. strings. Every element of a structure array contains the same structure of various «data containers» that are each referenced by a unique name. http://www. it is more clearly visible what the contents of a referenced data field are. Compared to cell arrays 13.2010 116 .ch/static/matlab/ . further cell arrays etc. 13 A data structure that consists of several cells arranged in a matrix.
Examples to try out: >> screensize.name='Alan Johnson' >> patient(2) recall of the field names address an element and do a transformation reference the elements of the matrix a new data set thereby.5. and a matrix with medical test data. >> patient.y = 600 >> screensize.2.00.name = 'John Doe'.test = [79 75 73. :)) >> patient(3). a scalar for an amount due. for instance. These fields can be seen as «data containers».billing = 127.edulap. 220 210 205] >> fieldnames(patient) >> lower(patient.x = 1024 >> screensize(2).ch/static/matlab/ . 180 178 177. they can hold all kinds of data items. An element of a structure array could.2010 117 .Version from: 11. it automatically assumes the same structure Creation of the above example (patient data): >> patient.x = 800 >> screensize. patient(2) has been filled with empty fields http://www.Introduction to Matlab Data Representation in Structure Arrays Every element of a structure array contains the same structure of distinctly named sub-elements. >> patient.y = 768 screensize only has two sub-elements they can be addressed like this create an additional element.x >> screensize(2). In a similar way as cells of a cell arrays. called fields.name) >> sum(patient. contain a name as a string.test(2.
age. That is. date. instead of: function [Mdata.Version from: 11.age expinfo.time http://www. eye. In this way.2. sex. time] = loaddata(filename) you could implement it in this way: function [Mdata.2010 118 .edulap.Introduction to Matlab Application example You could implement a function to import experiment data that stores all general data concerning the experiment trial in a structure array. expinfo] = loaddata(filename) expinfo would consist of the fields: expinfo.eye expinfo.sex expinfo.ch/static/matlab/ . you can avoid having to return the data in many individual variables.date expinfo.
2010 119 . Thus.ch/static/matlab/ .Introduction to Matlab Summary • Every element of a structure array contains the same structure of different «data containers» (fields) that are addressable with a name. it is clearly visible what a referenced data field contains. separated by a period: • patient.edulap.Version from: 11.2.name http://www. contrary to cell arrays. The fields are addressed by adding the field name to the variable name.
2.ch/static/matlab/ . The final goal is to have a program that imports data from files.Version from: 11. you know all basic building blocks to enable you to start writing a data processing program of your own.edulap. processes them (aggregation. conversion.2010 120 .Introduction to Matlab Your Data Processing Project Now. graphical display etc. The project will be realised in several parts Px (P for project): • • • • • Exercise P1: write the main program and the function to import the data Exercise P2: request user inputs Exercise P3: data processing and saving to an external file Exercise P4: computations Exercise P5: graphical visualisation of the data http://www.) and stores the results in a file.
you can create a hypothetical practice data set (e.edulap. In this way.Version from: 11.2010 121 .dat • http://www.Introduction to Matlab Data Base Considering the data to be processed. you can use the example project «EyeData Processing» provided by this course (it will be described later on). you can implement a kind of a template that might help you when you need to emplement a similar program later on.g. If you do not have such a data set available.2. there are several options for your project: • • You have data from your own research project that you want to process. Alternatively. in Open Office Calc or MS Excel). similar to exp1.ch/static/matlab/ .
that is. it can later be converted into a function.Version from: 11.2. http://www. these latter parts can also be realised by calling other functions.m You can again find this script with the example programs you have downloaded at the outset of this course.Introduction to Matlab Basic Structure A data processing program usually consists of a main program (a script or a function) that controls the overall flow of the program . The following script may serve as a framework: mainprog1. Obviously.ch/static/matlab/ .edulap. calls functions to import or save data. If it is necessary for your application to pass parameters to the main program. processes the data.2010 122 . it interacts with the user if necessary. visualises them etc.
g.e. This requires additional data columns that contain the subject number and other information that is provided in the file header of the individual data files.Version from: 11. calculation of mean values per subject. In this way. http://www.2.fix (vn are the initials of the subject. or plots of the visuo-spatial distribution of fixations on the images). Lower row: the four image sizes The goal of the exercise is to write a program that loads the data of several subjects and merges them into a single output file that can later be imported into other software packages such as SPSS for further processing.ch/static/matlab/ . Upper row: example images (shown in colour in the experiment). They were asked to view them in preparation for a recognition test (which was not evaluated).Introduction to Matlab Data Base: EyeData Processing Exercise in case you do not have your own data The to-be-processed data originate from an eye tracking experiment. bar graphs of fixation duration per condition. Moreover. The data files are contained in the zip file data. the data are prepared for statistical evaluations such as ANOVAs.zip (you should have downloaded this file in the beginning) and are named vnsizex. the program should contain features which graphically display the data (e. eye movements were recorded and registered as fixations. the data has to be aggregated. During viewing. x designates the trial block 1-6). Additionally. The subjects were shown natural scene images in different sizes on a video monitor (5.2010 123 . i.edulap. and saved in a way that there is only one row per subject.5 seconds for each image).
Introduction to Matlab
Exercise P1: Data Import
Take the framework mainprog1.m for the main program outlined above and save it under a new name that fits your project (eyedata.m for the example task «EyeData Processing». The sample solution for this task can be found under the file name eyedata_sol1.m). Write a new function to import your data from the external files. To do this, you can start from scratch, or you modify and extend load_data1.m used in an earlier example (it is recommended to save it with a new name as well). If you have your own data set, please first consider what you want to do with your data. This will influence the way your function will have to return the imported data to the calling script. Relevant questions are: • • • Which of the available data are needed for further processing? Are there certain data items that need to be recoded (typical case: conversion of experimental conditions coded in clear text into numerical codes)? Which data structures are best suited for further processing - single values, matrices, cell arrays, or structure arrays?
Guidelines for the «EyeData Processing» project Try to implement a function readfixdata.m that reads a single data file and returns the data in suitable form, e.g. as • • • a structure array with the fields study name, subject number, recording date, left/right eye, number of images, and screen resolution a cell array with the image names; and a matrix containing the eye movement data.
These suggestions refer to the sample solution, but - of course - there is not a single correct solution; it is just as well possible to pack everything into a cell array, for instance. The data to process have the following stucture (afsize1.fix, tab-separated file):
http://www.edulap.ch/static/matlab/ - Version from: 11.2.2010
Introduction to Matlab
Most items in the file header are self-explaining, others are irrelevant for our project (Binocular, Mousedata). Side designates the eye from which the movement data has been recorded (1 = left, 2 = right). The items in the main table (which continues until the end of the file) designate: • • • • • • • eventnb - fixations, consecutively numbered within each trial bmpnb - image number = trial number bmpname - image name. The last character indicates the image size start - start time of a fixation relative to the start of the trial (in ms) dur - fixation duration [ms] x, y - coordinates of the fixatins on the image in pixels skipcode - marker for data filtering due to calibration problems. -1 = ok, all other codes designate problematic data.
Sample solution (opens in a new window)
http://www.edulap.ch/static/matlab/ - Version from: 11.2.2010
Introduction to Matlab
The solution can also be found in the M-file readfixdata_sol.m.
http://www.edulap.ch/static/matlab/ - Version from: 11.2.2010
definition of «regions of interests» (ROIs) or calibration points by means of mouse clicks Selection of the location and file format for saving data or graphics Below. the implementation of integrated graphical user interfaces (GUIs) will not be discussed.ch/static/matlab/ . Typical examples are: • • • • Selections of data files to be processed Specification of parameters such as limits. e.edulap.Introduction to Matlab User Interaction Most larger applications require a certain amount of interaction with the user. the most important interactive elements are listed. http://www. However. selection of graphics options etc. Graphical inputs.2010 127 . Cf.Version from: 11.g. filter settings.2. the information given in the Help System under MATLAB > Function Reference > Creating Graphical User Interfaces.
only files with this extension are shown..e. Copy the code lines below into the Command Window (>> can also be copied ..Version from: 11. The selection process begins at the current path as it is set in Matlab as the «Current Directory».edulap.txt'.PathName] = . uigetfile({'*. If several file types should be available. Select a file: uigetfile [FileName. Opens the file selection dialog box. '*. All of them have a large number of configuration options.*' can be entered. i. 'File Selector').m'. 'Select the M-file'). For further options. The first argument '*.Matlab will ignore them). 0) >> disp('User selected ''Cancel''') >> else >> disp(['User selected '. you can specify this by means of a cell array. The desired file extensions are listed in the first column of the cell array: [filename. FileName = 0 results. pathname] = uigetfile('*. '*.2010 128 .*'}. If you want the selection to start at a different place in the file system. uigetfile('d:\matlab\data\*. fullfile(pathname. Example for a file selection dialog with output of the result. The function returns the file name and the path. PathName] = uigetfile('*. which cannot be discussed in detail here..m' is a filter.2. >> [filename.m'. If all files should be visible. please consult the Help System. filename)]) >> end http://www. >> if isequal(filename. '*.mdl'. thus only some typical application examples are shown. you can specify it like this: [FileName.mat'. If «Cancel» has been clicked. The second argument contains the text that will be shown in the window title..Introduction to Matlab Selection of Files and Directories Standard dialog boxes to select files or directory locations for loading and saving data as you know them from other applications are also available in Matlab. '*. 'Select data set'). pathname] = .txt'.ch/static/matlab/ . 'Pick a text file').
the value 0 is returned.Version from: 11. If the user hits «Cancel».2010 129 .2. http://www.edulap. The first argument designates the path where the selection process starts out.ch/static/matlab/ .Introduction to Matlab Resulting file selection window Select a directory: uigetdir directory_name = uigetdir('c:\data\'. 'Please select the directory') Opens a directory selection dialog box directory_name contains the selected path. The second argument holds the window title text.
a complete file name is suggested.2. 'Save as.dat'.Version from: 11. PathName] = uiputfile('*.edulap. http://www.dat'. In case «Cancel» has been pressed..2010 130 .. The second argument again specifies the window title text.. in the second example. The first argument specifies the file type. The function returns the selected file name and path.') Creates a dialog box to select the location for a file saving operation. FileName = 0 results..') [FileName. PathName] = uiputfile('vp27data. 'Save as.Introduction to Matlab Directory selection window Select a directory/file name to save a file: uiputfile [FileName.ch/static/matlab/ .
txt') And the converse: Generate a complete path from parts: fullfile >> filepath = fullfile(pathstr. 'myfile.Version from: 11. the queried file names have to be disassembled into their parts. there are helpful functions: Please try it out for yourself. [name ext]) >> filepath = fullfile('C:'.2.txt') http://www. Decompose a complete path into its constituents:fileparts >> [pathstr. or a complete path has to be assembled from parts.ch/static/matlab/ .edulap. To aid this.Introduction to Matlab Window to select the location to save a file Two useful functions to handle file and path names Often.2010 131 . 'new'. ext] = fileparts('c:\data\new\myfile. name. 'data'.
if filename(1) ~= '. .Introduction to Matlab Sample Code: Select All Files in a Directory Below you find the sample code for a function that might be helpful later when you implement a program.isdir == false filename = Mdir(entry_i). pathname = uigetdir(''..' [p. the if the user hits 'cancel'.' and '. 'Select directory'). nbentries = size(Mdir..tap for tab-separated ASCII files).name are relevant): http://www.name. it is often the case that you can simply store all to-be-evaluated data files in a certain folder. 1). the program will read the contents of the directory and builds a list of all files with a specified extension (e.g. Thus it is helpful if you can simply select this folder in the evaluation program. for entry_i = 1:nbentries if Mdir(entry_i). The file names are returned in the matrix Mfiles.. ext] = fileparts(filename). instead of selecting single files.isdir and . Later on in the program. '. In data evaluation projects.ch/static/matlab/ . The code shown below realises this: The user an select a directory. 1). Mfiles = [].2010 132 .tab') Mfiles = strvcat(Mfiles. You only have to modify the desired file extension.2. if strcmpi(ext.edulap. You can simply overtake this code into your own program. store the file name determine the number of found entries Weitere Erläuterungen (*) The function dir returns the contents of a directory as a structure array with the following fields (for us.' (**) determine the extension compare with the desired extension if matched.. . the number of contained file names is stored in nbfiles. terminate the program read all directory entries (*) determine their number pre-define the result matrix as empty matrix loop over all directory entries is this NO directory entry? --> then it must be a file name extract the current file name exclude '. end end end end nbfiles = size(Mfiles. these files can be imported and processed in a loop. n.. if pathname == 0 return end Mdir = dir(pathname). filename).Version from: 11. only the fields .
' (current directory).fix jlsize2.fix tlsize3.' (one directory level up) and '.fix rrsize4. aggr.Version from: 11.fix slsize3.fix slsize4.ch/static/matlab/ .2010 133 . bhsize1.fix tlsize1.fix .fix rrsize2..fix afsize1.2.fix slsize6.fix afsize5.dat slsize2.fix bhsize5.fix jlsize6.fix http://www.fix tlsize5. Typical output of dir: ..fix tlsize6.fix rrsize3.fix rrsize6.fix bhsize3.fix slsize1.fix bhsize4.fix jlsize5.dat jlsize3.).fix jlsize1..fix jlsize4.fix rawall.Introduction to Matlab (**) Mdir(.fix afsize4.fix afsize3.fix bhsize2.fix rrsize5.fix afsize6..fix rrsize1.fix afsize2. that are needed for navigation within the file system: '.edulap.fix slsize5.fix tlsize4.name always contains two special entries.fix tlsize2.
only exemplary cases can be shown. 'Not yet') http://www.Introduction to Matlab Other User Input Features Dialog box to input values: inputdlg This function also has many configuration options. >> answer = inputdlg(prompt.. Please note: The entered value is returned as String! Matlab cannot know whether a number or a text is to be entered. 'Alas.ch/static/matlab/ .'hsv'}. you will have to convert the input into a number by means of str2double or str2num! It is possible to query several values at once.'Enter colormap name:'}. If you want to proceed with a numerical value.def) The inputs are returned in a cell array. >> answer = inputdlg('Diameter:'. >> def = {'20'. >> dlg_title = 'Input for peaks function'.dlg_title.num_lines. 'Please enter the value') answer contains the entered value or {} (empty cell array) if «Cancel» has been clicked. Input request with buttons: questdlg >> button = questdlg('Older than 30?'.2010 134 . 'Please answer'. here. 'Not yet'.2. .. and to define default values: >> prompt = {'Enter matrix size:'. >> num_lines = 1. yes'.Version from: 11.edulap. For further details please refer to the Help System.
'. The coordinates are returned in the column vectors x and y.edulap. coordinates can be entered in an existing graph.ch/static/matlab/ .Introduction to Matlab Explanations: The last argument designates which button will be set as the «default». http://www. Please have a look at this: >> plot(peaks) % create any graphic >> hold on >> [x.2. It is just as well possible to create more than two buttons. y.2010 135 . button will return the clear text of the selected button. three values are queried. that is it will already be pre-selected (and can be confirmed with the enter key). Graphical input of coordinates: ginput With this function.Version from: 11. This argument cannot be omitted. y] = ginput(3) >> plot(x. the input process can be terminated earlier.-r') >In this example. You can find many more options in the Help System under the keyword «Predefined Dialog Boxes». By means of the return key.
fix). or the directory where the data are stored. the user should be able to select a fixation file (that is.2. Other erroneous inputs should either be made impossible. various inputs can be necessary: • • • • Selection of the file(s) to be processed. filter settings) Selection of the file name and/or the storing location for saving the processed data.2010 136 . Moreover. a file with the extension .e. the user has to enter where and under which name the data (the merged raw data file and the aggregated data) are to be saved. For the EyeData project • • • First. the program should exit and return an appropriate message.edulap.m http://www. or lead to an error message. the user has to be asked whether s/he wants the data to be filtered based on the data in the column skipcode. You can find the sample solution in the M-file eyedata_sol2. Dependent on your actual goals.Introduction to Matlab Exercise P2: User Inputs Integrate the necessary user inputs into your project's main program. As a parameter. Query any parameters that are necessary for data processing (i. Ask the user whether certain evaluations or graphical outputs are desired. If no file has been selected in the file selection process («cancel» has been pressed).Version from: 11.ch/static/matlab/ .
Introduction to Matlab Summary Summary of the most important commands: • • • • • • • • • uigetfile: dialog box to select a file uigetdir: dialog box to select s folder (directory) uiputfile: dialog box to select the location to save a file fileparts: decomposes a complete path into its parts fullfile: creates a complete path from parts inputdlg: dialog box to query values questdlg: dialog box with buttons ginput: graphical input of coordinates dir: read directory entries from the file system http://www.Version from: 11.2010 137 .ch/static/matlab/ .2.edulap.
2010 138 .2.Introduction to Matlab Writing Data to External Files Basically.Version from: 11. http://www. then the data is written. and finally. the file has to be closed again with fclose. the procedure is very similar to reading from external files: First.ch/static/matlab/ .edulap. the file is opened with fopen.
'%s\n'. % write the line break % output with maximally 6 integer digits and 2 decimal digits fprintf(fid. M. e. This example generates the data file C:\m\testdata. % Write text: % %s designates a string. % Schreiben von numerischen Daten: % %g stands for fixed point notation. \n generates a line break fprintf(fid. several values are written % and separated by a tabulator (\t). Some basic formats are shown in the example below. format. 'w' (write . mode) Opens a file. as mode.m % open the file in write mode fid = fopen('C:\m\testdata.please refer to the Help System if necessary.5:3234. % close the file fclose(fid). '%g\t'. pi.2010 139 .5]).ch/static/matlab/ . other applications can freely access the file. . 'w').273:20000]). Example: Writing to a file Also see the M-file m-File writedatafile.5:3:13. '%6. The format of the written data is controlled by the format string.) Writes the data contained in the matrix M (and any further matrices) to the file.Version from: 11.. '\n').2f\t'..txt'. There are extensive options how the data can be formatted by means of the format string. [737. fprintf(fid.Introduction to Matlab Basic Functions to Write to External Files Some of the commands described below have further parameters . fclose(fid) Closes the file.open a file for writing or creating) or 'a' (append data to the existing file) has to be selected.txt (as viewed in MS Excel): You can find further file functions in the Help System.edulap. fprintf(fid.2. 'Any text').g. under: MATLAB > Function Reference > File I/O > Text files http://www. [7. Only after closing. fprintf(fid. fid = fopen(filename. For the detailed format specifications and all further options please consult the Help System. Now.
The intermediate data processing steps depend on your specific task. Afterwards.2010 140 . http://www. The sample solution can be found in the m-File eyedata_sol3.edulap. As a practice task. Internally. the header lines are not to be saved. According the image below.m. Instead.ch/static/matlab/ .Version from: 11. the data have to be stored in a way that they can easily be re-called for saving. column 2 contains the study name (Study).Introduction to Matlab Exercise P3: Save Data Write the program code that allows for saving the imported and processed dagta to an external file. For the EyeData Processing project • • The fixation file selected by the user should be impoorted. two additional columns are added: Column 1 contains the subject number (Subject).2. you can start with saving the unchanged data (or data with minor changes). the program has to save the imported data to a file.
formatted according to the format string fclose(fid): close a file http://www. M): write the data in matrix M to the file.Version from: 11.ch/static/matlab/ .Introduction to Matlab Summary Summary of the most important points and commands: Points to remember • The procedure when writing data to a file is the almost the same as when reading: First.2010 141 . the file is opened by fopen. and finally. the file has to be closed by fclose. Commands • • • fid = fopen(filename. format. mode): open a file fprintf(fid.2.edulap. then data are written with fprintf.
Introduction to Matlab Glossary ASCII: American Standard Code for Information Interchange. cell array: A data structure that consists of several cells arranged in a matrix. structure array: Every element of a structure array contains the same structure of various sub-elements that can be accessed with a unique name. On Mac OS: cmd-C and cmd-V Debugger: Editor function to assist in finding and correcting errors in a program. that is only one row or one column http://www.Version from: 11.2010 142 . Usually. strings. vector). the expression «matrix» refers to two. a matrix is a table of numbers or other values. only one element string: Character string. further cell arrays etc.e. matrix: The most important way to represent data in Matlab. copy-and-paste: On PC/Windows: CTRL-C and CTRL-V. i. In the field of mathematics.2. A vector or a matrix whose elements are interpreted as ASCII coded characters.or higher-dimensional matrices (cf. scalar. the most common norm to represent alphanumerical characters. Every cell can contain various kinds of data such as complete matrices. vector: one-dimensional matrix. Matrices differ from ordinary tables in that they can be used for calculations. called fields. scalar: «null-dimensional» matrix.ch/static/matlab/ . These fields can be seen as «data containers» that can hold all kinds of contents.edulap.
edulap. You know the most important statistical functions. On the one hand.ch/static/matlab/ .2. conversion. basic methods of data visualisation are introduced. On the other hand. You know how to generate graphical figures and how to adapt them to your needs.Introduction to Matlab Lesson 4: Data Processing and Graphical Presentation This lesson will show you how to further process data. You know the most important graphical functions and can apply them to your data. it is about transformation.Version from: 11. or aggregation of data. Learning Objectives • • • • You know how to selectively access data. http://www. and computation of statistical characteristics.2010 143 .
your data processing project will be complemented by data evaluation functions.edulap.2.Version from: 11.Introduction to Matlab Data Selection: Logical Indexing and the «find» Function This section introduces important possibilities to selectively extract certain data from larger data fields. To this end. the following methods are available: • • • logical indexing the find function a dedicated function subM Afterwards.ch/static/matlab/ . http://www.2010 144 .
ch/static/matlab/ . http://www. extract the value from the desired column: Mdata = rand(50. section Comparison Operators in Lesson 2).5.3)>. you can address all elements fulfilling a certain condition at once.5.edulap. That is.Introduction to Matlab Logical Indexing This data access method allows for addressing specific elements of a matrix based on logical comparisons. An obvious solution for that problem is to write a loop and check every row by means of an if statement and. all columns whose corresponding entry contains true (a numerical value of 1) are selected. Mdata(row_i. Put more simply. 7). And how does it work? The comparison a < 10 yields a matrix of the same size that contains the truth values of that comparison for every element. Now try it out yourself: >> a = magic(7). This vector can now be used as a logical index into a matrix. This resulting truth value matrix can be used as logical index to access the values in the data matrix. end end This can be realised with logical indexing in a much shorter and thus more elegant (and faster) manner: >> Mdata = rand(50. if the condition is met.5 Mselect = vertcat(Mselect. e. 7). comparison operators can also be applied to whole vectors or matrices! (cf. 7)).2010 145 . >> a(a < 10) = 0 What has happened? All elements of a that are smaller than 10 are set to 0. 3) > . it yields a vector with the truth values of the comparison of all values in column 3 with the value 0. 7) To clearly see how this works.2. For example: >> a = magic(7).Version from: 11. we take a closer look at the «inner» expression: >> Mdata(:. Mselect = [].3)>. As you see now. [nbrows. the values from column 7 of all rows of a matrix Mdata whose column 3 contains a value larger than 0. >> a < 10 >> b = a(a > 20) result of the comparison extracts all elements that fulfill the condition It often happens that you need to extract data from a larger matrix according to certain criteria.5.5 As you see.g. nbcols] = size(Mdata). >> Mselect = Mdata(Mdata(:. for row_i = 1:nbrows if Mdata(row_i.
Introduction to Matlab The find Function The find function provides similar possibilities as the logical indexing discussed above. however.2010 146 . paragraph «Linear Indexing» all the way down on the page). find can be replaced by logical indexing.ch/static/matlab/ . Usually.Version from: 11. http://www. it does not return a matrix with logical indices. but a vector with the «linear indices» (cf. Again. Lesson 1.edulap. >> selected = find(a > 50) >> length(selected) find all elements of a that are > 50 number of matching elements This now results in a vector with the linear indices of the matching elements. It can be used for further operations: >> b = a(selected) >> a(selected) = inf extract the corresponding elements set those elements in a to inf In most cases. As a result.2. it is best to try it out: >> a = magic(10). section Matrices. this makes sense as this is processed faster.
Let's look at this in detail again: >> M1(:.Introduction to Matlab A Helpful Function: subM You can find this useful function (which is not included in the standard function set of Matlab) with the example programs (zip file). >> Mnew = subM(M1. This will later save time. minvalue = 10.ch/static/matlab/ . minvalue. and you get code that is easier to understand. :) Explanation: The results of the two comparisons are logically combined with & (AND operation). http://www.2. you see that . column) <= maxvalue If you have a look at the function subM in the Editor (by typing edit subM). >> column = 3.edulap. column) >= minvalue & M1(:. column) >= minvalue >> M1(:.it does not do anything else. >> M1 = magic(10). column. min. However. column) >= minvalue & M1(:.2010 147 . It is defined like this: function Mselected = subM(Min. column) <= maxvalue >> M1(:.except for a plausibility check . column) <= maxvalue.Version from: 11. maxvalue = 30. max) subM is a function that extracts all rows from a matrix Min whose value in column col lies within a defined range from min and max (inclusive). it can be helpful to write such often used operations as functions. this is less comfortable and results in a code that is more difficult to read : >> Mnew = M1(M1(:. maxvalue) Of course. col. Nevertheless. it is possible to program this directly using logical indexing.
reading all elements from a that are smaller than 10: b = a(a < 10) Commands • • find: Find elements in a matrix.ch/static/matlab/ . the linear indices to the matching elements are returned.g.Version from: 11.edulap.2010 148 . subM: A help function (not included in Matlab's library). http://www.Introduction to Matlab Summary Points to remember • Logical indexing: A data access method that is used to address at once all elements of a matrix that satisfy a certain condition. As a result. e. Extracts all rows from a matrix in which the value in a certain column lies in a defined range.2.
2.Version from: 11.2010 149 . basic statistical functions included in the base version of Matlab are introduced.ch/static/matlab/ .edulap. • • • functions to calculate statistical characteristics (descriptive statistics) calculation of correlation and covariance values functions to generate random data sets with defined distributions http://www.Introduction to Matlab Basic Statistical Functions In this chapter. That is.
you can find all necessary information in the Help System under Statistics Toolbox (main category in the Contents part) Minimum and maximum The functions are called min and max.2) matrix with normally distributed values mean in columns modal value. []. and modal values There are three functions that have the same structure: mean. you can specify the dimension of the calculation. A «logical solution» for this would be: m1 = reshape(m. >> min(a) >> max(max(a)) >> b=fix(rand(5)*25) >> max(a. Its functions are thus not discussed here.Introduction to Matlab Descriptive Statistics Even the basic version of Matlab offers a set of mainly descriptive statistics functions. you best see for yourself: >> m=fix(randn(200. 1 are columns (default).Version from: 11. >> mean(m) >> modeval=mode(m) >> [vals.ch/static/matlab/ . 2) calculates the minima in columns.2.6)*18+48). 2 are rows. the most frequent value in this way you can also get the numbers of values You can specify the dimension.e. 3 are «planes». median.freq]=mode(m) >> median(m. i. too.2010 150 . Mean. But there's a «short cut»: >> m1 = m(:) >> mode(m1) >> mean(m(:)) m(:) means: just take ALL values of m or even more directly Variance and standard deviation The two functions var and std are usually used in their most simple form (for details see the Help System). Please study the examples below: >> var(m) >> std(m) >> std(m1) variance standard deviation or over the one-column array http://www. Of course. etc.edulap. numel(m). median. It will also calculate the values in columns. and mode. which has to be licensed separately. Again. you first have to convert it into a column vector. a and b have to be of the same size. In this way. If you want to determine the value for a complete array. They can both be used in the same way: Try it out: >> a = magic(5). In case you have access to the Statistics Toolbox. b) >> min(a. calculates the minimum or maximum of a complete table define a second matrix Compares a and b element by element and writes the maximum of each comparison in a matrix of the same size. 1). Further functions are included in the Statistics Toolbox for Matlab.
edulap. 50%. 2) Calculates the 5%.Introduction to Matlab Percentiles The function prctile(data.ch/static/matlab/ .Version from: 11. Percentiles calculation: >> prctile(m. The calculation also runs over columns of a matrix data. percvalues) allows for computing percentiles in a comfortable way. Every row of the result contains the three percentile values of a column.2010 151 . [25 75]. You can also specify the dimension for prctile. The parameter percvalues is a row vector that contains the desired percent values.2. [5 50 95]) >> prctile(m. and 95% percentile for every column. http://www.
>> [r. 4). you obtain further values.05). the number of elements in both arrays need to be the same. rows) display their columns and rows http://www. The function runs over a two-dimensional matrix.edulap.the default value will then be . RUP] = corrcoef(X. P.Introduction to Matlab Correlation and Covariance The only inference statistics function of Matlab in its basic version is the calculation of correlations with corrcoef. . which is interpreted as follows: The columns represent the dependent variables.01) In this way. the measured values). an example from the Help System is shown.Version from: 11. you can find the details on further parameters in the Help System. RLO. >> [i.2010 152 .2. 'alpha'. To illustrate this. j] = find(p < 0. 4) = sum(x. 2). The most important formats are: R = corrcoef(X) Yields a matrix R with the correlation coefficients. R = corrcoef(x. if x and y are not column vectors. y) x and y are column vectors corresponding to two dependent variables. p] = corrcoef(x) >> [i. P contains the significance values based on the specified alpha value. j] uncorrelated random data now we generate a correlation calculate correlation coefficients and p values find the significant correlations (columns. they will automatically be converted into column vectors. As usual. More precisely. [R. Obviously. A data matrix which includes a correlation between column 4 and the other columns is used. and the rows represent the individual observations (that is. RLO and RUP contain the lower and upper limits for a 95% confidence interval for every correlation coefficient.ch/static/matlab/ . The parameter alpha can be omitted . >> x(:. >> x = randn(30.05 for 95% confidence interval.
it is often helpful to generate random data that have well-defined distributions. The syntax is: a = rand(rows. [3 2 6 4 1 5].ch/static/matlab/ .edulap.2. cols) * (UpperBound . Permutations If you want to obtain a randomly ordered sequence of numbers in a certain range. you can use the function randperm (random permutation). Equally distributed random numbers The basic function to generate equally distributed random numbers is called rand. or scale it by multiplying with a constant. e. To generate data in the range from LowerBound to UpperBound. random numbers in a specific range are needed. cols) This statement creates a matrix with the dimensions specified by rows and cols. randperm(n) This creates a randomly ordered sequence of the numbers 1 to n as a row vector. you can use this method: data = rand(rows.g. 1) * (37 .LowerBound) + LowerBound. Result of data = rand(4000.Introduction to Matlab Random Data with Defined Distributions To test an evaluation program.Version from: 11. You can shift this sequence into any range by simply adding a constant value. More often. It generates numbers between 0 and 1.2010 153 .12) + 12 http://www.
2.Introduction to Matlab For most applications. 1) * SD + M.ch/static/matlab/ .Version from: 11. this form suffices. >> data = randn(4000. >> SD = 10. In case you have to be sure that a different sequence is generated every time you call the function. proceed as shown below: >> M = 27. you always want the same sequence. cols) To create data with any mean and standard deviation. data = randn(rows. Normally distributed random data With the function randn you obtain normally distributed random data with a mean of 0 and a standard deviation of 1. >> mean(data) >> std(data) define the mean define the standard deviation generate the data verify the mean and the standard deviation http://www.edulap. or have to know the random generator algorithm precisely.2010 154 . please consult the Help System on rand.
calculation of average values or merging and regrouping of the data. you can also implement that the user can select a directory. All data with -1 are ok.fix files) should be selectable (end this process when the user clicks "Cancel"). You find the sample code for this in Lesson 3 Sample Code: Select All Files in a Directory (this is implemented in the sample solution for Exercise P5. 2. In a loop. one set after the other.Introduction to Matlab Exercise P4: Project Task .ch/static/matlab/ . all files selected by the user are imported.m). The filtered data of all subjects are to be saved in a single data file (= merged raw data file).fix files are imported. eyedata_sol5. For the EyeData Processing Project 1.Data Processing Implement the data processing parts in your project.Version from: 11. The data have to be internally stored in a way that they can later be easily accessed for saving. . the others are to be deleted. several data files (i. Image size is defined by tha last character of the image name (1 to 4). Extend the user interaction function for selecting the data: In a loop. 5. How the data are processes depends on your specific task: maybe transformations. (2) the median of the fixation duration (as the distribution is skewed!) of all fixations that were made on all images of a certain size.edulap. the following values are to be computed: (1) mean number of fixations per image. Per subject and image size.m http://www. The format remains the same as in Exercise P3. with the only difference that now there are the data sets of several subjects.2. aggregation. These values are to be saved as repeated mesurements data (as shown in the image below) into the file aggregated data. Alternatively. The sample solution can be found in the M-file eyedata_sol4. The program filters the data (if requested by the user) based on column skipcode. from which all present .2010 155 . 4. 3.e.
ch/static/matlab/ . and median value var.2010 156 .2. generating random numbers in a defined range + http://www. max: minimum and maximum mean. mode.edulap. median: mean. std: variance and standard deviation prctile: calculation of percentiles corrcoef: correlation coefficients randperm: randomly ordered sequence of the numbers 1 to n rand: equally distributed random numbers between 0 and 1 randn: normally distributed random numbers with mean 0 and standard deviation 1 data = rand(rows.Version from: 11.Introduction to Matlab Summary • • • • • • • • • min. modal. cols) * (UpperBound .LowerBound) LowerBound.
• • • • • • • handling figure windows interactive modification of graphics axes universal plots bar graphs a short demo of other graphs annotation and extension of graphics http://www. together with a demonstration of those graphics that are most often used in our field.edulap. Instead of that.2010 157 . It would go beyond the scope of this course to give a comprehensive overview of all features.Version from: 11.ch/static/matlab/ .Introduction to Matlab Graphics Basics: Figures and Axes General information on graphics in Matlab Matlab provides extensive possibilities to graphically display data.2. the basic mechanisms are introduced.
4)) A new figure can also be created by using the menu item of the current figure File > New > Figure. In the command line mode. However.1:pi)) >> hold on >> plot(sin(-pi:. in a program that uses graphical outputs. etc.this time. you have to create an additional figure: >> figure >> bar(rand(10.edulap.) are applied which often do not suit the necessities of the task. you can modify a graph according to your needs and afterwards print or save in various file formats. in the following called figure.Version from: 11. In this way. Thus. now in red . To better understand how Matlab deals with graphical outputs. every graphical output is directed to the currently active graphics window (that is. the figures are usually created explicitely and the needed properties are set accordingly. the explicit creation of a figure is often unnecessary. The display options of every graphics window can later be changed by using the built-in tools. background color.'r') Matlab automagically creates a figure with default settings the new graphical output replaces the previous one fixates the graphics (the counterpart is hold off) plot the sine again.1:pi)) >> plot(cos(-pi:. You might also want to consult the information provided in the Help System (docsearch 'interactive plotting').ch/static/matlab/ .Introduction to Matlab Creation and Manipulation of Figures Every graphical output takes place in a special window. http://www. Exercise: Have a look at the plotting tools now.2010 158 . as Matlab automatically creates a figure if none is available yet.1:pi). default values (window size.2. the one in focus / the last used one). a so-called figure graphics object. please have a look at the following exemples: >> plot(sin(-pi:. If you need an additional graphics window. the previous curve is not overwritten As you see.
close etc.g.3)) >> fig2=figure('Name'.'r') >> figure(fig1) >> grid off >> clf the parameters determine the title of the window (optional) a second figure change back to the 1st figure e. you can simply get the first window into the foreground «manually». you can directly specify which figure you want to access without explicitely making it active. >> bar3(rand(10.ch/static/matlab/ .g. by figure(fig1). http://www. switch off the grid clear the whole figure (clear figure) With functions such as clf. you proceed like this: Every figure is created separately and receives a so-called figure handle.'line graphs').1:pi). and continue with your graphics commands: >> bar(rand(10. or close(fig1). It is used to repeatedly reference a certain figure later. >> fig1=figure('Name'.'bar graphs').2. >> plot(sin(-pi:.edulap. e. clf(fig2).Version from: 11.1)) >> close all the plot goes to the first window again closes all open figures If you want to use several figures from within a program.2010 159 .Introduction to Matlab But what is if you want to plot to the first figure again? As long as you work in the command line mode.
'Visible'.[. For this. for instance under the keyword 'figure properties' (docsearch 'figure properties'). or you can recall the handle of the currently active figure with gcf (get current figure). You can either specify the handle directly (that is.ch/static/matlab/ . Example: >> set(fig2. 'titletext' Title of the figure window 'Color'.'line graphs'). For figures. The properties can either be set directly when creating a figure: >> fig2=figure('Name'. a plethora of modifiable properties are available. 'auto' is the default value.'ScreenSize') 'Resize'. bottom: distance in pixels from the left and bottom screen border width. 'Name'. Or you can modify them later by means of set. 'Another name'). The first argument of a pair indicates which property you want to change (e.edulap. width. you need the handle of the figure to be modified. The most important ones are briefly described in the next section. 'Another name'). For information on how to specify colours see the Help System: doc colorspec.8 . 'on' or 'off' With 'off'. >> set(gcf. the window can be hidden.8 . fig2). http://www. 'none' or 'auto' Determines whether the toolbar of the figure window is visible.2. the second argument specifies the value to be set. 'Name'. 'on' or 'off' Determines whether the user can manually change the window size. bottom. the window is visible. A useful assisting function: How to find out the screen size in case you want to size the window relative to the screen size: >> ss=get(0. height] Position and size of the window left. The most important figure properties 'Name'.Introduction to Matlab Figure Properties Changig the properties of figures is done with argument pairs.'r') >> set(gcf. 'Toolbar'. [100 100 800 600]). Examples: >> set(gcf. results in light gray 'Position'.'yellow') >> set(gcf. You find the complete overview in the Help System.2010 160 . [left.'Color'.'Color'.g. that is. but it is still available for graphic outputs. ColorSpec Background colour.'Color'. 'Name').8]) 'yellow' is one of the pre-defined colours 'r' is short for 'red' RGB colour triple.Version from: 11. height: width and height of the window in pixels Example: >> fig=figure('Position'. as you have seen in the above example with the window title.
[100 100 800 600]) >> plot(peaks) Now we can change the settings: >> title('The peaks function') >> grid off >> grid on >> axis off >> axis on >> axis([0 100 -20 20]) >> axis tight >> set(gca. y) or three (x.in Matlab terminology . Axes.2010 161 . see below).Version from: 11.g. but into the axes (or axes system) contained therein. plot(peaks).'blue') >> box on >> xlabel('Abscissa') >> ylabel('Ordinate) title of the graph switch off the grid switch it on again remove axis lines change the scales: [xmin xmax ymin ymax] tightly fit the scales to the data set background colour. bar(peaks) A different method for user interaction: the figure property currentcharacter (see Help System). but 'Color' is probably the only one you will ever use.a system of two (x.edulap. This should not be confused with axis. An axes is . For a demonstration.'Color'. a graphics output is not directed into a figure. gca = get current axes Further options of axis: see the Help System doc axis box(frame) around the graph label the axes Another useful function is Eine weitere nützliche Funktion ist waitforbuttonpress: It pauses program execution until the user clicks into the graphics window or presses a key when the figure is active: >> figure. All other axes properties can be changed by separate commands. y. waitforbuttonpress. too.Introduction to Matlab Axes Actually. with which you can set the properties of the actual axis (e. please close all open windows and create a new figure (simply use copy/paste): >> close all >> figure('Position'. http://www. z) axes.2. have a multitude of properties (docsearch 'axes properties').ch/static/matlab/ . the scales.
ch/static/matlab/ .2) >> barh(rand(10. clf would erase all axes from the figure. You can create several axes within a figure by means of the function subplot.3) >> scatter(randn(1.40).edulap. http://www.2. [100 100 800 600]) >> subplot(2.Introduction to Matlab Multiple Axes It is often useful to have a figure with several sub-plots (panels).40)) >> subplot(2.2.Version from: 11. Multiple axes Please go through the following example: >> close all.3)) >> subplot(2.2.2. randn(1.1) >> cla creates 2x2 sub-plots and activates the first one plots into the first sub-plot select the second sub-plot horizontal bar graph the bottom right sub-plot and the last one select the first one again only erases the contents of the current sub-plot (clear axes).1:pi)) >> subplot(2. figure('Position'.2.1) >> plot(sin(-pi:.2.4) >> plot(peaks) >> subplot(2.2010 162 .
Commands: figure properties • • • • figure: create a figure window clf: clear the contents of a figure window close.2010 163 . There can be more than one axes in a figure window. Change the properties of a figure window by means of argument pairs Some properties: Name.'Color'.Introduction to Matlab Summary Points to remember • • • Every graphics output takes place in a dedicated figure window. Color. Position. box off: show or hide the frame around the axes hold on.'blue') : change the properties of an axes. 'property'. the graphics output is directed to an axes system contained in the figure window.2. Visible gcf = get current figure handle waitforbuttonpress: Wait for key press or mouse click • Commands: axes • • • • • • • • • • • title: set the title of an axes xlabel. hold off: fixate graph. Changing most figure properties is done with argument pairs.edulap. the second argument specifies the value to be set. Toolbar.Version from: 11. ylabel. The first argument of a pair indicates which property you want to change. More precisely. parameter).ch/static/matlab/ . grid off: show or hide the grid axis on. or release fixation set(gca. axis off: show or hide the axes axis tight: tightly fit scales to data axis([xmin xmax ymin ymax]): set scales box on. zlabel: label an axis grid on. close all: close figure(s) set(gcf. gca = get current axes handle subplot: create or address sub-figures (= axes) cla: clear the current axes http://www.
Introduction to Matlab
Graphics Tools
Below, you will get to know some important graphics tools. Again: Matlab offers many options, and it is not possible here to explain all of them. As usual, you find everything in the Help System. An overview over all graphics commands is given in the Help System under Function reference > graphics > basic plots and graphs With the function plot as an example, the principle of most graphics commands are explained. After that, other frequently used graph types are briefly demonstrated.
http://www.edulap.ch/static/matlab/ - Version from: 11.2.2010
Introduction to Matlab
The Plot function
The plot function creates two-dimensional line graphs. The data have to be given as column vecors. The data points are connected by a line in the sequence as they are found in the vectors. In the following examples, you can see the two forms of the plot function: Form 1: plot(Y) If only one vector is given as argument, the data are interpreted as Y values and plotted against their index on the X axis. >> ydata = sin(-pi:.1:pi); >> plot(ydata) Form 2: plot(X, Y) If two vectors are given, they are interpreded as X and Y axis data. >> xdata = 20:39; ydata = rand(20, 1); >> plot(xdata, ydata) >> figure >> plot(sin(-pi:.1:pi), cos(-pi:.1:pi)) LineSpec: set the line properties plot(X1, Y1, LineSpec, ...) The plot function accepts one argument that allows to set three important properties of the curve: • • • Line style specifier: the style of the line (standard, dotted, dashed etc.) Marker specifier: the style of the data point markers (dot, circle, triangle, star, etc.) Color specifier: the colour of the curve
Example: To plot data with a red, dashed line and crosses as data markers, write: plot(x, y, '--xr')
http://www.edulap.ch/static/matlab/ - Version from: 11.2.2010
Introduction to Matlab
http://www.edulap.ch/static/matlab/ - Version from: 11.2.2010
Version from: 11. t.. y1.. '--'. ':') More properties Other properties of lines and markers can again be influenced by means of pairwise arguments: plot(.2010 167 . t.2.sin(tan(x)).Introduction to Matlab You can just as well draw plots without lines or without markers. 'PropertyName'. >> y3 = sin(t-0.edulap. >> plot(t.line colour Example: >> clf >> x = -pi:pi/10:pi. >> y1 = sin(t). '-'.fill colour of markers MarkerEdgeColor . PropertyValue.size of the markers LineWidth . y2. y3. Also see the information in the Help System (doc linespec). >> y = tan(sin(x)) .ch/static/matlab/ . This example shows how several data sets can be plotted with a single plot statement: >> t = 0:pi/100:2*pi.5). by omitting the corresponding specifiers. http://www.width of the line Color ..) • • • • • MarkerFaceColor . >> y2 = sin(t-0.edge colour of markers MarkerSize ....25).
'g'. ..ch/static/matlab/ ... '--rs'. 2. ..Version from: 11. 'MarkerSize'..Introduction to Matlab >> plot(x. 'MarkerEdgeColor'. 10) Other options can be found with doc plot. 'k'.2010 168 . http://www. 'LineWidth'.2.edulap... y. 'MarkerFaceColor'.
0.25.0. Examples for two-dimensional bar graphs: >> figure >> data=rand(10.edulap. >> bar(data(:.0 0 1]) http://www.25') subplot(2. barh plots horizontal bars.2) bar3(Y.2010 169 .3.3.3') colormap([1 0 0.'grouped') title('Grouped') subplot(2.'detached') title('Width = 0.ch/static/matlab/ .3. Copy all these lines at once into the Command Window.3.5.4) bar3(Y.'grouped') title('Width = 0.3)*20+5.5) bar3(Y.3.5) >> bar(10:10:100.6) bar3(Y.0.Introduction to Matlab Bar Graphs Another often used type of graph is the bar graph.1)) >> bar(data(:.0.1).'detached') title('Detached') subplot(2. but with three-dimensional bars.3. and bar3 and bar3h do the same. The two-dimensional form with vertical bars is called bar.5') subplot(2.1)) >> bar(data) one data column different bar width (the default is 0.data(:.3) bar3(Y.1) bar3(Y. Y = cool(7).2.'stacked') title('Stacked') subplot(2.'stacked') title('Width = 0.Version from: 11.3.8) re-label x axis several sets of data Examples for 3D bar graphs in various variants. subplot(2.0 1 0.
Introduction to Matlab http://www.edulap.Version from: 11.2.ch/static/matlab/ .2010 170 .
m and run it by hitting the F5 key. load the script graph_examples. http://www.Introduction to Matlab Brief Demonstration of Other Functions Below.Version from: 11.edulap. Please go to the Matlab Editor. a script is used to illustrate some more of Matlab's interesting graphics options.2.2010 171 . With a key press or mouse click into the figure window (function waitforbuttonpress) you can continue to the next graph.ch/static/matlab/ .
For further details. http://www.an underscore _ in the text is interpreted as a modifier that shows the following character in subscript. x. please refer to the Help System. '-. 'sin_x'.2. sin(x). 'Interpreter'. or legends. arrows. 'string2'.edulap. >> plot(x.. the strings are the text that describe the different curves. cos(x).for instance . lines. As this is not desired here..2010 172 . Example: >> x = -pi:pi/20:pi. .) h is the «handle» of the legend. By default.Introduction to Matlab Annotate and Extend Graphics Usually it makes sense to complement graphics with additional captions. 2). we disable the text interpreter. Below you get an outline of the most important functions.b') >> h = legend('cos_x'.ch/static/matlab/ .Version from: 11. it is TeX . >> set(h. '-ro'. 'none') Explanation: The last line relates to the text interpreter used by Matlab. Legend The function legend adds a legend to a graph. The most simple form of the statement is: h = legend('string1'.with the consequence that .
' \leftarrow sin(\pi)'. in case it hides relevant parts of the graph.2010 173 . Below you can see how the TeX interpreter can be used to display a formula. sin(0:pi/20:2*pi)) >> text(pi. as a complete description of all text options would go beyond the scope of this chapter.ch/static/matlab/ . you can place text anywhere in the current figure. The legend function has innumerable further options.e. the Help System. Geometrical Elements There are two elements that can be used to directly draw into a figure. The coordinates for text placement correspond to the data coordinates (i. With an additional parameter. it has to be pointed to the Help System. you can save the graph. cf. the text size is set.Introduction to Matlab A nice feature: In the graphics window.Version from: 11. as the scales indicate).2. >> plot(0:pi/20:2*pi. 'FontSize'. Afterwards. 18) Again. you can grab the legend with the mouse and move it around freely. Annotate graphs with text By means of the function text. 0. Again.edulap. the coordinates are the same as the axes coordinates. http://www.
.5 4 6].. Some examples: >> figure. 'EdgeColor'. axis([0 16 0 8]) >> rectangle('Position'. 'LineWidth'.. 'PropertyName'. 'Curvature'. The basic form of the function for two-dimensional applications is: line(X. propertyvalue. 'LineStyle'. . Y.2.h]. . 5) Rectangles and ellipses With the function rectangle.5].) X and Y are vectors specifying two or more coordinates that will be joined by straight lines. 'red') >> rectangle('Position'.w. rectangles (also with rounded corners) and ellipses can be constructed.edulap.8]. 'Color'. [11 2 4 3]. Example: >> line([0 1 .2. The properties are again given as argument pairs. 'blue'.Version from: 11. [1 1 4 3]. With the property Curvature the corners can be rounded.. [0 1 . 'PropertyName'. 'Curvature'.2010 174 .8]) http://www.. w and h are width and height of the rectangle. [1 1]. [6 . [x.Introduction to Matlab Lines The line function serves to draw lines into the figure.) x and y are the coordinates of the bottom left corner. '--'. 2) % default:schwarz >> rectangle('Position'. rectangle('Position'. [.4 . 'LineWidth'.4 . 'PropertyValue'.y. 'FaceColor'. These shapes can be filled with colour.ch/static/matlab/ .
lines.0 is the bottom left corner.8 . y) annotation('textarrow'. [.[. >> annotation('textarrow'.'HeadStyle'. y) annotation('arrow'. y) annotation('doublearrow'. 'EdgeColor'.ch/static/matlab/ . and ellipses. i. All annotations are applied with the same function annotation and the necessary parameters. It will not be changed even when the graph's scales are changed or deleted. 1.5]).Introduction to Matlab Annotations Annotations are another possibility to add texts and geometrical elements to figures. rand(100.2 .3 .1 is the top right one.2 . 'b'). 'g').[.'Text arrow'. [x y w h]) annotation('rectangle'.5].'. annotation('line'. [. that's why a semicolon is necessary at the end of the line to avoid its output to the Command Window.Version from: 11. 'This is a text box'). Remark: annotation always returns a handle.5 . x and y are the normalised coordinates.05 . 'FaceColor'. x. As with the above introduced functions.2]. >> annotation('textbox'. they lie between 0 and 1 for the whole figure (not the axes). [x y w h]) Examples to try out: >> figure.2010 175 . The basic form is: annotation(type. 'String'. scatter(rand(100.5]. Annotations are drawn on a layer of their own.8]. x. >> annotation('arrow'.e. http://www. x.05 . '-.2 .3 . [x y w h]) annotation('ellipse'. but «normalised» coordinates. [. plus the additional element arrows/text arrows. 1) * 30 . 0. [. [0 1]. 1) * 20 + 12. annotations can be used to draw text.'plain').9]. y) annotation('textbox'. x. >> annotation('ellipse'.10) >> annotation('rectangle'. [. Annotations differ from text/line/rectangle in that the coordinates for placement are not axis coordinates. 'LineStyle'.5 . 'r').9].edulap.9 . >> annotation('line'. 'color'. rectangles. [.5 .9 .2. parameters) The following types of annotations exist. w and h are width and height (also normalised).'String'.2 .15 ].
Introduction to Matlab http://www.ch/static/matlab/ .edulap.Version from: 11.2010 176 .2.
1028. With rectangle. Add a legend and error bars with the standard deviation. starty. stopx. 1052 Size 3: 385. use the median values you have already computed. • That's how the bar graph should look like http://www. Corresponding to your project's needs. over all subjects.Version from: 11. stopy) Size 1: full size 1600 x 1200 Size 2: 196. 148. 289. The corner coordinates are: (startx. can be necessary. line graphs. For the EyeData Processing Project • • Create a bar graph that displays fixation duration per condition (= image size).Graphical Data Display Implement in your project the graphical output of the data.edulap. either to a fixed location with a pre-defined file name. or to a location and with a file name selected by the user. 1402.Introduction to Matlab Exercise P5: Project Task . mark the image area as shown below.ch/static/matlab/ . 1213. or a location specified by the user). bar graphs etc. 771 Store the graphs to the hard disk drive. Draw a scatter plot of all fixations for all image sizes. Often it makes sense to automatically save the graphs to the hard disk drive (to a fixed location.2.2010 177 . 429. 909 Size 4: 571.
edulap.Introduction to Matlab Example for a scatter plot of fixation data per image size You can find the sample solution in the M-file eyedata_sol5.2.2010 178 .Version from: 11.ch/static/matlab/ .m http://www.
ch/static/matlab/ . 'EdgeColor'. rectangle: draw texts.05 .9 .Introduction to Matlab Summary Summary of the most important commands: • • • • • plot: plot data bar.2. line. legend: show the legend text.2010 179 .Version from: 11. or rectangles (and ellipses) in the current axes of a figure annotation: draw graphical elements in relative (normalised) coordinates of the whole figure. bar3h: bar graphs.g. http://www. annotation('rectangle'.edulap. horizontal. 'r'). 3D horizontal. [. lines. barh. and 3D. normal.05 . e.9]. bar3.
We hope that it has helped you to start with Matlab. as it was translated by a nonnative speaker of English (as you sure have noticed).edulap. [link] Thus. and are a native speaker of English: The course is in need of proofreading. If you have any comments. If you are willing to proofread a part (however small) of this course.2. suggestions. Thank you very much! http://www.ch/static/matlab/ . Only pictures can be viewed in the PDF version! For Flash etc. see online version. please let us know! If you would like to support our initiative to build this course.Introduction to Matlab Final Remarks You have now reached the end of this course.Version from: 11. please contact me.especially if you are new to programming. or if you have found errors. Only screenshots of animations will be displayed. We are fully aware that learning a new programming language is a very demanding undertaking . which is an open educational resource.2010 180 . we are very much interested in improving this course.