Introduction to MATLAB

Transcription

1 Introduction to MATLAB MATLAB stands for MATrix LABoratory. Originally written by Cleve Moler for college linear algebra courses, MATLAB has evolved into the premier software for linear algebra computations in science and industry all over the world. Using MATLAB in this course will save you time on homework, help you learn linear algebra, and give you a glimpse of how linear algebra is applied in practical work. At the end of many Study Guide sections, MATLAB boxes will show you how to avoid routine arithmetic calculations, so you can focus on new concepts. Later in the course, you will run several state-of-the-art programs. For instance, given a matrix A (which is small by today s standards), MATLAB s eigenvalue program provides important and accurate information about A in a fraction of a second, after performing about one million arithmetic operations. GETTING STARTED WITH MATLAB You need access to the MATLAB program, either on a personal computer (PC or Mac) or on a shared computer network system at your school. If the school network is prepared for your course, someone may have already installed special MATLAB programs written for this course, along with data for about 850 exercises in the text. Accessing a matrix or some vectors for a problem requires only a few keystrokes. (This avoids data entry error and saves you time.) And then MATLAB performs the computations for you. Once you see how much time you can save, you ll probably start using MATLAB for most of the numerical exercises! If you plan to work at a computer away from school, you can purchase a Student Version of MATLAB at modest cost. You need to download the special programs and exercise data from the Web, at These programs and data are in a folder called the Laydata4 Toolbox. Download the folder into the main MATLAB folder and then add the Laydata4 Toolbox to the MATLAB PATH. A ReadMe file in the Toolbox has instructions. When that is done, MATLAB will have immediate access to everything in the Toolbox. The following paragraphs provide basic information about the MATLAB environment, including how to save and print a copy of your work. After that, the MATLAB boxes in this Guide will form your lab manual for the use of MATLAB during the course. (Begin with Section 1.1.) For your reference, an index of commands is included at the end of this appendix. ML-1

2 ML-2 Getting Started with MATLAB How to Start, Stop, And Run MATLAB Once you start MATLAB (by clicking on a menu or icon), you will see the MATLAB logo as the program loads, followed by a prompt symbol >>, or EDU>>, in what is called the command window. Recent versions of MATLAB have two other windows, which you may close or resize. The Study Guide focuses mainly on the command window. Type a MATLAB command at the prompt and press <Enter>. MATLAB s response will follow. Here are some simple commands: x=2*3 X = 5*x Sets up a variable x in your workspace and stores 6 in it. The symbols +,, *, /, and ^ (for exponents) are used for arithmetic. Sets up a new variable with the value 30. MATLAB is case-sensitive. Extra spaces are ignored. They were inserted here for readability. A=[1 2 3; 4-5 6] Creates a matrix with 1,2,3 in the first row and 4, -5,6 in the second row. One or more spaces separate entries in each row. c1s1 who clear help clear help quit Requests data for exercises in Chapter 1 Section 1, for example. See the MATLAB box at the end of Study Guide notes for Section 1.1. Lists the variables in your workspace (a portion of computer memory that stores the variables created since you turned on the program). Removes all variables (and their contents) from the workspace. Tells you about the clear command. Displays a long list of topics for which help is available. Immediately clears the workspace and terminates MATLAB. exit does the same. You can place several commands on one line, if you wish, separated by commas or semicolons. A semicolon after a command instructs MATLAB not to display the result of the command. How To Format MATLAB Output Ordinarily, MATLAB displays up to 5 digits for each number and places a line feed between each object it displays. The following commands allow you to modify this standard display style. format compact Suppresses extra line-feeds, so you can see more output on one screen. Many students turn this on at the beginning of a work session.

3 Getting Started with MATLAB ML-3 format long format short format rat format Displays all 15 digits that were used in the calculation. Displays only 5 digits. Displays numbers as fractions, as accurately as possible. Restores the standard display style. Use help format to see other formatting options. How To Save and Print a Copy of Your Work You can save a record of every keystroke you make, along with MATLAB s responses, in a file you choose by turning on the diary feature. For instance, if you select the filename project1.txt, use the commands: diary project1.txt diary off diary on Writes output (following this command) to the file named. If the file already exists, the output is appended to the file. Stops the recording Starts writing output again to project1.txt, named earlier. Places new output at the end of the file. The file project1.txt will be located in the current directory, which initially is the main directory that holds MATLAB and all of its subdirectories. You can change this directory, but the easiest way to control where your file goes is to include a path at the front of the name. For example, if you have a USB flash drive in drive E, the command diary E:\project1.txt will store your work there. Alternatively, MATLAB version 7 displays the current directory in a toolbar at the top of the screen, and you can use the toolbar to change the current directory. Once your output is in a text file, you can use any convenient text editor to add comments to your work, delete extraneous output or errors in typing, and then print the file. If you want to print while working on a network, you may need to find out what special network commands are required. This concludes the main part of the MATLAB appendix. You should be ready to use MATLAB with your homework (as soon as the Laydata4 Toolbox is installed). Enjoy yourself!

4 ML-4 Getting Started with MATLAB SCRIPT M-FILES When you have some experience using MATLAB, you may wish to experiment with script m- files to prepare homework assignments and projects. The diary process works reasonably well for short homework assignments. However, for longer projects the diary file can be quite long and require extensive editing particularly if you make multiple attempts to get the project working A script M-file is simply a sequence of normal MATLAB commands stored in a text file that has.m as its extension. Instead of running these commands at the command prompt, you type the name of the script M-file at the prompt and press <Enter>. For example, if you name your script file project1.m and place it in the MATLAB working directory, then project1 becomes a new MATLAB command. Entering project1 at the prompt causes the commands in the file to be executed as if you had entered them one at a time. The main advantage of using a script M-file instead of the diary to create a project report is that errors in the script can be corrected easily and the entire script run again with no effort. If you discover a mistake in the middle of a project that is being recorded by the diary, you have to repeat all the commands. (Later, you ll also have to edit out the first set of commands that did not work properly.) A second reason for using a script is that you can reuse it later if you need to solve a similar problem. Just make a few appropriate edits and you are ready to go. How to Create a Script M-file M-files are ordinary text files that you can create and modify with any text editor or word processor that can save a file as plain ASCII text. On Unix or Linux systems, this includes pico, vi, textedit, and emacs. On Windows and Macintosh systems, MATLAB comes with its own M- file Editor/Debugger which you access from the toolbar or the File menu. The first line of a script M-file should be echo on Displays the commands along with results. Without this command, only the results will be displayed. Place the MATLAB commands next. The last line of the file should be echo off Turns off the previous echo command. Remember to place a.m extension on your file, and save it in the current working directory.

5 Getting Started with MATLAB ML-5 How to Prepare a Final Report When the script M-file is running satisfactorily, you need to document your work with comments, which are statements in the file that begin with a percent sign. Comments are used to outline the steps in your calculations and to interpret the results of various computations. For example: %The system is inconsistent, because 0 = 5/2 is not true. MATLAB ignores all such comments, but your instructor will appreciate them. To create a printed copy of your work, use the diary command. If your file is problem1.m, enter the following commands at the command prompt: diary problem1.txt problem1 diary off Records all commands and output that follow. Executes the commands in project1 and displays all comments in the file on the screen. The diary captures these comments as well. Stops the recording. Now you have a text file that shows all your work. Depending on the requirements of your course, you can either print the file for submission or attach the file to an . Index of MATLAB commands \ (backslash), 2-27, 4-15, 6-16, 6-19 : (colon), 2-4./ (divide entry-wise), 5-28 ^ (exponent), 2-4, 4-4, 6-20 (transpose), 2-4 (up-arrow), 1-14, 1-42, 5-32 abs, 5-32 ans, 1-6, 1-19 bgauss, 1-19 cond, 2-14 cos, 4-3, 6-20 det, 3-8 diag, 2-4, 3-8, 7-18 eig, 5-5, 5-15, 5-21, 5-28 exp, 6-20 eye, 2-4, 2-9, 5-4, 5-28 for...end, 5-25 format, 1-6 compact, 1-6, 5-32 long, 1-42, 2-14, 5-5 rat (rational), 1-27, 2-14, 5-5, 8-5 short, 1-27, 1-42, 2-14, 5-5 gauss, 1-19 grid, 4-3, 5-9, 5-25 gs, 6-12 hilb, 2-14 help, 2-4 hold, 4-4, 5-9, 5-25, 8-12 imag, 5-21, 5-28 inv, 2-14, 2-28 linspace, 4-3, 5-9, 6-26 log, 6-20 lu, 2-27 max, 5-32 mean, 7-18 norm, 6-2, 6-9

6 ML-6 Getting Started with MATLAB nulbasis, 5-4, 5-5, 5-15, 5-28 null, 7-15 ones, 2-4, 7-18, 8-3, 8-5 plot, 4-3, 5-9, 5-25, 6-26 poly, 5-9 polyval, 5-9 prod, 3-8 proj, 6-12 qr, 6-12 rand, 2-4, 2-14 randomint, 2-4, 4-22, 5-9 rank, 2-41, 4-22 real, 5-21, 5-28 ref, 2-38, 2-41, 4-10, 4-22, 4-26, 6-16, 6-19, 8-3 replace, 1-6, 1-14 roots, 4-31 rref, 2-38, 4-10 scale, 1-6, 1-4 size, 2-4, 7-15, 8-3, 8-5 sqrt, 7-15 sum, 8-3, 8-5 svd, 7-15 swap, 1-6, 1-14 zeros, 1-24, 2-4, 7-15