Mathworks (company that releases Matlab ) documentation website is:

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1 1 Getting Started The Mathematics Behind Biological Invasions Introduction to Matlab in UNIX Christina Cobbold and Tomas de Camino Beck as modified for UNIX by Fred Adler Logging in: This is what you do to start working on the computer. If your machine seems to be asleep, jiggle the mouse to wake it up. We ll tell you your login name and the secret default password. The local window: After a delay, a window named local or something similar may or may not appear. If not, randomly press buttons until one does, or ask somebody. You can move and resize the windows by clicking on the title bar with the right mouse button or grabbing the little box in the upper right corner. Changing your password Bring the local window to the front by moving the cursor there. Type passwd in your local window and follow instructions. Logging out: Just as important as logging in is logging out. Move the cursor to the background, press the left mouse button (maybe), and choose the last menu item: Exit X-Windows. Don t do this now. Opening netscape: Bring the local window to the front, and type the command netscape & in your local window. The little & at the end of the line runs the program in the background, meaning that you can issue other commands simultaneously. The ghost of a new window will appear in a kind of dotted outline form. Move the mouse to position it and click with left mouse button when satisfied. Navigate to the minicourse home page at adler/minicourse and check it out. 2 Matlab Matlab is a computer package with a nice programming language and easy graphics interface. It also does arithmetic. To open it, type the command matlab & in your local window. 2.1 Useful webpages and general help Mathworks (company that releases Matlab ) documentation website is: Matlab online help desk: Getting Started with Matlab is available on the minicourse web page and in hard copy. You can also obtain help within Matlab. To obtain help on logarithms for example, at the prompt type help log. Also try lookfor log, which will look for any documentation in the help pages that mentions log. The UNIX version of Matlab also has a decent help page via the Help menu on the Matlab window. The Matlab demo is also useful. Type demo at the prompt and you can explore. The demo gives examples of code for a whole range of topics. 1

2 2.2 Using the Editor and creating a file In addition to the command window (where the prompt is found) Matlab has an editor/debugger which can be used to create program files. To start the editor, either type edit at the prompt, or from the desktop, click File and follow the submenu arrows: New --> M-file. The Matlab Editor/Debugger window should open. Type the line below into it. avec=[1,2,3] Now save the file by clicking on File at the top left of the editor window, select Save As and a dialog box will open. You need to specify a file name. All Matlab files have the extension.m e.g. myprog.m. To run the program type myprog at the prompt in the command window,. If the program was saved correctly you should get the response avec = The short cut for saving a file is ctrl+x, ctrl+s. If you are familiar with UNIX commands a lot of these commands work with Matlab. Otherwise stick with the menu. If you want to open a file you have already saved, in the editor click: File > Open. Editing in the command window You can pick up a line by darkening it in with the left mouse button. To paste it, click on the spot where you want it (with the left mouse button again), and then click the middle button. If you want to change something in the line, use the mouse to find the spot you want, and then delete and add characters where the mouse is. All of this is handy when working with and debugging M-files. You can also use the up arrow to revive a previously executed line. 3 Some Matlab basics 3.1 Assigning and clearing variables etc. In the command window try typing 2*3 at the prompt. Matlab displays 2*3 6 The result is labelled ans by Matlab and can be used in another calculation. ans*5 30 You can assign your own names (variables) to store numbers too: x=2*3 x = 6 y=x*5 y = 2

3 30 So x has the value 6 and y has the value 30. These can be used in subsequent calculations. These are examples of assignment statements. Names can be a combination of letter and numbers, but not symbols. Allowed: NetCost, x3 Not allowed: Net-Cost, 3x, There are some special names that Matlab already uses, e.g. pi, so be careful. To clear a variable, x say, type clear x. To clear all variables you have assigned, type clear. To suppress the output, we use a semi colon. z=-78; s=10*z s = -780 z is hidden. We can also fit several statements on one line, separated by commas or semi colons. When writing a program you will want to add comments. To comment a line of code use the %. Any text which follows % is ignored. If you make an error in your typing, use the up arrow key to return to your previous line(s). 3.2 Matrices (arrays) Matlab lives for matrices. Try the following: x = [-2 4-8] % Creates a 1x3 matrix or row vector (1 row, 3 columns) y = 1:8 % Creates a 1x8 vector of numbers from 1 to 8. This is an example of the colon notation. It means all integers between 1 and 8, starting with 1 and ending with 8. If a,b and c are numbers, then a : b : c means all the numbers a,a+b,a+2b,... ending at or just before c. The syntax is first:increment:last. y = 1:2:8 % Creates a vector of numbers from 1 to 8 incremented by 2 z = [1; 2; 3] % Creates a 3x1 matrix, where ; tells Matlab to add a new row A = [-1 0; 3 1] % Creates a 2x2 matrix a = rand(3,3) % Creates a 3x3 matrix of random numbers B = ones(3,6) % Creates a 3x6 matrix of ones. Matlab variables are case sensitive, so that a and A are different quantities. Individual matrix entries can be referenced by indices in brackets: e.g. typing x(2) 4 A(2,1) % The entry in row 2 column 1 of matrix A 3 A matrix or vector will only accept positive integers as indices: B(0,1), B(2,-3) are not allowed. To extract an entire row or column of a matrix A type A(1,:) % Extracts the whole of row 1 3

4 -1 0 A(:,2) % Extracts the whole of column a(1:2,2) % Extracts the first two elements of column 2 Matrices and vectors can be gummed together if their sizes match. [A;A(1,:)] % Adds a new row to matrix A The size of a matrix can be checked: try typing size(a). Try typing size(ans). 3.3 Matrix operations Matrix operations include multiplication etc. Many of these commands can be made to work entry wise by typing dot. before the operation - e.g. A*A is the matrix A 2, while A.*A is the matrix with (i,j) entry equal to A(i,j) 2. These commands by also be typed as A A and A. A respectively. Check with the 2 x 2 matrix A. 3.4 Built-in functions Matlab has many built in functions, most of which apply entry-wise to matrices or vectors. Check the help under functions by category. Try out the following examples (use help to look up their meaning): exp(x) sy=sqrt(y) floor(sy) abs(a) sum(a) sum(sum(a)) 3.5 For loops Type the following lines in the edit window (then save and run the file) sum10 = 0 for i = 1:10 sum10 = sum10 + i end (the indentation is not necessary, but makes the code clearer). The code initializes the variable sum10 to zero; for each integer i between 1 and 10 it performs the command sum10 = sum10 + i. 3.6 Basic plotting The simplest plot has the form plot(x,y), where x and y are vectors of the same length, n say. It plots a graph of the points (x 1,y 1 ),(x 2,y 2 ),...,(x n,y n ). 4

5 Use the : to make a vector t of values from -6 to 6 with an increment of 0.1 (this could be a good time to practice suppressing output with ;). To get a plot of sin(t) against t, type plot(t,sin(t)). If you would prefer to see it with green dots, try plot(t,sin(t), go ). See help plot for more options. Axis labels and a title can be added using the xlabel, ylabel and title commands - use either the help command or the help pages to try these commands out. 3.7 Logical statements Matlab has some nifty features for checking logical conditions. Using the vector t made earlier, set sint=sin(t). If you type sint > 0 you get out a vector with zeros where the condition is false and ones where it is true. Figure out how to make a vector which is 0 when sin(t) < 0 and equal to sin(t) when sin(t) > 0 and plot it. To overlay this plot with a plot of sin(t), type hold on % Holds the plot plot(t,sint, r ) % Makes a red version of sin(t) hold off % Releases the plot. The other logical operators are == for equal, >= and <= for and, and = for. 3.8 Text strings The argument of xlabel, ylabel and title are examples of text strings i.e. a collection of characters surrounded by single quotes. Another example is: st = my name is Frankenstein Commands like disp, input and error use text strings. Another useful example is num2str, which converts a number into a string. As an example type: title([ Plot of sin t up to,num2str(2*pi)]) to label your graph. The square brackets are required in this command because there are two elements to be printed, so we store them in a vector. 3.9 M-files Matlab can be used in two main ways. You can either type instructions directly at the prompt or make up a file or files containing the instructions you want Matlab to execute and feed this file (called an M-file) to Matlab. In general you should use M-files to write all your commands/programmes. There are two different kinds of M-files, script files and function files, which act in slightly different ways. Script M-files store a sequence of commands that can be referenced and run with a single name. Function M-files are, not surprisingly, functions and are rather more confusing to use. All M-files end in.m and are created in the editor window. The little program you made to find sum10 is a script M-file. To make a nice output, open it up again and add the line disp([ The value of sum10 is,num2str(sum10)]) disp is to display output, and num2str converts numbers to strings for output. If you called this M-file summeup.m, typing summeup at the Matlab prompt will execute the M-file and will result in the output: The value of sum10 is 55 Typing help summeup will print any lines at the top of the file that start with a % (the comment lines), up to the first line that doesn t start with a %. Matlab programmers frown upon the use of unnecessary for loops. Figure out a way to add up the numbers from 1 to 10 using : and sum. 5

6 A sample function M-file The following file (mkvec.m) is a simple function file. Function files should always have the same name as the function itself. % MKVEC Takes input x and constructs the vector [1, x, x 2, x 3] % mkvec(x) returns the vector [1, x, x 2, x 3] function v = mkvec(x) v=[1, x, x 2 x 3]; write and save the file and then type mkvec(2) at the command line. You should get the result You can also use the M-file to assign a name to your output - for example type w=mkvec(6). If you want to use the output of a function file later you will need to assign it a name, otherwise it is just a local variable and Matlab will forget its value. Function M-files can have more than one input argument - e.g. the file mkvec2.m below % MKVEC2 Takes input x and n and constructs the vector [1, x, x 2,...,x n] % mkvec2(x) returns the vector [1, x, x 2,...,x n] function v = mkvec2(x,n) for k = 0:n v(k+1) = x k; end and more than one output argument - e.g. the file mkvec3.m below: % MKVEC3 Takes input x and n and constructs the vector [1, x, x 2,...,x n] % mkvec3(x) returns the vector [1, x, x 2,...,x n] and length len function [v,len] = mkvec3(x,n) for k = 0:n v(k+1) = x k; end len = length(v); Here you have two outputs, v and len. If you type mkvec3(4,3) at the command window prompt ( ) you will just get the output for v, because ans, in which Matlab temporarily stores the output is a 1x1 array so it can store only one output. To view both outputs type [v,len]=mkvec3(4,3). I have labelled the output as v and len, but you can use any valid variable name. If you assign output to an existing global variable then your output will overwrite what is already there. 6