MATLAB An introductory tutorial

Transcription

1 MATLAB An introductory tutorial By Carin Nilsson Dept. of Physical Geography and Ecosystems Analysis (taken from the tutorials for course NGE604 Climate Systems) And Chantal Donnelly (Dept. of Water Resources Engineering) The aim of this tutorial is to give the student a general glimpse of how to handle files and commands in MATLAB. The tutorial is short, so at the end there a few recommendations to further study MATLAB, such as on-line tutorials from the Mathworks homepage etc, for exploration at your own pace. 1

2 Starting up MATLAB Put the data you will be using into a temporary data folder, e.g. C:/TempData Start up MATLAB via the icon on the desktop, or by Start- Programs-MATLAB. 1. Settings Set the Current Directory to define your working folder (C:/TempData) Now all the files you have copied will appear in the Current Directory, in the left window. 2. Look around the workspace. If you wish to change the number of windows you see, it can be done through Desktop Layout from the menu at the top. Default is to show the Command Window, Current Directory, Command History and Workspace. 3. Warming up with calculations. MATLAB is a good calculation tool. Let us start with creating a matrix and then perform some calculations. Operate in the Command Window. a) Create a matrix with 4 rows and 3 columns. Choose any numbers you like. I have decided to make a matrix, A, which looks like this. >> A=[3 6 8; 2 5 3; 4 7 5; 2 6 8] ([ ] Those brackets you get with Alt Gr + 8) Press return at the end of the line. What happens? Is there any other way to write the same matrix? Write A in the Command Window what happens? Write A; in the Command Window what happens? (If the line finishes with a ; MATLAB does not print that variable on the screen.) b) You can refer to the different rows and columns in matrix A. For example >> A(2,3) = 3 This means row 2, column 3 of the matrix, A. >> A(1,:) = This means row 1, all columns of the matrix A. 2

3 >> A(:,3) = This means all rows, column 3 of matrix A >> A(:,:) This means all rows and all columns of matrix A. c) These are the most common operators +, -,.*,./,.^ Multiply the data in the matrix by 2. There are two ways to do this. Either you write >> A(:,:).*2 OR >>A.*2 which gives you an ans, and then the new matrix, or you assign a name, in this case B, to the answer, and write >> B=A(:,:).*2. Try both. Note that every time you get an ans from MATLAB, the old ans is over written, i.e. if you want to keep a result for long-term use, it is wise to give it a name. Remember to give it a name, which always start with a letter, and do not have any spaces in it. Note that Matlab differentiates between large and small letters, i.e. a is not the same as A Also, Matlab differentiates between the dot product (or scalar multiplication) and the cross product. To multiply a matrix by a scalar (or calculate the dot product) use.* For matrix multiplication (cross products), just use * The same is true for /. Use./ for scalar division. c) Now we have two matrices, A and B. A = B = Lets subtract the second column from A from the third column in B, and call the result C: >> C=(B(:,3)-A(:,2)) 3

4 C = Notice that it is not possible to subtract a column from a row. Matrix dimensions must always agree, which means that the columns must be of equal length; i.e. have the same number of rows. Maybe we want to add this C column to our earlier ones, as a forth column in A: Then write >> A=[A(:,:),C(:,1)] (This means include all rows and columns from A, and the column from C ) The [ ] angle brackets are important for joining two matrixes. Or, maybe you want to make C into a row vector instead of a column vector >> D=C d) Check how many variables we have by typing who, or whos. Look at the different answers. Make sure you understand the information. Save your work by writing save followed by the name you choose, followed by the variable names you want to save. If you do not define you variables, all of them will be saved. In my case it looks like this if I just want to save the vector C. >> save mywork C Now clear all variables, so that the Command Window has nothing left, by using clear and then the variable name, or even clear all. Programming in Matlab Matlab contains many small programs which you can use. For example: YI = INTERP1(X,Y,XI) interpolates to find YI, the values of the underlying function Y at the points in the vector XI. 4

5 The vector X specifies the points at which the data Y is given. To find out how to use a program, type help and then the name of the program, eg. >>help interp1 There are many similar programs for all sorts of functions within Matlab. Some are very simple, for example calculating the area of a circle from the radius, others calculate statistics, some analyse signals, some even can detect edges within an uploaded image file. You can also write your own program, like interp1, to make some calculations on some data. Let s try writing our own program to calculate the area of a circle. 1. What input do you need? The radius, R, and pi. (Pi is already defined with matlab, just type pi) 2. What output will we get? A, the area of the circle. 3. Create a new m file. Go to File, New, M-file 4. Type in the calculation A=pi*R^2 5. Add comments so you can understand the program later. Use % so the program knows that what follows is a comment, e.g. % This program calculates the area of a circle from the radius, R. 6. In the Matlab workspace, give R a value, e.g. R=2 7. In the m-file editor, go to Debug, Save and Run. This allows you to run the program to check that it works. You will have to give the program a name. Call it CircleArea.m 8. When you know the program works, you can define it as a function (a program which you can call within Matlab). In the first line of the program write: function [A]=CircleArea(R), Save the program. 9. Now you can run the program within the Matlab command window by typing: >>CircleArea(3) The output should be the area of a circle with radius 3. You can try again for a different circle >>CircleArea(8.46) 5

6 NOTE!!! Always remember to save an m-file, before running it, so that your latest commands are included. A quick way to run an m-file is to choose Debug - Save and Run from the top menu in the m-file window, or just press the key F5. If your script contains a fault, MATLAB will give you an error message, often referring to the line with the bug. You can always check your script by copying a couple of lines into the Command Window and in that way run the script step by step. 4. Understanding loops with for end Loops with for end commands are useful when we want to repeat a calculation, or a search, within a matrix. We will test this by first creating a matrix such as: >> Table=[ ; ; ] Table = Now we want to create a loop, which helps us to pick certain numbers from the matrix, and print them. Open an m-file, and write the following: for j=1:3 for i= 1:2 Table(i,j) end end Save the program and run it, by writing the filename in the command window. What does it mean? The script is made up of 2 loops, where the second one is nested in the first. The first line defines in which column (which we here have called j), the search should start and end, in this case column 1 to 3. This starts the first loop. The next row defines the row (called i), where we will start and end, in this case row 1 to 2. This is the nested loop. The third line says that we want to see our pick from the i rows in the j columns in our variable table. Then the loops are closed, with an end for each loop. After the loop is run the screen is showing: 1 6

7 Now try to modify the script to pick the 3 rd row in the 3 rd and 4 th columns. Which numbers do you get? For some reason you might want to swap the rows, so that they become columns. This is easily done by writing a ' just after the variable name, such as; Table'. Table' Please also look at using IF ELSEIF..END IF.END WHILE..END 5. Your own exploring time At the Mathworks homepage there are some lessons/tutorials which can be reached at You could also turn to the help in MATLAB directly. Make sure you know how to create a variable select certain rows or columns from a large matrix use the most common commands such as max min nanmin sum isnan isfinite find who whos (Also try length, size, datevec, datenum) 7

8 create a nice plot save and load data and files create and run an m-file understand the help in MATLAB know the basics of conditionals and loops (overview given in lecture) 8