EOSC 352 MATLAB Review

Transcription

1 EOSC 352 MATLAB Review To use MATLAB, you can either (1) type commands in the window (i.e., at the command line ) or (2) type in the name of a file you have made, whose name ends in.m and which contains a bunch of MATLAB commands. You can make a file of MATLAB commands in any editor as long as the file is saved as ascii text. To leave MATLAB type exit. In this document all MATLAB commands are in bold. Warning: your.m command files and data files (which I will provide for the homeworks) MUST be in the same directory you are running MATLAB from. Otherwise, MATLAB may not be able to find the files! Arithmetic and vectors Start by assigning numbers to variables and learning the format for math operations. a = 1 b = 2.3 a*b a/b Note that MATLAB names the answers ans and overwrites ans every time it calculates something. You can easily create vectors in MATLAB. The commands a = [ ] or a = [1,2,3,4] or a = (1:4) all do the same thing. They create a 1 row 4 column (1 by 4) vector: a = [ ] Okay - so MATLAB doesn t draw the brackets... Note that in the commands above, the colon (and round brackets) creates a vector with entries at intervals of 1 between the first and last entries. Typing b = (1:0.5:4) would create a vector with with 0.5 spacing (try it). To get the size (rows,columns) of this vector, type size(b). The transpose function is an apostrophe ( ) and it will change a row vector to a column vector. If you type a you will get a column vector: ans = We will use matrices a lot in this class. You will read several in from text files in this homework. If you type load SAF.ll then MATLAB will read the file into a variable called SAF (MATLAB chops off what is after the dot). How big is it? Note: to keep MATLAB from dumping its answers onto the screen, end each command line with a semicolon (;). This is especially important for big arrays. If you type SAF the whole 1

2 thing (6559 rows) will scroll by. If you type SAF; nothing will scroll (actually nothing will happen). Let s make a small array: a = zeros(3,3) This command makes a matrix of zeros: 3 rows and 3 columns. a(1:) = [1 2 3]; a(2,:) = [4 5 6]; a(3,:) = [10 2 4]; a MATLAB will print out a = See what the colon does: it stands in for all columns of row 1, all columns of row 2, and all columns of row 3. Type a(:,1) and MATLAB will print out a vector: it is all rows of column 1. This is a powerful tool for extracting rows and columns from matrices. For example, to get the longitudes of points along the San Andreas Fault (that is the first column in the N by 2 matrix SAF): lons = SAF(:,1); Similarly for latitudes (second column) type: lats = SAF(:,2); If you were to type SAF(1,:) (that is, without a semicolon) you would see one row containing two numbers: the lat and lon of the first point ( ). If you type SAF(1:10,:) then MATLAB will show you the first 10 rows of matrix SAF. MATLAB does more advanced matrix operations easily, too. To get the determinant of a, just type det(a). If you want to remember the determinant of a for future use, give the answer a name other than ans, which is always being overwritten, type mydeta = det(a) Other useful MATLAB functions are basic matrix arithmetic functions ( + - * / ), the dot product (dot(vec1,vec2)), cross product ( cross(a,b) ), and the gradient ( syntax is [FX,FY] = gradient(f) ). To learn how to use any command, type help and then the command name. For example, help gradient. Note that you have to create variables before trying out these commands, for example, you have to create vectors v1 and v2 before trying out the dot(vec1,vec2) command. One special function deserves note: if you want to multiply the vector entries by each other, but not do a full-blown matrix multiplication, you use the command.*. There is also a./ command which divides individual entries in vector or matrix a by individual entries in vector or matrix b. For example if we make matrix aa: 2

3 aa = then a./aa is ans = More info on doing simple arithmetic: clear deletes a variable, and clear all deletes all variables in your workspace. Figures The figure command gives you a new, empty figure window, and successive figure commands give you additional figures (figure 2, 3, etc.) (type help figure for more info if needed). clf clears the figure and close closes the most recently created figure. The command close all closes all figures. To practice making, destroying, and printing figures, type peaks at the prompt and an impressive color image will appear (dazzle your friends!). Congratulations - you have just run a MATLAB.m executable file. peaks.m is a canned MATLAB program, which is part of one of the Mathworks MATLAB tutorials. The plot command can make scatter and line plots. We use it in all of the MATLAB homeworks. There s a lot of info available on the plot command if you type help plot including different symbols, etc. Type plot(lons, lats) This makes a 2D line plot: a plain black line connects each of the (lon, lat) pairs in the file (all 6559 of them). The command plot(lons, lats, o ) plots a o at each (lat, lon) pair. The command hold on allows you to plot other quantities on the same figure without erasing what you just did. The axis command controls the size of the plotted region. The format is: axis ([ xmin xmax ymin ymax]); where xmin and xmax are the minimum and maximum x coordinates and ymin and ymax are the minimum and maximum y coordinates for the area you want to show. The Mathworks (company that makes MATLAB) has a useful MATLAB tutorial page for students. The URL is: This tutorial seems to assume that you ll be using Windows, and the lab computers are Windows boxes. 3

4 The Homework 2.m Files Open CA map.m in the text editing program of your choice. Go through it line by line. Everything in that file has been explained here, except some of the options in the plot commands (most of which are explained if you type help plot and look at the list of symbols and line styles). I renamed some things (e.g., f = CA flts; ) so I could use shorter names in the file (f instead of CA flts). The LineWidth option allows you to plot heavier or thinner lines (I want the SAF to stand out from the other faults). Open ll2xy for352.m. This file converts lon lat to (x,y), that is, (east, north). So why do I do the following: lons = lons - ones(lngth,1)*(lon 0);?? Answer: lons is a vector and lon 0 is a scalar value, which I want to subtract from each entry in the vector lons. If I want to subtract 3 (for example) from every entry in a vector, I must make a vector of 3 s which is the same size as the vector, and subtract it. The only other oddity is the fopen and fprintf command sequence, which writes tidily formatted output. A faster way to save the matrix xy in readable format is save xy xy -ascii -tabs which saves the values of variable xy in a file called xy. You can load xy by typing load xy An easy way to save all of the variables you have created is to type save allmyvariables This will create a file called allmyvariables.mat which contains all of your variables. To load them all, type load allmyvariables.mat The problem with this command is that you cannot open allmyvariables.mat in a text editor to see what s inside - only MATLAB can read a.mat file. This did not bother many students last year. To convert your files to x,y in kilometers you will have to change the input filename and the output filename as needed, save the file, and run the program. You will create 4 new files this way. For the lat lon file (vels scec3 t), use lats = p(:,1); lons = p(:,2); For the other files use lats = p(:,2); lons = p(:,1); Open CA map2.m. Every command in this file has been described. Open fastarrows 352.m. Everything in this file should look familiar except the quiver 4

5 command, which plots vectors (arrows) at specified (x,y) coordinates. Here is the command: quiver(v(:,1),v(:,2), east, north, 0, k ); v(:,1), v(:,2), east, and north are columns of length 840 (i.e., the number of GPS sites). v(:1) and v(:,2) are the x and y components of the position vector. East and north are the x and y (that is, east and north) components of the velocity vector. MATLAB automatically scales the lengths of these arrows to look good on the plot, if I set the fifth argument of the quiver function as 0. The k indicates that the arrows should be black (help plot tells you how to specify other colors). To add a scale arrow, you need another quiver command, which you can add yourself. quiver(50, 50, 60, 0, 0, k ); will make an arrow representing a velocity of 60 mm/yr (pointed east), at (x,y) = (50,50), that is, the southwest part of your plot. To label the scale arrow, use the gtext command. You would type gtext( 60 mm/yr ) and then click at the location on the figure where you want this text to go. You can move objects around in the figure by clicking and dragging using the edit figure tool on the figure window s menu bar (the icon is a boldface arrow pointed northwest, to the left of the A ). This is a good way to align things if you drop the text in an awkward spot on the figure. 5