Matlab Tutorial 1: Working with variables, arrays, and plotting

Transcription

1 Matlab Tutorial 1: Working with variables, arrays, and plotting Setting up Matlab First of all, let's make sure we all have the same layout of the different windows in Matlab. Go to Home Layout Default. On the top, you will see a bar with your current folder. At the beginning of each Matlab session, it is important to select your working folder. To make life easier, all files you save and load should be contained within this working folder. On the left of the Matlab window, you will see the contents of this folder. On the bottom (or througout the middle of the window if you don't have an open window in the editor), you will see the "Command Window". This gives you access to a command line, which basically can be thought of as a glorified calculator. Type, for example, the following line and press ENTER. 1+1 ans = 2 You will get the expected answer. Now, you could write your code in this Command Window. The problem is that, once you quit Matlab, you will lose everything you typed! Therefore, it's a much better idea to keep a record of your commands by writing scripts or functions. Writing scripts On the top left you will see a menu tab called "Home". Click on it and then click on "New Scipt". A new window should have opened. Let's now try to write a script for doing 1+1. First, type it into the script. Second, go to the "Editor" menu tab and click on the "Run" green arrow. If you're running this script for the first time, Matlab will prompt you to save the file within your working folder. Give it a name, keeping in mind that you cannot have spaces in the file name. After saving the file, Matlab will run the script and output the result in the Command Window. From now on, every time you want to run your script you can click on "Run". Matlab will save it automatically. As an alternative, you can also select the lines of code you want to run, right-click with your mouse and select "Evaluate Selection". Throughout these tutorials, we will be running lines one by one and showing you the result right below. Finally, one of the most important things to do with your code is to document it well! What this means is that you should always include information in your scripts that help others understand what you did and why you did it. This will be also useful for you if you need to come back to this script after some time. To write a comment in Matlab, you just start a line with "%". Matlab will ignore anything written afterwards such as % This is a comment Note that you can even write a comment inline with a command such as 1+1 %Adding one to one ans = 2

2 Again, commenting is a fundamental part of good programming ethiquette. Defining variables and operating on them In Matlab, most of the time we will want to store information such as numbers into variables so that we can do arithmetic operations on these variables. To get started, let's define a variable a and let's save the number 2 in it. a=2 a = 2 Note that the result you get in the Command Window. Also, not that the variable a is now shown in the "Workspace" to the right of the Matlab window. Here you can see all the variables that are being currently stored in memory. We can operate on this variable by doing a*2 ans = 4 and we could even save the result of this operation into a new variable b b=a*2 b = 4 Now, the result of our calculation is saved in the variable b. Note that every time we run each line, we get an output in the Command Window. However, we might not always want an output there. This will become useful when operating on large lists of numbers: we want to do math with them, but we don't want to display every step in the Command Window. To suppress the output, we just need to add semicolon at the end of each line we don't want an output for. For example, c=10; defines the variable c, but doesn't give any output in the Command Window. Later on, if we want to display the value of c, we just need to do c c = 10 to output it. Defining, accessing, and operating on lists of numbers Sometimes, we will want to save more than one number in a variable. For example, let's save a set of numbers in the variable d

3 d=[1,5,7,2,10]; This is called an array or a vector. If you want to extract the number stored in position 3 of vector d, you just need to do d(3) ans = 7 Conversely, if you want to modify the content of a specific element of d, you do d(4)=5 d = 1x5 double resulting in the replacement of the 4th element in this particular example. Finally, you can also ask Matlab to access a range of elements in a vector. For example, let's get the 3rd, 4th, and 5th element of the vector d. d([3,4,5]) ans = 1x3 double An alternative approach would have been to use the colon operator, which gives you a range of numbers. For example, 3:5 ans = 1x3 double such that we can also extract vector elements by doing d(3:5) ans = 1x3 double Note that, just like in the case of simple variables containing only one number, we can do arithmetic operations on the vector d. For example, we can sum d+1 ans = 1x5 double

4 which adds 1 to every element or the vector, or we can multiply each element by doing d*5 ans = 1x5 double However, we need to be careful when carrying out operations such as division and when raising vectors to a power. For example, we get an error if we try to do "1/d". The reason this error occurs is because Matlab is used to thinking about variables as matrices. Taking the inverse of a Matrix is an operation that only makes sense for a square matrix. d is a one-dimensional vector, for which this operation is not well defined. Of course, this wasn't our objective. We just wanted to calculate the inverse of each element inside d. This can be done using the operator "." such that we get 1./d ans = 1x5 double Note that what the operator "." did is just tell Matlab to perform the operation on each element of the vector. The same operator can be used for many other calculations such as taking the square of a vector d.^2 ans = 1x5 double Working with matrices Matlab can also work on sets of numbers arranged in a 2D matrix. When creating such a matrix, numbers within the same row are separated by a comma, while numbers in different rows are spearated by a semicolon. For example, a=[1,2,3;4,5,6;7,8,9] a = 3x3 double We can operate on matrices in the same way as with vectors, as explained in the previous section. In order to extract or modify a specific element of this matrix, it is important to remember that Matlab always operates on rows first, and then on columns. Basically, if we want to extract the number saved in row 2, column 3 of our matrix a, we do a(2,3)

5 ans = 6 We can also ask Matlab to give use all elements in one row or column using the colon operator. For example, let's get all elements in column 2 a(:,2) ans = 3x1 double This feature will become extremely useful later on as we need to extract different kinds of information from matrices. Making plots Finally, let's use what we learned to plot the simple function x^2. Remember that a curve on a plot is just a set of points with given x and y coordinates. Thus, if we want to plot the function x^2, we first need to define the values of x we want to plot this function for. Let's start then by defining these values x=[0,1,2,3,4,5,6,7,8,9,10]; and calculating the corresponding y values y=x.^2; noting that we used the "." operator. We're now ready to make our first plot using the function plot. This function can take two arguments: the x and y values. If you want to learn how to use a given function in Matlab, you can do multiple things. First, you can move your mouse cursor over plot in your script and press F1. Second, you can go the the help by clicking on the question mark on the top bar of the Matlab window and search for the function plot. Finally, you can just type help plot plot Linear plot. plot(x,y) plots vector Y versus vector X. If X or Y is a matrix, then the vector is plotted versus the rows or columns of the matrix, whichever line up. If X is a scalar and Y is a vector, disconnected line objects are created and plotted as discrete points vertically at X. plot(y) plots the columns of Y versus their index. If Y is complex, plot(y) is equivalent to plot(real(y),imag(y)). In all other uses of plot, the imaginary part is ignored. Various line types, plot symbols and colors may be obtained with plot(x,y,s) where S is a character string made from one element from any or all the following 3 columns: b blue. point - solid g green o circle : dotted r red x x-mark -. dashdot c cyan + plus -- dashed m magenta * star (none) no line

6 y yellow s square k black d diamond w white v triangle (down) ^ triangle (up) < triangle (left) > triangle (right) p pentagram h hexagram For example, plot(x,y,'c+:') plots a cyan dotted line with a plus at each data point; plot(x,y,'bd') plots blue diamond at each data point but does not draw any line. plot(x1,y1,s1,x2,y2,s2,x3,y3,s3,...) combines the plots defined by the (X,Y,S) triples, where the X's and Y's are vectors or matrices and the S's are strings. For example, plot(x,y,'y-',x,y,'go') plots the data twice, with a solid yellow line interpolating green circles at the data points. The plot command, if no color is specified, makes automatic use of the colors specified by the axes ColorOrder property. By default, plot cycles through the colors in the ColorOrder property. For monochrome systems, plot cycles over the axes LineStyleOrder property. Note that RGB colors in the ColorOrder property may differ from similarly-named colors in the (X,Y,S) triples. For example, the second axes ColorOrder property is medium green with RGB [0.5 0], while plot(x,y,'g') plots a green line with RGB [0 1 0]. If you do not specify a marker type, plot uses no marker. If you do not specify a line style, plot uses a solid line. plot(ax,...) plots into the axes with handle AX. plot returns a column vector of handles to lineseries objects, one handle per plotted line. The X,Y pairs, or X,Y,S triples, can be followed by parameter/value pairs to specify additional properties of the lines. For example, plot(x,y,'linewidth',2,'color',[.6 0 0]) will create a plot with a dark red line width of 2 points. Example x = -pi:pi/10:pi; y = tan(sin(x)) - sin(tan(x)); plot(x,y,'--rs','linewidth',2,... 'MarkerEdgeColor','k',... 'MarkerFaceColor','g',... 'MarkerSize',10) See also plottools, semilogx, semilogy, loglog, plotyy, plot3, grid, title, xlabel, ylabel, axis, axes, hold, legend, subplot, scatter. Reference page for plot Other functions named plot in the command window. You'll find all sorts of interesting information about the capabilities of the "plot" command. Let's give it a try. plot(x,y)

7 Note that Matlab connected the dots with lines. If we want it to just display the dots we can do plot(x,y,'.')

8 Finally, if we want dots connected by lines, we do plot(x,y,'.-') Our current plot presents a significant flaw: it has no axis labels! Let's add those by doing xlabel('x') ylabel('y')

9 Note that "x" and "y" were strings, which is a fancy name for text. That's why we had to input them into xlabel and ylabel between apostrophes. Finally, it will not always be a good idea to type all possible x values by hand, especially, if you have more than 10. Instead, we can use convenient functions such as linspace. Let's say that we want to create 100 equally spaced numbers between 0 and 10. We can do this by typing x=linspace(0,10); We now recalculate y y=x.^2; and make the plot plot(x,y,'.') xlabel('x')

10 Note how we have dramatically increased the density of x points without having to type them one by one. This will become very useful when we try to plot diverse functions.