## Plotting

In this tutorial we will assume that you know how to create vectors and matrices, know how to index into them, and know about loops. For more information on those topics see one of our tutorials on**vectors, matrices, vector operations, or loops.**

In this tutorial we will introduce the basic operations for creating plots. To show how the

*plot*command is used, an approximation using Euler's Method is found and the results plotted. We will approximate the solution to the D.E. y'= 1/y, y(0)=1. A step size of h=1/16 is specified and Euler's Method is used. Once done, the true solution is specified so that we can compare the approximation with the true value. (This example comes from the tutorial on loops.)

>> h = 1/16; >> x = 0:h:1; >> y = 0*x; >> size(y) ans = 1 17 >> max(size(y)) ans = 17 >> y(1) = 1; >> for i=2:max(size(y)), y(i) = y(i-1) + h/y(i-1); end >> true = sqrt(2*x+1);Now, we have an approximation and the true solution. To compare the two, the true solution is plotted with the approximation plotted at the grid points as a green 'o'. The

*plot*command is used to generate plots in matlab. There is a wide variety of arguments that it will accept. Here we just want one plot, so we give it the range, the domain, and the format.

>> plot(x,y,'go',x,true)That's nice, but it would also be nice to plot the error:

>> plot(x,abs(true-y),'mx')Okay, let's print everything on one plot. To do this, you have to tell matlab that you want two plots in the picture. This is done with the

*subplot*command. Matlab can treat the window as an array of plots. Here we will have one row and two columns giving us two plots. In plot #1 the function is plotted, while in plot #2 the error is plotted.

>> subplot(1,2,1); >> plot(x,y,'go',x,true) >> subplot(1,2,2); >> plot(x,abs(true-y),'mx')Figure 1.

*The two plots from the first approximation*

Let's start over. A new approximation is found by cutting the step size in half. But first, the picture is completely cleared and reset using the

*clf*comand. (Note that I am using new vectors

*x1*and

*y1*.)

>> clf >> h = h/2; >> x1 = 0:h:1; >> y1 = 0*x1; >> y1(1) = 1; >> for i=2:max(size(y1)), y1(i) = y1(i-1) + h/y1(i-1); end >> true1 = sqrt(2*x1+1);The new approximation is plotted, but be careful! The vectors passed to

*plot*have to match. The labels are given for the axis and a title is given to each plot in the following example. The following example was chosen to show how you can use the

*subplot*command to cycle through the plots at any time.

>> plot(x,y1,'go',x,true1) ??? Error using ==> plot Vectors must be the same lengths. >> plot(x1,y1,'go',x1,true1) >> plot(x1,abs(true1-y1),'mx') >> subplot(1,2,1); >> plot(x,abs(true-y),'mx') >> subplot(1,2,2); >> plot(x1,abs(true1-y1),'mx') >> title('Errors for h=1/32') >> xlabel('x'); >> ylabel('|Error|'); >> subplot(1,2,1); >> xlabel('x'); >> ylabel('|Error|'); >> title('Errors for h=1/16')Figure 2.

*The errors for the two approximations*

Finally, if you want to print the plot, you must first print the plot to a file. To print a postscript file of the current plot you can use the

>> print -dps error.ps

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