MATLAB Demystified phần 3 ppt

56 MATLAB Demystifi ed For the current example we replaced >> f = exp(-t)*sin(t); with y = exp(-1.2*x).*sin(10*x + 5);. The difference is that in the second case, we used matrix multiplication (indicated by typing .*). Well we are back to the old plot(x, y) command. What are some other ways we can spruce up your basic two-dimensional plot? One way is to add a grid to the plot. This is done by adding the phrase grid on to your plot statement. For the next example, we will plot y = tanh(x) over the range −6 ≤ x ≤ 6 with a grid display. First we define our interval: >> x = [–6:0.01:6]; Next, we define the function: >> y = tanh(x); The plot command looks like this, and produces the plot shown in Figure 3-7. Plot(x,y),grid on Figure 3-6 A labeled plot generated with the fplot command CHAPTER 3 Plotting and Graphics 57 The Axis Commands Figure 3-7 A plot made with the grid on command MATLAB allows you to adjust the axes used in two-dimensional plots in the following way. If we add axis square to the line containing the plot command, this will cause MATLAB to generate a square plot. If we type axis equal, then MATLAB will generate a plot that has the same scale factors and tick spacing on both axes. Let’s return to the example y = tanh(x), which we plotted in Figure 3-7. If you run this plot with axis square, you will get the same plot that we did using the default settings. But suppose that we typed: >> plot(x,y),grid on, axis equal In this case, we get the plot shown in Figure 3-8. Notice that the spacing used for the y axis in Figure 3-7 and Figure 3-8 are quite different. In the first case, the spacing used on the vertical or y axis is different than the spacing used on the x axis. In contrast, in Figure 3-8, the spacing is identical. 58 MATLAB Demystifi ed As you can see from this dramatic example, we can use the axis command to generate plots that differ quite a bit in appearance. Hence we can use the command to play with different plot styles and select what we need for the particular application. To let MATLAB set the axis limits automatically, type axis auto. This isn’t necessary, of course, unless you’ve been playing with the options described here. Showing Multiple Functions on One Plot In many cases, it is necessary to plot more than one curve on a single graph. The procedure used to do this in MATLAB is fairly straightforward. Let’s start by showing two functions on the same graph. In this case let’s plot the following two functions over 0 ≤ t ≤ 5: f(t) = e −t g(t) = e −2t Figure 3-8 Plotting y = tanh(x) using the axis equal option CHAPTER 3 Plotting and Graphics 59 We will differentiate between the two curves by plotting g with a dashed line. Following the usual procedure, we first define our interval: >> t = [0:0.01:5]; Next, we define the two functions: >> f = exp(–t); >> g = exp(–2*t); To plot multiple functions, we simply call the plot(x, y) command with multiple pairs x, y defining the independent and dependent variables used in the plot in pairs. This is followed by a character string enclosed in single quotes to tell us what kind of line to use to generate the second curve. In this case we have: >> plot(t,f,t,g,' ') This tells MATLAB to generate plots of f(t) and g(t) with the latter function displayed as a dashed line. Note that while we can’t show it in the book, MATLAB displays each curve with a unique color. The result is shown in Figure 3-9. MATLAB has four basic line types that can be defined in a plot. These are, along with the character strings, used to define them in the plot command: • Solid line ′-′ • Dashed line ′ ′ Figure 3-9 Plotting two curves on the same graph 60 MATLAB Demystifi ed • Dash-dot line ′ ′ • Dotted line ′:′ Let’s generate the same graph as in Figure 3-9 making the curve f(t) = e −t appear with a dotted line. The command is plot(t,f,':',t,g,' ') This generates the plot shown in Figure 3-10. If you want to plot all curves using solid lines and simply differentiate them by their colors, just leave off the character string specifying the curve type. The plot will be generated using solid lines, which is the default. Adding Legends A professionally done plot often has a legend that lets the reader know which curve is which. In the next example, let’s suppose that we are going to plot two potential energy functions that are defined in terms of the hyperbolic trig functions sinh(x) and cosh(x) for 0 ≤ x ≤ 2. First we define x: >> x = [0:0.01:2]; Figure 3-10 Using a dotted line to represent f(t) = e −t and a dashed line to represent g(t) = e −2t CHAPTER 3 Plotting and Graphics 61 Now we define our two functions. There is nothing magical about calling a function y or anything else in MATLAB, so let’s call the second function z. So we have >> y = sinh(x); >> z = cosh(x); The legend command is simple to use. Just add it to the line used for the plot(x, y) command and add a text string enclosed in single quotes for each curve you want to label. In our case we have: legend('sinh(x)','cosh(x)') We just add this to the plot command. For this example, we include x and y labels as well, and plot the curves using a solid line for the first curve and a dot-dash for the second curve: >> plot(x,y,x,z,' '),xlabel('x'),ylabel('Potential'),legend('sinh(x)','cosh(x)') The plot that results is shown in Figure 3-11. The legend didn’t originally show up where it is in the figure, and it probably won’t do so on your system either. To move the legend to a more favorable position that might be better for printing or display, just hold the mouse pointer over the legend and drag it to the location where you want it to display. Figure 3-11 A plot of two curves that includes a legend 62 MATLAB Demystifi ed Setting Colors The color of each curve can be set automatically by MATLAB or we can manually select which color we want. This is done by enclosing the appropriate letter assigned to each color used by MATLAB in single quotes immediately after the function to be plotted is specified. Let’s illustrate with an example. Let’s plot the hyperbolic sine and cosine functions again. This time we’ll use a different interval for our plot, we will take −5 ≤ x ≤ 5. So we define our data array as >> x = [–5:0.01:5]; Now we redefine the functions. Remember if we don’t do this and we’re in the same session of MATLAB, the program is going to think that the functions are defined in terms of the previous x we had used. So now we type: >> y = sinh(x); >> z = cosh(x); Now we will generate the plot representing y with a red curve and z with a blue curve. We do this by following our entries for y and z in the plot function by the character strings ′r′ and ′b′ respectively. The command looks like this: >> plot(x,y,'r',x,z,'b') Try this on your own system to see the plot it generates. Now, it is possible to set more than one option for each curve. So let’s use the colors red and blue for the curves, and set the cosh function (the blue curve) to draw with a dashed line. This is done in the following way, enclosing all of the plot options for the selected curve within the same set of quotes: >> plot(x,y,'r',x,z,'b ') This gives us the plot shown in Figure 3-12. You can’t see it in the black and white image, but the dashed line prints on screen as a blue curve. MATLAB gives the user eight basic color options for drawing curves. These are shown with their codes in Table 3-1. CHAPTER 3 Plotting and Graphics 63 Figure 3-12 A plot generated setting colors and line types with the same command Table 3-1 MATLAB specifiers for selecting plot colors. Color Specifier White w Black k Blue b Red r Cyan c Green g Magenta m Yellow y 64 MATLAB Demystifi ed Setting Axis Scales Let’s take another look at the axis command and see how to set the plot range. This is done by calling axis in the following way: axis ( [xmin xmax ymin ymax] ) Suppose that we want to generate a plot of y = sin(2x + 3) for 0 ≤ x ≤ 5. We might consider that the function ranges over −1 ≤ y ≤ 1. We can set the y axis to only show these values by using the following sequence of commands: >> x = [0:0.01:5]; >> y = sin(2*x + 3); >> plot(x,y), axis([0 5 –1 1]) This generates the plot shown in Figure 3-13. Now let’s make a plot of y = e −3/2x sin(5x + 3). First we try 0 ≤ x ≤ 5, −1 ≤ y ≤ 1. >> y = exp(–1.5*x).*sin(5*x+3); >> plot(x,y), axis([0 5 –1 1]) This generates the plot shown in Figure 3-14. As you can see from the figure, the range used for the y axis could be adjusted. Figure 3-13 A plot generated manually setting the limits on the x and y axes for a plot of y = sin(2x + 3) for 0 ≤ x ≤ 5 CHAPTER 3 Plotting and Graphics 65 Let’s try adjusting the range of y values on the plot, so that −0.7 ≤ y ≤ 0.3. We do this by adjusting the axis command as follows: >> plot(x,y), axis([0 5 –0.7 0.3]) This gives us a much tighter view of the graph, as shown in Figure 3-15. We aren’t restricted to plot only over the entire set of values of x we use to generate a function. To see what we mean by this, let’s generate a couple of plots of y = sin 2 (5x). First as an aside, let’s make a note of how one would square the sin function in MATLAB. If you type: >> y = sin(5*x)^2 MATLAB is going to lash out at you: ??? Error using ==> mpower Matrix must be square. The correct way to square the sin function is to use the arraywise power notation, which uses A. ^B to represent A B . Hence the following command will work >> y = sin(5*x).^2; Figure 3-14 A plot of y = e −3/2x sin(5x + 3). First we try 0 ≤ x ≤ 5, −1 ≤ y ≤ 1 [...]... the function, shown in Figure 3- 34 In situations like this, engineers often like to generate stem plots This is easily done in MATLAB using the stem(x,y) command The command we use in this case is: >> stem(t,f),xlabel('time(sec)'),ylabel('spring response') Figure 3- 34 The same function shown in Figure 3- 33, with a coarse sampling interval MATLAB Demystified 84 Figure 3- 35 The spring response example... function: >> contour(x,y,z),xlabel('x'),ylabel('y') MATLAB Demystified 88 Figure 3- 39 A contour map of z = cos(x)sin(y) with −5 ≤ x ≤ 5, 3 ≤ y ≤ 3 The result is shown in Figure 3- 41 Next, we will generate the three-dimensional contour plot If we just type in contour3(x, y, z, 30 ), we get the image shown in Figure 3- 42 Figure 3- 40 Our first call to contour3 for z = cos(x)sin(y) .. .MATLAB Demystified 66 Figure 3- 15 The plot of y = e 3/ 2x sin(5x + 3) with −0.7 ≤ y ≤ 0 .3, generated by using axis([0 5 –0.7 0 .3] ) This squares each element of the array, instead of the array as a whole Now let’s plot it using the automatic settings If we just type plot(x, y), then MATLAB generates the plot shown in Figure 3- 16 Figure 3- 16 The result of plot(x,y) where y = sin2(5x) CHAPTER 3 Plotting... specification of increment in each case So suppose that we’re going to plot some function z = f(x, y) where −5 ≤ x ≤ 5, 3 ≤ y ≤ 3 If we chose our increment in both cases to be 0.1, this simple call will do it: >> [x,y] = meshgrid(–5:0.1:5, 3: 0.1 :3) ; MATLAB Demystified 86 Figure 3- 37 A contour plot of z = x2 + y2 Next we enter the function we want to use For our first example, we try a simple function... set(h,'ShowText','on','TextStep',get(h,'LevelStep')*2) This time, MATLAB puts labels on each curve, as shown in Figure 3- 38 CHAPTER 3 Plotting and Graphics Figure 3- 38 87 Adding labels to contour lines Let’s try the same thing with z = cos(x)sin(y) The commands we use are: >> z = cos(x).*sin(y); >> [C,h] = contour(x,y,z); >> set(h,'ShowText','on','TextStep',get(h,'LevelStep')*2) This generates the contour map shown in Figure 3- 39 We can make the... filled diamonds, with green dashed lines We tell MATLAB to use green dashed lines by adding the string ‘—g’ to the arguments input to stem Redrawing the plot in Figure 3- 35 in this way produces the plot shown in Figure 3- 36 The command is: >> stem(t,f,' dg','fill'),xlabel('time(sec)'),ylabel('spring response') CHAPTER 3 Plotting and Graphics 85 Figure 3- 36 Stem plot generated using green, filled diamonds... = 0.01 and pretend it represents the response of a spring to some force Let’s plot it in the continuous case to see CHAPTER 3 Plotting and Graphics Figure 3- 31 A plot of test scores with labels generated with the set command Figure 3- 32 Test data shown on a bar chart 81 MATLAB Demystified 82 what it looks like when we take t out to 200 seconds The commands we enter for the continuous plot are: >>t =... time telling MATLAB to place this function in the second pane: >> subplot(1,2,2) MATLAB hasn’t put any data in there yet—remember we still have to call the plot command The figure now looks like that shown in Figure 3- 20 Now we plot it: >> plot(x,y),xlabel('x'),ylabel('exp(–2x)*sin(20x)'),axis([0 5 –1 1]) The result, two side-by-side plots, is shown in Figure 3- 21 70 MATLAB Demystified Figure 3- 20 The... graphics window has the plot shown in Figure 3- 23 A quick detour—notice that even though we defined our range of x values to be 0 ≤ x ≤ 2p, MATLAB has carried the graph out a bit further than where the function has been calculated We can fix that up by including the axis command in our call to plot(x,y): >> plot(x,sin(x)),axis([0 2*pi –1 1]) MATLAB Demystified 72 Figure 3- 22 A plot of cos(x) generated using... the nicer plot shown in Figure 3- 24 Returning to our dilemma, let’s say we have plotted cos(x) and want to overlay sin(x) on the same graphic We can do this with the following sequence of commands: >> x = linspace(0,2*pi); >> plot(x,cos(x)),axis([0 2*pi –1 1]) Figure 3- 23 We overwrite the previous plot by typing plot[x, sin(x)] CHAPTER 3 Plotting and Graphics Figure 3- 24 73 Now we fix the plot by calling . plot(x, y), then MATLAB generates the plot shown in Figure 3- 16. Figure 3- 15 The plot of y = e 3/ 2x sin(5x + 3) with −0.7 ≤ y ≤ 0 .3, generated by using axis([0 5 –0.7 0 .3] ) Figure 3- 16 The result. shown with their codes in Table 3- 1. CHAPTER 3 Plotting and Graphics 63 Figure 3- 12 A plot generated setting colors and line types with the same command Table 3- 1 MATLAB specifiers for selecting. [0:0.01:5]; >> y = sin(2*x + 3) ; >> plot(x,y), axis([0 5 –1 1]) This generates the plot shown in Figure 3- 13. Now let’s make a plot of y = e 3/ 2x sin(5x + 3) . First we try 0 ≤ x ≤ 5, −1