PLOT command

Withinthe Module functionswecouldhaveplacedasemicolon afterthe Plot commands. 

Activating the Define Plot command in the Output pull-down menu sets the button... 

Printer Setup... allows you to select and configure the output device from a list of all devices known to the MS-WINDOWS operating environment. Print... open.s the same dialog box, but includes the plot command. 

Develop a plotting code for Problem 1 that is based on the plotting commands in poly9.m on p. 27. (You will probably not need to use the subplot(.. . )... 

The command hold on after the first plot command ensures that all plots appear in the same graph. The command hold off at the end of our multiple plottings makes sure that the picture of one solveadiabxy run is not preserved in the figure window and that subsequent solveadiabxy plots for different data are not appended to the earlier plots, but rather drawn by themselves. 

These indicate the limit of our successful numerical BVP integrations near the bifurcation points. In between the x and o marks on the middle branch, the curve is drawn using interpolation of our successful BVP solutions data, while in between two adjacent x or two adjacent o marks, the curve is drawn by extrapolating nearby computed function data. This is done automatically by MATLAB s plot commands. 

There are several ways to create new graphs. The simplest is by a plotting command as discussed in the next sections. A new window consisting of a hgure is created. Unless indicated otherwise, each time a graphics command is executed, the graph in the figure window is overwritten. 

Plots can be made in Maple using the plot command > plot(y,y=0..1) ... 

Call Maple s plotting package by using the with(plots) command. 

Call with(linalg) and with(plots) commands. 

For a given set of parameters, one can plot the profiles by using Maple s plot command. 

Step 4 The result is shown in Figure 8.2. Now that you have a validated code, you can vary the parameters to see theii" effect. Figure 8.2 shows the concentrations, but it is difficult to distinguish between the curves when the figure is in black and white. You can plot each concentration with a different symbol by replacing the plot command with the following command. 

Now the output from ode45 is a vector, t, and a matrix, y. The vector y has as many columns as there are unknowns (here called TV), and it has as many rows as there are elements in the vector t. Once the solution is found, aU components of it can be plotted. See other commands under the plotting commands for other options. 

Sometimes you want to prepare several plots, examine them in turn, and decide whether to save them or print them. One way to do this is to insert the following command after the plot command ... 

Parameter estimation, that is the extraction of individual rate constants, was accomplished by a command ESTIMATE. Here the rate constants are varied until the best fit between the observed and calculated values are obtained. With the rate constants in this system covering five orders of magnitude in range, and somewhat limited amount of concentration data, it was often necessary to change the rate constants after the ESTIMATE procedure. This is done interactively through repeated use of SET, START, and PLOT commands. One such plot is shown in Figure 2. The lines in Figure 2 represent the calculated values, whereas the points represent the observed values. Arrhenius parameters for individual reactions are then calculated from the rate constants at three temperatures. These constants are then used in the REACTOR model. 

There are a host of different ways to adjust the look of the two-dimensional plots that we make in Mathematica. These adjustments are referred to as Graphics Options. To see what option we have in the Plot command we can use the double question mark command. 

Within the Module functions we could have placed a semicolon after the Plot commands. This would have allowed the graphs to be rendered, but the output "Graphics" would have been lost. We need the "Graphics" in order to plot arrays of these two functions with varying values of n. Therefore, we have left the semicolon out of the Modules. We can now use these in arrays and stacks. 

Another elegant way of saving the simulation to the workspace and then plotting the results proceeds as follows. Double click on the scope and select the Parameters option (second from the left). Select Data History and select the Save data to workspace option. Enter an appropriate name and select Array as format. Subsequently, select Apply and OK. After you run your simulation again, a variable with the name y will exist. The file y.mat contains three column, the first one is the time, the second one variable y 1, the second one variable y2. You can now use the plot command to visualize the process variables, for example plot (y( ,l),y( ,2), r, y( ,l),y( ,3), b ). 

Figure 1.12 The plot of the cosine function over the interval [-n, n] using the plot command. 

MATLAB allows users to change the color as well as the line style of graphs using a third argument in the plot command. For example, using the same arguments used to generate the plot shown in Fig. 

NOTE If you do not define the color attributes, then by default MATLAB currently cycles through the colors blue, green, red, cyan, magenta, yellow, and black when creating multiple lines with a plot command, as shown in Fig. 1.16b. 

Figure 3.6 The plot of f(x) using the MATLAB plot command. 

Second, create callmultiode.m (a script M-file) that contains the initial value for eachy the lower and upper limit for integration the options attributes, which is a structure of optional parameters that change the default integration properties a call to the MATLAB ode45 solver and a plot command fory as a function of t. Figure 7.7 embodies such a list of commands. 

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