PLOT statement

Only one variable can be plotted during program execution. In this case, concentration. A, is plotted versus time, using appropriate scaling commands of the PLOT statement... 

Program THERM solves the dynamic model equations. The initial values of concentration and temperature in the reactor can be changed after each run using the ISIM interactive commands. The plot statement causes a composite phase-plane graph of concentration versus temperature to be drawn. Note that for comparison both programs should be used with the same parameter values. 

The PLOT statement usually appears in the DYNAMIC part of the model and controls the output to the screen during a run after a START command. Only two variables may be specified. The format of this command is PLOT X variable, y variable, xmin, xmax, ymin, ymax... 

A variable listed in a PLOT statement or command does not appear in the symbol table of the main program. 

Note that PROC BOXPLOT uses SAS/GRAPH statements such as GOPTIONS and SYMBOL statements. There is a vast array of display options in the PROC BOXPLOT PLOT statement not used here. You may want to investigate those options if you decide to enhance the box plot further. 

This is how we may do the plots with time delay (details in MATLAB Session 7). Half of the work is taken up by the plotting statements. 

We can use the LTI Viewer to do all the plots, not only step and impulse responses, but also more general time response and frequency response plots in later chapters. If we know how to execute individual plot statements, it is arguable whether we really need the LTI Viewer. Nonetheless, that would be your personal choice. We will provide here the basic idea and some simple instructions. 

Let us say that we would like to have two functions, say, sin(x) and cos(x), superposed one above the other. In this case, the plot statement will be ... 

On the other hand, if we want to characteri2e objects which are described by the rather fuzzy statement "numbers dose to three", we then need a membership function which describes the doseness to three. An adequate membership function could be the one plotted in Figure 9-25 m x) has its maximum value of m x) = 1 for value x = 3. The greater the distance from x to 3 gets, the smaller is the value of m x). until it reaches its minimum m x) = 0 if the distance from x to 3 is greater than say 2, thus for x > 5 or x < 1. 

The amount of curvature in plots like Fig. 2.2 is a measure of the deviation from Newtonian behavior. We can use the logic of calculus to argue that such curvature becomes less apparent as we examine progressively smaller segments of the line. This statement leads us to two important conclusions ... 

As can be seen for infinite recycle ratio where C = Cl, all reactions will occur at a constant C. The resulting expression is simply the basic material balance statement for a CSTR, divided here by the catalyst quantity of W. On the other side, for no recycle at all, the integrated expression reverts to the usual and well known expression of tubular reactors. The two small graphs at the bottom show that the results should be illustrated for the CSTR case differently than for tubular reactor results. In CSTRs, rates are measured directly and this must be plotted against the driving force of... 

Figure 3-9 shows plots of Eqs. (3-135) and (3-136) for some hypothetical systems. Obviously the equilibrium approximation is poor in the early stages of the reaction, but in the later stages the assumption can be quite good. The preequilibrium assumption, applied to Scheme XIV, amounts to the statement that 2 is negligible relative to ki and i. 

As originally proposed, the Zucker-Hammett hypothesis states that for A1 reactions log kobs is linear in —Ho, whereas for A2 reactions log kobs is linear in log ch+. This latter statement is now known not to be generally correct. Moreover, the slopes of plots against —Ho often differ from unity. Bunnett and Olsen... 

According to Eq. (3-7), a plot of In [A], - [AL will be linear. The plot has, as the negative of its slope, the sum k + k-. The implication that this data treatment yields a sum is at first surprising, because this rate constant characteristic of the equilibration is clearly larger than the forward rate constant alone. The net rate itself, on the other hand, is smaller than the forward rate, since the reverse rate is subtracted from it, as in Eq. (3-2). These statements are not contradictory, and they illustrate the need to distinguish between a rate and a rate constant. 

Values of all the variables, stored by the PREPARE statement can be plotted at the end of the simulation or after an interrupt, using the GRAPH command. The GRAPH T,A,B,C,D, command, for example, plots a combined post-mortem graph of all the concentrations with respect to the independent variable time... 

This series of program statements will plot CA against T on the screen as the simulation progresses. Values of T, CA, CB, CC and RATE will also appear on the screen. Subsequently, any of the variables T, CA, CB, CC and RATE can be plotted against any other variable by using the GRAPH command. 

Produce a post-mortem plot using data stored by means of a PREPARE statement. 1, 3, 4 are the run numbers. If the run list is omitted, all runs are plotted. X, Z etc., are the vertical variables. The last four parameters specify axis scaling and are optional, i.e., GRAPH X,Y,Z plots all runs with automatic scaling. 

Are always regarded as real and treated in a floating-point form. Examples 21, 36, 123, -62, -0.562, -0.137E-21, 98E2 Always start with a letter which may be followed by further letters or digits up to a maximum of 8 characters. Differential identifiers are identifiers followed by one or more primes ( ). Each counts as one character, consist of up to eight digits and may precede most executable statements (not PLOT or OUTPUT). 

Store values of A, B and T in a workfile This prepares data for post-mortem plotting of A, B and T. This statement is effective when LPRP is TRUE. 

Plot Y against X on the specified axis (X axis annotated from XMIN to XMAX, Y axis from -100 to 100) as the simulation proceeds PLOT or OUTPUT statements may not be conditional or labelled. 

Statement duplicated (DYNAMIC, OUTPUT, PLOT or PREPARE. Wrong number of arguments in PLOT (should be 6) or too many arguments in OUTPUT, SUBROUTINE, FUNCTION or ARRAY. (OUTPUT limited to 10, others to 15). 

Mean values could be added to the preceding plot by calculating the means for each treatment by visit and then merging them back with the seizures data. Then, a PLOT2 statement could be used in PROC GPLOT to overlay the mean values. The following is an example of a box plot modified in these ways. 

ADD TWO NEW SYMBOL STATEMENTS TO PLOT THE MEAN VALUES. symbol3 color = black value = dot symbol4 color = gray value = dot ... 

ADD NEW AXIS FOR PL0T2 STATEMENT BELOW. WHITE IS USED TO MAKE THE AXIS INVISIBLE ON THE PLOT. axis3 color = white... 

CREATE BOX PLOT. VISIT IS ON THE X AXIS, SEIZURES ARE ON THE y AXIS, AND THE VALUES ARE PLOTTED BY TREATMENT. THE PLOT2 STATEMENT IS RESPONSIBLE FOR PLACING THE MEAN VALUES ON THE PLOT. proc gplot... 

The Kaplan-Meier survival estimates plots are instantiated by specifying PLOTS = (S) in the PROC LIFETEST statement. To show just the line itself, CENSOREDSYMBOL = NONE is specified to hide the censored observations in the plot. EVENTSYMBOL = NONE is specified here to hide the event points, although this is the default setting for... 

PROC LIFETEST. Note how the GOPTIONS and SYMBOL statements are used by the PROC LIFETEST plots. However, AXIS statements and LEGEND statements are not used by PROC LIFETEST plots. 

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