DELTAE allows for plotting by automatically incrementing (or decrementing) one or two independent variables, and tabulating these together with one or more output variables in a file named something.plt. Users can then manipulate and/or plot that file with their favorite graphics or spreadsheet software. We illustrate these features with a continuation of the same example, a plane-wave resonator.
We use the same input file as before, planewav.in. Execute DELTAE and choose this as input file. Check the vector status summary:
Iteration Vectors Summary: GUESS 0d 0e name BEGIN:|p|@0 BEGIN:Ph(p) value 1.00E+03 90. units Pa deg TARGET 4a 4b name HARDEND :R(1/Z HARDEND :I(1/Z units value .00 .00
Now inspect the Plotted parameter summary (type capital ``P"):
Dependent Variables (outputs): PLOTS 0A 0B name BEGIN:|p|@0 BEGIN:Ph(p) units Pa deg
Keep these parameters as the dependent variables to be plotted (they are copies of the guesses). To set up the independent variables, select ``plot another variable." We will make a two-dimensional plot, letting f go from 80 Hz to 339.5 Hz in 1.5-Hz steps in the inner loop, and using two values of mean pressure-1000 Pa and 100,000 Pa-in the outer loop. DELTAE prompts for these entries in the ``range" selection. As before, if you can't remember the segment-number and line-letter codes for frequency and mean pressure, ``display" segment 0 to find out. After entering these values, check the Plotted parameter summary again:
Dependent Variables (outputs): PLOTS 0A 0B name BEGIN:|p|@0 BEGIN:Ph(p) units Pa deg Indpendent Variables (inputs): Outer loop: 0a BEGIN:Mean Beg= 1.00E+03 End= 1.00E+05 Step= 9.90E+04 Inner Loop: 0b BEGIN:Freq. Beg= 80. End= 3.40E+02 Step= 1.5
Now do a (r)un. DELTAE will step through the variables selected (taking a minute or two on a 286). When it has finished, exit to the operating system, and find two new files. The file planewav.des gives headings of what has been tabulated:
BEGIN:Mean BEGIN:Freq. BEGIN:|p|@0 BEGIN:Ph(p)
Pa Hz Pa deg
0a 0b 0A 0B
and planewav.plt is the table of values:
* 1000.0 80.00 1000.0 90.00 * 1000.0 81.50 1000.0 90.00 * 1000.0 83.00 1000.0 90.00 * 1000.0 84.50 1000.0 90.00 * 1000.0 86.00 1000.0 90.00 1000.0 87.50 5.095 23.89 1000.0 89.00 5.398 16.33 1000.0 90.50 5.598 8.033 1000.0 92.00 5.656 -0.6461 . . . 1.0000E+05 87.50 -370.7 265.4 1.0000E+05 86.00 -328.6 265.8 1.0000E+05 84.50 -293.7 266.0 1.0000E+05 83.00 -264.1 266.3 1.0000E+05 81.50 -238.6 266.4 1.0000E+05 80.00 -216.4 266.6
Notice that the first few lines of planewav.plt begin with ``*" and their values do not make much sense. The asterisk signifies that DELTAE did not converge to a solution it judged accurate, so these data may be invalid. (We could have avoided this by giving DELTAE a better initial guess for |p| and phase(p/i> ), but we chose instead to let DELTAE seek a solution.) Warning messages on the screen as each of these points was calculated. Once it converged (at 87.5 Hz) DELTAE was in no danger of getting lost again because it always uses its previous solution as its initial guess, and with such small frequency increments the previous solution is an excellent guess. Notice also, that DELTAE alternates the order in which it calculates the points of the inner loop (frequency, here). This process is motivated by the quality of initial guesses; `zig-zagging' thus, DELTAE must spend only a brief time searching for the start point of the inner loop each time it begins a new cycle.
We brought this file into a spreadsheet/graphics program to fix it up for plotting. We removed the asterisked lines and the minus signs from |p| , then added 180 degrees to phase(p ) to improve the looks of the the graphs. We also plotted |p|/pm (instead of just |p/i>|). The resulting plots are shown in Figs. II.2. (The lower quality-factor curves are for the lower mean pressure, of course.)
Figure II.2: Pressure and phase vs. frequency for the plane-wave resonator.