pymininec 0.1.0

Test coverage: Making sure it is consistent with original Mininec

There are several tests against the original Basic source code, for the test cases see the subdirectory test. One of the test cases is a simple 7MHz wire dipole with half the wavelength and 10 segments. In one case the wire is 0.01m (1cm) thick, we use such a thick wire to make the mininec code work harder because it cannot use the thin wire assumptions. Another test is for the thin wire case. Also added are the inverted-L and the T antenna from the original Mininec reports. All these may also serve as examples. Tests statement coverage is currently at 100%.

There was a line that was flagged as not covered by the pytest framework. This is a continue statement in compute_impedance_matrix near the end (as of this writing line 1381). This looks like a bug in the test framework or in Python: When I set a breakpoint in the python debugger on the continue statement, the breakpoint is never reached. When I put an assignment statement before the continue statement, the continue statement is reported as covered by the tests and when I set a breakpoint it is reached. Note that the continue statement is executed properly, it is just not correctly reported to Python’s introspection. I’ve reported this as a bug in the pytest project and as a bug in python.

For all the test examples it was carefully verified that the results are close to the original results in Basic (see Running examples in Basic to see how you can run the original Basic code in the 21th century). The differences are due to rounding errors in the single precision implementation in Basic compared to a double precision implementation in Python. I’m using numeric code from numpy where possible to speed up computation, e.g. solving the impedance matrix is done using numpy.linalg.solve instead of a line-by-line translation from Basic. You can verify the differences yourself. In the test directory there are input files with extension .mini which are intended (after conversion to carriage-return convention) to be used as input to the original Basic code. The output of the Basic code is in files with the extension .bout while the output of the Python code is in files with the extension .pout. The .pout files are compared in the regression tests. The .pym files in the test directory are the command-line arguments to recreate the .pout files with mininec.py.

In his thesis [5], Zeineddin investigates numerical instabilities when comparing near and far field. He solves this by doing certain computations for the near field in double precision arithmetics. I’ve tried to replicate these experiments and the numerical instabilities are reproduceable in the Basic version. In the Python version the instabilities are not present (because everything is in double precision). But the absolute field values computed in Python are lower than the ones reported by Zeineddin (and the Basic code does reproduce Zeineddins values).

It doesn’t look like there is a problem in the computations of the currents in the Python code, the computed currents are lower than in Basic which leads to lower field values. But the computed impedance matrix when comparing both versions has very low error, see the test test_matrix_fill_ohio_example in test/test_mininec.py and the routine plot_z_errors to plot the errors (in percent) in test/ohio.py. Compared to the values computed by NEC [5], the Basic code produces slightly higher values for near and far field while the Python code produces slightly lower values than NEC. I’ve not tried to simulate this myself in NEC yet.

You can find the files in test/ohio* (the thesis was at Ohio University). This time there is a python script ohio.py to compute the near and far field values without recomputing the impedance matrix. This script can show the near and far field values in a plot and the difference in a second plot. There are two distances for which these are computed, so the code produces four plots. There is a second script to plot the Basic near and far field differences plot_bas_ohio.py.

The current Python code is still hard to understand – it’s the result of a line-by-line translation from Basic, especially where I didn’t (yet) understand the intention of the code. The same holds for Variable names which might not (yet) reflect the intention of the code. I did move things like computation of the angle of a complex number, or the computation of the absolute value, or multiplication/division of complex numbers to the corresponding complex arithmetic in python where I detected the pattern.

So the de-spaghettification was not successful in some parts of the code yet :-) My notes from the reverse-engineering can be found in the file basic-notes.txt which has explanations of some of the variables used in mininec and some sub routines with descriptions (mostly taken from REM statements) of the Basic code.

The code is also still quite slow: An example of a 12 element Yagi/Uda antenna used in modeling examples by Cebik [6] takes about 50 seconds on my PC (this has 264 segments, more than the original Mininec ever supported) when I’m using 5 degree increments for theta and phi angles and about 11 minutes (!) for 1 degree angles. The reason is that everything currently is implemented (like in Basic) as nested loops. This could (and should) be changed to use vector and matrix operations in numpy. In the inner loop of the matrix fill operation there are several integrals computed using gaussian quadrature or a numeric solution to an elliptic integral. These could be implemented by scipy library functions.

Notes on Elliptic Integral Parameters

The Mininec code uses the implementation of an elliptic integral when computing the impedance matrix and in several other places. The integral uses a set of E-vector coefficients that are cited differently in different places. In the latest version of the open source Basic code these parameters are in lines 1510–1512. They are also reprinted in the publication [2] about that version of Mininec which has a listing of the Basic source code (slightly different from the version available online) where it is on p. C-31 in lines 1512–1514.

In one of the first publications on Mininec [1] the authors give the parameters on p. 13 as:

This is consistent with the later Mininec paper [2] on version 3 of the Mininec code on p. 9, but large portions of that paper are copy & paste from the earlier paper.

The first paper [1] has a listing of the Basic code of that version and on p. 48 the parameters are given as:

In each case the first line are the a parameters, the second line are the b parameters. The a parameters are consistent in all versions but notice how in the b parameters (2nd line) the current Basic code has one more 3 in the second column. The rounding of the earlier Basic code suggests that the second 3 is a typo in the later Basic version. Also notice that in the 4th column the later Basic code has a 5 less than the version in the papers. The rounding in the earlier Basic code also suggests that the later Basic code is in error.

I’ve not investigated yet how these errors affect the computed values of the later Mininec code. Now Mininec is known to find a resonance point of an antenna some percent too high which means that usually in practice the computed wire lengths are a little too long. It may well be that the elliptic integral parameters have an influence there.

I’ve not investigated how to derive the elliptic integral parameters to correct possible errors in the elliptic integral implementation.

The reference for the elliptic integral parameters [3] cited in both reports lists the following table on p. 591:

Note that I could only locate the 1972 version of the Handbook, not the 1980 version cited by the reports. So there is a small chance that these parameters were corrected in a later version. It turns out that the reports are correct in the fourth column and the Basic program is wrong. But the second column contains still another version, note that there is a 5 in the 9th position after the comma, not a 3 like in the Basic program and not a missing digit like in the Mininec reports [1] [2].

Since I could not be sure that there was a typo in the handbook [3], I dug deeper: The handbook cites Approximations for Digital Computers by Hastings (without giving a year) [4]. The version of that book I found is from 1955 and lists the coefficients on p. 172:

So apparently the handbook [3] is correct. And the Basic version and both Mininec reports have at least one typo.

Running examples in Basic

The original Basic source code can still be run today, thanks to Rob Hagemans pcbasic project. It is written in Python and can be installed with pip. It is also packaged in some Linux distributions, e.g. in Debian.

Since Mininec reads all inputs for an antenna simulation from the command-line in Basic, I’m creating input files that contain reproduceable command-line input for an antenna simulation. An example of such a script is in dipole-01.mini, the suffix mini indicating a Mininec file.

Of course the input files only make sense if you actually run them with the mininec basic code as this displays all the prompts. Note that I had to change the dimensions of some arrays in the Basic code to not run into an out-of-memory condition with the Basic interpreter.

You can run pcbasic with the command-line option --input= to specify an input file. Note that the input file has to be converted to carriage return line endings (no newlines). I’ve described how I’m debugging the Basic code using the Python debugger in a contribution to pcbasic, this has been moved to the pcbasic wiki.

In the file debug-basic.txt you can find my notes on how to debug mininec using the python debugger. This is more or less a random cut&paste buffer.

The original basic source code can be obtained from the unofficial NEC archive by PA3KJ or from a Mininec github project, I’m using the version from the unofficial NEC archive and have not verified if the two links I’ve given contain the same code.