pymininec 1.0.0

Python version of the original MININEC Antenna Optimization code

Author:

Ralf Schlatterbeck <[e-mail]>

This is an attempt to rewrite the original MININEC3 basic sources in Python. Standard use-case like computation of feed impedance and far field are implemented and are quite well tested. There is only a command line interface.

An example of using the command-line interface uses the following 12-element Yagi/Uda antenna originally presented by Cebik [6] without the resistive element loading and with slight corrections to the element lengths to make the antenna symmetric (the errors in the display in Cebik’s article may be due to a display issue of the program used that displays negative numbers with less accuracy than positive numbers). You can get further help by calling pymininec with the --help option. The command-line options for the 12-element antenna example (also available in the file test/12-el.pym) are:

pymininec -f 148 \
-w 22,-.51943,0.00000,0,.51943,0.00000,0,.00238 \
-w 22,-.50165,0.22331,0,.50165,0.22331,0,.00238 \
-w 22,-.46991,0.34215,0,.46991,0.34215,0,.00238 \
-w 22,-.46136,0.64461,0,.46136,0.64461,0,.00238 \
-w 22,-.46224,1.03434,0,.46224,1.03434,0,.00238 \
-w 22,-.45989,1.55909,0,.45989,1.55909,0,.00238 \
-w 22,-.44704,2.19682,0,.44704,2.19682,0,.00238 \
-w 22,-.43561,2.94640,0,.43561,2.94640,0,.00238 \
-w 22,-.42672,3.72364,0,.42672,3.72364,0,.00238 \
-w 22,-.41783,4.53136,0,.41783,4.53136,0,.00238 \
-w 22,-.40894,5.33400,0,.40894,5.33400,0,.00238 \
-w 22,-.39624,6.0452,0,.39624,6.0452,0,.00238 \
--theta=0,5,37 --phi=0,5,73 \
--excitation-segment=33 > 12-el.pout

When the command line options are in a file, comments (using ‘#’ at the start of the line) can be added. Users on Linux can run this using (I’m sure Windows users can come up with a similar command-line on Windows):

pymininec $(sed '/^#/d' test/12-el.pym) > 12-el.pout

or using grep:

pymininec $(grep -v '#' test/12-el.pym) > 12-el.pout

This removes comments from the .pym file and passes the result as command-line parameters to pymininec. The resulting output file contains currents, impedance at the feedpoint and antenna far field in dBi as tables. The output tries to reproduce the format of the original Basic implementation of Mininec.

Measuring Timings

In the latest version there is a command-line option -T which outputs computation timings on the standard error output. This was used for measuring the results of recent vectorization of computations. Speed ups are roughly:

• About a factor of 50 for computation of the impedance matrix. So we’re down from around 23 seconds to 0.44 seconds for a 12 element Yagi/Uda with 22 segments per element.

• About a factor of 200 for computation of the far field. So we’re down from around 19 seconds to 0.09 seconds for the 12 element Yagi/Uda with 5° resolution of azimuth and elevation angles. Even the computation of a 1° resolution takes below 2s for this antenna.

• About a factor of 5 for near-field computations. This could be further improved by batching the near field coordinates in chunks. I’m currently not using near-field computations much, so further improvements will wait until I have more need…

Plotting

The output tables produced by pymininec are not very useful to get an idea of the far field behaviour of an antenna. The companion program plot-antenna used to be bundled with pymininec but was moved to its own project. You can currently plot elevation and azimuth diagram of an antenna, a 3D-plot, the geometry and VSWR. All either as a standalone program (using matplotlib) or exported as HTML to the browser (using plotly).

Ground (Media)

The latest version implements the option parsing for the mininec ground model for more than one medium. You also need to specify the --boundary option to set the type of boundary between media: The default linear boundary appends grounds in X-direction with the distance in the 4th parameter of the --medium option. The circular boundary has concentric media with the radius of each medium given in the 4th parameter of the --medium option. The third parameter of the --medium option is the height. Note that you typically want negative heights for media further out, this allows modelling of summits. Mininec allows the specification of higher grounds but the results will be questionable as no reflection at the higher ground is modelled. The ground implementation was not yet tested against the originally basic code (or any other modelling program implementing the mininec engine).

Test coverage and code quality

This section contains some notes on code quality and recent improvements.

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 is flagged as not covered by the pytest framework if the Python version is below 3.10. This is a continue statement in compute_impedance_matrix near the end (as of this writing line 1388). This is a bug in Python in versions below 3.10: When setting a breakpoint in the python debugger on the continue statement, the breakpoint is never reached although the continue statement is correctly executed. A workaround would be to put a dummy assignment before the continue statement and verify the test coverage now reports the continue statement as covered. I’ve reported this as a bug in the pytest project and as a bug in python, the bugs are closed now because Python3.9 does no longer get maintenance.

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.

Code quality before vectorization

Before the vectorization this was the state of the code:

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 are now implemented using methods (or at least constants in the case of gaussian quadrature) from scipy.integrate and scipy.special.ellipk.

Code quality after vectorization

Before beginning the vectorization I’ve changed the implicit pulse computations (this used a very complicated indexing schema to access pulse information) to an explicit data structure in mininec/pulse.py. This improved understandability of the code considerably (so that I was able to refactor it further to vectorize computations).

The current version still has obscure variable names from the Basic implementations and in many cases it is not clear what intermediate values in computations mean. Since Basic does not have complex numbers, the semantics of computations can only be guessed. I hope to improve on this when I get a version of [2] – the version available as ADA181682 contains many completely unreadable pages. If you have a source of that report with better readability, let me know!

Multiple Inverted-V Example

An old web-page from 1998 by Dr. Carol F. Milazzo, KP4MD has examples of antennas simulated with Mininec. The first of these examples is three crossed inverted-V (one of which has loading inductors to boost the effective length). The simulation results of pymininec are in the ballpark of the Mininec-based NEC4WIN which was used by KP4MD. But it looks like NEC4WIN might use what it prints as “Diam.” as the radius of the wire (see Fig. 1 in the website) as the radius (see Antenna Model Files in the Appendix). At least if this format is inherited from NEC the last column of the wire definition would hold the radius and this interpretation of the format also is more consistent with the simulation results of Pymininec. The following table shows the original data compared to using half of the diameter in the original model in Pymininec (“Pymininec r”) and the diameter as the radius (Pymininec 2r). When using the (supposed) diameter for the radius, the output data matches better to the website data.

Frequency		Original	Pymininec r	Pymininec 2r
7MHz	Gain Azimuth	-2.42 dBi	-2.52 dBi	-2.49 dBi
	Gain Elevation	7.21 dBi	7.21 dBi	7.21 dBi
	Impedance	38.74 +6.77j	38.82 -3.66j	39.28 +1.49j
14MHz	Gain Azimuth	4.33 dBi	4.60 dBi	4.37 dBi
	Gain Elevation	7.23 dBi	7.73 dBi	7.38 dBi
	Impedance	46.16 -326j	31.86 -307j	43.00 -313j

All of KP4MD’s examples have been converted to Pymininec and are available as inve802B.pym, hloop40-14.pym, hloop40-7.pym, vloop20.pym, and lzh20.pym in the test directory. Only the inve802B.pym (with the inverted-Vs) uses the diameter in the original example as the radius in Pymininec, all others use half of the value in the original example (which is supposed to be the diameter) as the radius. But most examples match better to the values computed by KP4MD when doubling the radius.

Running the Tests

You can run the tests with:

python3 -m pytest test

If coverage should be reported this becomes:

python3 -m pytest --cov mininec test

For a more detailed coverage report use:

python3 -m pytest --cov-report term-missing --cov mininec test

This will show a detailed report of the lines that are not covered by tests.

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.

1.38629436112	.09666344259	.03590092383	.03742563713	.01451196212
.5	.12498593397	.06880248576	.0332835346	.00441787012

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

1.38629436112	.09666344259	.03590092383	.03742563713	.01451196212
.5	.1249859397	.06880248576	.03328355346	.00441787012

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:

1.38629436	.09666344	.03590092	.03742563713	.01451196
.5	.12498594	.06880249	.0332836	.0041787

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.

The errors in the elliptic integral parameters do not have much effect on the computed values of the Mininec code. There are some minor differences but these are below the differences between Basic and Python implementation (single vs. double precision arithmetics). I had hoped that this has something to do with the well known fact that Mininec finds 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. This is apparently not the case. The resonance point is also wrong for very thin wires below the small radius modification condition which happens when the wire radius is below 1e-4 of the wavelength. Even in that case – where the elliptic integral is not used – the resonance is slightly wrong.

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

1.38629436112	.09666344259	.03590092383	.03742563713	.01451196212
.5	.12498593597	.06880248576	.03328355346	.00441787012

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:

1.38629436112	.09666344259	.03590092383	.03742563713	.01451196212
.5	.12498593597	.06880248576	.03328355346	.00441787012

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

Since this paragraph was written the implementation of the elliptic integral was removed and replace with a call to scipy.special.ellipk. The resulting differences in computed outputs were smaller than the differences between the Basic (single precision) and the Python (double precision) implementation.

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.

Release Notes

v1.0: Speed improvement by vectorization

• Vectorize far field computation

• Vectorize computation of the impedance matrix

• Vectorize near field computation

v0.6.1: Fix entry point for script

v0.6.0: Add pyproject.toml

• Add pyproject.toml

• Add LICENSE file

• Minor fixes

v0.5.0: Bug fixes and new load types

• New load types RLC load and Trap load: The first uses a series R-L-C (with each being optional), the second serial R-L parallel to a C (for a good emulation of traps in antennas)

• Bug-Fix in wire-end matching: If there are multiple wires connected to a single point the previous implementation would not build the data structures correctly

• Add more regression tests

• Get rid of unittest to avoid a mixture of the unittest and pytest testing frameworks

v0.4.0: Split plot-antenna into own project

• Own project plot-antenna

• Fix parsing of several medium options, mention ground in documentation

v0.3.0: Laplace loads correctly implemented

• Use scipy.special.ellipk for elliptic integral

• Use gaussian quadrature coefficients from scipy.integrate

• Test resonance (NEC vs. mininec)

v0.2.0: Add short paragraph on new plotting program

• Test coverage

• Expression simplification

v0.1.0: Initial release

[1] (1,2,3)

Alfredo J. Julian, James C. Logan, and John W. Rockway. Mininec: A mini-numerical electromagnetics code. Technical Report NOSC TD 516, Naval Ocean Systems Center (NOSC), San Diego, California, September 1982. Available as ADA121535 from the Defense Technical Information Center.

[2] (1,2,3,4)

J. C. Logan and J. W. Rockway. The new MININEC (version 3): A mini-numerical electromagnetic code. Technical Report NOSC TD 938, Naval Ocean Systems Center (NOSC), San Diego, California, September 1986. Available as ADA181682 from the Defense Technical Information Center. Note: The scan of that report is very bad. If you have access to a better version, please make it available!

[3] (1,2,3)

Milton Abramowitz and Irene A. Stegun, editors. Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables. Number 55 in Applied Mathematics Series. National Bureau of Standards, 1972.

[4]

Cecil Hastings, Jr. Approximations for Digital Computers. Princeton University Press, 1955.

[5] (1,2)

Rafik Paul Zeineddin. Numerical electromagnetics codes: Problems, solutions and applications. Master’s thesis, Ohio University, March 1993. Available from the OhioLINK Electronic Theses & Dissertations Center

[6] (1,2)

L. B. Cebik. Radiation plots: Polar or rectangular; log or linear. In Antenna Modeling Notes [7], chapter 48, pages 366–379. Available in Cebik’s Antenna modelling notes episode 48

[7]

L. B. Cebik. Antenna Modeling Notes, volume 2. antenneX Online Magazine, 2003. Available with antenna models from the Cebik collection.