# The Hodgkin-Huxley Model as a Performance Metric

13 November, 2018

The source code associated with this post is available on GitHub.

In the world of scientific computing, languages like Python, Julia, and even MATLAB have become the de facto standard. It’s understandable why these languages have become so popular too. For one, you don’t have to be a computer scientist to use them well; just about anyone can pick them up and start building useful tools. In addition, they’re all interpreted languages and don’t need to be compiled before being executed making it faster to iterate on.

While these languages have a lot going for them does performance suffer? Performance may not always be the most important metric when selecting a language to use, but as models become more complex performance starts to matter. In this post, I’ll be implementing the well-known Hodgkin-Huxley model in several different programming languages to see how their performance compares.

The Hodgkin-Huxley model is a mathematical model that describes the propagation of action potentials in neurons. It was developed by Alan Lloyd Hodgkin and Andrew Fielding Huxley in 1952 to describe the giant axon in squid. Since then, it has become a fairly standard model in mathematical neuroscience. I won’t be discussing the model itself in much more detail since we’re really only concerned with it’s performance but below are a few of the important equations. I do however highly recommend the Wikipedia page for a brief but thorough discussion on it.

Because this model is a complex derivative, we’re going to solve it numerically using the second-order Runge-Kutta method known as Heun’s method (sometimes referred to as the modified Euler method). In addition, we’ll be simulating it for a 10 seconds with an a constant applied current ($I_{app}$) of 12 nA (that’s nano-amperes if you didn’t know). All other values and equations are pulled from the original model.

All tests are executed on a Linode nanode instance running Debian 9 amd64 (I’m currently working to get MATLAB setup on a nanode instance). The table below briefly tabulates the average performance results across three attempts.

Language Version Run-time Memory usage
C float gcc 6.3.0 0.966 s 20.348 MB
C double gcc 6.3.0 0.919 s 39.901 MB
C++ float g++ 6.3.0 1.092 s 22.254 MB
C++ double g++ 6.3.0 1.273 s 41.723 MB
Julia 1.0.1 6.287 s 222.613 MB
Python 3.5.3 68.954 s 64.082 MB

Now let’s dive a little bit more into the results of each language.

### C

There’s nothing really all that surprising about C’s performance here in general. The combination of performance and low memory usage is something that C developers have raved about for years. After years of using C here and there I too have come to expect a result like this and I wasn’t disappointed. Also of note is that the performance when using double-precision values was actually faster on average than single-precision. Although I didn’t expect double-precision to be significantly slower I most definitely didn’t expect it to be faster. I wonder what the reasoning for this could be. Statistical error? Process scheduling? Aliens? We may never know.

What I did find challenging about implementing the model in C was the plotting. Although the plotting isn’t being taken into account with the performance test, I’m using plotting to visually validate that the model is working correctly. However, unlike Python, Julia, and other common data sciencpe languages, C doesn’t exactly have a plotting library that I can just link my program to and use. Instead, I had to open up a pipe stream to gnuplot and stream in the resulting model before plotting it to a PNG file. While this work file for me and for something simple like this, it’s definitely not as scalable as say Python’s matplotlib. Not to mention that I’m fairly comfortable coding in C and Linux, something that many data scientists and mathematicians can’t say.

To sum it all up, while C scores really highly on performance, it really suffers when it comes to usability. Not to mention that the C ecosystem is still fairly fragmented when it comes to operating system features and compilers.

### C++

Much like the results with C, C++ didn’t really provide any big surprises. It’s ever-so-slightly lower performance and small additional memory overhead are all characteristic of the relationship between C and C++. However, in a real-world situation, the addition of OOP and features added in C++11 and beyond make it a viable alternative for those who can afford the overhead. Notably, here we see that the double-precision version ran in just under 200 ms slower than the single-precision version. Even still, the C++ implementation comes out ahead of many of the other competitors (except for C, obviously).

Again though, I again experienced challenges with plotting and although C++ has slightly better offerings than C, I decided to stick with what I knew worked and ported over the gnuplot code (it wasn’t really a port, more like a Ctrl-C Ctrl-V but same idea).

I really don’t have much else to say about C++ since a lot of what was said about C applies here as well. If you want OOP and fancy “modern” language features but still really care about performance then C++ is the way to go. Otherwise, it’s probably best to stick with the more traditional data science languages.

### Julia

I’ll admit it, I was really expecting a lot from Julia. I’ve heard a lot of people say that it’s the future of data science. Instead of delivering on those expectations though it’s feels a bit like a mixed bag. I can’t really be too harsh on Julia though; this is my first time ever writing a line of code in Julia. I wouldn’t be surprised at all if I implemented the problem in a way that just doesn’t work well in Julia.

I’m not too concerned with the performance itself: 6 seconds is nothing to laugh at. What really concerns me is the memory usage. Although it ran 10x faster, Julia required over 3x as much memory as Python 3 (and almost 11x as much as C required). The Hodgkin-Huxley model is a rather simple model and there’s no reason it should be using that much memory.

In my opinion, Julia is a language that has a lot of potential when it comes to the computational sciences. Since I’ve never before used Julia I’m fully willing to admit that I did something wrong and that the 222 MB statistic can actually be lower. I really hope that this is the case too. Julia seems to be a language that fits nicely between C and Python in terms of performance and usability. It’s very well documented and it looks to have a fairly active community behind it. I’m definitely interested in learning more about it and using it in the future. Hopefully I’ll figure out a way to bring that memory usage down to a more reasonable level.

### Python

I’m not sure what I found more surprising: Julia’s memory usage or Python’s run-time. I mean, I didn’t expect anything near C or C++ level performance, but 10x slower than Julia seems a bit excessive. Python 3 is a language that I tend to feel fairly comfortable proficient in so I don’t believe that I wrote inherently poor code. Could my use of numpy be causing the slow down? In my past experiences with Python 3 as a data science language and using packages like numpy (and pandas in many cases), I found that it was generally faster than standard python lists.

I might have to take another look at the Python 3 implementation and see if there’s a more efficient and “python-ic” way to solving the equation. I know Python is relatively slow, but 68 seconds just seems way too damn slow compared to what I know and my own past experience. I really hope I just made some kind of newbie mistake or something with the Python implementation because otherwise I think I’ll have to re-evaluate my usage of Python for data science.

## Conclusion

Overall, I didn’t really find anything to be mid-boggling in any way. While Julia’s memory usage and Python’s run-time were pretty bad I can’t say I didn’t expect them (well the Python one at least, I didn’t really know what to expect from Julia). C and C++ are still king when it comes to raw performance but they really lack the approachability and easy-of-use that languages like Python 3 and Julia can offer. With the exception of the memory usage, I feel that Julia has the best balance between power and usability of the languages that were tested. Because of this, I’m really interested to learn about it more and maybe even start applying it to my data science needs both with my current research position and in my personal projects.

If I am able to find the time later on, I plan on diving more deeply into my concerns with Julia and Python 3 and figure out of I’m able to solve them. I also would like to test more languages like MATLAB, R, Ruby, Octave, and any others that I can think of between now and then. For now though, this simple performance test will have to suffice.