Approximate Entropy (ApEn) is a popular tool in analysing the complexity of time series data especially in clinical research.

This function is a very simple and efficient implementation of ApEn, based on vectorization concept that improves speed tremendously over for-loop implementation.

It also contains a test code (foo.m) for generating a plot of ApEn of different simulated time series data, to help understand the usage. The test code generates a plot similar to that appearing in Ki H. Chon's 2009 paper in IEEE Eng in Med Biol, that discusses what r value we should use.

I am interested in using this method to calculate approximate entropy for a boids model.
Can anyone suggest how I can complete the calculation for a specified number of boids in two dimensional space?

(I have txt files with lists of integer values for x and y co-ordinates.

I have been working with your program and testing it. I am a bit confused with your implementation. It is possible to get negative ApEn values, which make no sense to me. Could you please explain this to me. Also, it seems that each consecutive pattern is subtracted not only from the "future" coming patterns but also from the "past" or preceding patterns, which, in your implementation, would count the same matching pattern combination twice (you are finding and absolute value of the difference between two patterns). How does that work?

Thanks for details regarding the paper and the brief explanation on parameters. I have managed to find out a little bit about them from another paper that you may also be interested in:
doi:10.1016/j.ymssp.2006.02.009

It provides some investigation and then considerations in terms of efficiency of App Entr. when it comes to decide about values of parameters. It's been very useful to me.

The DOI of the paper is 10.1109/MEMB.2009.934629 so you can find it easily.

The first argument, dim, means embedded dimension. That is the length of the sequence to be compared, and typical value for that is 2 or 3.
The second argument, r, is the tolerance for matching. In other words, a pair of values whose difference is smaller than r is considered matching. Typically 0.2*std is used (std means standard deviation of the whole timeseries data), but this paper by Chon suggests that r value should be chosen carefully, and one should look for r value that maximizes the ApEn.

I am very grateful for this file that just saves a lot of time. However, could you please if this is not a problem to give some details of the paper you have mentioned? I am not sure if I understood the meaning of the first and the second argument of your function.

The new version (Ver 1) has corrected a minor error in the definition of ApEn, and included another input argument tau for multi-scale ApEn calculation. See inside for details.