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Ensemble averages

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CI Documentation Status Conda Version PyPi release


Hallmark feature

enstat is a library to facilitate the computation of

without storing the entire ensemble in memory.

Below you find a quick-start. For more information, see the documentation.

Ensemble average

The key feature is to store the sum of the first and second statistical moments and the number of samples. This gives access to the mean (and variance) at all times, while you can keep adding samples.

Suppose that we have 100 realisations, each with 1000 'blocks', and we want to know the ensemble average of each block:

import enstat
import numpy as np

ensemble = enstat.static()

for realisation in range(100):
    sample = np.random.random(1000)
    ensemble += sample


which will print a list of 1000 values, each around 0.5.

This is the equivalent of

import numpy as np

container = np.empty((100, 1000))

    sample = np.random.random(1000)
    container[realisation, :] = sample

print(np.mean(container, axis=0))

The key difference is that enstat only requires you to have 4 * N values in memory for a sample of size N: the sample itself, the sums of the first and second moment, and the normalisation. Instead the solution with the container uses much more memory.

A nice feature is also that you can keep adding samples to ensemble. You can even store it and continue later.

Ensemble histogram

Same example, but now we want the histogram for predefined bins:

import enstat
import numpy as np

bin_edges = np.linspace(0, 1, 11)
hist = enstat.histogram(bin_edges=bin_edges)

for realisation in range(100):
    sample = np.random.random(1000)
    hist += sample


which prints the probability density of each bin (so list of values around 0.1 for these bins).

The histogram class contains two additional nice features.

  1. It has several bin algorithms that NumPy does not have.

  2. It can be used for plotting with an ultra-sort interface, for example:

    import enstat
    import numpy as np
    import matplotlib.pyplot as plt
    data = np.random.random(1000)
    hist = enstat.histogram.from_data(data, bins=10, mode="log")
    fig, ax = plt.subplots()
    ax.plot(hist.x, hist.p)

    You can even use ax.plot(*hist.plot).

Average per bin

Suppose you have some time series (t) with multiple observables (a and b); e.g.;

import enstat
import numpy as np

t = np.linspace(0, 10, 100)
a = np.random.normal(loc=5, scale=0.1, size=t.size)
b = np.random.normal(loc=1, scale=0.5, size=t.size)

Now suppose that you want to compute the average a, b, and t based on a certain binning of t:

bin_edges = np.linspace(0, 12, 12)
binned = enstat.binned.from_data(t, a, b, names=["t", "a", "b"]m bin_edges=bin_edges)


  • Using conda

    conda install -c conda-forge enstat
  • Using PyPi

    python -m pip install enstat


This library is free to use under the MIT license. Any additions are very much appreciated. As always, the code comes with no guarantee. None of the developers can be held responsible for possible mistakes.

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