Ensemble averages

# enstat

## Overview

enstat is a library to facilitate the computation of ensemble averages (and their variances) or histograms.

The key feature is that a class stores 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.

For the histogram something similar holds, but this time the count per bin is stored.

### Ensemble average

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

print(ensemble.mean())


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))

for realisation in range(100):

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

print(hist.p)


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)
plt.show()


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

## Installation

• Using conda

conda install -c conda-forge enstat

• Using PyPi

python -m pip install enstat


## Disclaimer

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.

## Project details

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