cmomy#

A Python package to calculate and manipulate Central (co)moments. The main features of cmomy are as follows:

Numba accelerated computation of central moments and co-moments
Routines to combine, and resample central moments.
Both numpy array-like and xarray DataArray interfaces to Data.
Routines to convert between central and raw moments.

Overview#

cmomy is an open source package to calculate central moments and co-moments in a numerical stable and direct way. Behind the scenes, cmomy makes use of Numba to rapidly calculate moments. A good introduction to the type of formulas used can be found here.

Features#

Fast calculation of central moments and central co-moments with weights
Support for scalar or vector inputs
numpy and xarray api’s
bootstrap resampling

Status#

This package is actively used by the author. Please feel free to create a pull request for wanted features and suggestions!

Quick start#

Use one of the following

pip install cmomy

conda install -c conda-forge cmomy

Example usage#

>>> import numpy as np
>>> import cmomy
>>> rng = cmomy.random.default_rng(seed=0)
>>> x = rng.random(100)
>>> m = x.mean()
>>> mom = np.array([((x - m) ** i).mean() for i in range(4)])
>>> c = cmomy.CentralMoments.from_vals(x, mom=3)

>>> np.testing.assert_allclose(c.cmom(), mom, atol=1e-8)
>>> c.cmom()
array([ 1.    ,  0.    ,  0.0919, -0.0061])

# break up into chunks
>>> c = cmomy.CentralMoments.from_vals(x.reshape(-1, 2), mom=3)

>>> c
<CentralMoments(val_shape=(2,), mom=(3,))>
array([[ 5.0000e+01,  5.3019e-01,  8.0115e-02, -4.3748e-03],
       [ 5.0000e+01,  5.6639e-01,  1.0297e-01, -8.9911e-03]])

# Reduce along an axis
>>> c.reduce(axis=0).cmom()
array([ 1.    ,  0.    ,  0.0919, -0.0061])

# unequal chunks
>>> x0, x1, x2 = x[:20], x[20:60], x[60:]

>>> cs = [cmomy.CentralMoments.from_vals(_, mom=3) for _ in (x0, x1, x2)]

>>> c = cs[0] + cs[1] + cs[2]

>>> np.testing.assert_allclose(c.cmom(), mom, atol=1e-8)
>>> c.cmom()
array([ 1.    ,  0.    ,  0.0919, -0.0061])

Note on caching#

This code makes extensive use of the numba python package. This uses a jit compiler to speed up vital code sections. This means that the first time a function called, it has to compile the underlying code. However, caching has been implemented. Therefore, the very first time you run a function, it may be slow. But all subsequent uses (including other sessions) will be already compiled.

cmomy

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