Source code for photutils.morphology.non_parametric
# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
This module provides functions for measuring non-parametric morphologies
of sources.
"""
import numpy as np
__all__ = ['gini']
[docs]
def gini(data, mask=None):
r"""
Calculate the `Gini coefficient
<https://en.wikipedia.org/wiki/Gini_coefficient>`_ of a 2D array.
The Gini coefficient is calculated using the prescription from `Lotz
et al. 2004
<https://ui.adsabs.harvard.edu/abs/2004AJ....128..163L/abstract>`_
as:
.. math::
G = \frac{1}{\left | \bar{x} \right | n (n - 1)}
\sum^{n}_{i} (2i - n - 1) \left | x_i \right |
where :math:`\bar{x}` is the mean over all pixel values :math:`x_i`.
If the sum of all pixel values is zero, the Gini coefficient is
zero.
The Gini coefficient is a way of measuring the inequality in a given
set of values. In the context of galaxy morphology, it measures how
the light of a galaxy image is distributed among its pixels. A Gini
coefficient value of 0 corresponds to a galaxy image with the light
evenly distributed over all pixels while a Gini coefficient value of
1 represents a galaxy image with all its light concentrated in just
one pixel.
Usually Gini's measurement needs some sort of preprocessing for
defining the galaxy region in the image based on the quality of the
input data. As there is not a general standard for doing this, this
is left for the user.
Parameters
----------
data : array_like
The 2D data array or object that can be converted to an array.
mask : array_like, optional
A boolean mask with the same shape as ``data`` where `True`
values indicate masked pixels. Masked pixels are excluded from
the calculation.
Returns
-------
result : float
The Gini coefficient of the input 2D array.
"""
values = data[~mask] if mask is not None else np.ravel(data)
if np.all(np.isnan(values)):
return np.nan
npix = np.size(values)
normalization = np.abs(np.mean(values)) * npix * (npix - 1)
if normalization == 0:
return 0.0
kernel = ((2.0 * np.arange(1, npix + 1) - npix - 1)
* np.abs(np.sort(values)))
return np.sum(kernel) / normalization