Source code for segregation.multigroup.multi_info_theory

"""Multigroup Information index"""

__author__ = "Renan X. Cortes <renanc@ucr.edu>, Sergio J. Rey <sergio.rey@ucr.edu> and Elijah Knaap <elijah.knaap@ucr.edu>"

import numpy as np
from geopandas import GeoDataFrame

from .._base import MultiGroupIndex, SpatialImplicitIndex

np.seterr(divide="ignore", invalid="ignore")


def _multi_information_theory(data, groups):
    """Calculate Multigroup Information Theory index.

    Parameters
    ----------

    data   : a pandas DataFrame

    groups : list of strings.
             The variables names in data of the groups of interest of the analysis.

    Returns
    -------

    statistic : float
                Multigroup Information Theory Index

    core_data : a pandas DataFrame
                A pandas DataFrame that contains the columns used to perform the estimate.

    Notes
    -----
    Based on Reardon, Sean F., and Glenn Firebaugh. "Measures of multigroup segregation." Sociological methodology 32.1 (2002): 33-67.

    Reference: :cite:`reardon2002measures`.

    """
    data = data.copy()
    core_data = data[groups]
    df = np.array(core_data)

    T = df.sum()

    ti = df.sum(axis=1)
    pik = df / ti[:, None]
    Pk = df.sum(axis=0) / df.sum()

    # The natural logarithm is used, but this could be used with any base following Footnote 3 of pg. 37
    # of Reardon, Sean F., and Glenn Firebaugh. "Measures of multigroup segregation." Sociological methodology 32.1 (2002): 33-67.
    E = (Pk * np.log(1 / Pk)).sum()

    MIT = np.nansum(ti[:, None] * pik * np.log(pik / Pk)) / (T * E)
    if isinstance(data, GeoDataFrame):
        core_data = data[[data.geometry.name]].join(core_data)
    return MIT, core_data, groups


class MultiInfoTheory(MultiGroupIndex, SpatialImplicitIndex):
    """Multigroup Information Theory Index.

    Parameters
    ----------
    data : pandas.DataFrame or geopandas.GeoDataFrame, required
        dataframe or geodataframe if spatial index holding data for location of interest
    groups : list, required
        list of columns on dataframe holding population totals for each group
    w : libpysal.weights.KernelW, optional
        lipysal spatial kernel weights object used to define an egohood
    network : pandana.Network
        pandana Network object representing the study area
    distance : int
        Maximum distance (in units of geodataframe CRS) to consider the extent of the egohood
    decay : str
        type of decay function to apply. Options include
    precompute : bool
        Whether to precompute the pandana Network object

    Attributes
    ----------
    statistic : float
        Multigroup Dissimilarity Index value
    core_data : a pandas DataFrame
        DataFrame that contains the columns used to perform the estimate.

    Notes
    -----
    Based on Reardon, Sean F., and Glenn Firebaugh. "Measures of multigroup segregation." Sociological methodology 32.1 (2002): 33-67.

    Reference: :cite:`reardon2002measures`.
    """

    def __init__(
        self,
        data,
        groups,
        w=None,
        network=None,
        distance=None,
        decay='linear',
        function='triangular',
        precompute=False,
        **kwargs
    ):
        """Init."""
        MultiGroupIndex.__init__(self, data, groups)
        if any([w, network, distance]):
            SpatialImplicitIndex.__init__(self, w, network, distance, decay, function, precompute)
        aux = _multi_information_theory(self.data, self.groups)

        self.statistic = aux[0]
        self.data = aux[1]
        self.groups = aux[2]
        self._function = _multi_information_theory