kopia lustrzana https://github.com/crflynn/voting
131 wiersze
2.8 KiB
Python
131 wiersze
2.8 KiB
Python
"""Measures of diversity."""
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from math import exp
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from math import log
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from voting.util import normalize
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def berger_parker(groups):
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r"""Calculate the Berger-Parker index.
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.. math::
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max(p_i)
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:param list group: a list of integers representing populations of groups
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"""
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groups = normalize(groups)
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return max(groups)
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def general(groups, q=1):
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r"""Calculate the general diversity index.
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.. math::
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\left( \sum_{i=1}^n p_i^q \right) ^ {1/(1-q)}
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:param list groups: a list of integers representing populations of groups
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:param float q: weight value
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"""
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if q == 1:
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return exp(shannon(groups))
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groups = normalize(groups)
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return sum([g ** q for g in groups]) ** (1.0 / (1 - q))
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def gini_simpson(groups):
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r"""Calculate the Gini-Simpson index.
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.. math::
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1 - \sum_{i=1}^n p_i^2
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:param list group: a list of integers representing populations of groups
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"""
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return 1 - simpson(groups)
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def golosov(groups):
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r"""Calculate the effective number of parties using Golosov.
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.. math::
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\sum_{i=1}^n \frac{p_i}{p_i + p_1^2 - p_i^2}
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where :math:`p_1` is the largest proportion.
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:param list group: a list of integers representing populations of a group
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"""
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groups = normalize(groups)
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p1 = max(groups)
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return sum([g / (g + p1 ** 2 - g ** 2) for g in groups])
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def inverse_simpson(groups):
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r"""Calculate the Inverse-Simpson index.
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.. math::
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\frac{1}{\sum_{i=1}^n p_i^2}
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:param list group: a list of integers representing populations of groups
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"""
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return 1.0 / simpson(groups)
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def laakso_taagepera(groups):
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r"""Calculate the effective number of parties using Laakso-Taagepera.
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.. math::
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\frac{1}{\sum_{i=1}^n p_i^2}
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:param list group: a list of integers representing populations of groups
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"""
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groups = normalize(groups)
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return 1.0 / sum([g ** 2 for g in groups])
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def renyi(groups, q=0):
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r"""Calculate the Renyi entropy.
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.. math::
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\frac{1}{1-q} \ln \left( \sum_{i=1}^n p_i ^ q \right)
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:param list groups: a list of integers representing populations of groups
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:param float q: weight value
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"""
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if q == 1:
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return shannon(groups)
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groups = normalize(groups)
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return 1.0 / (1 - q) * log(sum([g ** q for g in groups]))
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def shannon(groups):
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r"""Calculate the Shannon index.
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.. math::
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\sum_{i=1}^n p_i \ln (p_i)
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:param list groups: a list of integers representing populations of groups
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"""
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groups = normalize(groups)
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return sum([g * log(g) for g in groups])
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def simpson(groups):
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r"""Calculate the Simpson index.
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.. math::
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\sum_{i=1}^n p_i^2
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:param list groups: a list of integers representing populations of groups
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"""
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groups = normalize(groups)
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return sum([g ** 2 for g in groups])
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