selection_functions.py

"""
Module containing various selection functions previously used in the literature.

@author davidrpugh

"""

import sympy as sym


class U(sym.Function):
    """Generic selection function"""

    is_real = True

    is_nonnegative = True

    @classmethod
    def eval(cls, x):
        """We require the U(0)=0 and U(1)=1"""
        if x.is_Number and x is sym.S.Zero:
            return sym.S.Zero
        elif x.is_Number and x is sym.S.One:
            return sym.S.One


class RandomSelection(U):

    @classmethod
    def eval(cls, x):
        """We require the U(0)=0 and U(1)=1"""
        if x.is_Number and x is sym.S.Zero:
            return sym.S.Zero
        elif x.is_Number and x is sym.S.One:
            return sym.S.One
        else:
            return x


class UGA(U):
    """Selection function for G females."""


class UgA(U):
    """Selection function for g females."""


def kirkpatrick_selection(x_A, d=1):
    return d * x_A / (1 + (d - 1) * x_A)


def kirkpatrick_selection_derivative(x_A, d=1):
    return d / (1 + (d - 1) * x_A)**2


def perfect_selection(x_A, d):
    return 1


def perfect_selection_derivative(x_A, d):
    return 0


def random_selection(x_A, d):
    return x_A


def random_selection_derivative(x_A, d):
    return 1


def seger_selection(x_A, d=0):
    return x_A * (1 + d * (1 - x_A))


def seger_selection_derivative(x_A, d=0):
    return 1 + d * (1 - 2 * x_A)


def wright_selection(x_A, d=0):
    return (d * x_A + (1 - d) * x_A**2)**0.5


def wright_selection_derivative(x_A, d=0):
    return 0.5 * (d + 2 * (1 - d) * x_A) * (d * x_A + (1 - d) * x_A**2)**(-0.5)