Source code for gerrychain.constraints.compactness

import math

from ..partition import Partition
from .bounds import SelfConfiguringLowerBound, SelfConfiguringUpperBound




def L1_reciprocal_polsby_popper(partition: Partition) -> float:
    """Returns the :math:`L^1` norm of the reciprocal Polsby-Popper scores for the given partition.

    Args:
        partition (Partition): Partition representing a districting plan

    Returns:
        float: :math:`L^1` norm of the reciprocal Polsby-Popper scores
    """
    return sum(1 / value for value in partition["polsby_popper"].values())





def L1_polsby_popper(partition: Partition) -> float:
    """Returns the :math:`L^1` norm of the Polsby-Popper scores for the given partition.

    Args:
        partition (Partition): Partition representing a districting plan

    Returns:
        float: :math:`L^1` norm of the reciprocal Polsby-Popper scores
    """
    return sum(value for value in partition["polsby_popper"].values())





def L2_polsby_popper(partition: Partition) -> float:
    """Returns the :math:`L^2` norm of the Polsby-Popper scores for the given partition.

    Args:
        partition (Partition): Partition representing a districting plan

    Returns:
        float: :math:`L^2` norm of the Polsby-Popper scores
    """
    return math.sqrt(sum(value**2 for value in partition["polsby_popper"].values()))





def L_minus_1_polsby_popper(partition: Partition) -> float:
    """Returns the :math:`L^{-1}` norm of the Polsby-Popper scores for the given partition.

    Args:
        partition (Partition): Partition representing a districting plan

    Returns:
        float: :math:`L^{-1}` norm of the Polsby-Popper scores
    """
    return len(partition.parts) / sum(1 / value for value in partition["polsby_popper"].values())



no_worse_L_minus_1_polsby_popper = SelfConfiguringLowerBound(L_minus_1_polsby_popper)

no_worse_L1_reciprocal_polsby_popper = SelfConfiguringUpperBound(L1_reciprocal_polsby_popper)