Module src.olaaaf.distance.distance_function.discreteL1DistanceFunction

Class representing a discretized l1 distance function, also called cityblock or Manhattan.

Classes

class DiscreteL1DistanceFunction (weights: dict[Variable, Fraction], epsilon: Fraction = Fraction(1, 1000), domaine: Domain = None)

Class representing a discretized l1 distance function d_\varepsilon, also called cityblock or Manhattan, defined as such:

d(x, y) = \sum_{j=1}^{n}w_j|y_j-x_j|\\ d_{\varepsilon}(x,y)=\varepsilon \biggl\lceil \frac{d(x,y)}{\varepsilon} \biggl\rceil

with w_j weights.

Parameters

weights : a dictionnary of fractions.Fraction with olaaaf.variable.variable.Variable as key
The weights of the l1 distance function
epsilon : fractions.Fraction
The value by which the l1 distance function will be discretized.
domain : olaaaf.distance.domain.domain.Domain
The olaaaf.distance.domain.domain.Domain on which the distance function is defined.
Expand source code 
class DiscreteL1DistanceFunction(DistanceFunctionOnNumericalTuple):
    r"""
    Class representing a discretized l1 distance function \(d_\varepsilon\), also called cityblock or Manhattan, defined as such:

    \[
        d(x, y) = \sum_{j=1}^{n}w_j|y_j-x_j|\\
        d_{\varepsilon}(x,y)=\varepsilon \biggl\lceil \frac{d(x,y)}{\varepsilon} \biggl\rceil
    \]

    with \(w_j\) weights.

    Parameters
    ----------
    weights : a dictionnary of fractions.Fraction with olaaaf.variable.variable.Variable as key
        The weights of the l1 distance function
    epsilon : fractions.Fraction
        The value by which the l1 distance function will be discretized.
    domain: olaaaf.distance.domain.domain.Domain
        The `olaaaf.distance.domain.domain.Domain` on which the distance function is defined.
    """

    def __init__(self, weights : dict[Variable, Fraction], epsilon : Fraction = Fraction("1e-3"), domaine : Domain = None):
        self._distance = l1DistanceFunction(weights, domaine)
        self._epsilon = epsilon

    def dist(self, x : tuple, y : tuple):
        r"""
        Main method of a distance funciton, allowing to get the distance between two points \(x\) and \(y\).

        Parameters
        ----------
        x, y : tuple of olaaaf.variable.variable.Variable
            The two tuples of `olaaaf.variable.variable.Variable` you which to get the distance between.

        Returns
        -------
        fractions.Fraction
            The distance between \(x\) and \(y\).
        """

        return self._epsilon * ceil(self._distance.dist(x,y) / self._epsilon)
    
    def getWeights(self) -> Fraction:
        return self._distance.getWeights()
    
    def getEpsilon(self) -> Fraction:
        return self._epsilon

Ancestors

Methods

def getEpsilon(self) ‑> fractions.Fraction
def getWeights(self) ‑> fractions.Fraction

Inherited members