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Class swarmauri_core.metrics.IMetric.IMetric

swarmauri_core.metrics.IMetric.IMetric

Bases: ABC

Interface for proper metric spaces.

This interface defines the contract enforcing the full metric axioms: - Non-negativity: d(x,y) ≥ 0 - Identity of indiscernibles (point separation): d(x,y) = 0 if and only if x = y - Symmetry: d(x,y) = d(y,x) - Triangle inequality: d(x,z) ≤ d(x,y) + d(y,z)

Implementations must support various input types including vectors, matrices, sequences, strings, and callables.

distance abstractmethod 

distance(x, y)

Calculate the distance between two points.

Parameters

x : MetricInput First point y : MetricInput Second point

Returns

float The distance between x and y

Raises

ValueError If inputs are incompatible with the metric TypeError If input types are not supported

Source code in swarmauri_core/metrics/IMetric.py 
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@abstractmethod
def distance(self, x: MetricInput, y: MetricInput) -> float:
    """
    Calculate the distance between two points.

    Parameters
    ----------
    x : MetricInput
        First point
    y : MetricInput
        Second point

    Returns
    -------
    float
        The distance between x and y

    Raises
    ------
    ValueError
        If inputs are incompatible with the metric
    TypeError
        If input types are not supported
    """
    pass

distances abstractmethod 

distances(x, y)

Calculate distances between collections of points.

Parameters

x : Union[MetricInput, MetricInputCollection] First collection of points y : Union[MetricInput, MetricInputCollection] Second collection of points

Returns

Union[List[float], IVector, IMatrix] Matrix or vector of distances between points in x and y

Raises

ValueError If inputs are incompatible with the metric TypeError If input types are not supported

Source code in swarmauri_core/metrics/IMetric.py 
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@abstractmethod
def distances(
    self,
    x: Union[MetricInput, MetricInputCollection],
    y: Union[MetricInput, MetricInputCollection],
) -> Union[List[float], IVector, IMatrix]:
    """
    Calculate distances between collections of points.

    Parameters
    ----------
    x : Union[MetricInput, MetricInputCollection]
        First collection of points
    y : Union[MetricInput, MetricInputCollection]
        Second collection of points

    Returns
    -------
    Union[List[float], IVector, IMatrix]
        Matrix or vector of distances between points in x and y

    Raises
    ------
    ValueError
        If inputs are incompatible with the metric
    TypeError
        If input types are not supported
    """
    pass

check_non_negativity abstractmethod 

check_non_negativity(x, y)

Check if the metric satisfies the non-negativity axiom: d(x,y) ≥ 0.

Parameters

x : MetricInput First point y : MetricInput Second point

Returns

bool True if the axiom is satisfied, False otherwise

Source code in swarmauri_core/metrics/IMetric.py 
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@abstractmethod
def check_non_negativity(self, x: MetricInput, y: MetricInput) -> bool:
    """
    Check if the metric satisfies the non-negativity axiom: d(x,y) ≥ 0.

    Parameters
    ----------
    x : MetricInput
        First point
    y : MetricInput
        Second point

    Returns
    -------
    bool
        True if the axiom is satisfied, False otherwise
    """
    pass

check_identity_of_indiscernibles abstractmethod 

check_identity_of_indiscernibles(x, y)

Check if the metric satisfies the identity of indiscernibles axiom: d(x,y) = 0 if and only if x = y.

Parameters

x : MetricInput First point y : MetricInput Second point

Returns

bool True if the axiom is satisfied, False otherwise

Source code in swarmauri_core/metrics/IMetric.py 
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@abstractmethod
def check_identity_of_indiscernibles(self, x: MetricInput, y: MetricInput) -> bool:
    """
    Check if the metric satisfies the identity of indiscernibles axiom:
    d(x,y) = 0 if and only if x = y.

    Parameters
    ----------
    x : MetricInput
        First point
    y : MetricInput
        Second point

    Returns
    -------
    bool
        True if the axiom is satisfied, False otherwise
    """
    pass

check_symmetry abstractmethod 

check_symmetry(x, y)

Check if the metric satisfies the symmetry axiom: d(x,y) = d(y,x).

Parameters

x : MetricInput First point y : MetricInput Second point

Returns

bool True if the axiom is satisfied, False otherwise

Source code in swarmauri_core/metrics/IMetric.py 
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@abstractmethod
def check_symmetry(self, x: MetricInput, y: MetricInput) -> bool:
    """
    Check if the metric satisfies the symmetry axiom: d(x,y) = d(y,x).

    Parameters
    ----------
    x : MetricInput
        First point
    y : MetricInput
        Second point

    Returns
    -------
    bool
        True if the axiom is satisfied, False otherwise
    """
    pass

check_triangle_inequality abstractmethod 

check_triangle_inequality(x, y, z)

Check if the metric satisfies the triangle inequality axiom: d(x,z) ≤ d(x,y) + d(y,z).

Parameters

x : MetricInput First point y : MetricInput Second point z : MetricInput Third point

Returns

bool True if the axiom is satisfied, False otherwise

Source code in swarmauri_core/metrics/IMetric.py 
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@abstractmethod
def check_triangle_inequality(
    self, x: MetricInput, y: MetricInput, z: MetricInput
) -> bool:
    """
    Check if the metric satisfies the triangle inequality axiom:
    d(x,z) ≤ d(x,y) + d(y,z).

    Parameters
    ----------
    x : MetricInput
        First point
    y : MetricInput
        Second point
    z : MetricInput
        Third point

    Returns
    -------
    bool
        True if the axiom is satisfied, False otherwise
    """
    pass