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Class swarmauri_core.pseudometrics.IPseudometric.IPseudometric

swarmauri_core.pseudometrics.IPseudometric.IPseudometric

Bases: ABC

Interface for a pseudometric distance function.

A pseudometric satisfies: 1. Non-negativity: d(x,y) ≥ 0 2. Symmetry: d(x,y) = d(y,x) 3. Triangle inequality: d(x,z) ≤ d(x,y) + d(y,z)

Unlike a metric, a pseudometric allows d(x,y) = 0 for x ≠ y, meaning it may not distinguish between distinct points.

distance abstractmethod 

distance(x, y)

Calculate the pseudometric distance between two objects.

Parameters

x : Union[VectorType, MatrixType, Sequence[T], str, Callable] The first object y : Union[VectorType, MatrixType, Sequence[T], str, Callable] The second object

Returns

float The distance between x and y

Raises

TypeError If inputs are of incompatible types ValueError If inputs have incompatible dimensions

Source code in swarmauri_core/pseudometrics/IPseudometric.py 
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@abstractmethod
def distance(
    self,
    x: Union[VectorType, MatrixType, Sequence[T], str, Callable],
    y: Union[VectorType, MatrixType, Sequence[T], str, Callable],
) -> float:
    """
    Calculate the pseudometric distance between two objects.

    Parameters
    ----------
    x : Union[VectorType, MatrixType, Sequence[T], str, Callable]
        The first object
    y : Union[VectorType, MatrixType, Sequence[T], str, Callable]
        The second object

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

    Raises
    ------
    TypeError
        If inputs are of incompatible types
    ValueError
        If inputs have incompatible dimensions
    """
    pass

distances abstractmethod 

distances(xs, ys)

Calculate the pairwise distances between two collections of objects.

Parameters

xs : Sequence[Union[VectorType, MatrixType, Sequence[T], str, Callable]] The first collection of objects ys : Sequence[Union[VectorType, MatrixType, Sequence[T], str, Callable]] The second collection of objects

Returns

List[List[float]] A matrix of distances where distances[i][j] is the distance between xs[i] and ys[j]

Raises

TypeError If inputs contain incompatible types ValueError If inputs have incompatible dimensions

Source code in swarmauri_core/pseudometrics/IPseudometric.py 
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@abstractmethod
def distances(
    self,
    xs: Sequence[Union[VectorType, MatrixType, Sequence[T], str, Callable]],
    ys: Sequence[Union[VectorType, MatrixType, Sequence[T], str, Callable]],
) -> List[List[float]]:
    """
    Calculate the pairwise distances between two collections of objects.

    Parameters
    ----------
    xs : Sequence[Union[VectorType, MatrixType, Sequence[T], str, Callable]]
        The first collection of objects
    ys : Sequence[Union[VectorType, MatrixType, Sequence[T], str, Callable]]
        The second collection of objects

    Returns
    -------
    List[List[float]]
        A matrix of distances where distances[i][j] is the distance between xs[i] and ys[j]

    Raises
    ------
    TypeError
        If inputs contain incompatible types
    ValueError
        If inputs have incompatible dimensions
    """
    pass

check_non_negativity abstractmethod 

check_non_negativity(x, y)

Check if the distance function satisfies the non-negativity property.

Parameters

x : Union[VectorType, MatrixType, Sequence[T], str, Callable] The first object y : Union[VectorType, MatrixType, Sequence[T], str, Callable] The second object

Returns

bool True if d(x,y) ≥ 0, False otherwise

Source code in swarmauri_core/pseudometrics/IPseudometric.py 
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@abstractmethod
def check_non_negativity(
    self,
    x: Union[VectorType, MatrixType, Sequence[T], str, Callable],
    y: Union[VectorType, MatrixType, Sequence[T], str, Callable],
) -> bool:
    """
    Check if the distance function satisfies the non-negativity property.

    Parameters
    ----------
    x : Union[VectorType, MatrixType, Sequence[T], str, Callable]
        The first object
    y : Union[VectorType, MatrixType, Sequence[T], str, Callable]
        The second object

    Returns
    -------
    bool
        True if d(x,y) ≥ 0, False otherwise
    """
    pass

check_symmetry abstractmethod 

check_symmetry(x, y, tolerance=1e-10)

Check if the distance function satisfies the symmetry property.

Parameters

x : Union[VectorType, MatrixType, Sequence[T], str, Callable] The first object y : Union[VectorType, MatrixType, Sequence[T], str, Callable] The second object tolerance : float, optional The tolerance for floating-point comparisons, by default 1e-10

Returns

bool True if d(x,y) = d(y,x) within tolerance, False otherwise

Source code in swarmauri_core/pseudometrics/IPseudometric.py 
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@abstractmethod
def check_symmetry(
    self,
    x: Union[VectorType, MatrixType, Sequence[T], str, Callable],
    y: Union[VectorType, MatrixType, Sequence[T], str, Callable],
    tolerance: float = 1e-10,
) -> bool:
    """
    Check if the distance function satisfies the symmetry property.

    Parameters
    ----------
    x : Union[VectorType, MatrixType, Sequence[T], str, Callable]
        The first object
    y : Union[VectorType, MatrixType, Sequence[T], str, Callable]
        The second object
    tolerance : float, optional
        The tolerance for floating-point comparisons, by default 1e-10

    Returns
    -------
    bool
        True if d(x,y) = d(y,x) within tolerance, False otherwise
    """
    pass

check_triangle_inequality abstractmethod 

check_triangle_inequality(x, y, z, tolerance=1e-10)

Check if the distance function satisfies the triangle inequality.

Parameters

x : Union[VectorType, MatrixType, Sequence[T], str, Callable] The first object y : Union[VectorType, MatrixType, Sequence[T], str, Callable] The second object z : Union[VectorType, MatrixType, Sequence[T], str, Callable] The third object tolerance : float, optional The tolerance for floating-point comparisons, by default 1e-10

Returns

bool True if d(x,z) ≤ d(x,y) + d(y,z) within tolerance, False otherwise

Source code in swarmauri_core/pseudometrics/IPseudometric.py 
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@abstractmethod
def check_triangle_inequality(
    self,
    x: Union[VectorType, MatrixType, Sequence[T], str, Callable],
    y: Union[VectorType, MatrixType, Sequence[T], str, Callable],
    z: Union[VectorType, MatrixType, Sequence[T], str, Callable],
    tolerance: float = 1e-10,
) -> bool:
    """
    Check if the distance function satisfies the triangle inequality.

    Parameters
    ----------
    x : Union[VectorType, MatrixType, Sequence[T], str, Callable]
        The first object
    y : Union[VectorType, MatrixType, Sequence[T], str, Callable]
        The second object
    z : Union[VectorType, MatrixType, Sequence[T], str, Callable]
        The third object
    tolerance : float, optional
        The tolerance for floating-point comparisons, by default 1e-10

    Returns
    -------
    bool
        True if d(x,z) ≤ d(x,y) + d(y,z) within tolerance, False otherwise
    """
    pass

check_weak_identity abstractmethod 

check_weak_identity(x, y)

Check if the distance function satisfies the weak identity property.

In a pseudometric, d(x,y) = 0 is allowed even when x ≠ y. This method verifies that this property is properly handled.

Parameters

x : Union[VectorType, MatrixType, Sequence[T], str, Callable] The first object y : Union[VectorType, MatrixType, Sequence[T], str, Callable] The second object

Returns

bool True if the pseudometric properly handles the weak identity property

Source code in swarmauri_core/pseudometrics/IPseudometric.py 
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@abstractmethod
def check_weak_identity(
    self,
    x: Union[VectorType, MatrixType, Sequence[T], str, Callable],
    y: Union[VectorType, MatrixType, Sequence[T], str, Callable],
) -> bool:
    """
    Check if the distance function satisfies the weak identity property.

    In a pseudometric, d(x,y) = 0 is allowed even when x ≠ y.
    This method verifies that this property is properly handled.

    Parameters
    ----------
    x : Union[VectorType, MatrixType, Sequence[T], str, Callable]
        The first object
    y : Union[VectorType, MatrixType, Sequence[T], str, Callable]
        The second object

    Returns
    -------
    bool
        True if the pseudometric properly handles the weak identity property
    """
    pass