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Class swarmauri_core.norms.INorm.INorm

swarmauri_core.norms.INorm.INorm

Bases: ABC

Interface for norm computations on vector spaces.

This interface defines the contract for norm behavior, enforcing point-separating distance logic. Norms provide a way to measure the "size" or "length" of elements in a vector space.

A norm must satisfy the following properties: 1. Non-negativity: norm(x) >= 0 for all x 2. Definiteness: norm(x) = 0 if and only if x = 0 3. Triangle inequality: norm(x + y) <= norm(x) + norm(y) 4. Absolute homogeneity: norm(ax) = |a|norm(x) for scalar a

compute abstractmethod 

compute(x)

Compute the norm of the input.

Parameters

x : Union[VectorType, MatrixType, SequenceType, StringType, CallableType] The input for which to compute the norm.

Returns

float The computed norm value.

Raises

TypeError If the input type is not supported. ValueError If the norm cannot be computed for the given input.

Source code in swarmauri_core/norms/INorm.py 
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@abstractmethod
def compute(
    self, x: Union[VectorType, MatrixType, SequenceType, StringType, CallableType]
) -> float:
    """
    Compute the norm of the input.

    Parameters
    ----------
    x : Union[VectorType, MatrixType, SequenceType, StringType, CallableType]
        The input for which to compute the norm.

    Returns
    -------
    float
        The computed norm value.

    Raises
    ------
    TypeError
        If the input type is not supported.
    ValueError
        If the norm cannot be computed for the given input.
    """
    pass

check_non_negativity abstractmethod 

check_non_negativity(x)

Check if the norm satisfies the non-negativity property.

Parameters

x : Union[VectorType, MatrixType, SequenceType, StringType, CallableType] The input to check.

Returns

bool True if the norm is non-negative, False otherwise.

Source code in swarmauri_core/norms/INorm.py 
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@abstractmethod
def check_non_negativity(
    self, x: Union[VectorType, MatrixType, SequenceType, StringType, CallableType]
) -> bool:
    """
    Check if the norm satisfies the non-negativity property.

    Parameters
    ----------
    x : Union[VectorType, MatrixType, SequenceType, StringType, CallableType]
        The input to check.

    Returns
    -------
    bool
        True if the norm is non-negative, False otherwise.
    """
    pass

check_definiteness abstractmethod 

check_definiteness(x)

Check if the norm satisfies the definiteness property.

The definiteness property states that the norm of x is 0 if and only if x is 0.

Parameters

x : Union[VectorType, MatrixType, SequenceType, StringType, CallableType] The input to check.

Returns

bool True if the norm satisfies the definiteness property, False otherwise.

Source code in swarmauri_core/norms/INorm.py 
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@abstractmethod
def check_definiteness(
    self, x: Union[VectorType, MatrixType, SequenceType, StringType, CallableType]
) -> bool:
    """
    Check if the norm satisfies the definiteness property.

    The definiteness property states that the norm of x is 0 if and only if x is 0.

    Parameters
    ----------
    x : Union[VectorType, MatrixType, SequenceType, StringType, CallableType]
        The input to check.

    Returns
    -------
    bool
        True if the norm satisfies the definiteness property, False otherwise.
    """
    pass

check_triangle_inequality abstractmethod 

check_triangle_inequality(x, y)

Check if the norm satisfies the triangle inequality.

The triangle inequality states that norm(x + y) <= norm(x) + norm(y).

Parameters

x : Union[VectorType, MatrixType, SequenceType, StringType, CallableType] The first input. y : Union[VectorType, MatrixType, SequenceType, StringType, CallableType] The second input.

Returns

bool True if the norm satisfies the triangle inequality, False otherwise.

Raises

TypeError If the inputs are not of the same type or cannot be added.

Source code in swarmauri_core/norms/INorm.py 
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@abstractmethod
def check_triangle_inequality(
    self,
    x: Union[VectorType, MatrixType, SequenceType, StringType, CallableType],
    y: Union[VectorType, MatrixType, SequenceType, StringType, CallableType],
) -> bool:
    """
    Check if the norm satisfies the triangle inequality.

    The triangle inequality states that norm(x + y) <= norm(x) + norm(y).

    Parameters
    ----------
    x : Union[VectorType, MatrixType, SequenceType, StringType, CallableType]
        The first input.
    y : Union[VectorType, MatrixType, SequenceType, StringType, CallableType]
        The second input.

    Returns
    -------
    bool
        True if the norm satisfies the triangle inequality, False otherwise.

    Raises
    ------
    TypeError
        If the inputs are not of the same type or cannot be added.
    """
    pass

check_absolute_homogeneity abstractmethod 

check_absolute_homogeneity(x, scalar)

Check if the norm satisfies the absolute homogeneity property.

The absolute homogeneity property states that norm(ax) = |a|norm(x) for scalar a.

Parameters

x : Union[VectorType, MatrixType, SequenceType, StringType, CallableType] The input. scalar : float The scalar value.

Returns

bool True if the norm satisfies the absolute homogeneity property, False otherwise.

Raises

TypeError If the input cannot be scaled by the scalar.

Source code in swarmauri_core/norms/INorm.py 
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@abstractmethod
def check_absolute_homogeneity(
    self,
    x: Union[VectorType, MatrixType, SequenceType, StringType, CallableType],
    scalar: float,
) -> bool:
    """
    Check if the norm satisfies the absolute homogeneity property.

    The absolute homogeneity property states that norm(a*x) = |a|*norm(x) for scalar a.

    Parameters
    ----------
    x : Union[VectorType, MatrixType, SequenceType, StringType, CallableType]
        The input.
    scalar : float
        The scalar value.

    Returns
    -------
    bool
        True if the norm satisfies the absolute homogeneity property, False otherwise.

    Raises
    ------
    TypeError
        If the input cannot be scaled by the scalar.
    """
    pass