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This is the API documentation for the gdtest_math_docs library.
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## Functions

Utility functions


euclidean_distance(x: list, y: list) -> float

Compute Euclidean distance between two vectors.

The Euclidean distance is defined as:

.. math::

    d(x, y) = \sqrt{\sum_{i=1}^{n} (x_i - y_i)^2}

Parameters
----------
x
    First vector.
y
    Second vector.

Returns
-------
float
    The Euclidean distance :math:`d(x, y)`.

sigmoid(x: float) -> float

Compute the sigmoid function.

The sigmoid function is :math:`\sigma(x) = \frac{1}{1 + e^{-x}}`.

Parameters
----------
x
    Input value.

Returns
-------
float
    Sigmoid output in range :math:`(0, 1)`.

softmax(values: list) -> list

Compute softmax probabilities.

For a vector :math:`z`, the softmax of element :math:`j` is:

.. math::

    \text{softmax}(z)_j = \frac{e^{z_j}}{\sum_{k=1}^{K} e^{z_k}}

Parameters
----------
values
    Input values.

Returns
-------
list
    Probability distribution that sums to 1.