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foapy.characteristics.average_remoteness

average_remoteness(intervals, dtype=None)

Calculates average remoteness of intervals.

\[ g = \frac{1}{n} * \sum_{i=1}^{n} \log_2 \Delta_{i} \]

where \( \Delta_{i} \) represents each interval and \( n \) is the total number of intervals.

Parameters:

Name Type Description Default

intervals

array_like

An array of intervals

 required

dtype

dtype

The dtype of the output

 None

Returns:

Type Description
float

The average remoteness of the input array of intervals.

Examples:

Calculate the average remoteness of intervals of a sequence.

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import foapy

source = ['a', 'b', 'a', 'c', 'a', 'd']
intervals = foapy.intervals(source, foapy.binding.start, foapy.mode.normal)
result = foapy.characteristics.average_remoteness(intervals)
print(result)
# 1.2641604167868594

# Improve precision by specifying a dtype.
result = foapy.characteristics.average_remoteness(intervals, dtype=np.longdouble)
print(result)
# 1.2641604167868593636
Source code in .tox/docs-deploy/lib/python3.11/site-packages/foapy/characteristics/_average_remoteness.py 
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def average_remoteness(intervals, dtype=None):
    """
    Calculates average remoteness of intervals.

    $$ g = \\frac{1}{n} * \\sum_{i=1}^{n} \\log_2 \\Delta_{i} $$


    where \\( \\Delta_{i} \\) represents each interval and \\( n \\)
    is the total number of intervals.

    Parameters
    ----------
    intervals : array_like
        An array of intervals
    dtype : dtype, optional
        The dtype of the output

    Returns
    -------
    : float
        The average remoteness of the input array of intervals.

    Examples
    --------

    Calculate the average remoteness of intervals of a sequence.

    ``` py linenums="1"
    import foapy

    source = ['a', 'b', 'a', 'c', 'a', 'd']
    intervals = foapy.intervals(source, foapy.binding.start, foapy.mode.normal)
    result = foapy.characteristics.average_remoteness(intervals)
    print(result)
    # 1.2641604167868594

    # Improve precision by specifying a dtype.
    result = foapy.characteristics.average_remoteness(intervals, dtype=np.longdouble)
    print(result)
    # 1.2641604167868593636
    ```
    """  # noqa: W605

    from foapy.characteristics import depth

    n = len(intervals)

    # Check for an empty list or a list with zeros
    if n == 0 or all(x == 0 for x in intervals):
        return 0

    return depth(intervals, dtype=dtype) / n