Skip to content

foapy.characteristics.geometric_mean

geometric_mean(intervals, dtype=None)

Calculates average geometric value of intervals lengths.

\[ \Delta_g=\sqrt[n]{\prod_{i=1}^{n} \Delta_{i}}\]

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 geometric mean of the input array of intervals.

Examples:

Calculate the geometric mean of intervals of a sequence.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
import foapy
import numpy as np

source = ['a', 'b', 'a', 'c', 'a', 'd']
intervals = foapy.intervals(source, foapy.binding.start, foapy.mode.normal)
result = foapy.characteristics.geometric_mean(intervals)
print(result)
# 2.4018739103520055

# Improve precision by specifying a dtype.
result = foapy.characteristics.geometric_mean(intervals, dtype=np.longdouble)
print(result)
# 2.4018739103520053365
Source code in .tox/docs-deploy/lib/python3.11/site-packages/foapy/characteristics/_geometric_mean.py 
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
def geometric_mean(intervals, dtype=None):
    """
    Calculates average geometric value of intervals lengths.

    $$ \\Delta_g=\\sqrt[n]{\\prod_{i=1}^{n} \\Delta_{i}}$$

    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 geometric mean of the input array of intervals.

    Examples
    --------

    Calculate the geometric mean of intervals of a sequence.

    ``` py linenums="1"
    import foapy
    import numpy as np

    source = ['a', 'b', 'a', 'c', 'a', 'd']
    intervals = foapy.intervals(source, foapy.binding.start, foapy.mode.normal)
    result = foapy.characteristics.geometric_mean(intervals)
    print(result)
    # 2.4018739103520055

    # Improve precision by specifying a dtype.
    result = foapy.characteristics.geometric_mean(intervals, dtype=np.longdouble)
    print(result)
    # 2.4018739103520053365
    ```
    """
    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

    from foapy.characteristics import depth

    return np.power(2, depth(intervals, dtype=dtype) / n, dtype=dtype)