Skip to content

foapy.characteristics.depth

depth(intervals, dtype=None)

Calculates depth of intervals.

\[ G=\sum_{i=1}^{n} \log_2 \Delta_{i} \]

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 depth of the input array of intervals.

Examples:

Calculate the depth 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.depth(intervals)
print(result)
# 7.584962500721156

# Improve precision by specifying a dtype.
result = foapy.characteristics.depth(intervals, dtype=np.longdouble)
print(result)
# 7.5849625007211561815
Source code in .tox/docs-deploy/lib/python3.11/site-packages/foapy/characteristics/_depth.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
def depth(intervals, dtype=None):
    """
    Calculates depth of intervals.

    $$ G=\\sum_{i=1}^{n} \\log_2 \\Delta_{i} $$

    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 depth of the input array of intervals.

    Examples
    --------

    Calculate the depth 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.depth(intervals)
    print(result)
    # 7.584962500721156

    # Improve precision by specifying a dtype.
    result = foapy.characteristics.depth(intervals, dtype=np.longdouble)
    print(result)
    # 7.5849625007211561815
    ```
    """
    return np.sum(np.log2(intervals, dtype=dtype), dtype=dtype)