Coverage for src/foapy/characteristics/_uniformity.py: 100%

1import numpy as np 

2 

3 

4def uniformity(intervals, dtype=None): 

5 """ 

6 Calculates uniformity of intervals grouped by element of the alphabet. 

7 

8 $$ u = \\frac {1} {n} * \\sum_{j=1}^{m}{\\log_2 \\frac{ (\\sum_{i=1}^{n_j} \\frac{\\Delta_{ij}}{n_j})^{n_j} } { \\prod_{i=1}^{n_j} \\Delta_{ij}}}$$ 

9 

10 where \\( m \\) is count of groups (alphabet power), \\( n_j \\) is count of intervals in group \\( j \\), 

11 \\( \\Delta_{ij} \\) represents an interval at index \\( i \\) in group \\( j \\) and \\( n \\) is total count of intervals across all groups. 

12 

13 $$n=\\sum_{j=1}^{m}{n_j} $$ 

14 

15 Parameters 

16 ---------- 

17 intervals_grouped : array_like 

18 An array of intervals grouped by element 

19 dtype : dtype, optional 

20 The dtype of the output 

21 

22 Returns 

23 ------- 

24 : float 

25 The uniformity of the input array of intervals_grouped. 

26 

27 Examples 

28 -------- 

29 

30 Calculate the uniformity of intervals_grouped of a sequence. 

31 

32 ``` py linenums="1" 

33 import foapy 

34 import numpy as np 

35 

36 source = np.array(['a', 'b', 'a', 'c', 'a', 'd']) 

37 order = foapy.ma.order(source) 

38 print(order) 

39 

40 #[[0 -- 0 -- 0 --] 

41 # [-- 1 -- -- -- --] 

42 # [-- -- -- 2 -- --] 

43 # [-- -- -- -- -- 3]] 

44 

45 intervals_grouped = foapy.ma.intervals(order, foapy.binding.start, foapy.mode.normal) 

46 

47 print(intervals_grouped) 

48 # [ 

49 # array([1, 2, 2]), 

50 # array([2]), 

51 # array([4]), 

52 # array([6]) 

53 # ] 

54 

55 # m = 4 

56 # n_0 = 3 

57 # n_1 = 1 

58 # n_2 = 1 

59 # n_3 = 1 

60 # n = 6 

61 

62 result = foapy.characteristics.uniformity(intervals_grouped) 

63 print(result) 

64 # 0.03514946374976957 

65 

66 # Improve precision by specifying a dtype. 

67 result = foapy.characteristics.uniformity(intervals_grouped, dtype=np.longdouble) 

68 print(result) 

69 # 0.03514946374976969819 

70 ``` 

71 """ # noqa: E501 

72 from foapy.characteristics import average_remoteness, identifying_information 

73 

74 total_elements = np.concatenate(intervals) 

75 

76 H = identifying_information(intervals, dtype=dtype) 

77 g = average_remoteness(total_elements, dtype=dtype) 

78 

79 return H - g