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

1import numpy as np 

2 

3 

4def regularity(intervals, dtype=None): 

5 """ 

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

7 

8 $$r= \\sqrt[n]{\\prod_{j=1}^{m} \\frac{ 

9 \\prod_{j=1}^{n_j} \\Delta_{ij}} 

10 {{\\left(\\frac{1}{n_j}\\sum_{i=1}^{n_j}{\\Delta_{ij}}\\right)^{n_j}} 

11 } 

12 }$$ 

13 

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

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

16 

17 $$ n=\\sum_{j=1}^{m}{n_j} $$ 

18 

19 Parameters 

20 ---------- 

21 intervals_grouped : array_like 

22 An array of intervals grouped by element 

23 dtype : dtype, optional 

24 The dtype of the output 

25 

26 Returns 

27 ------- 

28 : float 

29 The regularity of the input array of intervals_grouped. 

30 

31 Examples 

32 -------- 

33 

34 Calculate the regularity of intervals_grouped of a sequence. 

35 

36 ``` py linenums="1" 

37 import foapy 

38 import numpy as np 

39 

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

41 order = foapy.ma.order(source) 

42 print(order) 

43 

44 #[[0 -- 0 -- 0 --] 

45 # [-- 1 -- -- -- --] 

46 # [-- -- -- 2 -- --] 

47 # [-- -- -- -- -- 3]] 

48 

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

50 

51 print(intervals_grouped) 

52 # [ 

53 # array([1, 2, 2]), 

54 # array([2]), 

55 # array([4]), 

56 # array([6]) 

57 # ] 

58 

59 # m = 4 

60 # n_0 = 3 

61 # n_1 = 1 

62 # n_2 = 1 

63 # n_3 = 1 

64 # n = 6 

65 

66 result = foapy.characteristics.regularity(intervals_grouped) 

67 print(result) 

68 # 0.9759306487558016 

69 

70 # Improve precision by specifying a dtype. 

71 result = foapy.characteristics.regularity(intervals_grouped, dtype=np.longdouble) 

72 print(result) 

73 # 0.97593064875580153104 

74 ``` 

75 """ # noqa: E501 

76 from foapy.characteristics import descriptive_information, geometric_mean 

77 

78 total_elements = np.concatenate(intervals) 

79 g = geometric_mean(total_elements, dtype=dtype) 

80 D = descriptive_information(intervals, dtype=dtype) 

81 return g / D