Add Identifying Information (Amount of Information / Entropy) characteristic calculator for masked arrays

[ChainsManipulator]

Add calculator function for Identifying Information (Amount of Information / Entropy) characteristic for given intervals array using formula:
$$\displaystyle H_j=-\log_2 P_j= \log_2 \Delta_{a j}$$
Where $P_j$ is a frequency of the element and $\Delta_{a j}$ arithmetic mean of intervals of $j$-th element of the alphabet.

Examples

X = [2, 4, 2, 2, 4]
masked_X = ma.masked_array(X)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> [0.415037499, 1.321928094887]

X = [1, 2, 3]
masked_X = ma.masked_array(X)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> [0, 1, 1.5849625]

X = [1, 2, 3]
masked_X = ma.masked_array(X)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'End', 'Normal')
result = identifying_information(x_intervals)
print(result)
> [1.5849625, 1, 0]

X = ['B','B','B','A','A','B','B','A','B','B']
mask = [1, 1, 1, 0, 0, 1, 1, 0, 1, 1]
masked_X = ma.masked_array(X, mask)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Lossy')
result = identifying_information(x_intervals)
print(result)
> [1]

X = ['B','B','B','A','A','B','B','A','B','B']
mask = [1, 1, 1, 0, 0, 1, 1, 0, 1, 1]
masked_X = ma.masked_array(X, mask)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> [1.415037499]

X = ['B','B','B','A','A','B','B','A','B','B']
mask = [1, 1, 1, 0, 0, 1, 1, 0, 1, 1]
masked_X = ma.masked_array(X, mask)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'End', 'Normal')
result = identifying_information(x_intervals)
print(result)
> [1.222392421336]

X = ['B','B','B','A','A','B','B','A','B','B']
mask = [1, 1, 1, 0, 0, 1, 1, 0, 1, 1]
masked_X = ma.masked_array(X, mask)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Redundant')
result = identifying_information(x_intervals)
print(result)
> [1.459431618637297]

X = ['B','B','B','A','A','B','B','A','B','B']
mask = [1, 1, 1, 0, 0, 1, 1, 0, 1, 1]
masked_X = ma.masked_array(X, mask)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Cycle')
result = identifying_information(x_intervals)
print(result)
> [1.736965594]

X = ['B']
masked_X = ma.masked_array(X,)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Lossy')
result = identifying_information(x_intervals)
print(result)
> [0]

X = ['B']
masked_X = ma.masked_array(X,)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> [0]

X = ['B']
masked_X = ma.masked_array(X,)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'End', 'Normal')
result = identifying_information(x_intervals)
print(result)
> [0]

X = ['B']
masked_X = ma.masked_array(X,)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Redundant')
result = identifying_information(x_intervals)
print(result)
> [0]

X = ['B']
masked_X = ma.masked_array(X,)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Cycle')
result = identifying_information(x_intervals)
print(result)
> [0]

X = ['A','A','A','A','A','A','A','B']
mask = [1, 1, 1, 1, 1, 1, 1, 0]
masked_X = ma.masked_array(X, mask)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Lossy')
result = identifying_information(x_intervals)
print(result)
> [0]

X = ['A','A','A','A','A','A','A','B']
mask = [1, 1, 1, 1, 1, 1, 1, 0]
masked_X = ma.masked_array(X, mask)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> [3]

X = ['A','A','A','A','A','A','A','B']
mask = [1, 1, 1, 1, 1, 1, 1, 0]
masked_X = ma.masked_array(X, mask)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'End', 'Normal')
result = identifying_information(x_intervals)
print(result)
> [0]

X = ['A','A','A','A','A','A','A','B']
mask = [1, 1, 1, 1, 1, 1, 1, 0]
masked_X = ma.masked_array(X, mask)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Redundant')
result = identifying_information(x_intervals)
print(result)
> [2.169925]

X = ['A','A','A','A','A','A','A','B']
mask = [1, 1, 1, 1, 1, 1, 1, 0]
masked_X = ma.masked_array(X, mask)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Cycle')
result = identifying_information(x_intervals)
print(result)
> [3]

X = ['A','A','A','A','A']
masked_X = ma.masked_array(X)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Lossy')
result = identifying_information(x_intervals)
print(result)
> [0]

X = ['A','A','A','A','A']
masked_X = ma.masked_array(X)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> [0]

X = ['A','A','A','A','A']
masked_X = ma.masked_array(X)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'End', 'Normal')
result = identifying_information(x_intervals)
print(result)
> [0]

X = ['A','A','A','A','A']
masked_X = ma.masked_array(X)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Redundant')
result = identifying_information(x_intervals)
print(result)
> [0]

X = ['A','A','A','A','A']
masked_X = ma.masked_array(X)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Cycle')
result = identifying_information(x_intervals)
print(result)
> [0]