Add Amount of identifying information (Amount of Information / Entropy) characteristic calculator

[ChainsManipulator]

Add calculator function for Identifying Information (Amount of Information / Entropy) characteristic for given intervals array using formula:
$$\displaystyle H=\sum_{j=1}^{m}{\frac {n_j} {n} * \log_2 \Delta_{a j}}$$
Where $n_j$ is a number of intervals in the given congeneric sequence, $n$ is a number of intervals in the whole sequence, $m$ is a number of different elements in the sequence and $\Delta_{a j}$ arithmetic mean of intervals of $j$-th element of the alphabet.

Examples

X = [2, 4, 2, 2, 4]
x_intervals = intervals(X, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 0,77779373752225

X = ['B','B','A','A','C','B','A','C','C','B']
x_intervals = intervals(X, 'Start', 'Lossy')
result = identifying_information(x_intervals)
print(result)
> 1.25069821459

X = ['B','B','A','A','C','B','A','C','C','B']
x_intervals = intervals(X, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 1.3709777

X = ['B','B','A','A','C','B','A','C','C','B']
x_intervals = intervals(X, 'End', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 1.2532824857

X = ['B','B','A','A','C','B','A','C','C','B']
x_intervals = intervals(X, 'Start', 'Redundant')
result = identifying_information(x_intervals)
print(result)
> 1.335618955

X = ['B','B','A','A','C','B','A','C','C','B']
x_intervals = intervals(X, 'Start', 'Cycle')
result = identifying_information(x_intervals)
print(result)
> 1.571

---

X = ['A','C','T','T','G','A','T','A','C','G']  
x_intervals = intervals(X, 'Start', 'Lossy')
result = identifying_information(x_intervals)
print(result)
> 1.7906654768

X = ['A','C','T','T','G','A','T','A','C','G'] 
x_intervals = intervals(X, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 1.6895995955

X = ['A','C','T','T','G','A','T','A','C','G'] 
x_intervals = intervals(X, 'End', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 1.6965784285

X = ['A','C','T','T','G','A','T','A','C','G'] 
x_intervals = intervals(X, 'End', 'Redundant')
result = identifying_information(x_intervals)
print(result)
> 1.6373048326

X = ['A','C','T','T','G','A','T','A','C','G'] 
x_intervals = intervals(X, 'End', 'Cycle')
result = identifying_information(x_intervals)
print(result)
> 1.9709505945

---

X = ['C','C','A','C','G','C','T','T','A','C']
x_intervals = intervals(X, 'Start', 'Lossy')
result = identifying_information(x_intervals)
print(result)
> 1.210777084415

X = ['C','C','A','C','G','C','T','T','A','C']
x_intervals = intervals(X, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 1.5661778097771987

X = ['C','C','A','C','G','C','T','T','A','C']
x_intervals = intervals(X, 'End', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 1.35849625

X = ['C','C','A','C','G','C','T','T','A','C']
x_intervals = intervals(X, 'End', 'Redundant')
result = identifying_information(x_intervals)
print(result)
> 1.5294637608763

X = ['C','C','A','C','G','C','T','T','A','C'] 
x_intervals = intervals(X, 'End', 'Cycle')
result = identifying_information(x_intervals)
print(result)
> 1.76096404744368

---

X = ['C','G'] 
x_intervals = intervals(X, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 0.5

X = ['C','G'] 
x_intervals = intervals(X, 'End', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 0.5

X = ['C','G'] 
x_intervals = intervals(X, 'End', 'Redundant')
result = identifying_information(x_intervals)
print(result)
> 0.5849625007

X = ['C','G'] 
x_intervals = intervals(X, 'End', 'Cycle')
result = identifying_information(x_intervals)
print(result)
> 1

---

X = ['C','C','C','C'] 
x_intervals = intervals(X, 'Start', 'Lossy')
result = identifying_information(x_intervals)
print(result)
> 0

X =['C','C','C','C']  
x_intervals = intervals(X, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 0

X = ['C','C','C','C'] 
x_intervals = intervals(X, 'End', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 0

X = ['C','C','C','C'] 
x_intervals = intervals(X, 'End', 'Redundant')
result = identifying_information(x_intervals)
print(result)
> 0

X = ['C','C','C','C'] 
x_intervals = intervals(X, 'End', 'Cycle')
result = identifying_information(x_intervals)
print(result)
> 0

---

X =  ['A','C','G','T'] 
x_intervals = intervals(X, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 1.1462406252

X = ['A','C','G','T'] 
x_intervals = intervals(X, 'End', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 1.1462406252

X = ['A','C','G','T'] 
x_intervals = intervals(X, 'End', 'Redundant')
result = identifying_information(x_intervals)
print(result)
> 1.3219280949

X = ['A','C','G','T'] 
x_intervals = intervals(X, 'End', 'Cycle')
result = identifying_information(x_intervals)
print(result)
> 2

---

X = ['A','A','A','A','C','G','T'] 
x_intervals = intervals(X, 'Start', 'Lossy')
result = identifying_information(x_intervals)
print(result)
> 0

X = ['A','A','A','A','C','G','T'] 
x_intervals = intervals(X, 'Start', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 1.102035074

X = ['A','A','A','A','C','G','T'] 
x_intervals = intervals(X, 'End', 'Normal')
result = identifying_information(x_intervals)
print(result)
> 0.830626027

X = ['A','A','A','A','C','G','T'] 
x_intervals = intervals(X, 'End', 'Redundant')
result = identifying_information(x_intervals)
print(result)
> 1.3991235932

X = ['A','A','A','A','C','G','T'] 
x_intervals = intervals(X, 'End', 'Cycle')
result = identifying_information(x_intervals)
print(result)
> 1.6644977792

No intervals

X = ['C','G'] 
x_intervals = intervals(X, 'End', 'Lossy')
result = identifying_information(x_intervals)
print(result)
> 1

X = ['A','C','G','T'] 
x_intervals = intervals(X, 'End', 'Lossy')
result = identifying_information(x_intervals)
print(result)
> 1

X = [2, 1] 
x_intervals = intervals(X, 'End', 'Lossy')
result = identifying_information(x_intervals)
print(result)
> 1