Add Geometric Mean characteristic calculator

[ChainsManipulator]

Add calculator function for Geometric Mean characteristic for given intervals array using formula:
$$\displaystyle \Delta_g=\sqrt[n]{V}= \sqrt[n]{\prod_{j=1}^{m} \prod_{i=1}^{n_j} \Delta_{ij}}$$
Where $\Delta_{ij}$ is an interval and $n$ is number of intervals in the sequence.

Examples

X = [2, 4, 2, 2, 4]
x_intervals = intervals(X, 'Start', 'Normal')
result = geometric_mean(x_intervals)
print(result)
> 1,64375

X = ['B','B','A','A','C','B','A','C','C','B']
x_intervals = intervals(X, 'Start', 'Lossy')
result = geometric_mean(x_intervals)
print(result)
> 2.0339

X = ['B','B','A','A','C','B','A','C','C','B']
x_intervals = intervals(X, 'Start', 'Normal')
result = geometric_mean(x_intervals)
print(result)
> 2.155

X = ['B','B','A','A','C','B','A','C','C','B']
x_intervals = intervals(X, 'End', 'Normal')
result = geometric_mean(x_intervals)
print(result)
> 2.0237

X = ['B','B','A','A','C','B','A','C','C','B']
x_intervals = intervals(X, 'Start', 'Redundant')
result = geometric_mean(x_intervals)
print(result)
> 2.1182

X = ['B','B','A','A','C','B','A','C','C','B']
x_intervals = intervals(X, 'Start', 'Cycle')
result = geometric_mean(x_intervals)
print(result)
> 2.3522

---

X = ['C','C','A','C','G','C','T','T','A','C']
x_intervals = intervals(X, 'Start', 'Lossy')
result = geometric_mean(x_intervals)
print(result)
> 2.139826387867

X = ['C','C','A','C','G','C','T','T','A','C']
x_intervals = intervals(X, 'Start', 'Normal')
result = geometric_mean(x_intervals)
print(result)
> 2.513888742864

X = ['C','C','A','C','G','C','T','T','A','C']
x_intervals = intervals(X, 'End', 'Normal')
result = geometric_mean(x_intervals)
print(result)
> 2.25869387

X = ['C','C','A','C','G','C','T','T','A','C']
x_intervals = intervals(X, 'End', 'Redundant')
result = geometric_mean(x_intervals)
print(result)
> 2.4953181811241978

X = ['C','C','A','C','G','C','T','T','A','C']
x_intervals = intervals(X, 'End', 'Cycle')
result = geometric_mean(x_intervals)
print(result)
> 2.843527111557

---

X = ['C','C','C','C'] 
x_intervals = intervals(X, 'Start', 'Lossy')
result = geometric_mean(x_intervals)
print(result)
> 1

X =['C','C','C','C']  
x_intervals = intervals(X, 'Start', 'Normal')
result = geometric_mean(x_intervals)
print(result)
> 1

X = ['C','C','C','C'] 
x_intervals = intervals(X, 'End', 'Normal')
result = geometric_mean(x_intervals)
print(result)
> 1

X = ['C','C','C','C'] 
x_intervals = intervals(X, 'End', 'Redundant')
result = geometric_mean(x_intervals)
print(result)
> 1

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

No intervals

X = ['C','G'] 
x_intervals = intervals(X, 'End', 'Lossy')
result = geometric_mean(x_intervals)
print(result)
> 0

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

X = [2, 1] 
x_intervals = intervals(X, 'End', 'Lossy')
result = geometric_mean(x_intervals)
print(result)
> 0

Inequalities with arithmetic mean

X = [10, 87, 10, 87, 10, 87] 
x_intervals = intervals(X, 'Start', 'Lossy')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [10, 87, 10, 87, 10, 87] 
x_intervals = intervals(X, 'End', 'Lossy')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [10, 87, 10, 87, 10, 87] 
x_intervals = intervals(X, 'Start', 'Normal')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [10, 87, 10, 87, 10, 87] 
x_intervals = intervals(X, 'End', 'Normal')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [10, 87, 10, 87, 10, 87] 
x_intervals = intervals(X, 'Start', 'Redundant')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [10, 87, 10, 87, 10, 87] 
x_intervals = intervals(X, 'End', 'Redundant')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [10, 87, 10, 87, 10, 87] 
x_intervals = intervals(X, 'Start', 'Cycle')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [10, 87, 10, 87, 10, 87] 
x_intervals = intervals(X, 'End', 'Cycle')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

---

X = [1, 1, 3, 1, 1] 
x_intervals = intervals(X, 'Start', 'Lossy')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [1, 1, 3, 1, 1] 
x_intervals = intervals(X, 'End', 'Lossy')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [1, 1, 3, 1, 1] 
x_intervals = intervals(X, 'Start', 'Normal')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [1, 1, 3, 1, 1] 
x_intervals = intervals(X, 'End', 'Normal')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [1, 1, 3, 1, 1] 
x_intervals = intervals(X, 'Start', 'Redundant')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [1, 1, 3, 1, 1] 
x_intervals = intervals(X, 'End', 'Redundant')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [1, 1, 3, 1, 1] 
x_intervals = intervals(X, 'Start', 'Cycle')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [1, 1, 3, 1, 1] 
x_intervals = intervals(X, 'End', 'Cycle')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

---

X = [13, 13, 13, 13] 
x_intervals = intervals(X, 'Start', 'Lossy')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [13, 13, 13, 13] 
x_intervals = intervals(X, 'End', 'Lossy')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [13, 13, 13, 13] 
x_intervals = intervals(X, 'Start', 'Normal')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [13, 13, 13, 13] 
x_intervals = intervals(X, 'End', 'Normal')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [13, 13, 13, 13] 
x_intervals = intervals(X, 'Start', 'Redundant')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [13, 13, 13, 13] 
x_intervals = intervals(X, 'End', 'Redundant')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [13, 13, 13, 13]  
x_intervals = intervals(X, 'Start', 'Cycle')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = [13, 13, 13, 13] 
x_intervals = intervals(X, 'End', 'Cycle')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

---

X = ['A', 'A', 'B', 'B'] 
x_intervals = intervals(X, 'Start', 'Lossy')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['A', 'A', 'B', 'B'] 
x_intervals = intervals(X, 'End', 'Lossy')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['A', 'A', 'B', 'B'] 
x_intervals = intervals(X, 'Start', 'Normal')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['A', 'A', 'B', 'B'] 
x_intervals = intervals(X, 'End', 'Normal')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['A', 'A', 'B', 'B'] 
x_intervals = intervals(X, 'Start', 'Redundant')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['A', 'A', 'B', 'B'] 
x_intervals = intervals(X, 'End', 'Redundant')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['A', 'A', 'B', 'B'] 
x_intervals = intervals(X, 'Start', 'Cycle')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['A', 'A', 'B', 'B'] 
x_intervals = intervals(X, 'End', 'Cycle')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

---

X = ['B'] 
x_intervals = intervals(X, 'Start', 'Lossy')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['B'] 
x_intervals = intervals(X, 'End', 'Lossy')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['B'] 
x_intervals = intervals(X, 'Start', 'Normal')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['B'] 
x_intervals = intervals(X, 'End', 'Normal')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['B'] 
x_intervals = intervals(X, 'Start', 'Redundant')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['B'] 
x_intervals = intervals(X, 'End', 'Redundant')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['B'] 
x_intervals = intervals(X, 'Start', 'Cycle')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true

X = ['B'] 
x_intervals = intervals(X, 'End', 'Cycle')
delta_g = geometric_mean(x_intervals)
delta_a = arithmetic_mean(x_intervals)
print(delta_g  <= delta_a)
> true