Add Arigthmetic Mean Interval characteristic calculator for masked arrays

[ChainsManipulator]

Add calculator function for Arithmetic Mean Interval characteristic for given intervals array using formula:
$$\Delta_{a j}=\displaystyle \frac{1}{n_j} * \sum_{i=1}^{n_j} \Delta_{ij}$$
Where $\Delta_{ij}$ is an interval and $n_j$ is a number of intervals in the given congeneric sequence.

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 = arithmetic_mean(x_intervals)
print(result)
> [3.333, 2.5]

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 = arithmetic_mean(x_intervals)
print(result)
> [1,2,3]

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 = arithmetic_mean(x_intervals)
print(result)
> [3,2,1]

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', 'Lossy')
result = arithmetic_mean(x_intervals)
print(result)
> [2]

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 = arithmetic_mean(x_intervals)
print(result)
> [2.6667]

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 = arithmetic_mean(x_intervals)
print(result)
> [2.3333]

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 = arithmetic_mean(x_intervals)
print(result)
> [2.75]

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 = arithmetic_mean(x_intervals)
print(result)
> [3.3333]

X = ['A','A','A','B','A','B','B','A','A','A','A','B','A','A','A']
mask = [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1]
masked_X = ma.masked_array(X, mask)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Lossy')
result = arithmetic_mean(x_intervals)
print(result)
> [2.6667]

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

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

X = ['A','A','A','B','A','B','B','A','A','A','A','B','A','A','A']
mask = [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1]
masked_X = ma.masked_array(X, mask)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Redundant')
result = arithmetic_mean(x_intervals)
print(result)
> [3.2]

X = ['A','A','A','B','A','B','B','A','A','A','A','B','A','A','A']
mask = [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1]
masked_X = ma.masked_array(X, mask)
order, alphabet = ma.order(masked_X, True)
x_intervals = ma.intervals(order, 'Start', 'Cycle')
result = arithmetic_mean(x_intervals)
print(result)
> [3.75]

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

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

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

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

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 = arithmetic_mean(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 = arithmetic_mean(x_intervals)
print(result)
> [8]

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 = arithmetic_mean(x_intervals)
print(result)
> [1]

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 = arithmetic_mean(x_intervals)
print(result)
> [4.5]

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 = arithmetic_mean(x_intervals)
print(result)
> [8]

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 = arithmetic_mean(x_intervals)
print(result)
> [1]

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 = arithmetic_mean(x_intervals)
print(result)
> [1]

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 = arithmetic_mean(x_intervals)
print(result)
> [1]

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 = arithmetic_mean(x_intervals)
print(result)
> [1]

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 = arithmetic_mean(x_intervals)
print(result)
> [1]