Looping in a 3D matrix - desperate for assistance!

[killerrex]

What you are looking for is a moving average. I use normally variations of this answer in stackoverflow

def moving_avg(a, n):
    # Notice that in the original here forces dtype=float...
    # I prefer to keep dtype of a, as not always work with float
    acc = np.cumsum(a)
    acc[n:] = acc[n:] - acc[:-n]
    return acc[n-1:] / n

Notice that this is fast but can be problematic when the array has many elements or outliers and the accumulated sum is too big and produces a degradation in the accuracy of the result.

when I have to deal with that type of arrays I prefer this version:

def ha_moving_avg(a, n):
    sz = len(a) - n + 1
    # acc = a[:sz].copy()
    acc = 0
    for k in range(n):
        acc += a[k:sz+k]
    return acc / n

Is slower, but if your data has big values or can contain outliers you can have disgusting surprises... consider the following:

def demo():

    n = 3
    # Just to print nice the arrays
    fmt = {'all': lambda x: '%.1g' % x}
    
    print("Nice inputs")
    # Let's try something nice...
    # m[k] = k so the average of 3 elements is:
    # (k + k+1 + k+2) / 3 = k + 1
    m = np.arange(10)
    ma = moving_avg(m, n)
    print("\tNormal:   " + np.array2string(ma, formatter=fmt))
    ma = ha_moving_avg(m, n)
    print("\tHigh Acc: " + np.array2string(ma, formatter=fmt))
    
    print("Broken Inputs")
    m = np.ones(10)
    m[4] = 1E20
    ma = moving_avg(m, n)
    print("\tNormal:   " + np.array2string(ma, formatter=fmt))
    ma = ha_moving_avg(m, n)
    print("\tHigh Acc: " + np.array2string(ma, formatter=fmt))


if __name__ == '__main__':
    demo()

Output:
Nice inputs
	Normal:   [1 2 3 4 5 6 7 8]
	High Acc: [1 2 3 4 5 6 7 8]
Broken Inputs
	Normal:   [1 1 3e+19 3e+19 3e+19 0 0 0]
	High Acc: [1 1 3e+19 3e+19 3e+19 1 1 1]

See the surprise?