Finding Moving Average from Data Points in Python

Finding moving average from data points in Python

Before reading this answer, bear in mind that there is another answer below, from Roman Kh, which uses numpy.cumsum and is MUCH MUCH FASTER than this one.

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Best One common way to apply a moving/sliding average (or any other sliding window function) to a signal is by using numpy.convolve().

def movingaverage(interval, window_size):
    window = numpy.ones(int(window_size))/float(window_size)
    return numpy.convolve(interval, window, 'same')

Here, interval is your x array, and window_size is the number of samples to consider. The window will be centered on each sample, so it takes samples before and after the current sample in order to calculate the average. Your code would become:

plot(x,y)
xlim(0,1000)

x_av = movingaverage(interval, r)
plot(x_av, y)

xlabel("Months since Jan 1749.")
ylabel("No. of Sun spots")
show()

Moving average or running mean

For a short, fast solution that does the whole thing in one loop, without dependencies, the code below works great.

mylist = [1, 2, 3, 4, 5, 6, 7]
N = 3
cumsum, moving_aves = [0], []

for i, x in enumerate(mylist, 1):
    cumsum.append(cumsum[i-1] + x)
    if i>=N:
        moving_ave = (cumsum[i] - cumsum[i-N])/N
        #can do stuff with moving_ave here
        moving_aves.append(moving_ave)

Moving average on list of (x,y) points in python

Here is an example using a convolution of size s:

v = np.array([(0, 4), (1, 5), (2, 6), (-1, 9), (3, 7), (4, 8), (5, 9)])
s = 2

kernel = np.ones(s)
x = np.convolve(v[:,0], kernel, 'valid') / s
y = np.convolve(v[:,1], kernel, 'valid') / s
res = np.hstack((x[:, None], y[:, None]))

print(res)

Output:

[[0.5 4.5]
 [1.5 5.5]
 [0.5 7.5]
 [1.  8. ]
 [3.5 7.5]
 [4.5 8.5]]

The bigger s, the smoother the path. However, the bigger s, the shorter the path.

How to calculate rolling / moving average using python + NumPy / SciPy?

A simple way to achieve this is by using np.convolve.
The idea behind this is to leverage the way the discrete convolution is computed and use it to return a rolling mean. This can be done by convolving with a sequence of np.ones of a length equal to the sliding window length we want.

In order to do so we could define the following function:

def moving_average(x, w):
    return np.convolve(x, np.ones(w), 'valid') / w

This function will be taking the convolution of the sequence x and a sequence of ones of length w. Note that the chosen mode is valid so that the convolution product is only given for points where the sequences overlap completely.

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Some examples:

x = np.array([5,3,8,10,2,1,5,1,0,2])

For a moving average with a window of length 2 we would have:

moving_average(x, 2)
# array([4. , 5.5, 9. , 6. , 1.5, 3. , 3. , 0.5, 1. ])

And for a window of length 4:

moving_average(x, 4)
# array([6.5 , 5.75, 5.25, 4.5 , 2.25, 1.75, 2.  ])

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How does convolve work?

Lets have a more in depth look at the way the discrete convolution is being computed.
The following function aims to replicate the way np.convolve is computing the output values:

def mov_avg(x, w):
    for m in range(len(x)-(w-1)):
        yield sum(np.ones(w) * x[m:m+w]) / w 

Which, for the same example above would also yield:

list(mov_avg(x, 2))
# [4.0, 5.5, 9.0, 6.0, 1.5, 3.0, 3.0, 0.5, 1.0]

So what is being done at each step is to take the inner product between the array of ones and the current window. In this case the multiplication by np.ones(w) is superfluous given that we are directly taking the sum of the sequence.

Bellow is an example of how the first outputs are computed so that it is a little clearer. Lets suppose we want a window of w=4:

[1,1,1,1]
[5,3,8,10,2,1,5,1,0,2]
= (1*5 + 1*3 + 1*8 + 1*10) / w = 6.5

And the following output would be computed as:

  [1,1,1,1]
[5,3,8,10,2,1,5,1,0,2]
= (1*3 + 1*8 + 1*10 + 1*2) / w = 5.75

And so on, returning a moving average of the sequence once all overlaps have been performed.

moving average in python

if lst[i] < n:

You do not define i

but I guess i is a index of lst so try:

for i, _ in enumerate(lst):
  if lst[i] < n:
    s += lst[n - (n-i)]

EDIT:

def gen(lst, n):
    if n > len(lst):
        print("Sorry can't do this")
    try:
        for i, _ in enumerate(lst[:-(n-1)]):
            s = sum(lst[i:i+n])
            yield s/n
    except ZeroDivisionError:
        print("Sorry can't do this")

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