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Element layout for calculating average value in Python / NumPy

I have a 1st list as follows:

data = [1,5,9,13, 2,6,10,14, 3,7,11,15, 4,8,12,16]

I want to make the following list of tuples and calculate the average value of each tuple separately.

 [(1,5,2,6), (3,7,4,8), (9,13,10,14), (11,15,12,16)]

Expected Result:

 [3.5, 5.5, 11.5, 13.5]

What is easier to do?

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3 answers

Put the data in a 4-dimensional numpy array with the shape (2, 2, 2, 2), then take the average of this array over the axes 1 and 3:

 In [25]: data Out[25]: [1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15, 4, 8, 12, 16] In [26]: a = np.array(data).reshape(2, 2, 2, 2) In [27]: a Out[27]: array([[[[ 1, 5], [ 9, 13]], [[ 2, 6], [10, 14]]], [[[ 3, 7], [11, 15]], [[ 4, 8], [12, 16]]]]) In [28]: a.mean(axis=(1, 3)) Out[28]: array([[ 3.5, 11.5], [ 5.5, 13.5]])

You can use the ravel() method if you need the final result as the 1st array:

 In [31]: a.mean(axis=(1, 3)).ravel() Out[31]: array([ 3.5, 11.5, 5.5, 13.5])

See How can I vectorize the averaging of 2x2 numpy arrays? for a similar question.

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Here is one approach

 In [29]: a = np.array(data) In [30]: a2 = a.reshape(4,4) In [31]: a3 = np.vstack((a2[:, :2], a2[:, 2:])) In [32]: a4 = a3.reshape(4,4) In [33]: np.mean(a4, axis=1) Out[33]: array([ 3.5, 5.5, 11.5, 13.5])
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This post lists some solution options -

 def grouped_mean(data,M2,N1,N2): # Paramters: # M2 = Columns in input data # N1, N2 = Blocksize into which data is to be divided and averaged # Get grouped mean values; transpose and flatten for final output grouped_mean = np.array(data).reshape(-1,N2).sum(1).reshape(-1,N1,M2/N2).sum(1)/(N1*N2) # Return transposed and flattened version as output (as per OP) return grouped_mean.T.ravel()

Now grouped_mean can be calculated using np.einsum instead of np.sum , like this -

 stage1_sum = np.einsum('ij->i',np.array(data).reshape(-1,N2)) grouped_mean = np.einsum('ijk->ik',stage1_sum.reshape(-1,N1,M2/N2))/(N1*N2)

Or you can enter with the splitting of the 2D input array into a 4D array, as suggested by the @Warren Weckesser solution , and then use np.einsum in the same way -

 split_data = np.array(data).reshape(-1, N1, M2/N2, N2) grouped_mean = np.einsum('ijkl->ik',split_data)/(N1*N2)

Run Example -

 In [182]: data = np.array([[1,5,9,13], ...: [2,6,10,14], ...: [3,7,11,15], ...: [4,8,12,16]]) In [183]: grouped_mean(data,4,2,2) Out[183]: array([ 3.5, 5.5, 11.5, 13.5])

Runtime tests

Computing grouped_mean seems to be the most computationally intensive piece of code. So here are some run-time tests for calculating with these three approaches -

 In [174]: import numpy as np ...: # Setup parameters and input list ...: M2 = 4000 ...: N1 = 2 ...: N2 = 2 ...: data = np.random.randint(0,9,(16000000)).tolist() ...: In [175]: %timeit np.array(data).reshape(-1,N2).sum(1).reshape(-1,N1,M2/N2).sum(1)/(N1*N2) ...: %timeit np.einsum('ijk->ik',np.einsum('ij->i',np.array(data).reshape(-1,N2)).reshape(-1,N1,M2/N2))/(N1*N2) ...: %timeit np.einsum('ijkl->ik',np.array(data).reshape(-1, N1, M2/N2, N2))/(N1*N2) ...: 1 loops, best of 3: 2.2 s per loop 1 loops, best of 3: 2.12 s per loop 1 loops, best of 3: 2.1 s per loop
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