Question

I am looking for a fast formulation to do a numerical binning of a 2D numpy array. By binning I mean calculate submatrix averages or cumulative values. For ex. x = numpy.arange(16).reshape(4, 4) would have been splitted in 4 submatrix of 2×2 each and gives numpy.array([[2.5,4.5],[10.5,12.5]]) where 2.5=numpy.average([0,1,4,5]) etc…

How to perform such an operation in an efficient way… I don’t have really any ideay how to perform this …

Many thanks…

Answer 1

You can use a higher dimensional view of your array and take the average along the extra dimensions:

In [12]: a = np.arange(36).reshape(6, 6)

In [13]: a
Out[13]: 
array([[ 0,  1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10, 11],
       [12, 13, 14, 15, 16, 17],
       [18, 19, 20, 21, 22, 23],
       [24, 25, 26, 27, 28, 29],
       [30, 31, 32, 33, 34, 35]])

In [14]: a_view = a.reshape(3, 2, 3, 2)

In [15]: a_view.mean(axis=3).mean(axis=1)
Out[15]: 
array([[  3.5,   5.5,   7.5],
       [ 15.5,  17.5,  19.5],
       [ 27.5,  29.5,  31.5]])

In general, if you want bins of shape (a, b) for an array of (rows, cols), your reshaping of it should be .reshape(rows // a, a, cols // b, b). Note also that the order of the .mean is important, e.g. a_view.mean(axis=1).mean(axis=3) will raise an error, because a_view.mean(axis=1) only has three dimensions, although a_view.mean(axis=1).mean(axis=2) will work fine, but it makes it harder to understand what is going on.

As is, the above code only works if you can fit an integer number of bins inside your array, i.e. if a divides rows and b divides cols. There are ways to deal with other cases, but you will have to define the behavior you want then.