Apply function n items at a time along axis

Question

I am looking for a way to apply a function n items at the time along an axis. E.g.

array([[ 1,  2], 
       [ 3,  4],
       [ 5,  6],
       [ 7,  8]])

If I apply sum across the rows 2 items at a time I get:

array([[  4,   6], 
       [ 12,  14]])

Which is the sum of 1st 2 rows and the last 2 rows.

NB: I am dealing with much larger array and I have to apply the function to n items which I can be decided at runtime.

---

The data extends along different axis. E.g.

array([[... [ 1,  2, ...], 
            [ 3,  4, ...],
            [ 5,  6, ...],
            [ 7,  8, ...],
            ...], ...])

Answer 1

This is a reduction:

numpy.add.reduceat(a, [0,2])
>>> array([[ 4,  6],
           [12, 14]], dtype=int32)

As long as by "larger" you mean longer in the "y" axis, you can extend:

a = numpy.array([[ 1,  2],
                 [ 3,  4],
                 [ 5,  6],
                 [ 7,  8],
                 [ 9, 10],
                 [11, 12]])
numpy.add.reduceat(a, [0,2,4])
>>> array([[ 4,  6],
           [12, 14],
           [20, 22]], dtype=int32)

EDIT: actually, this works fine for "larger in both dimensions", too:

a = numpy.arange(24).reshape(6,4)
numpy.add.reduceat(a, [0,2,4])
>>> array([[ 4,  6,  8, 10],
           [20, 22, 24, 26],
           [36, 38, 40, 42]], dtype=int32)

I will leave it up to you to adapt the indices to your specific case.

Answer 2

Reshape splitting the first axis into two axes, such that the second split axis is of length n to have a 3D array and then sum along that split axis, like so -

a.reshape(a.shape[0]//n,n,a.shape[1]).sum(1)

It should be pretty efficient as reshaping just creates a view into input array.

Sample run -

In [55]: a
Out[55]: 
array([[2, 8, 0, 0],
       [1, 5, 3, 3],
       [6, 1, 4, 7],
       [0, 4, 0, 7],
       [8, 0, 8, 1],
       [8, 3, 3, 8]])

In [56]: n = 2 # Sum every two rows

In [57]: a.reshape(a.shape[0]//n,n,a.shape[1]).sum(1)
Out[57]: 
array([[ 3, 13,  3,  3],
       [ 6,  5,  4, 14],
       [16,  3, 11,  9]])

Answer 3

How about something like this?

n = 2
# calculate the cumsum along axis 0 and take one row from every n rows
cumarr = arr.cumsum(axis = 0)[(n-1)::n]                

# calculate the difference of the resulting numpy array along axis 0   
np.vstack((cumarr[0][None, :], np.diff(cumarr, axis=0)))

# array([[ 4,  6],
#        [12, 14]])