How to combine two columsn/rows of a matrix in numpy by summing values?

Question

I\'m using numpy and am trying to figure out an issue I\'m having with matrices. Say I have a 3 x 3 matrix and want to transform it into a 2 x 2 matrix through summing the first

Answer 1

You can do this using integer array indexing and the "axis" option in numpy's sum. For example, starting with:

import numpy as np
a = np.arange(16).reshape(4,4)
list0 = [0,1,2]
list1 = [3]

The initial array is

array([[ 0,  1,  2,  3],
   [ 4,  5,  6,  7],
   [ 8,  9, 10, 11],
   [12, 13, 14, 15]])

The lists of indices can be used to "select" only the rows you want from an array. For example,

a[list0,:]

is

array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])

Also, rows of an array can be added together using the "axis=0" argument in numpy's sum, and the result is a 1D array. For example,

np.sum(a[list0,:],axis=0)

results in

array([12, 15, 18, 21])

Summing like this we can build the row-summed array row by row:

b = np.zeros((2,a.shape[1]))
b[0,:] = np.sum(a[list0,:],axis=0)
b[1,:] = np.sum(a[list1,:],axis=0)

The resulting array is

array([[12., 15., 18., 21.],
   [12., 13., 14., 15.]])

A similar thing can be done for the columns, but with "axis=1" to add the columns:

c = np.zeros((2,2))
c[:,0] = np.sum(b[:,list0],axis=1)
c[:,1] = np.sum(b[:,list1],axis=1)

which yields the 2x2 array:

array([[45., 21.],
       [39., 15.]])

If you want to do it in a more compact way, you could loop over the lists and combine them into a single array using vstack:

idx_lists = [list0, list1]
b = np.vstack([np.sum(a[idx_lists[n],:],0) for n in range(2)])

Stacking together the columns is a little trickier, since sum returns a 1D array, which is treated as a row. One solution is to vertically stack the rows together and take a transpose at the end:

c = np.vstack([np.sum(b[:,idx_lists[n]],1) for n in range(2)]).T