Absolute difference of two NumPy arrays

Question

Is there an efficient way/function to subtract one matrix from another and writing the absolute values in a new matrix? I can do it entry by entry but for big matrices, this will be fairly slow...

For example:

X = [[12,7,3],
[4 ,5,6],
[7 ,8,9]]

Y = [[5,8,1],
[6,7,3],
[4,5,9]]

for i in range(len(r_0)):
    for j in range(len(r)):
        delta_r[i][j]= sqrt((r[i][j])**2 - (r_0[i][j])**2)

Answer 1

If you want the absolute element-wise difference between both matrices, you can easily subtract them with NumPy and use numpy.absolute on the resulting matrix.

import numpy as np

X = [[12,7,3],
[4 ,5,6],
[7 ,8,9]]

Y = [[5,8,1],
[6,7,3],
[4,5,9]]

result = np.absolute(np.array(X) - np.array(Y))

Outputs:

[[7 1 2]
 [2 2 3]
 [3 3 0]]

---

Alternatively (although unnecessary), if you were required to do so in native Python you could zip the dimensions together in a nested list comprehension.

result = [[abs(a-b) for a, b in zip(xrow, yrow)]
          for xrow, yrow in zip(X,Y)]

Outputs:

[[7, 1, 2], [2, 2, 3], [3, 3, 0]]

Answer 2

Doing this becomes trivial if you cast your 2D arrays to numpy arrays:

import numpy as np

X = [[12, 7, 3],
     [4,  5, 6],
     [7,  8, 9]]

Y = [[5,  8, 1],
     [6,  7, 3],
     [4,  5, 9]]

X, Y = map(np.array, (X, Y))

result = X - Y

Numpy is designed to work easily and efficiently with matrices.

Also, you spoke about subtracting matrices, but you also seemed to want to square the individual elements and then take the square root on the result. This is also easy with numpy:

result = np.sqrt((A ** 2) - (B ** 2))