numpy数组：有效分配值

Question

I have an array and I want to loop through its values to update it as follows:

import numpy as np
arr=np.ones((5,7))
for i in range(1,arr.shape[0]-1):
    for j in range(1,arr.shape[1]-1):
        arr[i,j]=arr[i+1,j]+arr[i,j+1]

The result is, as desired,

[[1. 1. 1. 1. 1. 1. 1.]
 [1. 2. 2. 2. 2. 2. 1.]
 [1. 2. 2. 2. 2. 2. 1.]
 [1. 2. 2. 2. 2. 2. 1.]
 [1. 1. 1. 1. 1. 1. 1.]]

However, for-loops are quite slow and I'd like to know if there is a way to make this more efficient.

Edit: The input is not always np.ones((5,7)) , it will be something more heterogeneous in general.

Answer 1

If you draw a box around the "inner" elements, your code is setting the new value of those elements to be the sum of (a) that box "shifted one row down", and (b) that box "shifted one column to the right".

For example:

-----     -----     -----
-XXX-     -----     --XXX
-XXX-  =  -XXX-  +  --XXX
-XXX-     -XXX-     --XXX
-----     -XXX-     -----

And you can do that without loops as follows:

arr[1:-1,1:-1] = arr[2:,1:-1] + arr[1:-1,2:]

Answer 2

Here is the code for question.

import numpy as np 
a=np.random.randn(5, 7)
a1=a
a2=a
mid_mat= a[1:, :][:, :-1]+a[:, :-1][:-1, :]
a1[1:-1, 1:-1] = mid_mat[:-1, :-1]

# Assert Code

for i in range(1,a.shape[0]-1):
    for j in range(1,a.shape[1]-1):
        a2[i,j]=a[i+1,j]+a[i,j+1]

np.testing.assert_array_equal(a1, a2)