Strange comportement of list/array

Question

I want to understand why the comportement of my array is like that:

import numpy as np
import math
n=10
P=np.array([[0]*n]*n)
P[2][2]=1 #It works as I want
for i in range(n):
 for j in range(n):
 P[i][j]=math.comb(n,j+1)*((i+1)/n)**(j+1)*(1-(i+1)/n)**(n-j-1)
 print(math.comb(n,j+1)*((i+1)/n)**(j+1)*(1-(i+1)/n)**(n-j-1))
print(P)

I get as a result for P an array with only 0 except 1 for the (n,n) position but values printed are not 0.

I suppose it comes from the fact that I use [[0]*n]*n for my list with mutable/immutable variable because it works well when I use np.zeros() but I don't understand why it works when I set value manually (with P[2][2]=1 for example)

Thanks

Answer 1

The way you are creating the array is defaulting to an integer dtype because it uses the first value to determine the type if you don't explicitly set it. You can demonstrate this by trying to assign a float instead of an int with

P[2][2]=1 #It works as I want
P[2][2]=0.3 #It doesn't work

To use your approach you need to create an array with a dtype of float so values don't get clipped: P=np.array([[0.0]*n]*n) or P=np.array([[0]*n]*n, dtype=float).

This will produce an array of the expected values:

array([[3.87420489e-01, 1.93710245e-01, 5.73956280e-02, 1.11602610e-02,
 1.48803480e-03, 1.37781000e-04, 8.74800000e-06, 3.64500000e-07,
 9.00000000e-09, 1.00000000e-10],
 [2.68435456e-01, 3.01989888e-01, 2.01326592e-01, 8.80803840e-02,
 2.64241152e-02, 5.50502400e-03, 7.86432000e-04, 7.37280000e-05,
 4.09600000e-06, 1.02400000e-07], 
 ...

• Wick: Thanks for that answer! I thought de default type would have been float
• chepner: Another approach would be to use P = np.zeros((n, n)) for initialization, which does use float as the default dtype. This is also more efficient than having to build a possibly large nested list first.
• Mark: Yes, @chepner the OP says as much..."it works well when I use np.zeros()", but worth highlighting.
• chepner: Oh, yeah, I missed that in the middle of the question.