Computing the distance between each pair of points

[Truman]

X = rand.rand(10, 2)
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn; seaborn.set() # Plot styling
plt.scatter(X[:, 0], X[:, 1], s=100);
dist_sq = np.sum((X[:, np.newaxis, :] - X[np.newaxis, :, :]) ** 2, axis=-1)

what I don't undersand is this part:

differences = X[:, np.newaxis, :] - X[np.newaxis, :, :]

what's happening between these two brackets, these two colons. Help is appreciated.

[buran]

https://numpy.org/doc/stable/reference/a...exing.html

Each newaxis object in the selection tuple serves to expand the dimensions of the resulting selection by one unit-length dimension. The added dimension is the position of the newaxis object in the selection tuple.

Example

>>>x[:,np.newaxis,:,:].shape
(2, 1, 3, 1)

This example depends on previous examples, so check it from the start

[Truman]

Yes, I know what newaxis stands for but these two colons in each bracket are making me headache. Thank you anyway. I asked the same question on the biggest python facebook group and noone was able to answer exactly.

[buran]

Ah, I misunderstood your question
At the very start of the link in my previous post it explains slicing. I am sure you are familiar.
So basically it is a slice at each axis of the multidimensional array, slices are separated with commas.
Inside [], colon is translated into slice and it is passed to __getitem__ as tuple. See also https://stackoverflow.com/a/39482568/4046632

[buran]

one example

import numpy as np
rand = np.random.RandomState(42)
X = rand.rand(10, 5)
print(X)
print(X[:2, ::2])

Output:
[[0.37454012 0.95071431 0.73199394 0.59865848 0.15601864]
 [0.15599452 0.05808361 0.86617615 0.60111501 0.70807258]
 [0.02058449 0.96990985 0.83244264 0.21233911 0.18182497]
 [0.18340451 0.30424224 0.52475643 0.43194502 0.29122914]
 [0.61185289 0.13949386 0.29214465 0.36636184 0.45606998]
 [0.78517596 0.19967378 0.51423444 0.59241457 0.04645041]
 [0.60754485 0.17052412 0.06505159 0.94888554 0.96563203]
 [0.80839735 0.30461377 0.09767211 0.68423303 0.44015249]
 [0.12203823 0.49517691 0.03438852 0.9093204  0.25877998]
 [0.66252228 0.31171108 0.52006802 0.54671028 0.18485446]]
[[0.37454012 0.73199394 0.15601864]
 [0.15599452 0.86617615 0.70807258]]

as you can see on the first axis :2 is translated into 0:2:1 slice and it takes only first 2 elements
the second ::2 is translated into 0::2 slice so on second axis it takes elements with index 0, 2, 4

[Truman]

This last example of yours is perfectly clear. Now I'll have to go back to the one from the book. But first to read given docs.

[Truman]

It looks that this operation adds an axis to my array, turning it from 2D into 3D

X[:, np.newaxis, :]

Output:
array([[[0.37454012, 0.95071431]],

       [[0.73199394, 0.59865848]],

       [[0.15601864, 0.15599452]],

       [[0.05808361, 0.86617615]],

       [[0.60111501, 0.70807258]],

       [[0.02058449, 0.96990985]],

       [[0.83244264, 0.21233911]],

       [[0.18182497, 0.18340451]],

       [[0.30424224, 0.52475643]],

       [[0.43194502, 0.29122914]]])

[buran]

Yes, that's the effect of np.newaxis. You said you know it...

[Truman]

Yes, it's just that I still don't understand the contest...

[Truman]

I'm now reading docs that you provided and smth doesn't work well.

import numpy as np 
x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
x[:,np.newaxis,:,:].shape

Error:
IndexError                                Traceback (most recent call last)
 in 
      2 x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
      3 print(x[...,0])
----> 4 x[:,np.newaxis,:,:].shape

IndexError: too many indices for array