what is happening in the given numpy code. I'm confused for the last line print() statement

Question

the print() statement will print the rows of array X??

import numpy as np
X = np.arange(12).reshape((3, 4))
row = np.array([0, 1, 2])
mask = np.array([1, 0, 1, 0], dtype=bool)
print(X[row[:, np.newaxis], mask])

X = [[0, 1, 2, 3],
     [4, 5, 6, 7],
     [8, 9, 10, 11]]

row = [0, 1, 2]
mask = [True, False, True, False]

array row changes to a 2d array after adding a new axis. shape of row is (3,1)

row = [[0],
       [1],
       [2]]

after print(), the result HOW??

  [[0, 2],
   [4, 6],
   [8, 10]]

Answer 1

To understand the given Python code and the output it generates, let's break down the process step by step, focusing on the key components involved: NumPy arrays, indexing, and the manipulation of shapes for advanced selection.

1. NumPy Array Creation

The code starts by creating a 2D NumPy array named X:

X = np.arange(12).reshape((3, 4))

• np.arange(12) generates a 1D array with numbers from 0 to 11.
• .reshape((3, 4)) reshapes this array into a 2D array with 3 rows and 4 columns:

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

2. Index Arrays

Two additional arrays are defined:

• row = np.array([0, 1, 2]) specifies row indices.
• mask = np.array([1, 0, 1, 0], dtype=bool) is a boolean mask for selecting columns.

Since True corresponds to 1 and False to 0, it effectively becomes [True, False, True, False], meaning that it will select the first and third columns and skip the second and fourth.

3. Adding a New Axis

• row[:, np.newaxis] transforms row from a 1D array ([0, 1, 2]) into a 2D array by adding a new axis:

[[0], [1], [2]]

This change in shape is crucial for the next step.

4. Advanced Indexing

The expression X[row[:, np.newaxis], mask] performs advanced indexing on X:

• row[:, np.newaxis] indicates which rows to select, and its 2D shape allows for broadcasting.
• mask selects columns based on its boolean values.

Because row has been reshaped to a 2D array, and mask is a 1D boolean array, NumPy broadcasts them to perform element-wise selection. This means for each row specified by row, it selects elements where mask is True.

5. Result Explanation

The final output is:

[[ 0, 2], [ 4, 6], [ 8, 10]]

Here's how the result is achieved:

• For the first row [0, 1, 2, 3], applying the mask [True, False, True, False] results in [0, 2].
• For the second row [4, 5, 6, 7], the same mask yields [4, 6].
• For the third row [8, 9, 10, 11], again, the mask results in [8, 10].

Thus, the operation selects elements [0, 2] from the first row, [4, 6] from the second row, and [8, 10] from the third row, aligning with the specified row indices and column mask. This demonstrates a powerful aspect of NumPy's advanced indexing capabilities, enabling complex selections through broadcasting and boolean masking.