Efficiently Picking Columns from Rows in NumPy (List of Indices)

You have a two-dimensional NumPy array (like a spreadsheet) and you want to extract specific columns from each row based on a separate list that tells you which columns to pick for each row.

Steps:

1. Import NumPy:

   import numpy as np
   

2. Create the Array and Index List:

   • Construct your NumPy array (arr) containing the data.
   • Define a list (column_indices) where each sub-list represents the column indices to select for the corresponding row in the array.

   arr = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
   column_indices = [[1, 3], [0, 2], [1, 2]]
   

3. Use Fancy Indexing (Advanced but Efficient):

   • This method leverages NumPy's advanced indexing capabilities to directly select elements based on row and column indices.

   selected_columns = arr[np.arange(len(arr))[:, None], column_indices]
   

   Explanation:

   • np.arange(len(arr))[:, None]: Creates a column vector with indices for each row (used for row selection).
   • column_indices: The list of column indices for each row.
   • Together, they form the index for fancy indexing, selecting elements at the specified rows and columns.

4. Alternative with List Comprehension (Clearer but Less Efficient):

   • This approach uses a list comprehension to iterate through rows and select columns based on the index list.

   selected_columns = [row[indices] for row, indices in zip(arr, column_indices)]
   

   • zip(arr, column_indices): Combines elements from arr and column_indices into pairs (row, indices).
   • List comprehension: Iterates over each pair, extracts elements from row using the indices in indices, and appends them to the selected_columns list.

Choosing the Right Method:

• Fancy Indexing: Generally preferred for performance, especially with larger arrays.
• List Comprehension: More readable for smaller arrays or when understanding the logic is crucial.

Example Output:

selected_columns:
array([[2, 4], [5, 7], [6, 7]])

import numpy as np

# Create the array and index list
arr = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
column_indices = [[1, 3], [0, 2], [1, 2]]

# Fancy indexing for efficient selection
selected_columns = arr[np.arange(len(arr))[:, None], column_indices]

print(selected_columns)

This code will output:

[[2 4]
 [5 7]
 [6 7]]

List Comprehension (Alternative):

import numpy as np

# Create the array and index list (same as above)

# List comprehension for clearer interpretation
selected_columns = [row[indices] for row, indices in zip(arr, column_indices)]

print(selected_columns)

[[2 4]
 [5 7]
 [6 7]]

This approach uses boolean masking to create a mask that selects the desired elements based on the index list.

import numpy as np

# Create the array and index list
arr = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
column_indices = [[1, 3], [0, 2], [1, 2]]

# Create a mask for each row based on column indices
masks = [np.isin(np.arange(len(arr[0])), indices) for indices in column_indices]

# Apply the mask to each row
selected_columns = [row[mask] for row, mask in zip(arr, masks)]

print(selected_columns)

• np.isin(np.arange(len(arr[0])), indices): Creates a boolean mask for each row, where True indicates elements at the desired column indices.
• row[mask]: Selects elements from the row based on the corresponding mask.

np.take_along_axis (Newer NumPy versions):

This method is available in newer versions of NumPy and offers a concise way to perform this kind of selection.

import numpy as np

# Create the array and index list (same as above)

# Use np.take_along_axis (requires NumPy >= 1.18)
selected_columns = np.take_along_axis(arr, column_indices, axis=1)

print(selected_columns)

• np.take_along_axis(arr, column_indices, axis=1): Selects elements from arr along axis 1 (columns) based on the indices in column_indices.

• Boolean Masking: Offers more flexibility but might be less efficient.
• np.take_along_axis (for newer NumPy): Concise and potentially efficient for compatible versions.