np.ix_() converts a sequence of 1D index arrays into a form suitable for building an 'open mesh', letting you select a full rectangular cross-section of specific rows and specific columns at once.

Syntax

np.ix_(rows, cols)

Deep Dive Course

Ordinary fancy indexing with two index arrays pairs them up element-wise, selecting specific (row, column) coordinate pairs rather than a rectangular block. np.ix_() reshapes each input array into a compatible broadcasting shape, a column vector for the first, a row vector for the second, and so on, so that indexing with the result instead selects every combination of the given rows crossed with the given columns — exactly the rectangular sub-block that naive two-array fancy indexing does not give you.

1Understanding np.ix_()

💡

Whenever you want 'these specific rows and these specific columns, every combination', reach for np.ix_() — plain fancy indexing with two lists gives you paired coordinates instead, which is a very different, easy-to-miss result.

editor.html

import numpy as np

matrix = np.arange(16).reshape(4, 4)
rows = [0, 2]
cols = [1, 3]
print(matrix[np.ix_(rows, cols)])

localhost:3000

2Practical Example

Here is a real-world application of np.ix_() showing how it is used in production NumPy code.

editor.html

import numpy as np

matrix = np.arange(16).reshape(4, 4)
rows = [0, 2]
cols = [1, 3]
print(matrix[rows, cols])

localhost:3000

3Best Practices

Follow these guidelines when working with np.ix_():

1. Use np.ix_() specifically when you want a rectangular cross-section of chosen rows and chosen columns, not paired coordinates

2. Compare the result's shape against your expectation after using np.ix_(), since the broadcasting-based mechanism it relies on can be non-obvious at first

3. Prefer simple slicing when the rows/columns you want happen to be contiguous — reach for np.ix_() specifically for arbitrary, non-contiguous selections

⚠️

Tip: Whenever you want 'these specific rows and these specific columns, every combination', reach for np.ix_() — plain fancy indexing with two lists gives you paired coordinates instead, which is a very different, easy-to-miss result.

editor.html

import numpy as np

matrix = np.arange(16).reshape(4, 4)
rows = [0, 2]
cols = [1, 3]
print(matrix[np.ix_(rows, cols)])

localhost:3000

Examples

Example 01Basic Usage

import numpy as np

matrix = np.arange(16).reshape(4, 4)
rows = [0, 2]
cols = [1, 3]
print(matrix[np.ix_(rows, cols)])

Example 02Advanced Example

import numpy as np

matrix = np.arange(16).reshape(4, 4)
rows = [0, 2]
cols = [1, 3]
print(matrix[rows, cols])

Best Practices

Use np.ix_() specifically when you want a rectangular cross-section of chosen rows and chosen columns, not paired coordinates
Compare the result's shape against your expectation after using np.ix_(), since the broadcasting-based mechanism it relies on can be non-obvious at first
Prefer simple slicing when the rows/columns you want happen to be contiguous — reach for np.ix_() specifically for arbitrary, non-contiguous selections

Interview Question

For the same rows and columns lists, why does using np.ix_() return a different result than plain fancy indexing with those same lists?▼

Hint: Think about paired coordinates versus every possible combination.

Plain fancy indexing with two lists pairs them up element-wise, selecting only the specific coordinates (rows[0], cols[0]), (rows[1], cols[1]), and so on, as many results as there are elements in each list. Wrapping the same lists in np.ix_() instead reshapes the index arrays so that indexing produces every combination of a row from rows with a column from cols, forming a full rectangular sub-block with as many results as the product of the two lists' lengths, which is usually the more intuitive 'give me this subset of rows and this subset of columns' behavior people actually want.

Exercises

MediumPractice using np.ix_() in a real scenario.

View Solution

import numpy as np

matrix = np.arange(16).reshape(4, 4)
rows = [0, 2]
cols = [1, 3]
print(matrix[np.ix_(rows, cols)])

Frequently Asked Questions

For the same rows and columns lists, why does using np.ix_() return a different result than plain fancy indexing with those same lists?▼

Related Functions

fancy-indexingbasic-slicingndarray-shape