np.ix_() for open mesh indexing in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of np.ix_() for 2D mesh indexing

What is the output of the following code snippet using np.ix_() to create an open mesh grid?

NumPy

import numpy as np
rows = np.array([1, 3, 5])
cols = np.array([2, 4])
mesh = np.ix_(rows, cols)
result = mesh[0] + mesh[1]
print(result)

A

[[3 5]
 [5 7]
 [7 9]]

B

[[3 5 7]
 [5 7 9]]

C

[[3 5]
 [4 6]
 [5 7]]

D

[[3 5]
 [4 6]]

💡 Hint

Remember that np.ix_ creates open mesh grids that broadcast arrays for indexing.

np.ix_ creates two arrays: one column vector from rows and one row vector from cols. Adding them broadcasts to a 3x2 array where each element is sum of row and column indices.

❓ data_output

intermediate

Shape of arrays from np.ix_()

Given a = np.array([0, 1, 2]) and b = np.array([10, 20, 30, 40]), what are the shapes of the arrays returned by np.ix_(a, b)?

NumPy

import numpy as np
a = np.array([0, 1, 2])
b = np.array([10, 20, 30, 40])
mesh = np.ix_(a, b)
shapes = (mesh[0].shape, mesh[1].shape)
print(shapes)

A ((4, 1), (3, 1))

B ((3, 1), (1, 4))

C ((1, 3), (4, 1))

D ((3, 4), (3, 4))

💡 Hint

np.ix_ returns arrays shaped to broadcast for indexing: one column vector and one row vector.

np.ix_ returns arrays shaped (len(a),1) and (1,len(b)) to create an open mesh grid for indexing.

🔧 Debug

advanced

Identify the error in using np.ix_() for 3D indexing

What error will the following code raise when using np.ix_() for 3D indexing?

NumPy

import numpy as np
x = np.array([0, 1])
y = np.array([2, 3])
z = np.array([4, 5])
mesh = np.ix_(x, y, z)
arr = np.arange(60).reshape(3,4,5)
result = arr[mesh]
print(result.shape)

A ValueError: cannot reshape array of size 60 into shape (3,4,5)

B TypeError: unhashable type: 'numpy.ndarray'

C IndexError: shape mismatch: indexing arrays could not be broadcast together

D No error, prints (2, 2, 2)

💡 Hint

Check how np.ix_ arrays broadcast with the target array shape.

np.ix_ returns arrays shaped (2,1,1), (1,2,1), (1,1,2). Using these to index a (3,4,5) array causes shape mismatch because the indexing arrays cannot broadcast to the same shape.

🚀 Application

advanced

Using np.ix_() to select submatrix

You have a 5x5 matrix mat. Which option correctly uses np.ix_() to select rows 1, 3 and columns 0, 4 to create a 3x2 submatrix?

NumPy

import numpy as np
mat = np.arange(25).reshape(5,5)

A mat[[0,4]][[1,3]]

B mat[[1,3], [0,4]]

C mat[np.ix_([0,4], [1,3])]

D mat[np.ix_([1,3], [0,4])]

💡 Hint

np.ix_ creates open mesh indexing for selecting multiple rows and columns.

Option D uses np.ix_ with correct row and column indices to select a 2x2 submatrix. Option D selects elements at paired indices, not a mesh. Options C and D select wrong rows/columns or slice incorrectly.

🧠 Conceptual

expert

Why use np.ix_() instead of broadcasting arrays directly?

Why is np.ix_() preferred for open mesh indexing over directly broadcasting arrays for indexing in NumPy?

A np.ix_ ensures the indexing arrays have correct shapes to broadcast without ambiguity, preventing shape mismatch errors.

B np.ix_ compresses the indexing arrays to reduce memory usage.

C np.ix_ converts arrays to lists for compatibility with older NumPy versions.

D np.ix_ automatically sorts the indices to optimize indexing speed.

💡 Hint

Think about how np.ix_ shapes arrays for broadcasting.

np.ix_ reshapes 1D arrays into N-dimensional open mesh grids with singleton dimensions, ensuring they broadcast correctly for indexing without shape conflicts.