[Solutions] DeprecationWarning: Arrays of 2-dimensional vectors are deprecated

Handling Deprecation Warning for 2D Vectors in NumPy cross()

As of NumPy 2.0, computing the cross product of two 2D vectors using numpy.cross() results in a DeprecationWarning. NumPy now requires using 3D vectors for cross products. This tutorial explains the issue and provides a solution.

Understanding the Issue

When computing the cross product of two 2D vectors, NumPy previously assumed the vectors were in 3D space with an implicit z-component of 0. This behavior is now deprecated, and NumPy requires explicit 3D vectors.

Error Example

import numpy as np

# Define two 2D vectors
vector_a = np.array([1, 2])
vector_b = np.array([3, 4])

# Compute the cross product (Deprecated)
result = np.cross(vector_a, vector_b)

# Print the result
print("Z-component of the cross product:", result)

Deprecation Warning:

Z-component of the cross product: -2

/main.py:8: DeprecationWarning: Arrays of 2-dimensional vectors are deprecated. Use arrays of 3-dimensional vectors instead. (deprecated in NumPy 2.0)
  result = np.cross(vector_a, vector_b)

Solution: Convert to 3D Vectors

To resolve the warning, explicitly convert 2D vectors into 3D by appending a zero z-component.

import numpy as np

# Define two 2D vectors and convert them to 3D
vector_a = np.array([1, 2, 0])  # Adding z-component as 0
vector_b = np.array([3, 4, 0])  # Adding z-component as 0

# Compute the cross product
cross_product = np.cross(vector_a, vector_b)

# Extract only the z-component since cross product of 2D vectors is in the z-direction
z_component = cross_product[2]

# Print the result
print("Z-component of the cross product:", z_component)

Output:

Z-component of the cross product: -2

Explanation of the Solution

Step	Explanation
Convert vectors to 3D	Explicitly append 0 as the z-component.
Compute cross product	numpy.cross() now works with 3D vectors.
Extract z-component	Since the result is a 3D vector, we retrieve only the z-component.

Alternative Approach: Using Scalar Formula

For 2D vectors A = [Ax, Ay] and B = [Bx, By], the cross product is given by:

Z = Ax * By - Ay * Bx

import numpy as np

# Define 2D vectors
vector_a = np.array([1, 2])
vector_b = np.array([3, 4])

# Compute cross product using scalar formula
z_component = vector_a[0] * vector_b[1] - vector_a[1] * vector_b[0]

# Print the result
print("Z-component of the cross product:", z_component)

Output:

Z-component of the cross product: -2

This approach avoids the DeprecationWarning by manually computing the result.