Confusion with broadcasting when adding a 1D array to a 2D NumPy array with differing shapes
Could someone explain I'm upgrading from an older version and I'm stuck on something that should probably be simple... I'm having trouble understanding how NumPy's broadcasting rules apply when I'm trying to add a 1D array to a 2D array. I have a 2D array of shape (4, 3) and a 1D array of shape (3,). When I try to perform the addition, I expect it to work element-wise, but instead, I'm getting an unexpected result. Here's the code I'm using: ```python import numpy as np array_2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]) array_1d = np.array([1, 2, 3]) result = array_2d + array_1d print(result) ``` I expected the output to be: ``` [[ 2, 4, 6], [ 5, 7, 9], [ 8, 10, 12], [11, 13, 15]] ``` However, I got: ``` [[ 2, 4, 6], [ 5, 7, 9], [ 8, 10, 12], [10, 12, 14]] ``` It seems like the addition is not being broadcasted correctly across the rows of the 2D array, and I don't understand why. I've checked the shapes, and they seem compatible. I've also read through the broadcasting rules in the NumPy documentation, but I'm still confused. Can someone help clarify what's happening here? Also, how can I ensure that I get the expected result without changing the shape of either array? Is there a better approach? This is part of a larger service I'm building. How would you solve this? For context: I'm using Python on macOS. This is for a application running on Ubuntu 20.04. Thanks, I really appreciate it! This is my first time working with Python 3.11. Any ideas how to fix this? I'm using Python LTS in this project. What's the correct way to implement this? The project is a REST API built with Python.