Understanding the broadcast behavior of np.multiply with higher-dimensional arrays
This might be a silly question, but I'm stuck trying to Could someone explain I've been banging my head against this for hours... I'm having trouble understanding how NumPy's broadcasting rules apply when using `np.multiply` on arrays of different dimensions. I've defined two arrays as follows: ```python import numpy as np a = np.array([1, 2, 3]) # Shape (3,) b = np.array([[1, 2], [3, 4]]) # Shape (2, 2) ``` When I try to multiply these two arrays using `np.multiply(a, b)`, I encounter a `ValueError`: ``` ValueError: shapes (3,) and (2,2) not aligned: 3 (dim 0) != 2 (dim 0) ``` From what I understand, for broadcasting to work, the dimensions should match from the end, but I'm not sure how to reshape or manipulate the arrays to make this operation successful. I've attempted reshaping `a` using `a.reshape(1, 3)` to get its shape to `(1, 3)`, but this still doesn't resolve the alignment scenario. I also experimented with stacking `b` along a new axis using `np.stack(b, axis=0)`, but I'm not clear why this didn't help either. Can someone explain how I can successfully use `np.multiply` for these arrays, or how I should adjust their shapes to work together? Any insights into the broadcasting rules in this context would be greatly appreciated. I'm currently using NumPy version 1.23.0. I'd really appreciate any guidance on this. I recently upgraded to Python stable. Thanks for taking the time to read this! My development environment is Ubuntu 20.04. Am I approaching this the right way? I'm on Debian using the latest version of Python. Am I approaching this the right way?