如何让Numpy生成与MATLAB一致的D变量？逐元素乘法问题

Let's break down why your current NumPy code isn't matching MATLAB's output, then adjust it to get the correct D array.

Understanding the MATLAB Behavior #

First, let's recap what MATLAB is doing:

• A is a 3x3 matrix.
• C gets reshaped to 1x3x2 (a 3D array with 1 row, 3 columns, 2 slices).
• bsxfun(@times, A, C) automatically broadcasts the arrays to compatible dimensions:
  • A (3x3) is expanded to a 3x3x2 array (repeating its values across the 3rd dimension twice).
  • C (1x3x2) is expanded to a 3x3x2 array (repeating its values across the 1st dimension three times).
  • Element-wise multiplication happens, resulting in a 3x3x2 array where:
    • D(:,:,1) is A multiplied column-wise by [100, 10, 1]
    • D(:,:,2) is A multiplied column-wise by [1, 0.1, 0.01]

What's Wrong with the Current NumPy Code? #

Your current code uses C.T, which transposes the (1,3,2) array into (2,3,1). When multiplied with A (3x3), NumPy broadcasts to a (2,3,3) array—this flips the dimensions compared to MATLAB's output, leading to mismatched values.

Corrected NumPy Code #

To replicate MATLAB's broadcasting logic, we need to align the dimensions properly. We'll expand A to have a singleton 3rd dimension (so it matches the 3rd dimension of C), then perform element-wise multiplication:

import numpy as np

A = np.array([[1,2,3],[4,5,6],[7,8,9]])
# C matches the reshaped MATLAB version: shape (1, 3, 2)
C = np.array([[[100, 1], [10, 0.1], [1, 0.01]]])

# Expand A to shape (3,3,1) to broadcast with C (1,3,2)
D = A[:, :, np.newaxis] * C

Verifying the Result #

Let's check the output:

• D[:,:,0] will be:

  [[100.  20.   3.]
   [400.  50.   6.]
   [700.  80.   9.]]
  

• D[:,:,1] will be:

  [[1.    0.2   0.03]
   [4.    0.5   0.06]
   [7.    0.8   0.09]]
  

This exactly matches the MATLAB output you provided.

Alternative Approach (Using Reshape for Clarity) #

If you prefer to start with the original C values (before MATLAB's reshape), you can do this:

import numpy as np

A = np.array([[1,2,3],[4,5,6],[7,8,9]])
# Original C from MATLAB: 3x2 array
C_original = np.array([[100, 1], [10, 0.1], [1, 0.01]])
# Reshape to match MATLAB's (1,3,2)
C = C_original.reshape(1, 3, 2)

D = A[:, :, np.newaxis] * C

This gives the same correct result.

内容的提问来源于stack exchange，提问作者rafidude