numpy Matrix Multiplication n x m * m x p = n x p

Question

I am trying to multiply two numpy arrays as matrices. I expect that if A is an n x m matrix and B is an m x p matrix, then A*B yields an n x p matrix.

This code creates a 5x3 matrix and a 3x1 matrix, as verified by the shape property. I was careful to create both arrays in two dimensions. The final line performs the multiplication, and I expect a 5x1 matrix.

A = np.array([[1,1,1],[2,2,2],[3,3,3],[4,4,4],[5,5,5]])
print(A)
print(A.shape)
B = np.array([[2],[3],[4]])
print(B)
print(B.shape)
print(A*B)

Result

[[1 1 1]
 [2 2 2]
 [3 3 3]
 [4 4 4]
 [5 5 5]]
(5, 3)
[[2]
 [3]
 [4]]
(3, 1)

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-38-653ff6c66fb7> in <module>()
      5 print(B)
      6 print(B.shape)
----> 7 print(A*B)

ValueError: operands could not be broadcast together with shapes (5,3) (3,1)

Even the exception message indicates that the inner dimensions (3 and 3) match. Why did multiplication throw an exception? How should I generate a 5x1 matrix?

I am using Python 3.6.2 and Jupyter Notebook server 5.2.2.

If you want matrix-multiplication, you either need to do ```A.dot(B)``` or use the [new operator](https://stackoverflow.com/questions/34142485/difference-between-numpy-dot-and-python-3-5-matrix-multiplication) introduced. This behaves differently if A would be of type np.matrix or a scipy sparse matrix (where A*B is actually matrix-multiplication) [numpy-docs: basic operations](https://docs.scipy.org/doc/numpy-1.12.0/user/quickstart.html#basic-operations). — sascha, Feb 06 '18 at 00:49

Matt Hall · Accepted Answer · 2018-02-06T01:09:42.323

The * operator provides elementwise multiplication, which requires that the arrays are the same shape, or are 'broadcastable'.

For the dot product, use A.dot(B) or in many cases you can use A @ B (in Python 3.5; read how it differs from dot.

>>> import numpy as np
>>> A = np.array([[1,1,1],[2,2,2],[3,3,3],[4,4,4],[5,5,5]])
>>> B = np.array([[2],[3],[4]])
>>> A @ B
array([[ 9],
       [18],
       [27],
       [36],
       [45]])

For even more options, especially for handling higher dimensional arrays, there's also np.matmul.

numpy Matrix Multiplication n x m * m x p = n x p

1 Answers1