user3272574 user3272574 - 3 months ago 31
Python Question

numpy matrix vector multiplication

When I multiply two numpy arrays of sizes (n x n)*(n x 1), I get a matrix of size (n x n). Following normal matrix multiplication rules, a (n x 1) vector is expected, but I simply cannot find any information about how this is done in Python's Numpy module.

The thing is that I don't want to implement it manually to preserve the speed of the program.

Example code is shown below:

a = np.array([[ 5, 1 ,3], [ 1, 1 ,1], [ 1, 2 ,1]])
b = np.array([1, 2, 3])

print a*b
>>
[[5 2 9]
[1 2 3]
[1 4 3]]


What i want is:

print a*b
>>
[16 6 8]

Answer

Use numpy.dot or a.dot(b). See the documentation here.

>>> a = np.array([[ 5, 1 ,3], [ 1, 1 ,1], [ 1, 2 ,1]])
>>> b = np.array([1, 2, 3])
>>> print a.dot(b)
array([16, 6, 8])

This occurs because numpy arrays are not matrices, and the standard operations *, +, -, / work element-wise on arrays. Instead, you could try using numpy.matrix, and * will be treated like matrix multiplication.


Also know there are other options:

  • As noted below, if using python3 the @ operator works as you'd expect:

    >>> print(a @ b)
    array([16, 6, 8])
    
  • If you want overkill, you can use numpy.einsum. The documentation will give you a flavor for how it works, but honestly, I didn't fully understand how to use it until reading this answer and just playing around with it on my own.

    >>> np.einsum('ji,i->j', a, b)
    array([16, 6, 8])
    
  • As of mid 2016 (numpy 1.10.1), you can try the experimental numpy.matmul, which works like numpy.dot with two major exceptions: no scalar multiplication but it works with stacks of matrices.

    >>> np.matmul(a, b)
    array([16, 6, 8])
    
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