user3272574 - 1 year ago 689
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 Source

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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