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])
[[5 2 9]
[1 2 3]
[1 4 3]]
[16 6 8]
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
* 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])