What is the multiplication operator actually doing with numpy arrays?
numpy, python
Solution
It's a little bit complicated and has to do with the concept of broadcasting and the fact that all numpy operations are element wise.
- `a` is a 2D array with 1 row and 3 columns and `b` is a 2D array with 1 column and 3 rows.
- If you try to multiply them element by element (which is what numpy tries to do if you do `a * b` because every basic operation except the `dot` operation is element wise), it must broadcast the arrays so that they match in all their dimensions.
- Since the first array is 1x3 and the second is 3x1 they can be broadcasted to 3x3 matrix according to the broadcasting rules. They will look like:
a = [[1, 2, 3],
[1, 2, 3],
[1, 2, 3]]
b = [[4, 4, 4],
[5, 5, 5],
[6, 6, 6]]
And now Numpy can multiply them element by element, giving you the result:
[[ 4, 8, 12],
[ 5, 10, 15],
[ 6, 12, 18]]
When you are doing a `.dot` operation it does the standard matrix multiplication. More in docs
Problem
I am learning NumPy and I am not really sure what is the operator `*` actually doing. It seems like some form of multiplication, but I am not sure how is it determined. From ipython: ``` In [1]: import numpy as np In [2]: a=np.array([[1,2,3]]) In [3]: b=np.array([[4],[5],[6]]) In [4]: a*b Out[4]: array([[ 4, 8, 12], [ 5, 10, 15], [ 6, 12, 18]]) In [5]: b*a Out[5]: array([[ 4, 8, 12], [ 5, 10, 15], [ 6, 12, 18]]) In [6]: b.dot(a) Out[6]: array([[ 4, 8, 12], [ 5, 10, 15], [ 6, 12, 18]]) In [7]: a.dot(b) Out[7]: array([[32]]) ``` It seems like it is doing matrix multiplication, but only `b` multiplied by `a`, not the other way around. What is going on?