# [Numpy-discussion] For broadcasting, can m by n by k matrix be multiplied with n by k matrix?

C W tmrsg11 at gmail.com
Fri Apr 19 18:58:06 EDT 2019

```Thanks, you are right. I overlooked it's for addition.

The original problem was that I have matrix X (RBG image, 3 layers), and
vector y.

I wanted to do np(X, y.T).
>>> X.shape   # 100 of 28 x 28 matrix
(100, 28, 28)
>>> y.shape   # Just one 28 x 28 matrix
(1, 28, 28)

But, np.dot() gives me four axis shown below,
>>> z = np.dot(X, y.T)
>>> z.shape
(100, 28, 28, 1)

The fourth axis is unexpected. Should y.shape be (28, 28), not (1, 28, 28)?

Thanks again!

On Fri, Apr 19, 2019 at 6:39 PM Andras Deak <deak.andris at gmail.com> wrote:

> On Sat, Apr 20, 2019 at 12:24 AM C W <tmrsg11 at gmail.com> wrote:
> >
> > Am I miss reading something? Thank you in advance!
>
> Hey,
>
> You are missing that the broadcasting rules typically apply to
> arithmetic operations and methods that are specified explicitly to
> broadcast. There is no mention of broadcasting in the docs of np.dot
> [1], and its behaviour is a bit more complicated.
> Specifically for multidimensional arrays (which you have), the doc says
>
> If a is an N-D array and b is an M-D array (where M>=2), it is a sum
> product over the last axis of a and the second-to-last axis of b:
> dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])
>
> So your (3,4,5) @ (3,5) would want to collapse the 4-length axis of
> `a` with the 3-length axis of `b`; this won't work. If you want
> elementwise multiplication according to the broadcasting rules, just
> use `a * b`:
>
> >>> a = np.arange(3*4*5).reshape(3,4,5)
> ... b = np.arange(4*5).reshape(4,5)
> ... (a * b).shape
> (3, 4, 5)
>
>
> [1]: https://docs.scipy.org/doc/numpy/reference/generated/numpy.dot.html
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