On Tue, 2022-07-05 at 23:36 +0000, rmccampbe...@gmail.com wrote: > Maybe I wasn't clear, I'm talking about the 1-dimensional vector > product, but applied to N-D arrays of vectors. Certainly dot products > can be realized as matrix products, and often are in mathematics for > convenience, but matrices and vectors are not the same thing, > theoretically or coding wise. If I have two (M, N, k) arrays a and b > where k is the vector dimension, to dot product them using matrix > notation I have to do: > > (a[:, :, np.newaxis, :] @ b[:, :, :, np.newaxis])[:, :, 0, 0] >
You can make it more readable for example with:
res = a[..., np.newaxis, :] @ b[..., :, np.newaxis]
res = res[..., 0, 0]
(could remove the `:`). Maybe even more tricks like:
rowmat = np.s_[..., np.newaxis, :]
colmat = np.s_[..., :, np.newaxis]
res = a[rowmat] @ a[colmat]
> Which I certainly don't find readable (I always have to scratch my
> head a little bit to figure out whether the newaxis's are in the
> right places). If this is a common operation in larger expressions,
> then it basically has to be written as a separate function, which
> then someone reading the code may have to look at for the semantics.
> It also breaks down if you want to write generic vector functions
> that may be applied along different axes; then you need to do
> something like
>
I would suggest using `np.moveaxis` to implement a helper.
Now of course there may be a point to put that helper into NumPy as
`np.vecdot` (or similar), even if it is probably a 3 line function if
implemented in terms of `matmul`.
Cheers,
Sebastian
> np.squeeze(np.expand_dims(a, axis=axis) @ np.expand_dims(b,
> axis=axis+1), (axis, axis+1))
>
> (after normalizing the axis; if it's negative you'd need to do axis-1
> and axis instead).
>
> Compare this to the simplicity, composability and consistency of:
>
> a.dot(b, axis=-1) * np.cross(c, d, axis=-1).dot(e, axis=-1) /
> np.linalg.norm(f, axis=-1)
>
> (the cross and norm operators already support an axis parameter)
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