[Numpy-discussion] Feature request: dot product along arbitrary axes
Currently there are lots of ways to compute dot products (dot, vdot, inner, tensordot, einsum...), but none of them are really convenient for the case of arrays of vectors, where one dimension (usually the last or the first) is the vector dimension. The simplest way to do this currently is `np.sum(a * b, axis=axis)`, but this makes vector algebra less readable without a wrapper function, and it's probably not optimized as much as matrix products. Another way to do it is by adding appropriate dimensions and using matmul, but that's arguably less readable and not obvious to do generically for arbitrary axes. I think either np.dot or np.vdot could easily be extended with an `axis` parameter that would convert it into a bulk vector operation, with the same semantics as `np.sum(a * b, axis=axis)`. It should also maybe have a `keep_dims` parameter, which is useful for preserving broadcasting. I submitted a corresponding issue at https://github.com/numpy/numpy/issues/21915 ___ NumPy-Discussion mailing list -- numpy-discussion@python.org To unsubscribe send an email to numpy-discussion-le...@python.org https://mail.python.org/mailman3/lists/numpy-discussion.python.org/ Member address: arch...@mail-archive.com
[Numpy-discussion] Re: Feature request: dot product along arbitrary axes
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] 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 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) ___ NumPy-Discussion mailing list -- numpy-discussion@python.org To unsubscribe send an email to numpy-discussion-le...@python.org https://mail.python.org/mailman3/lists/numpy-discussion.python.org/ Member address: arch...@mail-archive.com
[Numpy-discussion] Re: Feature request: dot product along arbitrary axes
I'm unaware of the context here, is this a specification for functions that it is hoped will eventually be made consistent across numpy/tensorflow/etc? If that's the idea then yeah, I'm all for it, but I would suggest also adding a keepdim parameter (as I mentioned above it helps with broadcasting, i.e. vec_array1.dot(vec_array2, keepdims=True) * vec_array3 would work as expected). But is there an active effort to incorporate these APIs back into numpy? ___ NumPy-Discussion mailing list -- numpy-discussion@python.org To unsubscribe send an email to numpy-discussion-le...@python.org https://mail.python.org/mailman3/lists/numpy-discussion.python.org/ Member address: arch...@mail-archive.com
[Numpy-discussion] Re: Feature request: dot product along arbitrary axes
Yes, if I am doing this more than once in some code I would make a helper. But it's much better I think to have a common function that people can learn and use consistently instead of having to roll their own functions all the time. Especially because numpy otherwise usually just works when you write the algorithm how you write it on paper. There shouldn't need to be too much thinking involved in the translation. Also yeah using fancy index tricks like `rowmat` and `colmat` simplifies the code a bit, but is still obscure and esoteric looking to somebody who's not intimately familiar with numpy indexing. ___ NumPy-Discussion mailing list -- numpy-discussion@python.org To unsubscribe send an email to numpy-discussion-le...@python.org https://mail.python.org/mailman3/lists/numpy-discussion.python.org/ Member address: arch...@mail-archive.com
[Numpy-discussion] Re: Feature request: dot product along arbitrary axes
Oh nevermind, I see that this is added as an experimental module in the latest numpy version. It would be nice to not have to have another whole set of APIs, but on the other hand the numpy API is so messy and inconsistent that maybe it is a good thing :) But it does mean now we have at least 9 different functions/methods/operators that can compute dot products š¢ (not even including theĀ other array_api functions...) I see that currently the vecdot function returns a 2x2 array from two 2x3 APIs, which matches np.inner but is not what I would expect. Does your fix make it instead return a 1-d length-2 array? ___ NumPy-Discussion mailing list -- numpy-discussion@python.org To unsubscribe send an email to numpy-discussion-le...@python.org https://mail.python.org/mailman3/lists/numpy-discussion.python.org/ Member address: arch...@mail-archive.com
