Hi all.

As discussed in today's community meeting, I plan to start working on
adding some useful functions to NumPy which are part of the array API
standard https://data-apis.org/array-api/latest/index.html.

Although these are all things that will be needed for NumPy to be
standard compliant, my focus for now at least is going to be on new
functionality that is useful for NumPy independent of the standard.
The things that I (and possibly others) plan on working on are:

- A new function matrix_transpose() and corresponding ndarray
attribute x.mT. Unlike transpose(), matrix_transpose() will require at
least 2 dimensions and only operate on the last two dimensions (it's
effectively an alias for swapaxes(x, -1, -2)). This was discussed in
the past at https://github.com/numpy/numpy/issues/9530 and
https://github.com/numpy/numpy/issues/13797. See
https://data-apis.org/array-api/latest/API_specification/generated/signatures.linear_algebra_functions.matrix_transpose.html

- namedtuple outputs for eigh, qr, slogdet and svd. This would only
apply to the instances where they currently return a tuple (e.g.,
svd(compute_uv=False) would still just return an array). See the
corresponding pages at
https://data-apis.org/array-api/latest/extensions/index.html for the
namedtuple names. These four functions are the ones that are part of
the array API spec, but if there are other functions that aren't part
of the spec which we'd like to update to namedtuples as well for
consistency, I can look into that.

- New functions matrix_norm() and vector_norm(), which split off the
behavior of norm() between vector and matrix specific functionalities.
This is a cleaner API and would allow these functions to be proper
gufuncs. See https://data-apis.org/array-api/latest/extensions/generated/signatures.linalg.vector_norm.html
and https://data-apis.org/array-api/latest/extensions/generated/signatures.linalg.matrix_norm.html.

- New function vecdot() which does a broadcasted 1-D dot product along
a specified axis
https://data-apis.org/array-api/latest/API_specification/generated/signatures.linear_algebra_functions.vecdot.html#signatures.linear_algebra_functions.vecdot

- New function svdvals(), which is equivalent to
svd(compute_uv=False). The idea here is that functions that have
different return types depending on keyword arguments are problematic
for various reasons (e.g., they are hard to type annotate), so it's
cleaner to split these APIs. Functionality-wise there's not much new
here, so this is lower priority than the rest.

- New function permute_dims(), which works just like transpose() but
it has a required axis argument. This is more explicit and can't be
confused with doing a matrix transpose, which transpose() does not do
for stacked matrices by default.

- Adding a copy argument to reshape(). This has already been discussed
at https://github.com/numpy/numpy/issues/9818. The main motivation is
to replace the current usage of modifying array.shape inplace. (side
note: this also still needs to be added to numpy.array_api)

You can see the source code of numpy.array_api for an idea of what
pure Python implementations of these changes look like, but to be
clear, the proposal here is to add these to the main NumPy namespace,
not to numpy.array_api.

One question I have is which of the new functions proposed should be
implemented as pure Python wrappers and which should be implemented in
C as ufuncs/gufuncs?

Unless there are any objections, I plan to start working on
implementing these right away.

Aaron Meurer
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