[Numpy-discussion] NEP: Dispatch Mechanism for NumPy’s high level API
Marten van Kerkwijk
m.h.vankerkwijk at gmail.com
Sun Jun 3 11:19:01 EDT 2018
Hi Stephan,
Thanks for posting. Overall, this is great!
My more general comment is one of speed: for *normal* operation performance
should be impacted as minimally as possible. I think this is a serious
issue and feel strongly it *has* to be possible to avoid all arguments
being checked for the `__array_function__` attribute, i.e., there should be
an obvious way to ensure no type checking dance is done. Some possible
solutions (which I think should be in the NEP, even if as discounted
options):
A. Two "namespaces", one for the undecorated base functions, and one
completely trivial one for the decorated ones. The idea would be that if
one knows one is dealing with arrays only, one would do `import
numpy.array_only as np` (i.e., the reverse of the suggestion currently in
the NEP, where the decorated ones are in their own namespace - I agree with
the reasons for discounting that one). Note that in this suggestion the
array-only namespace serves as the one used for
`ndarray.__array_function__`.
B. Automatic insertion by the decorator of an `array_only=np._NoValue` (or
`coerce` and perhaps `subok=...` if not present) in the function signature,
so that users who know that they have arrays only could pass
`array_only=True` (name to be decided). This would be most useful if there
were also some type of configuration parameter that could set the default
of `array_only`.
Note that both A and B could also address, at least partially, the problem
of sometimes wanting to just use the old coercion methods, i.e., not having
to implement every possible numpy function in one go in a new
`__array_function__` on one's class.
Two other general comments:
1. I'm rather unclear about the use of `types`. It can help me decide what
to do, but I would still have to find the argument in question (e.g., for
Quantity, the unit of the relevant argument). I'd recommend passing instead
a tuple of all arguments that were inspected, in the inspection order;
after all, it is just a `arg.__class__` away from the type, and in your
example you'd only have to replace `issubclass` by `isinstance`.
2. For subclasses, it would be very handy to have
`ndarray.__array_function__`, so one can call super after changing
arguments. (For `__array_ufunc__`, there was lots of question about whether
this was useful, but it really is!!). [I think you already agreed with
this, but want to have it in-place, as for subclasses of ndarray this is
just as useful as it would be for subclasses of dask arrays.)
Note that any `ndarray.__array_function__` might also help solve the
problem of cases where coercion is fine: it could have an extra keyword
argument (say `coerce`) that would call the function with coercion in
place. Indeed, if the `ndarray.__array_function__` were used inside the
"dance" function, and then the actual implementation of a given function
would just be a separate, private one.
Again, overall a great idea, and thanks to all those involved for taking it
on.
All the best,
Marten
On Sat, Jun 2, 2018 at 6:55 PM, Stephan Hoyer <shoyer at gmail.com> wrote:
> Matthew Rocklin and I have written NEP-18, which proposes a new dispatch
> mechanism for NumPy's high level API: http://www.numpy.org/neps/nep-
> 0018-array-function-protocol.html
>
> There has already been a little bit of scattered discussion on the pull
> request (https://github.com/numpy/numpy/pull/11189), but per NEP-0 let's
> try to keep high-level discussion here on the mailing list.
>
> The full text of the NEP is reproduced below:
>
> ==================================================
> NEP: Dispatch Mechanism for NumPy's high level API
> ==================================================
>
> :Author: Stephan Hoyer <shoyer at google.com>
> :Author: Matthew Rocklin <mrocklin at gmail.com>
> :Status: Draft
> :Type: Standards Track
> :Created: 2018-05-29
>
> Abstact
> -------
>
> We propose a protocol to allow arguments of numpy functions to define
> how that function operates on them. This allows other libraries that
> implement NumPy's high level API to reuse Numpy functions. This allows
> libraries that extend NumPy's high level API to apply to more NumPy-like
> libraries.
>
> Detailed description
> --------------------
>
> Numpy's high level ndarray API has been implemented several times
> outside of NumPy itself for different architectures, such as for GPU
> arrays (CuPy), Sparse arrays (scipy.sparse, pydata/sparse) and parallel
> arrays (Dask array) as well as various Numpy-like implementations in the
> deep learning frameworks, like TensorFlow and PyTorch.
>
> Similarly there are several projects that build on top of the Numpy API
> for labeled and indexed arrays (XArray), automatic differentation
> (Autograd, Tangent), higher order array factorizations (TensorLy), etc.
> that add additional functionality on top of the Numpy API.
>
> We would like to be able to use these libraries together, for example we
> would like to be able to place a CuPy array within XArray, or perform
> automatic differentiation on Dask array code. This would be easier to
> accomplish if code written for NumPy ndarrays could also be used by
> other NumPy-like projects.
>
> For example, we would like for the following code example to work
> equally well with any Numpy-like array object:
>
> .. code:: python
>
> def f(x):
> y = np.tensordot(x, x.T)
> return np.mean(np.exp(y))
>
> Some of this is possible today with various protocol mechanisms within
> Numpy.
>
> - The ``np.exp`` function checks the ``__array_ufunc__`` protocol
> - The ``.T`` method works using Python's method dispatch
> - The ``np.mean`` function explicitly checks for a ``.mean`` method on
> the argument
>
> However other functions, like ``np.tensordot`` do not dispatch, and
> instead are likely to coerce to a Numpy array (using the ``__array__``)
> protocol, or err outright. To achieve enough coverage of the NumPy API
> to support downstream projects like XArray and autograd we want to
> support *almost all* functions within Numpy, which calls for a more
> reaching protocol than just ``__array_ufunc__``. We would like a
> protocol that allows arguments of a NumPy function to take control and
> divert execution to another function (for example a GPU or parallel
> implementation) in a way that is safe and consistent across projects.
>
> Implementation
> --------------
>
> We propose adding support for a new protocol in NumPy,
> ``__array_function__``.
>
> This protocol is intended to be a catch-all for NumPy functionality that
> is not covered by existing protocols, like reductions (like ``np.sum``)
> or universal functions (like ``np.exp``). The semantics are very similar
> to ``__array_ufunc__``, except the operation is specified by an
> arbitrary callable object rather than a ufunc instance and method.
>
> The interface
> ~~~~~~~~~~~~~
>
> We propose the following signature for implementations of
> ``__array_function__``:
>
> .. code-block:: python
>
> def __array_function__(self, func, types, args, kwargs)
>
> - ``func`` is an arbitrary callable exposed by NumPy's public API,
> which was called in the form ``func(*args, **kwargs)``.
> - ``types`` is a list of types for all arguments to the original NumPy
> function call that will be checked for an ``__array_function__``
> implementation.
> - The tuple ``args`` and dict ``**kwargs`` are directly passed on from the
> original call.
>
> Unlike ``__array_ufunc__``, there are no high-level guarantees about the
> type of ``func``, or about which of ``args`` and ``kwargs`` may contain
> objects
> implementing the array API. As a convenience for ``__array_function__``
> implementors of the NumPy API, the ``types`` keyword contains a list of all
> types that implement the ``__array_function__`` protocol. This allows
> downstream implementations to quickly determine if they are likely able to
> support the operation.
>
> Still be determined: what guarantees can we offer for ``types``? Should
> we promise that types are unique, and appear in the order in which they
> are checked?
>
> Example for a project implementing the NumPy API
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
> Most implementations of ``__array_function__`` will start with two
> checks:
>
> 1. Is the given function something that we know how to overload?
> 2. Are all arguments of a type that we know how to handle?
>
> If these conditions hold, ``__array_function__`` should return
> the result from calling its implementation for ``func(*args, **kwargs)``.
> Otherwise, it should return the sentinel value ``NotImplemented``,
> indicating
> that the function is not implemented by these types.
>
> .. code:: python
>
> class MyArray:
> def __array_function__(self, func, types, args, kwargs):
> if func not in HANDLED_FUNCTIONS:
> return NotImplemented
> if not all(issubclass(t, MyArray) for t in types):
> return NotImplemented
> return HANDLED_FUNCTIONS[func](*args, **kwargs)
>
> HANDLED_FUNCTIONS = {
> np.concatenate: my_concatenate,
> np.broadcast_to: my_broadcast_to,
> np.sum: my_sum,
> ...
> }
>
> Necessary changes within the Numpy codebase itself
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
> This will require two changes within the Numpy codebase:
>
> 1. A function to inspect available inputs, look for the
> ``__array_function__`` attribute on those inputs, and call those
> methods appropriately until one succeeds. This needs to be fast in the
> common all-NumPy case.
>
> This is one additional function of moderate complexity.
> 2. Calling this function within all relevant Numpy functions.
>
> This affects many parts of the Numpy codebase, although with very low
> complexity.
>
> Finding and calling the right ``__array_function__``
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
> Given a Numpy function, ``*args`` and ``**kwargs`` inputs, we need to
> search through ``*args`` and ``**kwargs`` for all appropriate inputs
> that might have the ``__array_function__`` attribute. Then we need to
> select among those possible methods and execute the right one.
> Negotiating between several possible implementations can be complex.
>
> Finding arguments
> '''''''''''''''''
>
> Valid arguments may be directly in the ``*args`` and ``**kwargs``, such
> as in the case for ``np.tensordot(left, right, out=out)``, or they may
> be nested within lists or dictionaries, such as in the case of
> ``np.concatenate([x, y, z])``. This can be problematic for two reasons:
>
> 1. Some functions are given long lists of values, and traversing them
> might be prohibitively expensive
> 2. Some function may have arguments that we don't want to inspect, even
> if they have the ``__array_function__`` method
>
> To resolve these we ask the functions to provide an explicit list of
> arguments that should be traversed. This is the ``relevant_arguments=``
> keyword in the examples below.
>
> Trying ``__array_function__`` methods until the right one works
> '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
>
> Many arguments may implement the ``__array_function__`` protocol. Some
> of these may decide that, given the available inputs, they are unable to
> determine the correct result. How do we call the right one? If several
> are valid then which has precedence?
>
> The rules for dispatch with ``__array_function__`` match those for
> ``__array_ufunc__`` (see
> `NEP-13 <http://www.numpy.org/neps/nep-0013-ufunc-overrides.html>`_).
> In particular:
>
> - NumPy will gather implementations of ``__array_function__`` from all
> specified inputs and call them in order: subclasses before
> superclasses, and otherwise left to right. Note that in some edge cases,
> this differs slightly from the
> `current behavior <https://bugs.python.org/issue30140>`_ of Python.
> - Implementations of ``__array_function__`` indicate that they can
> handle the operation by returning any value other than
> ``NotImplemented``.
> - If all ``__array_function__`` methods return ``NotImplemented``,
> NumPy will raise ``TypeError``.
>
> Changes within Numpy functions
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
> Given a function defined above, for now call it
> ``do_array_function_dance``, we now need to call that function from
> within every relevant Numpy function. This is a pervasive change, but of
> fairly simple and innocuous code that should complete quickly and
> without effect if no arguments implement the ``__array_function__``
> protocol. Let us consider a few examples of NumPy functions and how they
> might be affected by this change:
>
> .. code:: python
>
> def broadcast_to(array, shape, subok=False):
> success, value = do_array_function_dance(
> func=broadcast_to,
> relevant_arguments=[array],
> args=(array,),
> kwargs=dict(shape=shape, subok=subok))
> if success:
> return value
>
> ... # continue with the definition of broadcast_to
>
> def concatenate(arrays, axis=0, out=None)
> success, value = do_array_function_dance(
> func=concatenate,
> relevant_arguments=[arrays, out],
> args=(arrays,),
> kwargs=dict(axis=axis, out=out))
> if success:
> return value
>
> ... # continue with the definition of concatenate
>
> The list of objects passed to ``relevant_arguments`` are those that should
> be inspected for ``__array_function__`` implementations.
>
> Alternatively, we could write these overloads with a decorator, e.g.,
>
> .. code:: python
>
> @overload_for_array_function(['array'])
> def broadcast_to(array, shape, subok=False):
> ... # continue with the definition of broadcast_to
>
> @overload_for_array_function(['arrays', 'out'])
> def concatenate(arrays, axis=0, out=None):
> ... # continue with the definition of concatenate
>
> The decorator ``overload_for_array_function`` would be written in terms
> of ``do_array_function_dance``.
>
> The downside of this approach would be a loss of introspection capability
> for NumPy functions on Python 2, since this requires the use of
> ``inspect.Signature`` (only available on Python 3). However, NumPy won't
> be supporting Python 2 for `very much longer <http://www.numpy.org/neps/
> nep-0014-dropping-python2.7-proposal.html>`_.
>
> Use outside of NumPy
> ~~~~~~~~~~~~~~~~~~~~
>
> Nothing about this protocol that is particular to NumPy itself. Should
> we enourage use of the same ``__array_function__`` protocol third-party
> libraries for overloading non-NumPy functions, e.g., for making
> array-implementation generic functionality in SciPy?
>
> This would offer significant advantages (SciPy wouldn't need to invent
> its own dispatch system) and no downsides that we can think of, because
> every function that dispatches with ``__array_function__`` already needs
> to be explicitly recognized. Libraries like Dask, CuPy, and Autograd
> already wrap a limited subset of SciPy functionality (e.g.,
> ``scipy.linalg``) similarly to how they wrap NumPy.
>
> If we want to do this, we should consider exposing the helper function
> ``do_array_function_dance()`` above as a public API.
>
> Non-goals
> ---------
>
> We are aiming for basic strategy that can be relatively mechanistically
> applied to almost all functions in NumPy's API in a relatively short
> period of time, the development cycle of a single NumPy release.
>
> We hope to get both the ``__array_function__`` protocol and all specific
> overloads right on the first try, but our explicit aim here is to get
> something that mostly works (and can be iterated upon), rather than to
> wait for an optimal implementation. The price of moving fast is that for
> now **this protocol should be considered strictly experimental**. We
> reserve the right to change the details of this protocol and how
> specific NumPy functions use it at any time in the future -- even in
> otherwise bug-fix only releases of NumPy.
>
> In particular, we don't plan to write additional NEPs that list all
> specific functions to overload, with exactly how they should be
> overloaded. We will leave this up to the discretion of committers on
> individual pull requests, trusting that they will surface any
> controversies for discussion by interested parties.
>
> However, we already know several families of functions that should be
> explicitly exclude from ``__array_function__``. These will need their
> own protocols:
>
> - universal functions, which already have their own protocol.
> - ``array`` and ``asarray``, because they are explicitly intended for
> coercion to actual ``numpy.ndarray`` object.
> - dispatch for methods of any kind, e.g., methods on
> ``np.random.RandomState`` objects.
>
> As a concrete example of how we expect to break behavior in the future,
> some functions such as ``np.where`` are currently not NumPy universal
> functions, but conceivably could become universal functions in the
> future. When/if this happens, we will change such overloads from using
> ``__array_function__`` to the more specialized ``__array_ufunc__``.
>
>
> Backward compatibility
> ----------------------
>
> This proposal does not change existing semantics, except for those
> arguments
> that currently have ``__array_function__`` methods, which should be rare.
>
>
> Alternatives
> ------------
>
> Specialized protocols
> ~~~~~~~~~~~~~~~~~~~~~
>
> We could (and should) continue to develop protocols like
> ``__array_ufunc__`` for cohesive subsets of Numpy functionality.
>
> As mentioned above, if this means that some functions that we overload
> with ``__array_function__`` should switch to a new protocol instead,
> that is explicitly OK for as long as ``__array_function__`` retains its
> experimental status.
>
> Separate namespace
> ~~~~~~~~~~~~~~~~~~
>
> A separate namespace for overloaded functions is another possibility,
> either inside or outside of NumPy.
>
> This has the advantage of alleviating any possible concerns about
> backwards compatibility and would provide the maximum freedom for quick
> experimentation. In the long term, it would provide a clean abstration
> layer, separating NumPy's high level API from default implementations on
> ``numpy.ndarray`` objects.
>
> The downsides are that this would require an explicit opt-in from all
> existing code, e.g., ``import numpy.api as np``, and in the long term
> would result in the maintainence of two separate NumPy APIs. Also, many
> functions from ``numpy`` itself are already overloaded (but
> inadequately), so confusion about high vs. low level APIs in NumPy would
> still persist.
>
> Multiple dispatch
> ~~~~~~~~~~~~~~~~~
>
> An alternative to our suggestion of the ``__array_function__`` protocol
> would be implementing NumPy's core functions as
> `multi-methods <https://en.wikipedia.org/wiki/Multiple_dispatch>`_.
> Although one of us wrote a `multiple dispatch
> library <https://github.com/mrocklin/multipledispatch>`_ for Python, we
> don't think this approach makes sense for NumPy in the near term.
>
> The main reason is that NumPy already has a well-proven dispatching
> mechanism with ``__array_ufunc__``, based on Python's own dispatching
> system for arithemtic, and it would be confusing to add another
> mechanism that works in a very different way. This would also be more
> invasive change to NumPy itself, which would need to gain a multiple
> dispatch implementation.
>
> It is possible that multiple dispatch implementation for NumPy's high
> level API could make sense in the future. Fortunately,
> ``__array_function__`` does not preclude this possibility, because it
> would be straightforward to write a shim for a default
> ``__array_function__`` implementation in terms of multiple dispatch.
>
> Implementations in terms of a limited core API
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
> The internal implemenations of some NumPy functions is extremely simple.
> For example: - ``np.stack()`` is implemented in only a few lines of code
> by combining indexing with ``np.newaxis``, ``np.concatenate`` and the
> ``shape`` attribute. - ``np.mean()`` is implemented internally in terms
> of ``np.sum()``, ``np.divide()``, ``.astype()`` and ``.shape``.
>
> This suggests the possibility of defining a minimal "core" ndarray
> interface, and relying upon it internally in NumPy to implement the full
> API. This is an attractive option, because it could significantly reduce
> the work required for new array implementations.
>
> However, this also comes with several downsides: 1. The details of how
> NumPy implements a high-level function in terms of overloaded functions
> now becomes an implicit part of NumPy's public API. For example,
> refactoring ``stack`` to use ``np.block()`` instead of
> ``np.concatenate()`` internally would now become a breaking change. 2.
> Array libraries may prefer to implement high level functions differently
> than NumPy. For example, a library might prefer to implement a
> fundamental operations like ``mean()`` directly rather than relying on
> ``sum()`` followed by division. More generally, it's not clear yet what
> exactly qualifies as core functionality, and figuring this out could be
> a large project. 3. We don't yet have an overloading system for
> attributes and methods on array objects, e.g., for accessing ``.dtype``
> and ``.shape``. This should be the subject of a future NEP, but until
> then we should be reluctant to rely on these properties.
>
> Given these concerns, we encourage relying on this approach only in
> limited cases.
>
> Coersion to a NumPy array as a catch-all fallback
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
> With the current design, classes that implement ``__array_function__``
> to overload at least one function implicitly declare an intent to
> implement the entire NumPy API. It's not possible to implement *only*
> ``np.concatenate()`` on a type, but fall back to NumPy's default
> behavior of casting with ``np.asarray()`` for all other functions.
>
> This could present a backwards compatibility concern that would
> discourage libraries from adopting ``__array_function__`` in an
> incremental fashion. For example, currently most numpy functions will
> implicitly convert ``pandas.Series`` objects into NumPy arrays, behavior
> that assuredly many pandas users rely on. If pandas implemented
> ``__array_function__`` only for ``np.concatenate``, unrelated NumPy
> functions like ``np.nanmean`` would suddenly break on pandas objects by
> raising TypeError.
>
> With ``__array_ufunc__``, it's possible to alleviate this concern by
> casting all arguments to numpy arrays and re-calling the ufunc, but the
> heterogeneous function signatures supported by ``__array_function__``
> make it impossible to implement this generic fallback behavior for
> ``__array_function__``.
>
> We could resolve this issue by change the handling of return values in
> ``__array_function__`` in either of two possible ways: 1. Change the
> meaning of all arguments returning ``NotImplemented`` to indicate that
> all arguments should be coerced to NumPy arrays instead. However, many
> array libraries (e.g., scipy.sparse) really don't want implicit
> conversions to NumPy arrays, and often avoid implementing ``__array__``
> for exactly this reason. Implicit conversions can result in silent bugs
> and performance degradation. 2. Use another sentinel value of some sort
> to indicate that a class implementing part of the higher level array API
> is coercible as a fallback, e.g., a return value of
> ``np.NotImplementedButCoercible`` from ``__array_function__``.
>
> If we take this second approach, we would need to define additional
> rules for how coercible array arguments are coerced, e.g., - Would we
> try for ``__array_function__`` overloads again after coercing coercible
> arguments? - If so, would we coerce coercible arguments one-at-a-time,
> or all-at-once?
>
> These are slightly tricky design questions, so for now we propose to
> defer this issue. We can always implement
> ``np.NotImplementedButCoercible`` at some later time if it proves
> critical to the numpy community in the future. Importantly, we don't
> think this will stop critical libraries that desire to implement most of
> the high level NumPy API from adopting this proposal.
>
> NOTE: If you are reading this NEP in its draft state and disagree,
> please speak up on the mailing list!
>
> Drawbacks of this approach
> --------------------------
>
> Future difficulty extending NumPy's API
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
> One downside of passing on all arguments directly on to
> ``__array_function__`` is that it makes it hard to extend the signatures
> of overloaded NumPy functions with new arguments, because adding even an
> optional keyword argument would break existing overloads.
>
> This is not a new problem for NumPy. NumPy has occasionally changed the
> signature for functions in the past, including functions like
> ``numpy.sum`` which support overloads.
>
> For adding new keyword arguments that do not change default behavior, we
> would only include these as keyword arguments when they have changed
> from default values. This is similar to `what NumPy already has
> done <https://github.com/numpy/numpy/blob/v1.14.2/numpy/core/
> fromnumeric.py#L1865-L1867>`_,
> e.g., for the optional ``keepdims`` argument in ``sum``:
>
> .. code:: python
>
> def sum(array, ..., keepdims=np._NoValue):
> kwargs = {}
> if keepdims is not np._NoValue:
> kwargs['keepdims'] = keepdims
> return array.sum(..., **kwargs)
>
> In other cases, such as deprecated arguments, preserving the existing
> behavior of overloaded functions may not be possible. Libraries that use
> ``__array_function__`` should be aware of this risk: we don't propose to
> freeze NumPy's API in stone any more than it already is.
>
> Difficulty adding implementation specific arguments
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
> Some array implementations generally follow NumPy's API, but have
> additional optional keyword arguments (e.g., ``dask.array.sum()`` has
> ``split_every`` and ``tensorflow.reduce_sum()`` has ``name``). A generic
> dispatching library could potentially pass on all unrecognized keyword
> argument directly to the implementation, but extending ``np.sum()`` to
> pass on ``**kwargs`` would entail public facing changes in NumPy.
> Customizing the detailed behavior of array libraries will require using
> library specific functions, which could be limiting in the case of
> libraries that consume the NumPy API such as xarray.
>
>
> Discussion
> ----------
>
> Various alternatives to this proposal were discussed in a few Github
> issues:
>
> 1. `pydata/sparse #1 <https://github.com/pydata/sparse/issues/1>`_
> 2. `numpy/numpy #11129 <https://github.com/numpy/numpy/issues/11129>`_
>
> Additionally it was the subject of `a blogpost
> <http://matthewrocklin.com/blog/work/2018/05/27/beyond-numpy>`_ Following
> this
> it was discussed at a `NumPy developer sprint
> <https://scisprints.github.io/#may-numpy-developer-sprint>`_ at the `UC
> Berkeley Institute for Data Science (BIDS) <https://bids.berkeley.edu/>`_.
>
>
> References and Footnotes
> ------------------------
>
> .. [1] Each NEP must either be explicitly labeled as placed in the public
> domain (see
> this NEP as an example) or licensed under the `Open Publication
> License`_.
>
> .. _Open Publication License: http://www.opencontent.org/openpub/
>
>
> Copyright
> ---------
>
> This document has been placed in the public domain. [1]_
>
> _______________________________________________
> NumPy-Discussion mailing list
> NumPy-Discussion at python.org
> https://mail.python.org/mailman/listinfo/numpy-discussion
>
>
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