NumPy

NEP 37 — A dispatch protocol for NumPy-like modules

Author

Stephan Hoyer <shoyer@google.com>

Author

Hameer Abbasi

Author

Sebastian Berg

Status

Draft

Type

Standards Track

Created

2019-12-29

Abstract

NEP-18’s __array_function__ has been a mixed success. Some projects (e.g., dask, CuPy, xarray, sparse, Pint, MXNet) have enthusiastically adopted it. Others (e.g., JAX) have been more reluctant. Here we propose a new protocol, __array_module__, that we expect could eventually subsume most use-cases for __array_function__. The protocol requires explicit adoption by both users and library authors, which ensures backwards compatibility, and is also significantly simpler than __array_function__, both of which we expect will make it easier to adopt.

Why __array_function__ hasn’t been enough

There are two broad ways in which NEP-18 has fallen short of its goals:

  1. Backwards compatibility concerns. __array_function__ has significant implications for libraries that use it:

    • JAX has been reluctant to implement __array_function__ in part because it is concerned about breaking existing code: users expect NumPy functions like np.concatenate to return NumPy arrays. This is a fundamental limitation of the __array_function__ design, which we chose to allow overriding the existing numpy namespace. Libraries like Dask and CuPy have looked at and accepted the backwards incompatibility impact of __array_function__; it would still have been better for them if that impact didn’t exist.

      Note that projects like PyTorch and scipy.sparse have also not adopted __array_function__ yet, because they don’t have a NumPy-compatible API or semantics. In the case of PyTorch, that is likely to be added in the future. scipy.sparse is in the same situation as numpy.matrix: its semantics are not compatible with numpy.ndarray and therefore adding __array_function__ (except to return NotImplemented perhaps) is not a healthy idea.

    • __array_function__ currently requires an “all or nothing” approach to implementing NumPy’s API. There is no good pathway for incremental adoption, which is particularly problematic for established projects for which adopting __array_function__ would result in breaking changes.

  2. Limitations on what can be overridden. __array_function__ has some important gaps, most notably array creation and coercion functions:

    • Array creation routines (e.g., np.arange and those in np.random) need some other mechanism for indicating what type of arrays to create. NEP 35 proposed adding optional like= arguments to functions without existing array arguments. However, we still lack any mechanism to override methods on objects, such as those needed by np.random.RandomState.

    • Array conversion can’t reuse the existing coercion functions like np.asarray, because np.asarray sometimes means “convert to an exact np.ndarray” and other times means “convert to something _like_ a NumPy array.” This led to the NEP 30 proposal for a separate np.duckarray function, but this still does not resolve how to cast one duck array into a type matching another duck array.

Other maintainability concerns that were raised include:

  • It is no longer possible to use aliases to NumPy functions within modules that support overrides. For example, both CuPy and JAX set result_type = np.result_type and now have to wrap use of np.result_type in their own result_type function instead.

  • Implementing fall-back mechanisms for unimplemented NumPy functions by using NumPy’s implementation is hard to get right (but see the version from dask), because __array_function__ does not present a consistent interface. Converting all arguments of array type requires recursing into generic arguments of the form *args, **kwargs.

get_array_module and the __array_module__ protocol

We propose a new user-facing mechanism for dispatching to a duck-array implementation, numpy.get_array_module. get_array_module performs the same type resolution as __array_function__ and returns a module with an API promised to match the standard interface of numpy that can implement operations on all provided array types.

The protocol itself is both simpler and more powerful than __array_function__, because it doesn’t need to worry about actually implementing functions. We believe it resolves most of the maintainability and functionality limitations of __array_function__.

The new protocol is opt-in, explicit and with local control; see Appendix: design choices for API overrides for discussion on the importance of these design features.

The array module contract

Modules returned by get_array_module/__array_module__ should make a best effort to implement NumPy’s core functionality on new array types(s). Unimplemented functionality should simply be omitted (e.g., accessing an unimplemented function should raise AttributeError). In the future, we anticipate codifying a protocol for requesting restricted subsets of numpy; see Requesting restricted subsets of NumPy’s API for more details.

How to use get_array_module

Code that wants to support generic duck arrays should explicitly call get_array_module to determine an appropriate array module from which to call functions, rather than using the numpy namespace directly. For example:

# calls the appropriate version of np.something for x and y
module = np.get_array_module(x, y)
module.something(x, y)

Both array creation and array conversion are supported, because dispatching is handled by get_array_module rather than via the types of function arguments. For example, to use random number generation functions or methods, we can simply pull out the appropriate submodule:

def duckarray_add_random(array):
    module = np.get_array_module(array)
    noise = module.random.randn(*array.shape)
    return array + noise

We can also write the duck-array stack function from NEP 30, without the need for a new np.duckarray function:

def duckarray_stack(arrays):
    module = np.get_array_module(*arrays)
    arrays = [module.asarray(arr) for arr in arrays]
    shapes = {arr.shape for arr in arrays}
    if len(shapes) != 1:
        raise ValueError('all input arrays must have the same shape')
    expanded_arrays = [arr[module.newaxis, ...] for arr in arrays]
    return module.concatenate(expanded_arrays, axis=0)

By default, get_array_module will return the numpy module if no arguments are arrays. This fall-back can be explicitly controlled by providing the module keyword-only argument. It is also possible to indicate that an exception should be raised instead of returning a default array module by setting module=None.

How to implement __array_module__

Libraries implementing a duck array type that want to support get_array_module need to implement the corresponding protocol, __array_module__. This new protocol is based on Python’s dispatch protocol for arithmetic, and is essentially a simpler version of __array_function__.

Only one argument is passed into __array_module__, a Python collection of unique array types passed into get_array_module, i.e., all arguments with an __array_module__ attribute.

The special method should either return a namespace with an API matching numpy, or NotImplemented, indicating that it does not know how to handle the operation:

class MyArray:
    def __array_module__(self, types):
        if not all(issubclass(t, MyArray) for t in types):
            return NotImplemented
        return my_array_module

Returning custom objects from __array_module__

my_array_module will typically, but need not always, be a Python module. Returning a custom objects (e.g., with functions implemented via __getattr__) may be useful for some advanced use cases.

For example, custom objects could allow for partial implementations of duck array modules that fall-back to NumPy (although this is not recommended in general because such fall-back behavior can be error prone):

class MyArray:
    def __array_module__(self, types):
        if all(issubclass(t, MyArray) for t in types):
            return ArrayModule()
        else:
            return NotImplemented

class ArrayModule:
    def __getattr__(self, name):
        import base_module
        return getattr(base_module, name, getattr(numpy, name))

Subclassing from numpy.ndarray

All of the same guidance about well-defined type casting hierarchies from NEP-18 still applies. numpy.ndarray itself contains a matching implementation of __array_module__, which is convenient for subclasses:

class ndarray:
    def __array_module__(self, types):
        if all(issubclass(t, ndarray) for t in types):
            return numpy
        else:
            return NotImplemented

NumPy’s internal machinery

The type resolution rules of get_array_module follow the same model as Python and NumPy’s existing dispatch protocols: subclasses are called before super-classes, and otherwise left to right. __array_module__ is guaranteed to be called only a single time on each unique type.

The actual implementation of get_array_module will be in C, but should be equivalent to this Python code:

def get_array_module(*arrays, default=numpy):
    implementing_arrays, types = _implementing_arrays_and_types(arrays)
    if not implementing_arrays and default is not None:
        return default
    for array in implementing_arrays:
        module = array.__array_module__(types)
        if module is not NotImplemented:
            return module
    raise TypeError("no common array module found")

def _implementing_arrays_and_types(relevant_arrays):
    types = []
    implementing_arrays = []
    for array in relevant_arrays:
        t = type(array)
        if t not in types and hasattr(t, '__array_module__'):
            types.append(t)
            # Subclasses before superclasses, otherwise left to right
            index = len(implementing_arrays)
            for i, old_array in enumerate(implementing_arrays):
                if issubclass(t, type(old_array)):
                    index = i
                    break
            implementing_arrays.insert(index, array)
    return implementing_arrays, types

Relationship with __array_ufunc__ and __array_function__

These older protocols have distinct use-cases and should remain

__array_module__ is intended to resolve limitations of __array_function__, so it is natural to consider whether it could entirely replace __array_function__. This would offer dual benefits: (1) simplifying the user-story about how to override NumPy and (2) removing the slowdown associated with checking for dispatch when calling every NumPy function.

However, __array_module__ and __array_function__ are pretty different from a user perspective: it requires explicit calls to get_array_function, rather than simply reusing original numpy functions. This is probably fine for libraries that rely on duck-arrays, but may be frustratingly verbose for interactive use.

Some of the dispatching use-cases for __array_ufunc__ are also solved by __array_module__, but not all of them. For example, it is still useful to be able to define non-NumPy ufuncs (e.g., from Numba or SciPy) in a generic way on non-NumPy arrays (e.g., with dask.array).

Given their existing adoption and distinct use cases, we don’t think it makes sense to remove or deprecate __array_function__ and __array_ufunc__ at this time.

Mixin classes to implement __array_function__ and __array_ufunc__

Despite the user-facing differences, __array_module__ and a module implementing NumPy’s API still contain sufficient functionality needed to implement dispatching with the existing duck array protocols.

For example, the following mixin classes would provide sensible defaults for these special methods in terms of get_array_module and __array_module__:

class ArrayUfuncFromModuleMixin:

    def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
        arrays = inputs + kwargs.get('out', ())
        try:
            array_module = np.get_array_module(*arrays)
        except TypeError:
            return NotImplemented

        try:
            # Note this may have false positive matches, if ufunc.__name__
            # matches the name of a ufunc defined by NumPy. Unfortunately
            # there is no way to determine in which module a ufunc was
            # defined.
            new_ufunc = getattr(array_module, ufunc.__name__)
        except AttributeError:
            return NotImplemented

        try:
            callable = getattr(new_ufunc, method)
        except AttributeError:
            return NotImplemented

        return callable(*inputs, **kwargs)

class ArrayFunctionFromModuleMixin:

    def __array_function__(self, func, types, args, kwargs):
        array_module = self.__array_module__(types)
        if array_module is NotImplemented:
            return NotImplemented

        # Traverse submodules to find the appropriate function
        modules = func.__module__.split('.')
        assert modules[0] == 'numpy'
        for submodule in modules[1:]:
            module = getattr(module, submodule, None)
        new_func = getattr(module, func.__name__, None)
        if new_func is None:
            return NotImplemented

        return new_func(*args, **kwargs)

To make it easier to write duck arrays, we could also add these mixin classes into numpy.lib.mixins (but the examples above may suffice).

Alternatives considered

Naming

We like the name __array_module__ because it mirrors the existing __array_function__ and __array_ufunc__ protocols. Another reasonable choice could be __array_namespace__.

It is less clear what the NumPy function that calls this protocol should be called (get_array_module in this proposal). Some possible alternatives: array_module, common_array_module, resolve_array_module, get_namespace, get_numpy, get_numpylike_module, get_duck_array_module.

Requesting restricted subsets of NumPy’s API

Over time, NumPy has accumulated a very large API surface, with over 600 attributes in the top level numpy module alone. It is unlikely that any duck array library could or would want to implement all of these functions and classes, because the frequently used subset of NumPy is much smaller.

We think it would be useful exercise to define “minimal” subset(s) of NumPy’s API, omitting rarely used or non-recommended functionality. For example, minimal NumPy might include stack, but not the other stacking functions column_stack, dstack, hstack and vstack. This could clearly indicate to duck array authors and users what functionality is core and what functionality they can skip.

Support for requesting a restricted subset of NumPy’s API would be a natural feature to include in get_array_function and __array_module__, e.g.,

# array_module is only guaranteed to contain "minimal" NumPy
array_module = np.get_array_module(*arrays, request='minimal')

To facilitate testing with NumPy and use with any valid duck array library, NumPy itself would return restricted versions of the numpy module when get_array_module is called only on NumPy arrays. Omitted functions would simply not exist.

Unfortunately, we have not yet figured out what these restricted subsets should be, so it doesn’t make sense to do this yet. When/if we do, we could either add new keyword arguments to get_array_module or add new top level functions, e.g., get_minimal_array_module. We would also need to add either a new protocol patterned off of __array_module__ (e.g., __array_module_minimal__), or could add an optional second argument to __array_module__ (catching errors with try/except).

A new namespace for implicit dispatch

Instead of supporting overrides in the main numpy namespace with __array_function__, we could create a new opt-in namespace, e.g., numpy.api, with versions of NumPy functions that support dispatching. These overrides would need new opt-in protocols, e.g., __array_function_api__ patterned off of __array_function__.

This would resolve the biggest limitations of __array_function__ by being opt-in and would also allow for unambiguously overriding functions like asarray, because np.api.asarray would always mean “convert an array-like object.” But it wouldn’t solve all the dispatching needs met by __array_module__, and would leave us with supporting a considerably more complex protocol both for array users and implementors.

We could potentially implement such a new namespace via the __array_module__ protocol. Certainly some users would find this convenient, because it is slightly less boilerplate. But this would leave users with a confusing choice: when should they use get_array_module vs. np.api.something. Also, we would have to add and maintain a whole new module, which is considerably more expensive than merely adding a function.

Dispatching on both types and arrays instead of only types

Instead of supporting dispatch only via unique array types, we could also support dispatch via array objects, e.g., by passing an arrays argument as part of the __array_module__ protocol. This could potentially be useful for dispatch for arrays with metadata, such provided by Dask and Pint, but would impose costs in terms of type safety and complexity.

For example, a library that supports arrays on both CPUs and GPUs might decide on which device to create a new arrays from functions like ones based on input arguments:

class Array:
    def __array_module__(self, types, arrays):
        useful_arrays = tuple(a in arrays if isinstance(a, Array))
        if not useful_arrays:
            return NotImplemented
        prefer_gpu = any(a.prefer_gpu for a in useful_arrays)
        return ArrayModule(prefer_gpu)

class ArrayModule:
    def __init__(self, prefer_gpu):
        self.prefer_gpu = prefer_gpu

    def __getattr__(self, name):
        import base_module
        base_func = getattr(base_module, name)
        return functools.partial(base_func, prefer_gpu=self.prefer_gpu)

This might be useful, but it’s not clear if we really need it. Pint seems to get along OK without any explicit array creation routines (favoring multiplication by units, e.g., np.ones(5) * ureg.m), and for the most part Dask is also OK with existing __array_function__ style overrides (e.g., favoring np.ones_like over np.ones). Choosing whether to place an array on the CPU or GPU could be solved by making array creation lazy.

Appendix: design choices for API overrides

There is a large range of possible design choices for overriding NumPy’s API. Here we discuss three major axes of the design decision that guided our design for __array_module__.

Opt-in vs. opt-out for users

The __array_ufunc__ and __array_function__ protocols provide a mechanism for overriding NumPy functions within NumPy’s existing namespace. This means that users need to explicitly opt-out if they do not want any overridden behavior, e.g., by casting arrays with np.asarray().

In theory, this approach lowers the barrier for adopting these protocols in user code and libraries, because code that uses the standard NumPy namespace is automatically compatible. But in practice, this hasn’t worked out. For example, most well-maintained libraries that use NumPy follow the best practice of casting all inputs with np.asarray(), which they would have to explicitly relax to use __array_function__. Our experience has been that making a library compatible with a new duck array type typically requires at least a small amount of work to accommodate differences in the data model and operations that can be implemented efficiently.

These opt-out approaches also considerably complicate backwards compatibility for libraries that adopt these protocols, because by opting in as a library they also opt-in their users, whether they expect it or not. For winning over libraries that have been unable to adopt __array_function__, an opt-in approach seems like a must.

Explicit vs. implicit choice of implementation

Both __array_ufunc__ and __array_function__ have implicit control over dispatching: the dispatched functions are determined via the appropriate protocols in every function call. This generalizes well to handling many different types of objects, as evidenced by its use for implementing arithmetic operators in Python, but it has an important downside for readability: it is not longer immediately evident to readers of code what happens when a function is called, because the function’s implementation could be overridden by any of its arguments.

The speed implications are:

  • When using a duck-array type, get_array_module means type checking only needs to happen once inside each function that supports duck typing, whereas with __array_function__ it happens every time a NumPy function is called. Obvious it’s going to depend on the function, but if a typical duck-array supporting function calls into other NumPy functions 3-5 times this is a factor of 3-5x more overhead.

  • When using NumPy arrays, get_array_module is one extra call per function (__array_function__ overhead remains the same), which means a small amount of extra overhead.

Explicit and implicit choice of implementations are not mutually exclusive options. Indeed, most implementations of NumPy API overrides via __array_function__ that we are familiar with (namely, Dask, CuPy and Sparse, but not Pint) also include an explicit way to use their version of NumPy’s API by importing a module directly (dask.array, cupy or sparse, respectively).

Local vs. non-local vs. global control

The final design axis is how users control the choice of API:

  • Local control, as exemplified by multiple dispatch and Python protocols for arithmetic, determines which implementation to use either by checking types or calling methods on the direct arguments of a function.

  • Non-local control such as np.errstate overrides behavior with global-state via function decorators or context-managers. Control is determined hierarchically, via the inner-most context.

  • Global control provides a mechanism for users to set default behavior, either via function calls or configuration files. For example, matplotlib allows setting a global choice of plotting backend.

Local control is generally considered a best practice for API design, because control flow is entirely explicit, which makes it the easiest to understand. Non-local and global control are occasionally used, but generally either due to ignorance or a lack of better alternatives.

In the case of duck typing for NumPy’s public API, we think non-local or global control would be mistakes, mostly because they don’t compose well. If one library sets/needs one set of overrides and then internally calls a routine that expects another set of overrides, the resulting behavior may be very surprising. Higher order functions are especially problematic, because the context in which functions are evaluated may not be the context in which they are defined.

One class of override use cases where we think non-local and global control are appropriate is for choosing a backend system that is guaranteed to have an entirely consistent interface, such as a faster alternative implementation of numpy.fft on NumPy arrays. However, these are out of scope for the current proposal, which is focused on duck arrays.