Write numeric code that automatically works with any numpy-ish libraries.

A lightweight python AUTOmatic-arRAY library. Write numeric code that works for:

As an example consider this function that orthogonalizes a matrix using the modified Gram-Schmidt algorithm:

from autoray import do

def modified_gram_schmidt(X):
    # n.b. performance-wise this particular function is *not*
    # a good candidate for a pure python implementation

    Q = []
    for j in range(0, X.shape[0]):

        q = X[j, :]
        for i in range(0, j):
            rij = do('tensordot', do('conj', Q[i]), q, 1)
            q = q - rij * Q[i]

        rjj = do('linalg.norm', q, 2)
        Q.append(q / rjj)

    return do('stack', Q, axis=0)

Which is now compatible with all of the above mentioned libraries! Abstracting out the array interface also allows the following functionality:

  • swap custom versions of functions for specific backends
  • trace through computations lazily without actually running them
  • automatically share intermediates and fold constants in computations
  • compile functions with a unified interface for different backends

... all implemented in a lightweight manner with an emphasis on minimizing overhead. Of course complete compatibility is not going to be possible for all functions, operations and libraries, but autoray hopefully makes the job much easier. Of the above, tensorflow has quite a different interface and pytorch probably the most different. Whilst for example not every function will work out-of-the-box for these two, autoray is also designed with the easy addition of new functions in mind (for example adding new translations is often a one-liner).

Basic Usage

How does it work?

autoray works using essentially a single dispatch mechanism on the first argument for do, or the like keyword argument if specified, fetching functions from the whichever module defined that supplied array. Additionally, it caches a few custom translations and lookups so as to handle libraries like tensorflow that don't exactly replicate the numpy api (for example sum gets translated to tensorflow.reduce_sum). Due to the caching, each do call only adds 1 or 2 dict look-ups as overhead - much less than using functools.singledispatch for example.

Essentially you call your numpy-style array functions in one of four ways:

1. Automatic backend:

do('sqrt', x)

Here the backend is inferred from x. Usually dispatch happens on the first argument, but several functions (such as stack and einsum) know to override this and look elsewhere.

2. Backend 'like' another array:

do('random.normal', size=(2, 3, 4), like=x)

Here the backend is inferred from another array and can thus be implicitly propagated, even when functions take no array arguments.

3. Explicit backend:

do('einsum', eq, x, y, like='customlib')

Here one simply supplies the desired function backend explicitly.

4. Context manager

with backend_like('autoray.lazy'):
    xy = do('tensordot', x, y, 1)
    z = do('trace', xy)

Here you set a default backend for a whole block of code. This default overrides method 1. above but 2. and 3. still take precedence.

If you don't like the explicit do syntax, then you can import the fake numpy object as a drop-in replacement instead:

from autoray import numpy as np

x = np.random.uniform(size=(2, 3, 4), like='tensorflow')
np.tensordot(x, x, [(2, 1), (2, 1)])
# <tf.Tensor 'Tensordot:0' shape=(2, 2) dtype=float32>

np.eye(3, like=x)  # many functions obviously can't dispatch without the `like` keyword
# <tf.Tensor 'eye/MatrixDiag:0' shape=(3, 3) dtype=float32>

Customizing functions

If you want to directly provide a missing or alternative implementation of some function for a particular backend you can swap one in with autoray.register_function:

def my_custom_torch_svd(x):
    import torch

    print('Hello SVD!')
    u, s, v = torch.svd(x)

    return u, s, v.T

ar.register_function('torch', 'linalg.svd', my_custom_torch_svd)

x ='random.uniform', size=(3, 4), like='torch')'linalg.svd', x)
# Hello SVD!
# (tensor([[-0.5832,  0.6188, -0.5262],
#          [-0.5787, -0.7711, -0.2655],
#          [-0.5701,  0.1497,  0.8078]]),
#  tensor([2.0336, 0.8518, 0.4572]),
#  tensor([[-0.4568, -0.3166, -0.6835, -0.4732],
#          [-0.5477,  0.2825, -0.2756,  0.7377],
#          [ 0.2468, -0.8423, -0.0993,  0.4687]]))

If you want to make use of the existing function you can supply wrap=True in which case the custom function supplied should act like a decorator:

def my_custom_sum_wrapper(old_fn):

    def new_fn(*args, **kwargs):
        print('Hello sum!')
        return old_fn(*args **kwargs)

    return new_fn

ar.register_function('torch', 'sum', my_custom_sum_wrapper, wrap=True)'sum', x)
# Hello sum!
# tensor(5.4099)

Though be careful, if you call register_function again it will now wrap the new function!

Lazy Computation

Abstracting out the array interface also affords an opportunity to run any computations utilizing completely lazily. autoray provides the lazy submodule and LazyArray class for this purpose:

from autoray import lazy

# input array - can be anything supports
x = do('random.normal', size=(5, 5), like='torch')

# convert it to a lazy 'computational node'
lx = lazy.array(x)

# supply this to our function
ly = modified_gram_schmidt(lx)
# <LazyArray(fn=stack, shape=(5, 5), dtype=float32, backend='torch')>

None of the functions have been called yet - simply the shapes and dtypes have been propagated through. ly represents the final stack call, and tracks which other LazyArray instances it needs to materialize before it can compute itself. At this point one can perform various bits of introspection:

# --> the largest array encountered
# 25

# number of unique computational nodes
# 57

# --> traverse the computational graph and collect statistics
from collections import Counter
Counter(node.fn_name for node in ly)
# Counter({'stack': 1,
#          'truediv': 5,
#          'norm': 5,
#          'sub': 10,
#          'mul': 10,
#          'getitem': 5,
#          'None': 1,
#          'tensordot': 10,
#          'conjugate': 10})

# --> plot the full computation graph

Finally, if we want to compute the actual value we call:

# tensor([[-0.4225,  0.1371, -0.2307,  0.5892,  0.6343],
#         [ 0.4079, -0.5103,  0.5924,  0.4261,  0.2016],
#         [ 0.2569, -0.5173, -0.4875, -0.4238,  0.4992],
#         [-0.2778, -0.5870, -0.3928,  0.3645, -0.5396],
#         [ 0.7155,  0.3297, -0.4515,  0.3986, -0.1291]])

Note that once a node is computed, it only stores the actual result and clears all references to other LazyArray instances.

Sharing intermediates

If the computation might involve repeated computations then you can call it in a shared_intermediates context:

with lazy.shared_intermediates():
    ly = modified_gram_schmidt(lx)

# --> a few nodes can be reused here (c.f. 57 previously)
# 51

this caches the computational nodes as they are created based on a hash of their input arguments (note this uses id for array like things, i.e. assumes they are immutable). Unlike eagerly caching function calls in real time, which might consume large amounts of memory, now when the computation runs (i.e. ly.compute() is called) data is only kept as long as its needed.

Why not use e.g. dask?

There are many reasons to use dask, but it incurs a pretty large overhead for big computational graphs with comparatively small operations. Calling and computing the modified_gram_schmidt function for a 100x100 matrix (20,102 computational nodes) with dask.array takes ~25sec whereas with lazy.array it takes ~0.25sec:

import dask.array as da

dx = da.array(x)
dy = modified_gram_schmidt(dx)
y = dy.compute()
# CPU times: user 25.6 s, sys: 137 ms, total: 25.8 s
# Wall time: 25.5 s

lx = lazy.array(x)
ly = modified_gram_schmidt(lx)
y = ly.compute()
# CPU times: user 256 ms, sys: 0 ns, total: 256 ms
# Wall time: 255 ms

This is enabled by autoray's very minimal implementation.


Various libraries provide tools for tracing numeric functions and turning the resulting computation into a more efficient, compiled function. Notably:

autoray is obviously very well suited to these since it just dispatches functions to whichever library is doing the tracing - functions written using autoray should be immediately compatible with all of them.

The autojit wrapper

Moreover, autoray also provides a unified interface for compiling functions so that the compilation backend can be easily switched or automatically identified:

from autoray import autojit

mgs = autojit(modified_gram_schmidt)

Currently autojit supports functions with the signature fn(*args, **kwargs) -> array where both args and kwargs can be any nested combination of tuple, list and dict objects containings arrays.
We can compare different compiled versions of this simply by changing the backend option:

x = do("random.normal", size=(50, 50), like='numpy')

# first the uncompiled version
# 23.5 ms ± 241 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

# 'python' mode unravels computation into source then uses compile+exec
mgs(x)  # backend='python'
# 17.8 ms ± 191 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

mgs(x, backend='torch')
# 11.9 ms ± 80.5 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)

mgs(x, backend='tensorflow')
# 1.87 ms ± 441 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)

# need to config jax to run on same footing
from jax.config import config
config.update("jax_enable_x64", True)
config.update('jax_platform_name', 'cpu')

mgs(x, backend='jax')
# 226 µs ± 14.8 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)

do('linalg.qr', x, like='numpy')[0]  # appriximately the 'C' version
# 156 µs ± 32.1 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

Here you see (with this very for-loop heavy function), that there are significant gains to be made for all the compilations options. Whilst jax for example achieves fantastic performance, it should be noted the compilation step takes a lot of time and scales badly (super-linearly) with the number of computational nodes.


Special Functions

The main function is do, but the following special (i.e. not in numpy) functions are also implemented that may be useful:

  • autoray.infer_backend - check what library is being inferred for a given array
  • autoray.to_backend_dtype - convert a string specified dtype like 'float32' to torch.float32 for example
  • autoray.get_dtype_name - convert a backend dtype back into the equivalent string specifier like 'complex64'
  • autoray.astype - backend agnostic dtype conversion of arrays
  • autoray.to_numpy - convert any array to a numpy.ndarray

Here are all of those in action:

import autoray as ar

backend = 'torch'
dtype = ar.to_backend_dtype('float64', like=backend)
# torch.float64

x ='random.normal', size=(4,), dtype=dtype, like=backend)
# tensor([ 0.0461,  0.3028,  0.1790, -0.1494], dtype=torch.float64)

# 'torch'

# 'float64'

x32 = ar.astype(x, 'float32')
# array([ 0.04605161,  0.30280888,  0.17903718, -0.14936243], dtype=float32)

Deviations from numpy

autoray doesn't have an API as such, since it is essentially just a fancy single dispatch mechanism. On the other hand, where translations are in place, they generally use the numpy API. So'stack', arrays=pytorch_tensors, axis=0) gets automatically translated into torch.stack(tensors=pytorch_tensors, dims=0) and so forth.

Currently the one place this isn't true is'linalg.svd', x) where instead full_matrices=False is used as the default since this generally makes more sense and many libraries don't even implement the other case. Autoray also dispatches 'linalg.expm' for numpy arrays to scipy, and may well do with other scipy-only functions at some point.


You can install autoray via conda-forge as well as with pip. Alternatively, simply copy the monolithic into your project internally (if dependencies aren't your thing) to provide do.


  • The __array_function__ protocol has been suggested and now implemented in numpy. Hopefully this will eventually negate the need for autoray. On the other hand, third party libraries themselves need to implement the interface, which has not been done, for example, in tensorflow yet.
  • The uarray project aims to develop a generic array interface but comes with the warning "This is experimental and very early research code. Don't use this.".