Backends & GPU Support¶
The following is a brief overview of libraries which have been tested with
opt_einsum
:
- tensorflow: compiled tensor expressions that can run on GPU.
- theano: compiled tensor expressions that can run on GPU.
- cupy: numpy-like api for GPU tensors.
- dask: larger-than-memory tensor computations, distributed scheduling, and potential reuse of intermediaries.
- sparse: sparse tensors.
- pytorch: numpy-like api for GPU tensors.
opt_einsum
is quite agnostic to the type of n-dimensional arrays (tensors)
it uses, since finding the contraction path only relies on getting the shape
attribute of each array supplied.
It can perform the underlying tensor contractions with various
libraries. In fact, any library that provides a tensordot()
and
transpose()
implementation can perform most normal contractions.
While more special functionality such as axes reduction is reliant on a
einsum()
implementation.
Note
For a contraction to be possible without using a backend einsum, it must satisfy the following rule: in the full expression (so including output indices) each index must appear twice. In other words, each dimension must be contracted with one other dimension, or left alone.
General backend for any ndarray¶
This ‘duck-typing’ support just requires specifying the correct backend
argument for the type of arrays supplied when calling
contract()
. For example, if you had a library installed
called 'foo'
which provided an ndarray
like object with a
.shape
attribute as well as foo.tensordot
and foo.transpose
then
you could contract then with something like:
contract(einsum_str, *foo_arrays, backend='foo')
Behind the scenes opt_einsum
will find the contraction path, perform
pairwise contractions using e.g. foo.tensordot
and finally return whatever
type those functions return.
Dask¶
dask is an example of a library which satisfies these requirements. For example:
>>> import opt_einsum as oe
>>> import dask.array as da
>>> shapes = (3, 200), (200, 300), (300, 4)
>>> dxs = [da.random.normal(0, 1, shp, chunks=(100, 100)) for shp in shapes]
>>> dxs
[dask.array<da.random.normal, shape=(3, 200), dtype=float64, chunksize=(3, 100)>,
dask.array<da.random.normal, shape=(200, 300), dtype=float64, chunksize=(100, 100)>,
dask.array<da.random.normal, shape=(300, 4), dtype=float64, chunksize=(100, 4)>]
>>> dy = oe.contract("ab,bc,cd", *dxs, backend='dask')
>>> dy
dask.array<transpose, shape=(3, 4), dtype=float64, chunksize=(3, 4)>
>>> dy.compute()
array([[ 470.71404665, 2.44931372, -28.47577265, 424.37716615],
[ 64.38328345, -287.40753131, 144.46515642, 324.88169821],
[-142.07153553, -180.41739259, 125.0973783 , -239.16754541]])
In this case, dask arrays in = dask array out, since dask arrays have a shape
attribute, and opt_einsum
can find dask.array.tensordot
and
dask.array.transpose
.
Sparse¶
The sparse library also fits the bill and is supported. An example:
>>> import opt_einsum as oe
>>> import sparse as sp
>>> shapes = (3, 200), (200, 300), (300, 4)
>>> sxs = [sp.random(shp) for shp in shapes]
[<COO: shape=(3, 200), dtype=float64, nnz=6, sorted=False, duplicates=True>,
<COO: shape=(200, 300), dtype=float64, nnz=600, sorted=False, duplicates=True>,
<COO: shape=(300, 4), dtype=float64, nnz=12, sorted=False, duplicates=True>]
>>> sy = oe.contract("ab,bc,cd", *sxs, backend='sparse')
<COO: shape=(3, 4), dtype=float64, nnz=0, sorted=False, duplicates=False>
Special (GPU) backends for numpy arrays¶
A special case is if you want to supply numpy arrays and get numpy arrays back,
but use a different backend, such as performing a contraction on a GPU.
Unless the specified backend works on numpy arrays this requires converting to
and from the backend array type. Currently opt_einsum
can handle this
automatically for:
which all offer GPU support. Since tensorflow
and theano
both require
compiling the expression, this functionality is encapsulated in generating a
ContractExpression
using
contract_expression()
, which can then be called using numpy
arrays whilst specifiying backend='tensorflow'
etc.
Additionally, if arrays are marked as constant
(see Specifying Constants), then these arrays will be kept on the device
for optimal performance.
Theano¶
If theano
is installed, using it as backend is as simple as specifiying
backend='theano'
:
>>> import opt_einsum as oe
>>> shapes = (3, 200), (200, 300), (300, 4)
>>> expr = oe.contract_expression("ab,bc,cd", *shapes)
>>> expr
<ContractExpression('ab,bc,cd')>
>>> import numpy as np
>>> # GPU advantage mainly for low precision numbers
>>> xs = [np.random.randn(*shp).astype(np.float32) for shp in shapes]
>>> expr(*xs, backend='theano') # might see some fluff on first run
...
array([[ 129.28352 , -128.00702 , -164.62917 , -335.11682 ],
[-462.52344 , -121.12657 , -67.847626 , 624.5457 ],
[ 5.2838974, 36.441578 , 81.62851 , 703.1576 ]],
dtype=float32)
Note that you can still supply theano.tensor.TensorType
directly to
opt_einsum
(with backend='theano'
), and it will return the
relevant theano
type.
Tensorflow¶
To run the expression with tensorflow, you need to register a default session:
>>> import tensorflow as tf
>>> sess = tf.Session() # might see some fluff
...
>>> with sess.as_default(): out = expr(*xs, backend='tensorflow')
>>> out
array([[ 129.28357 , -128.00684 , -164.62903 , -335.1167 ],
[-462.52362 , -121.12659 , -67.84769 , 624.5455 ],
[ 5.2839584, 36.44155 , 81.62852 , 703.15784 ]],
dtype=float32)
Note that you can still supply this expression with, for example, a
tensorflow.placeholder
using backend='tensorflow'
, and then no
conversion would take place, instead you’d get a tensorflow.Tensor
back.
Version 1.9 of tensorflow also added support for eager execution of computations. If compilation of the contraction expression tensorflow graph is taking a substantial amount of time up then it can be advantageous to use this, especially since tensor contractions are quite compute-bound. This is achieved by running the following snippet:
import tensorflow as tf
tf.enable_eager_execution()
After which opt_einsum
will automatically detect eager mode if
backend='tensorflow'
is supplied to a
ContractExpression
.
Pytorch & Cupy¶
Both pytorch and cupy
offer numpy-like, GPU-enabled arrays which execute eagerly rather than
requiring any compilation. If they are installed, no steps are required to
utilize them other than specifiying the backend
keyword:
>>> expr(*xs, backend='torch')
array([[ 129.28357 , -128.00684 , -164.62903 , -335.1167 ],
[-462.52362 , -121.12659 , -67.84769 , 624.5455 ],
[ 5.2839584, 36.44155 , 81.62852 , 703.15784 ]],
dtype=float32)
>>> expr(*xs, backend='cupy')
array([[ 129.28357 , -128.00684 , -164.62903 , -335.1167 ],
[-462.52362 , -121.12659 , -67.84769 , 624.5455 ],
[ 5.2839584, 36.44155 , 81.62852 , 703.15784 ]],
dtype=float32)
And as with the other GPU backends, if raw cupy
or pytorch
arrays are
supplied the returned array will be of the same type, with no conversion
to or from numpy
arrays.