Optimized Einsum: A tensor contraction order optimizer
Optimized einsum can significantly reduce the overall execution time of einsum-like expressions (e.g.,
by optimizing the expression's contraction order and dispatching many
operations to canonical BLAS, cuBLAS, or other specialized routines. Optimized
einsum is agnostic to the backend and can handle NumPy, Dask, PyTorch,
Tensorflow, CuPy, Sparse, Theano, JAX, and Autograd arrays as well as potentially
any library which conforms to a standard API. See the
documentation for more
function can often act as a drop-in replacement for
functions without further changes to the code while providing superior performance.
Here, a tensor contraction is preformed with and without optimization:
import numpy as np from opt_einsum import contract N = 10 C = np.random.rand(N, N) I = np.random.rand(N, N, N, N) %timeit np.einsum('pi,qj,ijkl,rk,sl->pqrs', C, C, I, C, C) 1 loops, best of 3: 934 ms per loop %timeit contract('pi,qj,ijkl,rk,sl->pqrs', C, C, I, C, C) 1000 loops, best of 3: 324 us per loop
In this particular example, we see a ~3000x performance improvement which is not uncommon when compared against unoptimized contractions. See the backend examples for more information on using other backends.
The algorithms found in this repository often power the
in many of the above projects. For example, the optimization of
has been passed upstream and most of the same features that can be found in
this repository can be enabled with
np.einsum(..., optimize=True). However,
this repository often has more up to date algorithms for complex contractions.
The following capabilities are enabled by
- Inspect detailed information about the path chosen.
- Perform contractions with numerous backends, including on the GPU and with libraries such as TensorFlow and PyTorch.
- Generate reusable expressions, potentially with constant tensors, that can be compiled for greater performance.
- Use an arbitrary number of indices to find contractions for hundreds or even thousands of tensors.
- Share intermediate computations among multiple contractions.
- Compute gradients of tensor contractions using autograd or jax
Please see the documentation for more features!
opt_einsum can either be installed via
pip install opt_einsum or from conda
conda install opt_einsum -c conda-forge. See the installation documenation for further methods.
If this code has benefited your research, please support us by citing:
Daniel G. A. Smith and Johnnie Gray, opt_einsum - A Python package for optimizing contraction order for einsum-like expressions. Journal of Open Source Software, 2018, 3(26), 753
All contributions, bug reports, bug fixes, documentation improvements, enhancements, and ideas are welcome.
A detailed overview on how to contribute can be found in the contributing guide.