OMEinsum.jl

This package provides

  • The einsum notation, which is similar to the einsum function in numpy, although some details are different.
  • Highly optimized algorithms to optimize the contraction of tensors.

The source code is available at OMEinsum.jl.

Quick start

You can find a set up guide in the README. To get started, open a Julia REPL and type the following code.

julia> using OMEinsum
julia> code = ein"ij,jk,kl,lm->im" # define the einsum operationij, jk, kl, lm -> im
julia> optcode = optimize_code(code, uniformsize(code, 100), TreeSA())  # optimize the contraction orderki, mk -> im
├─ jk, ij -> ki
│  ├─ jk
│  └─ ij
└─ lm, kl -> mk
   ├─ lm
   └─ kl
julia> optcode(randn(100, 100), randn(100, 100), randn(100, 100), randn(100, 100))  # compute the result100×100 Matrix{Float64}:
    -6.12125   -525.686   -2286.76   …    146.241    -26.4623   -762.849
  1063.56       930.139     689.342       943.279     47.5721    173.718
 -1657.45      1690.49    -1044.98       -764.243    932.333    1259.96
   463.346     1619.63    -1493.31      -1728.53    2208.31     -806.461
   989.323    -1951.2      -505.067      -447.405   -716.807    1064.86
  -497.002      -20.2953  -1178.23   …    243.524    555.58     -960.441
 -1980.8      -1187.67      357.042       503.557    698.557   -1095.35
  -506.512      770.852     319.192      -434.015   1541.9      2495.87
  -684.9       3500.08     1349.35        995.611    706.008     -66.8325
  -754.877     3204.44    -1012.24       1160.67     981.198    -242.511
     ⋮                               ⋱
   -79.5721    -119.495    1855.57        601.924    -19.8216   -472.667
 -1996.99       121.316     432.117      1312.41    1313.94     -496.394
   690.789      -11.4183    151.871       730.008     54.0171    711.313
    -8.78545  -1173.33     -266.005       338.171   -100.816   -1049.33
 -1194.03       611.395   -2417.73   …    660.685   -876.977    -549.798
  -520.547    -1703.17      873.316       804.774  -1015.9     -1600.47
   -66.4216    1835.61      785.689      -211.848   2108.11     -258.689
   540.475     2837.18      324.604     -1052.65     738.322    -454.541
 -1215.74       799.773    -548.443      -731.715    419.708    -696.118