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 ordermk, ik -> im
├─ lm, kl -> mk
│  ├─ lm
│  └─ kl
└─ ij, jk -> ik
   ├─ ij
   └─ jk
julia> optcode(randn(100, 100), randn(100, 100), randn(100, 100), randn(100, 100))  # compute the result100×100 Matrix{Float64}:
   151.512   2103.93     -2214.4     …   -285.673     275.653     441.982
   439.348    573.14     -1859.41        1553.26      249.342    2137.6
  1457.67    -502.481      419.077       -384.421    1471.96     -214.815
  -318.705   2137.72      1281.19         679.203     -21.0916  -1319.04
   577.902   -612.43      2378.37         783.074     274.311    -210.546
  -805.414    616.457    -1068.59    …  -2045.74      330.723     474.063
  -147.947     -1.97531   -256.96        -558.785    -592.616     550.787
   670.388     47.4396     653.086        186.745     524.375     255.19
 -2218.99     355.199     -513.5          153.449     -13.7413   -920.403
   222.407    206.364      284.386       -926.037      -1.1118   -795.344
     ⋮                               ⋱
   617.991    415.75      1770.55        1079.34     -320.741   -1806.99
 -1215.92    1204.16      -184.121       -627.257    -189.33      415.793
  -693.861   1301.42     -1333.86          74.9894   -750.022    -386.86
  -341.376    -95.1462     998.508       1649.11      533.217     194.88
 -1155.49   -1232.2        884.039   …    635.235    -516.53      127.896
  -346.221   -259.517       13.9123       811.065   -1072.15       52.6132
   583.526   1154.87      1409.93       -1881.99      943.825   -1922.72
  -955.509   1855.08       167.713        542.434      47.6894   -286.298
  -171.148   1107.24      -550.19        1261.72     -680.209    1058.93