name = string

The value of option name specifies an optional name for this Tensor to be displayed in output and when visualizing the dataflow graph.

The EinsteinSummation(rule,t1,...,tn,opts) command creates a Tensor in the active dataflow graph which is obtained by applying the generalized contraction rule rule to the Tensor arguments t1,...,tn.

This function is part of the DeepLearning package, so it can be used in the short form EinsteinSummation(..) only after executing the command with(DeepLearning). However, it can always be accessed through the long form of the command by using DeepLearning[EinsteinSummation](..).

The implementation of EinsteinSummation uses the tf.einsum command from the TensorFlow Python API. Consult the TensorFlow Python API documentation for tf.einsum for more information on Einstein summation and the syntax for rule specifically.

$\mathrm{with}\left(\mathrm{DeepLearning}\right)\:$

$a≔\mathrm{Constant}\left(⟨1.02342476022\,0.34935719689\,0.88659081013\,0.59299726719\,0.63322441838⟩\right)$

$a≔\left[\begin{array}{c}\mathrm{DeepLearning\; Tensor}\\ \mathrm{Shape:\; [5]}\\ \mathrm{Data\; Type:\; float[8]}\end{array}\right]$

$b≔\mathrm{Constant}\left(⟨1.82052532615\,-0.02883818599\,1.09669226315\,1.39986207979\,1.62917836656⟩\right)$

$b≔\left[\begin{array}{c}\mathrm{DeepLearning\; Tensor}\\ \mathrm{Shape:\; [5]}\\ \mathrm{Data\; Type:\; float[8]}\end{array}\right]$

$\mathrm{EinsteinSummation}\left(''i,i->''\,a\,b\right)$

$\left[\begin{array}{c}\mathrm{DeepLearning\; Tensor}\\ \mathrm{Shape:\; []}\\ \mathrm{Data\; Type:\; float[8]}\end{array}\right]$

$\mathrm{EinsteinSummation}\left(''i,j->ij''\,a\,b\right)$

$\left[\begin{array}{c}\mathrm{DeepLearning\; Tensor}\\ \mathrm{Shape:\; [5,\; 5]}\\ \mathrm{Data\; Type:\; float[8]}\end{array}\right]$

$c≔\mathrm{Constant}\left(⟨⟨1.73965\,1.08139\,0.65633⟩\left|⟨0.87144\,0.60517\,1.13247⟩\right|⟨1.32978\,1.94794\,1.14978⟩⟩\right)$

$c≔\left[\begin{array}{c}\mathrm{DeepLearning\; Tensor}\\ \mathrm{Shape:\; [3,\; 3]}\\ \mathrm{Data\; Type:\; float[8]}\end{array}\right]$

$d≔\mathrm{Constant}\left(⟨⟨1.42797\,0.43478\,0.56673⟩\left|⟨1.32968\,1.98237\,1.29244⟩\right|⟨0.78380\,1.03537\,1.17197⟩⟩\right)$

$d≔\left[\begin{array}{c}\mathrm{DeepLearning\; Tensor}\\ \mathrm{Shape:\; [3,\; 3]}\\ \mathrm{Data\; Type:\; float[8]}\end{array}\right]$

$\mathrm{res}≔\mathrm{EinsteinSummation}\left(''ij,jk->ik''\,c\,d\right)$

$\mathrm{res}≔\left[\begin{array}{c}\mathrm{DeepLearning\; Tensor}\\ \mathrm{Shape:\; [3,\; 3]}\\ \mathrm{Data\; Type:\; float[8]}\end{array}\right]$

$\mathrm{res}≔\mathrm{EinsteinSummation}\left(''ij->ji''\,c\right)$

$\mathrm{res}≔\left[\begin{array}{c}\mathrm{DeepLearning\; Tensor}\\ \mathrm{Shape:\; [3,\; 3]}\\ \mathrm{Data\; Type:\; float[8]}\end{array}\right]$

The DeepLearning[EinsteinSummation] command was introduced in Maple 2018.

For more information on Maple 2018 changes, see Updates in Maple 2018.