Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`
TensorNetworkAdd  |
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▪
The length of must equal the rank of ; otherwise the resulting expression is held and not a valid network.
indices
tensor
▪
Any index in that already occurs in the network becomes a contraction in the result; indices not yet present are added to the free-index set.
indices
▪
If was constructed with an explicit list, the output of the new network drops any index that is no longer free and appends the new free indices contributed by ; otherwise it stays .
tn
"Output"
tensor
▪
In the Graph form, each new edge is directed: the new vertex receives a -indexed leg where it meets a -indexed leg of the existing graph, and vice versa, so that every contracted edge connects one output index to one input index.
▪
When is in the Graph form, indices are taken in order from [], up to the rank of . Any remaining slots become fresh free indices on the new vertex.
index
graph
tensor
▪
Calling with a list of disjoint indices is the incremental analogue of constructing the whole network at once with [,].
{tensors,…}
{indices,…}
Examples
(10)
Basic Examples
(1)
Build a triangle tensor network with three free indices contracted pairwise:
In[]:=
t1=RandomReal[1,{2,3}];t2=RandomReal[1,{3,4}];t3=RandomReal[1,{4,2}];t4=RandomReal[1,{2,2}];tn=
[{t1,t2,t3},{{idx1,idx2},{idx2,idx3},{idx3,idx1}}]
 | TensorNetwork |
Out[]=
TensorNetwork
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Append a fourth tensor sharing index idx1; idx1 becomes contracted and idx5 enters the free-index set:
In[]:=
newTN=
[tn,t4,{idx1,idx5}]
 | TensorNetworkAdd |
Out[]=
TensorNetwork
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Append the same tensor on two fresh indices instead, leaving the existing network untouched and adding two new free indices:
In[]:=
 | TensorNetworkAdd |
Out[]=
TensorNetwork
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Move to the annotated Graph form via ToTensorNetworkGraph and inspect its free indices:
In[]:=
chain=
[{RandomReal[1,{2,3}],RandomReal[1,{3,4}]},{{a,b},{b,c}}];g=
[chain]
| TensorNetwork |
| ToTensorNetworkGraph |
Out[]=
Append a rank-2 tensor to the Graph at one of its free legs; the result is a new annotated Graph:
In[]:=
| TensorNetworkAdd |
Out[]=
Scope
(4)
Applications
(2)
Properties & Relations
(3)
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