Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`
TensorNetwork  |
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Repeated indices in the hyperedge lists denote contractions; indices appearing exactly once are free (output) indices.
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Hyperedge entries can be integers or symbols, but every entry of a single hyperedge list must have length equal to the rank of the corresponding tensor.
h
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When the third argument is (the default), the free indices of the network are derived from the hyperedge structure in their order of first appearance.
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objects support property access via the syntax ; use to list every supported key.
tn["Property"]
tn["Properties"]
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Use to evaluate the network to a single tensor; the contraction path can be supplied explicitly or chosen by or .
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A network is binary when every index appears in at most two tensors; use to convert a hyper-edge network (an index shared by three or more tensors) to its binary equivalent by inserting copy tensors. tests for that condition.
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Output cells display a summary box (icon, tensor count, free-index count, binary/sparse flags, output dimension) generated by an upvalue on ; the icon is the network's hypergraph for binary networks with at most ten tensors and a placeholder graph otherwise.
Examples
(35)
Basic Examples
(2)
Create a tensor network representing matrix multiplication:
In[1]:=
tn=BlockRandomRandomSeed[1];
[RandomReal[1,#]&/@{{2,3},{3,2,3},{3,4}},{{i,j},{j,k,l},{l,m}}]
 | TensorNetwork |
Out[1]=
TensorNetwork
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Visualize the tensor network structure:
In[2]:=
tn["Hypergraph"]
Out[2]=
Contract the network to get the result:
In[3]:=
 | TensorNetworkContract |
Out[3]=
{{{0.450216,0.244854,1.07489,1.38969},{0.549743,0.329563,1.08865,1.23591}},{{0.568642,0.316769,1.33932,1.76742},{0.611233,0.371568,1.17524,1.30506}}}
Define a collection of randomly-generated complex tensors with some given dimensions:
In[1]:=
tensors=SparseArray[RandomComplex[{-1-I,1+I},#]]&/@{{3,4},{3,3,4},{3,3,4},{3,4}};
Given tensors, define the tensor network by feeding indices:
In[2]:=
tn=
[tensors,{{1,5},{1,2,6},{2,3,7},{3,8}}]
 | TensorNetwork |
Out[2]=
TensorNetwork
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Visualize its hypergraph:
In[3]:=
tn["Hypergraph"]
Out[3]=
Contract the tensor network:
In[4]:=
| TensorNetworkContract |
Out[4]=
SparseArray
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Scope
(9)
Applications
(3)
Properties & Relations
(20)
Neat Examples
(1)
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