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TensorNetworks

Guides

  • TensorNetworks

Tech Notes

  • Building Tensor Networks
  • Contraction Paths and Execution
  • Matrix Product States
  • Tensor Networks Overview
  • Young Tableaux and Tensor Symmetries

Symbols

  • ActivateTensors
  • BinaryTensorNetwork
  • BinaryTensorNetworkQ
  • CanonicalPath
  • CanonicalPathQ
  • ContractIndices
  • ContractionTree
  • EinsteinSummation
  • GreedyContractionPath
  • HookFactor
  • HookLength
  • HookLengths
  • IndexedMultiply
  • InitializeTensorNetwork
  • MetricTensor
  • MetricTensorQ
  • MPSCanonicalForm
  • MPSCanonicalQ
  • MPSEntanglementEntropy
  • MPSNormalize
  • MPSNorm
  • MPSOverlap
  • MPSSchmidtValues
  • MPSTruncate
  • OptimalContractionPath
  • PartitionQ
  • PathIndexContractions
  • PathQ
  • PathToTreePath
  • RandomTensorNetwork
  • SparseTensorNetwork
  • TableauColumns
  • TableauDimension
  • TableauRows
  • TableauShape
  • TableauSize
  • TensorNetworkAdd
  • TensorNetworkContraction
  • TensorNetworkContractions
  • TensorNetworkContract
  • TensorNetworkData
  • TensorNetworkDelete
  • TensorNetworkFreeIndices
  • TensorNetworkGraphData
  • TensorNetworkGraphQ
  • TensorNetworkIndexDimensions
  • TensorNetworkIndexGraph
  • TensorNetworkIndices
  • TensorNetwork
  • TensorNetworkQ
  • TensorNetworkRemoveCycles
  • TensorNetworkReplaceIndices
  • TensorNetworkSize
  • TensorNetworkTensors
  • TensorNetworkToNetGraph
  • ToTensorNetworkGraph
  • TransposePartition
  • TreePathQ
  • TreePathToPath
  • YoungProject
  • YoungSymmetrize
  • YoungTableau
  • YoungTableauQ
Wolfram`TensorNetworks`
IndexedMultiply
​
IndexedMultiply
[{i,j,…},{A,B,…}]
joins the tensors
A,B,…
by broadcasting along shared indices and returns the pair
{indices,tensor}
.
​
Details and Options
Examples  
(23)
Basic Examples  
(3)
Join two matrices over a shared index:
In[1]:=
Amat={{1,1},{3,2}};Bmat={{1,0,1},{0,2,2}};
In[2]:=
IndexedMultiply[{{"i","j"},{"j","k"}},{Amat,Bmat}]
Out[2]=
{{i,j,k},{{{1,0,1},{0,2,2}},{{3,0,3},{0,4,4}}}}
​
Scale the columns of a matrix by a vector
A
i,j
v
j
:
In[1]:=
IndexedMultiply[{{"i","j"},{"j"}},{{{10,20,30},{40,50,60}},{1,10,100}}]
Out[1]=
{{i,j},{{10,200,3000},{40,500,6000}}}
​
Disjoint indices give a pure outer product
C
i,j
=
u
i
v
j
:
In[1]:=
IndexedMultiply[{{"i"},{"j"}},{{10,20},{1,2,3}}]
Out[1]=
{{i,j},{{10,20,30},{20,40,60}}}
Scope  
(16)

Applications  
(2)

Properties & Relations  
(2)

SeeAlso
EinsteinSummation
 
▪
ActivateTensors
 
▪
TensorNetwork
 
▪
TensorProduct
 
▪
ArrayPad
 
▪
Transpose
 
▪
ArraySymbol
TechNotes
▪
Building Tensor Networks
RelatedGuides
▪
TensorNetworks
""

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