Wolfram/TensorNetworks | Paclet Repository

Wolfram`TensorNetworks`

TensorNetworkData

TensorNetworkData [tn]
	returns an Association containing the complete data of the tensor network tn : its tensors, dimensions, indices, vertices, bonds, contractions, and free indices.

Details and Options

▪

The returned

Association

has nine keys, each describing one view of the tensor network

	"Tensors"	the list of tensors that form the network
	"Dimensions"	per-tensor list of array dimensions
	"Hyperedges"	the hyperedge index lists with their raw labels (integers or symbols)
	"Indices"	per-tensor index lists labelled by Superscript [v,k] for tensor v , slot k
	"Vertices"	the integers 1,2,…,n enumerating the tensors
	"Bonds"	list of group  dim pairs, one per shared index
	"Contractions"	per-tensor index lists with each shared index replaced by its full labelled group
	"ContractionIndices"	per-tensor index lists with each shared index replaced by the raw label of its first occurrence
	"FreeIndices"	the uncontracted (output) indices, in output order

▪

Each key is also reachable through property dispatch on the

TensorNetwork

object:

TensorNetworkData

[tn]

is equivalent to

tn["Data"]

, and individual entries can be retrieved as

tn["Key"]

▪

The result of

TensorNetworkData

is cached on first call through

tn["Data"]

, so repeated access from any of the per-key dispatch shortcuts (

tn["Indices"]

tn["Bonds"]

tn["Contractions"]

tn["ContractionIndices"]

) is free after the first evaluation.

▪

The

"Indices"

and

"Contractions"

keys carry the qualified form

Superscript

[v,k]

, which records both the tensor index

and the raw hyperedge label

;

"Hyperedges"

and

"ContractionIndices"

carry only the raw label.

Examples

(17)

Basic Examples

(1)

Get the complete data of a tensor network as an association:

In[1]:=

t1=RandomReal[1,{2,3}];t2=RandomReal[1,{3,4}];t3=RandomReal[1,{4,2}];t4=RandomReal[1,{2,2}];indices={{idx1,idx2},{idx2,idx3},{idx3,idx1}};tn=

TensorNetwork

[{t1,t2,t3},indices]

Out[1]=

TensorNetwork

Tensors: 3	Binary: Yes
Free indices: 0	Sparse: No
Output dimension: 1



In[2]:=

TensorNetworkData

[tn]

Out[2]=

Tensors{{{0.612809,0.130458,0.260095},{0.657812,0.265318,0.462577}},{{0.253323,0.438937,0.839983,0.931607},{0.444777,0.100304,0.618537,0.835115},{0.748834,0.00609525,0.0887644,0.724669}},{{0.102168,0.77641},{0.570572,0.0947489},{0.957574,0.913492},{0.608683,0.925448}}},Dimensions{{2,3},{3,4},{4,2}},Hyperedges{{idx1,idx2},{idx2,idx3},{idx3,idx1}},Indices

idx1

idx2

,

idx2

idx3

,

idx3

idx1

,Vertices{1,2,3},Bonds

idx1

2,

idx2

3,

idx3

4,Contractions

idx1

,

idx2

,

idx2

,

idx3

,

idx3

,

idx1

,ContractionIndices{{idx1,idx2},{idx2,idx3},{idx3,idx1}},FreeIndices{}

Add a new tensor into the previous tensor network:

In[3]:=

TensorNetworkData



TensorNetworkAdd

[tn,t4,{idx1,idx5}]

Out[3]=

Tensors{{{0.612809,0.130458,0.260095},{0.657812,0.265318,0.462577}},{{0.253323,0.438937,0.839983,0.931607},{0.444777,0.100304,0.618537,0.835115},{0.748834,0.00609525,0.0887644,0.724669}},{{0.102168,0.77641},{0.570572,0.0947489},{0.957574,0.913492},{0.608683,0.925448}},{{0.249091,0.606372},{0.263592,0.657744}}},Dimensions{{2,3},{3,4},{4,2},{2,2}},Hyperedges{{idx1,idx2},{idx2,idx3},{idx3,idx1},{idx1,idx5}},Indices

idx1

idx2

,

idx2

idx3

,

idx3

idx1

,

idx1

idx5