Wolfram/TensorNetworks | Paclet Repository

Wolfram`TensorNetworks`

OptimalContractionPath

OptimalContractionPath [tn]
	finds an optimal contraction path through the TensorNetwork tn by dynamic-programming search.

OptimalContractionPath [graph]
	works directly on a tensor-network Graph graph .

OptimalContractionPath [data]
	accepts the low-level Association data with keys "Dimensions" , "Indices" , and "Contractions" .

OptimalContractionPath [expr]
	finds a path for an Inactive TensorContract over a TensorProduct , optionally wrapped in Transpose with a Cycles permutation.

Details and Options

▪

Returns a canonical contraction path — a list of pairs {{i, j}, …} where each step removes the tensors at positions i and j from the working list and appends their pairwise contraction (the opt_einsum convention).

▪

The path is optimal under the chosen

Method

. Search uses dynamic programming and is exponential in the number of tensors in the worst case; use

GreedyContractionPath

for networks where exhaustive search is impractical.

▪

The default

Method

"size"

minimizes the size of the largest intermediate tensor produced during contraction.

▪

When the input has a hyper-edge (an index that appears in three or more tensors),

OptimalContractionPath

first applies

BinaryTensorNetwork

to insert copy tensors and reduce the network to pairwise edges before searching.

▪

The search backend is a Rust library function loaded from the

Wolfram/PacletExtensions

paclet; the library function is called

optimize_optimal

▪

The following options can be given:

Method	"size"	cost function: "size" , "flops" , "max" , "write" , "combo" , or "limit" .
"PruningThreshold"	None	prune search branches whose running cost exceeds this value.
"AllowOuterProducts"	None	when True , the search may pair tensors that share no index.
"PreSimplify"	None	when True , fuse duplicate indices and trivial dimensions before searching.
"FixedIndexing"	None	when True , use static single-assignment (SSA) index allocation.