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Wolfram`TensorNetworks`

$TensorNetworkContractionMethods

$TensorNetworkContractionMethods
	is the list of binary-contraction engines available as the Method option to TensorNetworkContraction and TensorNetworkContract .

Details and Options

▪

The constant value is

{"ArrayDotTranspose","ArrayDot","Dot","TensorContract","TableSum"}

▪

All five engines produce numerically identical results; they differ only in the shape of the

Inactive

expression tree returned by

TensorNetworkContraction

and in the runtime cost of evaluation.

▪

The default engine is

"ArrayDot"

▪

Each engine has the following form and use case:

"ArrayDot"	ArrayDot [a, b, axes] (default)	general-purpose dense contraction.
"ArrayDotTranspose"	permutes axes to a canonical layout, then ArrayDot with a flat contraction count.	uniform-layout audit of intermediate transposes.
"Dot"	reshape to matrices, apply Dot , reshape back.	BLAS performance critical for large dense tensors.
"TensorContract"	TensorContract [ TensorProduct […], axes]	symbolic/pedagogical inspection closest to the textbook definition.
"TableSum"	Table [ Sum […], iterators]	explicit-form audit of the underlying scalar arithmetic.

▪

All five engines must produce numerically identical results. Any non-zero difference outside floating-point rounding is a bug; the diagnostic is the

AssociationMap

sweep shown in Basic Examples.

▪

The

"TableSum"

engine emits an explicit

Table

Sum

of scalar

Part

accesses; evaluation cost is

O(∏dims)

without BLAS acceleration, so this engine is slow for high-rank dense tensors. Use it for audit and pedagogy, not for production contractions.

Examples

(2)

Basic Examples

(1)

List the available binary-contraction engines:

In[1]:=

$TensorNetworkContractionMethods

Out[1]=

{ArrayDotTranspose,ArrayDot,Dot,TensorContract,TableSum}

Build a small two-tensor network used in the examples below:

In[2]:=

tn=

TensorNetwork

[{{{0.5,-0.2,0.3},{0.1,0.8,-0.4}},{{0.6,0.4,-0.1,0.2},{-0.3,0.5,0.7,-0.2},{0.1,-0.4,0.3,0.5}}},{{i,j},{j,k}}]

Out[2]=

TensorNetwork

Tensors: 2	Binary: Yes
Free indices: 2	Sparse: No
Output dimension: 8



Use the first available engine as the Method value:

In[3]:=

TensorNetworkContract

[tn,MethodFirst[$TensorNetworkContractionMethods]]

Out[3]=

{{0.39,-0.02,-0.1,0.29},{-0.22,0.6,0.43,-0.34}}

Iterate over every engine and collect the contracted tensors:

In[4]:=

AssociationMap

TensorNetworkContract

[tn,Method#1]&,$TensorNetworkContractionMethods

Out[4]=

ArrayDotTranspose{{0.39,-0.02,-0.1,0.29},{-0.22,0.6,0.43,-0.34}},ArrayDot{{0.39,-0.02,-0.1,0.29},{-0.22,0.6,0.43,-0.34}},Dot{{0.39,-0.02,-0.1,0.29},{-0.22,0.6,0.43,-0.34}},TensorContract{{0.39,-0.02,-0.1,0.29},{-0.22,0.6,0.43,-0.34}},TableSum{{0.39,-0.02,-0.1,0.29},{-0.22,0.6,0.43,-0.34}}

All five engines produce numerically identical results. The maximum absolute difference between any two is zero up to floating-point noise:

In[5]:=