Wolfram/TensorNetworks | Paclet Repository

Wolfram`TensorNetworks`

PathToTreePath

PathToTreePath [path]
	converts a linear pairwise contraction path to a nested tree-form path with auto-derived integer leaves.

PathToTreePath [path,indices]
	uses the explicit list indices as the leaf labels.

Details and Options

▪

The tree form is a nested list whose leaves are singleton lists

{x}

and whose non-leaf nodes group two or more children. It is the same form recognised by

TreePathQ

and consumed by

TreePathToPath

▪

The required arity — the number of leaves of the resulting tree — is

Count

[path,{_,_}]

+ 1: one leaf for each binary contraction step in

path

, plus one for the initial tensor count.

▪

When

indices

is omitted it defaults to

Automatic

, and the leaves are taken from

Range

[required]

▪

If an explicit

indices

list is given whose length does not match the required arity,

PathToTreePath

issues

PathToTreePath::indlen

and returns

$Failed

▪

At each step the underlying fold deletes the contracted positions from the working list and appends either the chosen leaf (singleton step) or the pair of children (binary step) as a tree-level node, so the order in which leaves appear in the output is determined by the path.

Examples

(10)

Basic Examples

(4)

The simplest pairwise path produces a two-leaf tree:

In[1]:=