Tensor Transpose

Shipping

tensor_transpose

Permute or reverse array axes (numpy transpose / .T); a pure reindex that preserves the unit

Signature

Inputs

aVector|Matrix|Tensorrequired— The array whose axes are permuted.

Outputs

resultVector|Matrix|Tensor— The axis-permuted view materialized as a new array; same elements, reordered shape, unit unchanged.

Parameters

Key	Type	Default	Notes
`order`	text		Comma-separated axis permutation, e.g. "1, 0" or "2, 0, 1". Empty = reverse all axes (numpy .T). Negative axes count from the end.

Description

Tensor Transpose permutes the axes of an array, matching numpy's transpose. The order parameter is a comma-separated axis permutation: "1, 0" swaps the two axes of a matrix (an ordinary transpose), "2, 0, 1" rotates a rank-3 tensor's axes. An empty order reverses all axes — exactly numpy's .T. Negative axes count from the end, so "-1, 0" addresses the last axis first.

This is a pure reindex: no arithmetic touches the values, they are merely relabeled by position. Consequently the physical unit is preserved unchanged. For a 2-D matrix the operation is the familiar $A^{T}$ where $(A^{T})_{ij} = A_{ji}$ ; for higher ranks it generalizes to an arbitrary axis relabeling.

Mathematics

(result)_{i_{p_{0}}, i_{p_{1}}, \dots} = a_{i_{0}, i_{1}, \dots}, p = order

2-D transpose : (A^{T})_{ij} = A_{ji}

empty order \Rightarrow p = (n - 1, n - 2, \dots, 0) (reverse all n axes)

Examples

Matrix transpose

Feed the $2 \times 3$ matrix [[0,1,2],[3,4,5]] with order = "1, 0" (or empty). The result is the $3 \times 2$ transpose:

[[0, 3],
 [1, 4],
 [2, 5]]

Rank-3 axis rotation

A tensor of shape $(2, 3, 4)$ with order = "2, 0, 1" becomes shape $(4, 2, 3)$ : the old last axis moves to front, and the first two shift back one position.

Applications

Turning a row layout into a column layout (or vice versa) before matmul or concatenation so shapes align.
Reordering the axes of a data cube (e.g. moving a channel/time axis to the front) to match a downstream node's expected layout.
Realizing a numpy .T with no parameters for a quick full-axis reversal of any rank.

Neat

Because it is a metadata-only reindex on the value side, the unit rides through untouched — unlike stack/concat which drop or must reconcile units.

The empty-order fast path calls a dedicated full-reverse transpose, while an explicit list dispatches to a general permute — the same axis-list parser as tensor_reduce.

Negative-axis support means you can address 'the last axis' without knowing the rank, useful in rank-agnostic subgraphs.

Known issues

An `order` that is not a valid permutation of the array's axes (wrong length, repeats, or out-of-range index) is a hard error rather than a partial reorder.