Principle:LaurentMazare Tch rs Tensor Iteration

Knowledge Sources	LaurentMazare_Tch_rs
Domains	Software Engineering, Functional Programming, Data Structures
Last Updated	2026-02-08 00:00 GMT

Overview

Element-wise iteration over tensor data bridges tensor abstractions with standard iteration protocols, enabling functional programming patterns like map, fold, and sum on tensor contents.

Description

Tensor iteration provides a way to access individual elements of a tensor through the standard iterator protocol of the host language. This creates a bridge between the bulk-operation paradigm of tensor computing (where operations are applied to entire tensors at once) and the element-wise paradigm of general-purpose programming (where individual elements are processed sequentially).

By implementing the standard iteration interface, tensors become compatible with the full ecosystem of functional combinators:

map -- Transform each element individually
fold / reduce -- Accumulate elements into a single value
sum / product -- Aggregate all elements
filter -- Select elements meeting a condition
zip -- Pair elements from two tensors
enumerate -- Pair each element with its index
collect -- Gather elements into a standard collection type

The iterator typically works by first ensuring the tensor data is in a contiguous memory layout, then providing sequential access to each element as a native typed value. This involves an implicit type conversion from the tensor's internal representation to the native element type.

An important design consideration is the ownership model. Iteration may require either a reference to the tensor (borrowing its data) or ownership of the tensor (consuming it). The choice affects whether the original tensor remains usable after iteration.

Usage

Apply tensor iteration when:

Performing element-wise inspection or transformation that does not map to a built-in tensor operation
Converting tensor data to standard collections for use with non-tensor APIs
Computing custom aggregations that are not available as tensor operations
Debugging or logging individual tensor values
Bridging between tensor computation and general-purpose algorithms

Theoretical Basis

Iterator Protocol

An iterator over a tensor of type $T$ with $n$ elements provides a sequence:

$⟨ e_{1}, e_{2}, \dots, e_{n} ⟩$

where each $e_{i}$ is a native value of type $T$ corresponding to element $i$ in the linearized tensor.

Linearization

For a tensor with shape $(d_{1}, d_{2}, \dots, d_{k})$ , elements are accessed in row-major order. The multi-dimensional index $(i_{1}, i_{2}, \dots, i_{k})$ maps to linear index:

$linear (i_{1}, \dots, i_{k}) = \sum_{j = 1}^{k} i_{j} \cdot \prod_{m = j + 1}^{k} d_{m}$

The total number of elements is $n = \prod_{j = 1}^{k} d_{j}$ .

Functional Combinators

Standard functional operations compose through the iterator:

Map: $map (f, ⟨ e_{1}, \dots, e_{n} ⟩) = ⟨ f (e_{1}), \dots, f (e_{n}) ⟩$

Fold: $fold (g, a_{0}, ⟨ e_{1}, \dots, e_{n} ⟩) = g (\dots g (g (a_{0}, e_{1}), e_{2}) \dots, e_{n})$

Sum: $sum (⟨ e_{1}, \dots, e_{n} ⟩) = fold (+, 0, ⟨ e_{1}, \dots, e_{n} ⟩)$

Performance Considerations

Element-wise iteration is inherently sequential and does not benefit from hardware parallelism (SIMD, GPU). It should be used for small tensors, debugging, or cases where the operation cannot be expressed as a tensor operation. For large-scale computation, prefer vectorized tensor operations.

Related Pages

Implementation:LaurentMazare_Tch_rs_Tensor_Iter

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