fourindex

Fourindex is a concept used to describe an indexing approach for four-dimensional data structures. It refers to both a methodological way to address elements by a four-tuple (i, j, k, l) and to the software abstractions that map such coordinates to a single linear storage location. In practice, fourindex supports accessing or storing data in four-dimensional arrays, tensors, or other multi-dimensional containers.

For a storage dimensionality of D1 × D2 × D3 × D4, a common linearization under row-major order is index = ((i * D2 + j) * D3 + k) * D4 + l, assuming 0-based indices. Column-major order uses a different stride pattern. Variants may include non-zero-based indexing and padding. The choice of order affects memory locality and performance, especially in high-performance computing.

Applications include numerical simulations, time-varying volumetric data, color-video data, and machine learning tasks that operate on 4D tensors (batches, channels, height, width) or spatiotemporal data.

Implementation notes: Many programming languages provide 4D arrays or tensor types that inherently implement fourindex-like access. When implementing custom storage, attention to stride, cache lines, and alignment matters. Nested arrays offer flexibility but can incur pointer indirection overhead; flat contiguous storage improves spatial locality.

Limitations: The abstraction can obscure underlying memory layout; debugging 4D indexing errors can be nontrivial. The term fourindex is sometimes used informally in literature to discuss index mapping in four dimensions, rather than to denote a single standard construct.

See also: Multidimensional arrays; Tensor; Linearization; Memory layout.