alongadd

Alongadd is a term used in data processing and numerical computing to denote performing addition along a specified axis of a multidimensional array, resulting in a running total that preserves the array’s shape. In its common interpretation, alongadd computes a prefix sum along the chosen axis: for each position, it adds all preceding elements along that axis up to the current index, producing an output array of the same dimensions. Variants include inclusive alongadd, which includes the current element, and exclusive alongadd, which sums only the elements before the current index.

Axis selection and semantics are central to alongadd. The operation can be applied along any axis of a tensor, typically axis 0, 1, etc., and can be implemented for 1D sequences as well as higher-dimensional arrays. In practice, alongadd is closely related to the concept known in computing as a prefix sum or scan. Many software libraries provide a cumulative-sum function along a specified axis, which is a concrete realization of alongadd in different ecosystems.

Common applications of alongadd include time-series analysis, where cumulative totals are tracked over time; image processing, where running sums along rows or columns can aid in smoothing or feature extraction; and numerical simulations that require preserved-shape accumulations rather than reduced totals. Understanding alongadd helps distinguish it from a simple axis-reduction sum, which collapses the axis rather than preserving it.

See also: cumulative sum, prefix sum, scan, axis-based reductions.