flatvector

Flatvector is a term used in mathematics and computer science with multiple related meanings. In geometry, a flat denotes an affine subspace of a vector space; a vector that lies entirely within a given flat may be described informally as a flatvector. In software and data representation, flatvector refers to a one-dimensional, contiguous array layout used to store the coordinates of multiple vectors, rather than a nested or structured array.

In mathematical usage, a flat is a subset of a vector space closed under affine combinations; the concept of a flatvector emphasizes coordinates within that affine subspace, often when performing linear operations restricted to the flat.

In computing usage, flatvector describes a memory layout where a batch of vectors is stored in a single contiguous array. For example, N vectors of dimension D are stored as a vector of size N*D. This layout improves cache performance and compatibility with low-level linear algebra libraries. It also means that operations must account for the stride between vectors.

Advantages of the flatvector layout include fast traversal, better cache locality, and straightforward serialization; drawbacks include reduced type-safety, manual indexing, and potential inefficiency when dimensions vary within a dataset. Common applications include numerical processing, graphics pipelines, and machine learning preprocessing, where efficient bulk vector operations are important.

Note that the term flatvector is not standardized and can refer to different concepts depending on context. See also vector, affine subspace, contiguous memory, and flat array.