Rowbycolumn

Rowbycolumn is a term used in data processing and programming to describe a two-dimensional data access and processing pattern that emphasizes traversal along rows and columns. The phrase is used descriptively to refer to strategies that operate on one axis at a time, with row-first or column-first variants. In practice, row-by-column patterns are often realized as row-major traversal, where an outer loop iterates over rows and an inner loop over columns, and as column-major traversal, where the outer loop iterates over columns and the inner loop over rows. The choice of pattern has implications for performance, particularly memory locality and cache utilization, because different languages and data layouts expose different access efficiencies.

Common applications include numerical computing with matrices, processing two-dimensional tables in spreadsheets or databases, and image processing workflows that apply per-row or per-column operations. Many libraries offer explicit row-wise or column-wise operations, reflecting this distinction.

Although rowbycolumn is not a formal standard term, it is used as a practical label in discussions of data layout and loop optimization. Related concepts include row-major order, column-major order, memory locality, and transposition.

Example: In a 3x3 matrix, a row-by-column traversal processes all elements of the first row, then all elements of the second row, and so on, resulting in the access order (0,0),(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,1),(2,2).