AllMround

AllMround is a numeric utility function designed to round every element of a numeric collection to the nearest multiple of a specified base. It is used in data processing, numerical analysis, and grid-based computations to align values to a common spacing.

Definition: Given a numeric collection x and a nonzero real base b, AllMround(x, b) returns a collection where each element x_i is replaced by b times the nearest integer to x_i/b. In effect, y_i = b * Round(x_i / b). The function preserves the original data structure, applying the operation elementwise.

Behavior: The base b may be positive or negative; the set of multiples is the same either way. Elements that are non-numeric are usually left unchanged or cause an error depending on the implementation. The exact handling of ties (when a value lies exactly halfway between two multiples) follows the language’s standard rounding rule.

Example: AllMround([0.3, 0.7, 1.2, -0.4], 0.5) yields [0.5, 0.5, 1.0, -0.5].

Implementation notes: In pseudocode, y = [b * Round(a / b) for a in x]. In many languages, this can be implemented with elementwise operations, for instance using y = b * Round(x / b). If the input is a matrix or nested list, the operation is applied recursively in an elementwise fashion.

Applications: Common uses include preparing data for histogram binning, aligning measurements to a grid for visualization, and simplifying numerical comparisons by snapping values to fixed spacings.

See also: Round, grid snapping, rounding to multiples.

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