proportionswhile

Proportionswhile is a neologism used in algorithm design and mathematical modeling to describe a loop-driven technique for preserving proportional relationships between multiple variables during iterative computation. The core idea is to perform updates within a loop while a stated condition holds, in such a way that the ratios among selected variables remain fixed or follow a predefined scaling pattern.

Origin and usage: The term combines proportion with the programming keyword while. It is used mainly in discussions of constraint propagation, responsive sizing, and simulations where maintaining aspect or quantity ratios is essential. The concept is not tied to a single language or library but describes a family of methods that enforce invariants across iterations.

Mechanics: In a proportionswhile procedure, the invariants are set at the outset (for example, x1:x2:...:xn = a1:a2:...:an). During each iteration, the variables are updated by a common scale factor or by proportional adjustments that preserve the specified ratios. A typical pattern uses a constant scale s > 0 applied uniformly, or a scale computed to meet a bound without breaking the ratios.

Applications and examples: It is used in graphic layout to resize elements while preserving aspect ratios, in simulations where composition ratios matter, and in optimization problems that require proportional resource allocation. Example: given width w and height h with w:h = 4:3, repeatedly multiply both by s until w exceeds a maximum width; the aspect ratio remains 4:3. In images or UI, it ensures consistent appearance across sizes.

Limitations: Floating-point drift can gradually distort ratios; care is needed to enforce constraints and to avoid infinite loops. It can be less flexible than methods that allow small proportional deviations or adaptive adjustments. See also: aspect ratio, proportional control, constraint programming.