Movie-based representation of reduction operations in numerical computing

Movie-based visual programming is an approach for creating computational programs utilizing animation frames of space structure scanning correlated with arithmetic and logical operations. The assignment of the operations on the frame structure nodes is implemented by coloring corresponding structure areas and specifying appropriate formulas on those areas. This programming is based on special acquisition of data/knowledge to generate executable code and to help application programmers in decision making. In this paper, an approach is considered for representing group reduction procedures (reduction and prefix sums, products, maximum/minimum search, etc.) that are widely used in various applications and libraries oriented to parallel and distributed computations. Within a process, new visual constructs and symbols including their syntax and semantics are introduced to define the procedures. In addition, a method of automatic production of template programs supporting the code generation is presented. The applicability of the procedures for high-level visual programming is demonstrated by an algorithm implementing the least-squares fitting method.