kmath/docs/expressions.md

Expressions

Expressions is a feature, which allows constructing lazily or immediately calculated parametric mathematical expressions.

The potential use-cases for it (so far) are following:

• lazy evaluation (in general simple lambda is better, but there are some border cases);
• automatic differentiation in single-dimension and in multiple dimensions;
• generation of mathematical syntax trees with subsequent code generation for other languages;
• symbolic computations, especially differentiation (and some other actions with kmath-symja integration with Symja's IExpr—integration, simplification, and more);
• visualization with kmath-jupyter.

The workhorse of this API is Expression interface, which exposes single operator fun invoke(arguments: Map<Symbol, T>): T method. ExpressionAlgebra is used to generate expressions and introduce variables.

Currently there are two implementations:

• Generic ExpressionField in kmath-core which allows construction of custom lazy expressions

• Auto-differentiation expression in kmath-commons module allows using full power of DerivativeStructure from commons-math. TODO: add example