Analytic Expression Format

Introduction

In many cases, the coordinates, the sizes, locations and other numeric values can be represented as real numbers. However, often an analytic expression which is evaluated at runtime is needed. Example use cases are parametric building blocks and compact models describing bulding block performance. Therefore, openEPDA defines a standardized analytic expression format, which can be used anywhere where a numeric value is expected.

Grammar

Informal summary

The expression grammar was chosen to cover a minimum yet comprehensive set of expressions. It supports standard mathematical operations, basic mathematical functions and variables defined at runtime.

Expressions can include the following items:

  • basic binary arithmetic operations (addition +, subtraction -, multiplication *, division /, exponentiation ^, and modulus %);

  • unary negation -;

  • mathematical functions (1 argument): abs, acos, asin, ceil, cos, cosh, exp, fac, floor, ln, log10, sin, sinh, sqrt, tan, tanh;

  • mathematical functions (2 arguments): atan2, pow;

  • constants: e, pi;

  • numbers (as defined in RFC 7159 - The JSON Data Interchange Format, Section 6. Numbers);

  • arbitrary variable identifiers, starting with a letter, and containing small and capital letters [a-zA-Z], digits [0-9], and an underscore _;

  • combinations of the above enclosed in the parentheses ( and ).

Formal description

To be added soon.

Evaluation

A result of expression evaluation should be a real numeric value. This means that the information required for expression evaluation (such as variable values) should be available prior to evaluation.

A valid expression can be evaluated using the standard python’s eval function. When using this function, care should be taken of the variable names identical to the python keywords. See the list of keywords here: here.

A pure-python parser (e.g. to check expression validity) and an evaluator are available in the openepda package.

Also, a valid openEPDA expression is possible to evaluate using tinyexpr C parser. Note that we use ln for the natural logarithm.