Terminology
SymbolicIndexingInterface.jl uses various library-specific terminology throughout its documentation. This page attempts to provide comprehensive explanations of the terms used.
Indexes
An index is an object that defines how to extract specific data from a data structure. Indexes may be anything from integer indexes into arrays, to custom types that contain information specific to a particular data structure.
In code samples, an index is typically denoted with the name idx or i.
Symbolic variables
Symbolic variables are objects that represent quantities (states, parameters, time, etc.) or collections of quantities used in a numerical simulation in a more human-accessible manner. Typically the values of these quantities are stored in custom data structures and referred to using indexes that do not convey any semantic meaning to users. Symbolic variables cannot directly be used to access values from these data structures and need to be translated into indexes.
In code samples, a symbolic variable is typically denoted with the name sym.
Symbolic variables are also sometimes referred to as "symbolic indices".
Index providers
Index providers translate symbolic variables into indexes. In general, an "index" can be anything from integer indexes into an array, or custom types that define how to index into complicated data structures. nothing is reserved to denote the absence of an index, in cases where the index provider is unaware of a particular symbolic variable. It cannot be used as an index. ModelingToolkit.jl systems are examples of index providers.
In code samples, an index provider is typically denoted with the name indp.
Value providers
Value providers store values of symbolic variables. Given an appropriate index from an index provider, value providers return the value (or values) stored at that index. The problem, integrator and solution types in SciML are all examples of value providers. Each value provider is (directly or indirectly) associated with an index provider that defines the set of valid symbolic variables for that value provider, and the corresponding indexes.
A value provider may not store values for all symbolic variables in the corresponding index provider. For example, a parameter object (even a plain Array storing parameter values) is a value provider specifically for the symbolic variables referring to parameters.
In code samples, a value provider is typically denoted with the name valp.
It is important to note that an object may be both a value- and index- provider. For example, SciML's problem, integrator and solution types are both value- and index- providers. This allows for several syntactic improvements. The symbolic_container function is useful in defining such objects.
Timeseries objects
Timeseries objects are value providers which implement the Timeseries variant of the is_timeseries trait.
Parameter timeseries objects
Parameter timeseries objects are timeseries objects which implement the Timeseries variant of the is_parameter_timeseries trait.