SymbolicIndexingInterface.jl: Standardized Symbolic Indexing of Julia

SymbolicIndexingInterface.jl is a set of interface functions for handling containers of symbolic variables.

To install SymbolicIndexingInterface.jl, use the Julia package manager:

using Pkg
Pkg.add("SymbolicIndexingInterface")

The symbolic indexing interface has 2 levels:

1. The user level. At the user level, a modeler or engineer simply uses terms from a domain-specific language (DSL) inside of SciML functionality and will receive the requested values. For example, if a DSL defines a symbol x, then sol[x] returns the solution value(s) for x.
2. The DSL system structure level. This is the structure which defines the symbolic indexing for a given problem/solution. DSLs can tag a constructed problem/solution with this object in order to endow the SciML tools with the ability to index symbolically according to the definitions the DSL writer wants.

# Use ModelingToolkit to make a solution

using ModelingToolkit, OrdinaryDiffEq, SymbolicIndexingInterface, Plots

@parameters σ ρ β
@variables t x(t) y(t) z(t) w(t)
D = Differential(t)

eqs = [D(D(x)) ~ σ * (y - x),
    D(y) ~ x * (ρ - z) - y,
    D(z) ~ x * y - β * z,
    w ~ x + y + z]

@mtkbuild sys = ODESystem(eqs)

u0 = [D(x) => 2.0,
    x => 1.0,
    y => 0.0,
    z => 0.0]

p = [σ => 28.0,
    ρ => 10.0,
    β => 8 / 3]

tspan = (0.0, 100.0)
prob = ODEProblem(sys, u0, tspan, p, jac = true)
sol = solve(prob, Tsit5())

# Now index it symbolically

sol[x]