Indexing hooks for symbolic DSLs

[ChrisRackauckas]

using ModelingToolkit, OrdinaryDiffEq

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

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

lorenz1 = ODESystem(eqs,name=:lorenz1)
lorenz2 = ODESystem(eqs,name=:lorenz2)

@variables a
@parameters γ
connections = [0 ~ lorenz1.x + lorenz2.y + a*γ]
connected = ODESystem(connections,t,[a],[γ],systems=[lorenz1,lorenz2])

u0 = [lorenz1.x => 1.0,
      lorenz1.y => 0.0,
      lorenz1.z => 0.0,
      lorenz2.x => 0.0,
      lorenz2.y => 1.0,
      lorenz2.z => 0.0,
      a => 2.0]

p  = [lorenz1.σ => 10.0,
      lorenz1.ρ => 28.0,
      lorenz1.β => 8/3,
      lorenz2.σ => 10.0,
      lorenz2.ρ => 28.0,
      lorenz2.β => 8/3,
      γ => 2.0]

tspan = (0.0,100.0)
prob = ODEProblem(connected,u0,tspan,p)
sol = solve(prob,Rodas5())

sol[lorenz1.x]
sol[lorenz1.x,2]
sol[lorenz1.x,:]
sol[lorenz1.x,1:5]

Now for observed functions.

[codecov]

Codecov Report

Merging #8 (9ecf223) into master (6f068d0) will decrease coverage by 0.02%.
The diff coverage is 0.00%.

@@            Coverage Diff            @@
##           master      #8      +/-   ##
=========================================
- Coverage    3.01%   2.99%   -0.03%     
=========================================
  Files          37      37              
  Lines        2584    2605      +21     
=========================================
  Hits           78      78              
- Misses       2506    2527      +21     

Impacted Files	Coverage Δ
src/solutions/solution_interface.jl	0.00% <0.00%> (ø)

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