Repair documentation example setup (#481)

* Fix callable interpolation builder symtype

Register CachedInterpolation's symbolic result as a callable Real-to-Real value, derived through public SymbolicUtils APIs. Add a regression that calls the bound interpolator before building and solving the ODEProblem.

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

* Repair documentation example setup

Supply the position-domain initialization equations, bind OnePort's extended names explicitly, and make OrdinaryDiffEqSDIRK a direct documentation dependency for ImplicitEuler.

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

---------

Co-authored-by: ChrisRackauckas-Claude <accounts@chrisrackauckas.com>

Author: ChrisRackauckas-Claude

docs/Project.toml

@@ -7,6 +7,7 @@ IfElse = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
 ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 ModelingToolkitStandardLibrary = "16a59e39-deab-5bd0-87e4-056b12336739"
 OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+OrdinaryDiffEqSDIRK = "2d112036-d095-4a1e-ab9a-08536f3ecdbf"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 SciCompDSL = "91a8cdf1-4ca6-467b-a780-87fda3fff15e"
 
@@ -19,5 +20,6 @@ IfElse = "0.1"
 ModelingToolkit = "11"
 ModelingToolkitStandardLibrary = "2.28.0"
 OrdinaryDiffEq = "6, 7"
+OrdinaryDiffEqSDIRK = "1, 2"
 Plots = "1.36"
 SciCompDSL = "1"

docs/src/connectors/connections.md

@@ -191,7 +191,8 @@ nothing # hide
 As can be seen, we get exactly the same result.  The only difference here is that we are solving an extra equation, which allows us to plot the body position as well.
 
 ```@example connections
-prob = ODEProblem(sys, [], (0, 10.0), fully_determined = true)
+prob = ODEProblem(
+    sys, [], (0, 10.0); initialization_eqs = [sys.body.s ~ 0, sys.body.v ~ 1])
 sol_p = solve(prob)
 
 p1 = plot(sol_p, idxs = [body.v])

docs/src/tutorials/custom_component.md

@@ -36,7 +36,7 @@ this can almost be directly translated to the syntax of `ModelingToolkit`.
 
 ```@example components
 @mtkmodel NonlinearResistor begin
-    @extend OnePort()
+    @extend v, i = oneport = OnePort()
     @parameters begin
         Ga
         Gb
@@ -58,7 +58,7 @@ nothing # hide
 Since the non-linear resistor is essentially a standard electrical component with two ports, we can extend from the `OnePort` component of the library.
 
 ```julia
-@extend OnePort()
+@extend v, i = oneport = OnePort()
 ```
 
 This extends `OnePort` and unpacks `v` and `i` variables.

src/Blocks/Blocks.jl

@@ -5,6 +5,7 @@ module Blocks
 using ModelingToolkitBase: ModelingToolkitBase, @component, @connector, @named,
     @parameters, @unpack, System, compose, connect, extend,
     getdefault, t_nounits as t, D_nounits as D
+using SymbolicUtils: @syms, symtype
 using Symbolics: Symbolics, @register_symbolic, @variables, Differential, Equation
 import Base: ifelse
 import ..@symcheck

src/Blocks/sources.jl

@@ -864,7 +864,15 @@ end
 
 Base.nameof(::CachedInterpolation) = :CachedInterpolation
 
-@register_symbolic (f::CachedInterpolation)(u::AbstractArray, x::AbstractArray, args::Tuple)
+const _INTERPOLATOR_SYMTYPE = let
+    @syms interpolator(::Real)::Real
+    symtype(interpolator)
+end
+
+# Calling the builder returns the interpolation function, not an interpolated scalar.
+@register_symbolic (f::CachedInterpolation)(
+    u::AbstractArray, x::AbstractArray, args::Tuple
+)::_INTERPOLATOR_SYMTYPE
 
 """
     ParametrizedInterpolation(interp_type, u, x, args...; name, t = ModelingToolkitBase.t_nounits)

test/sources.jl

@@ -14,6 +14,7 @@ using SymbolicIndexingInterface
 using SciMLStructures: SciMLStructures, Tunable
 using ForwardDiff
 using ADTypes
+using SymbolicUtils: symtype
 
 @testset "Constant" begin
     @named src = Constant(k = 2)
@@ -650,6 +651,9 @@ end
 
     @testset "LinearInterpolation" begin
         @named i = ParametrizedInterpolation(LinearInterpolation, u, x)
+        interpolator = only(values(bindings(i)))
+        @test symtype(interpolator(0.0)) === Real
+
         eqs = [i.input.u ~ t, D(y) ~ i.output.u]
 
         @named model = System(eqs, t, systems = [i])