Merge pull request #154 from ChrisRackauckas-Claude/update-vanderpol-documentation

Remove ModelingToolkit dependency from ODEProblemLibrary for faster compilation

Author: ChrisRackauckas

lib/ODEProblemLibrary/Project.toml

@@ -4,23 +4,17 @@ version = "0.1.12"
 
 [deps]
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
-Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
-ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
-RuntimeGeneratedFunctions = "7e49a35a-f44a-4d26-94aa-eba1b4ca6b47"
 
 [compat]
 Aqua = "0.5"
 DiffEqBase = "6"
-Latexify = "0.16"
-ModelingToolkit = "10"
-RuntimeGeneratedFunctions = "0.5"
 julia = "1.10"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 
 [targets]
-test = ["Aqua"]
+test = ["Aqua"]

lib/ODEProblemLibrary/src/ODEProblemLibrary.jl

@@ -1,17 +1,10 @@
 module ODEProblemLibrary
 
 using DiffEqBase
-using Latexify
-using ModelingToolkit
-using ModelingToolkit: t_nounits as t, D_nounits as D
-
 using LinearAlgebra
 using Markdown
 using Random
 
-import RuntimeGeneratedFunctions
-RuntimeGeneratedFunctions.init(@__MODULE__)
-
 Random.seed!(100)
 
 #ODE Example Problems
@@ -30,19 +23,13 @@ export prob_ode_linear, prob_ode_bigfloatlinear, prob_ode_2Dlinear,
        prob_ode_chen, prob_ode_rossler, prob_ode_rabinovich_fabrikant, prob_ode_sprott,
        prob_ode_hindmarsh_rose
 
-# For MTKv9 compatibility
-@static if !isdefined(ModelingToolkit, :mtkcompile)
-    function mtkcompile(args...; kwargs...)
-        structural_simplify(args...; kwargs...)
-    end
-end
-
+# Include all problem definitions
 include("ode_linear_prob.jl")
+include("nonlinchem.jl")
 include("ode_simple_nonlinear_prob.jl")
 include("brusselator_prob.jl")
 include("pollution_prob.jl")
 include("filament_prob.jl")
-include("nonlinchem.jl")
 include("strange_attractors.jl")
 
-end # module
+end # module

lib/ODEProblemLibrary/src/ode_simple_nonlinear_prob.jl

@@ -48,13 +48,15 @@ with initial condition ``v=w=1``
 prob_ode_fitzhughnagumo = ODEProblem(fitz, [1.0; 1.0], (0.0, 1.0),
     (0.7, 0.8, 1 / 12.5, 0.5))
 
-#Van der Pol Equations
-@parameters μ
-@variables x(t) y(t)
+## Van der Pol Equations
 
-eqs = [D(y) ~ μ * ((1 - x^2) * y - x),
-    D(x) ~ y]
-van = System(eqs, t; name = :van_der_pol) |> mtkcompile
+function vanderpol(du, u, p, t)
+    x = u[1]
+    y = u[2]
+    μ = p[1]
+    du[1] = y
+    du[2] = μ * ((1 - x^2) * y - x)
+end
 
 """
 Van der Pol Equations
@@ -66,12 +68,11 @@ Van der Pol Equations
 \\frac{dy}{dt} = μ((1-x^2)y -x)
 ```
 
-with ``μ=1.0`` and ``u_0=[x => \\sqrt{3}, y => 0]``
+with ``μ=1.0`` and ``u_0=[\\sqrt{3}, 0]`` (where ``u[1] = x``, ``u[2] = y``)
 
 Non-stiff parameters.
 """
-prob_ode_vanderpol = ODEProblem(van, [y => 0, x => sqrt(3), μ => 1.0], (0.0, 1.0),
-    jac = true, eval_module = @__MODULE__)
+prob_ode_vanderpol = ODEProblem(vanderpol, [sqrt(3), 0.0], (0.0, 1.0), [1.0])
 
 """
 Van der Pol Equations
@@ -83,21 +84,25 @@ Van der Pol Equations
 \\frac{dy}{dt} = μ((1-x^2)y -x)
 ```
 
-with ``μ=10^6`` and ``u_0=[x => \\sqrt{3}, y => 0]``
+with ``μ=10^6`` and ``u_0=[\\sqrt{3}, 0]`` (where ``u[1] = x``, ``u[2] = y``)
 
 Stiff parameters.
 """
-prob_ode_vanderpol_stiff = ODEProblem(van, [y => 0, x => sqrt(3), μ => 1e6], (0.0, 1.0),
-    jac = true, eval_module = @__MODULE__)
-
-# ROBER
-@parameters k₁ k₂ k₃
-@variables y₁(t) y₂(t) y₃(t)
-
-eqs = [D(y₁) ~ -k₁ * y₁ + k₃ * y₂ * y₃,
-    D(y₂) ~ k₁ * y₁ - k₂ * y₂^2 - k₃ * y₂ * y₃,
-    D(y₃) ~ k₂ * y₂^2]
-rober = System(eqs, t; name = :rober) |> mtkcompile
+prob_ode_vanderpol_stiff = ODEProblem(vanderpol, [sqrt(3), 0.0], (0.0, 1.0), [1e6])
+
+## ROBER
+
+function rober(du, u, p, t)
+    y₁ = u[1]
+    y₂ = u[2]
+    y₃ = u[3]
+    k₁ = p[1]
+    k₂ = p[2]
+    k₃ = p[3]
+    du[1] = -k₁ * y₁ + k₃ * y₂ * y₃
+    du[2] = k₁ * y₁ - k₂ * y₂^2 - k₃ * y₂ * y₃
+    du[3] = k₂ * y₂^2
+end
 
 """
 The Robertson biochemical reactions: (Stiff)
@@ -118,9 +123,7 @@ Hairer Norsett Wanner Solving Ordinary Differential Equations I - Nonstiff Probl
 
 Usually solved on ``[0,1e11]``
 """
-prob_ode_rober = ODEProblem(
-    rober, [[y₁, y₂, y₃] .=> [1.0; 0.0; 0.0]; [k₁, k₂, k₃] .=> (0.04, 3e7, 1e4)],
-    (0.0, 1e11), jac = true, eval_module = @__MODULE__)
+prob_ode_rober = ODEProblem(rober, [1.0, 0.0, 0.0], (0.0, 1e11), [0.04, 3e7, 1e4])
 
 # Three Body
 const threebody_μ = big(0.012277471);
@@ -174,15 +177,19 @@ prob_ode_threebody = ODEProblem(threebody,
     [0.994, 0.0, 0.0, big(-2.00158510637908252240537862224)],
     (big(0.0), big(17.0652165601579625588917206249)))
 
-# Rigid Body Equations
-
-@parameters I₁ I₂ I₃
-@variables y₁(t) y₂(t) y₃(t)
-
-eqs = [D(y₁) ~ I₁ * y₂ * y₃,
-    D(y₂) ~ I₂ * y₁ * y₃,
-    D(y₃) ~ I₃ * y₁ * y₂]
-rigid = System(eqs, t; name = :rigid_body) |> mtkcompile
+## Rigid Body Equations
+
+function rigidbody(du, u, p, t)
+    y₁ = u[1]
+    y₂ = u[2]
+    y₃ = u[3]
+    I₁ = p[1]
+    I₂ = p[2]
+    I₃ = p[3]
+    du[1] = I₁ * y₂ * y₃
+    du[2] = I₂ * y₁ * y₃
+    du[3] = I₃ * y₁ * y₂
+end
 
 """
 Rigid Body Equations (Non-stiff)
@@ -207,10 +214,7 @@ or Hairer Norsett Wanner Solving Ordinary Differential Equations I - Nonstiff Pr
 
 Usually solved from 0 to 20.
 """
-prob_ode_rigidbody = ODEProblem(
-    rigid, [[y₁, y₂, y₃] .=> [1.0, 0.0, 0.9]; [I₁, I₂, I₃] .=> (-2.0, 1.25, -0.5)],
-    (0.0, 20.0),
-    jac = true, eval_module = @__MODULE__)
+prob_ode_rigidbody = ODEProblem(rigidbody, [1.0, 0.0, 0.9], (0.0, 20.0), [-2.0, 1.25, -0.5])
 
 # Pleiades Problem
 
@@ -356,28 +360,27 @@ mm_f = ODEFunction(mm_linear; analytic = (u0, p, t) -> exp(inv(MM_linear) * mm_A
     mass_matrix = MM_linear)
 prob_ode_mm_linear = ODEProblem(mm_f, rand(4), (0.0, 1.0))
 
-@parameters p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12
-@variables y1(t) y2(t) y3(t) y4(t) y5(t) y6(t) y7(t) y8(t)
-
-eqs = [D(y1) ~ -p1 * y1 + p2 * y2 + p3 * y3 + p4,
-    D(y2) ~ p1 * y1 - p5 * y2,
-    D(y3) ~ -p6 * y3 + p2 * y4 + p7 * y5,
-    D(y4) ~ p3 * y2 + p1 * y3 - p8 * y4,
-    D(y5) ~ -p9 * y5 + p2 * y6 + p2 * y7,
-    D(y6) ~ -p10 * y6 * y8 + p11 * y4 + p1 * y5 -
-            p2 * y6 + p11 * y7,
-    D(y7) ~ p10 * y6 * y8 - p12 * y7,
-    D(y8) ~ -p10 * y6 * y8 + p12 * y7]
-hires = System(eqs, t; name = :hires) |> mtkcompile
+## Hires Problem
+
+function hires(du, u, p, t)
+    y1, y2, y3, y4, y5, y6, y7, y8 = u
+    p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12 = p
+    
+    du[1] = -p1 * y1 + p2 * y2 + p3 * y3 + p4
+    du[2] = p1 * y1 - p5 * y2
+    du[3] = -p6 * y3 + p2 * y4 + p7 * y5
+    du[4] = p3 * y2 + p1 * y3 - p8 * y4
+    du[5] = -p9 * y5 + p2 * y6 + p2 * y7
+    du[6] = -p10 * y6 * y8 + p11 * y4 + p1 * y5 - p2 * y6 + p11 * y7
+    du[7] = p10 * y6 * y8 - p12 * y7
+    du[8] = -p10 * y6 * y8 + p12 * y7
+end
 
 u0 = zeros(8)
 u0[1] = 1
 u0[8] = 0.0057
 
-u0 = [y1, y2, y3, y4, y5, y6, y7, y8] .=> u0
-p = [p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11,
-    p12] .=> (1.71, 0.43, 8.32, 0.0007, 8.75,
-    10.03, 0.035, 1.12, 1.745, 280.0, 0.69, 1.81)
+p = (1.71, 0.43, 8.32, 0.0007, 8.75, 10.03, 0.035, 1.12, 1.745, 280.0, 0.69, 1.81)
 
 """
 Hires Problem (Stiff)
@@ -401,16 +404,18 @@ where ``f`` is defined by
 Reference: [demohires.pdf](http://www.radford.edu/~thompson/vodef90web/problems/demosnodislin/Demos_Pitagora/DemoHires/demohires.pdf)
 Notebook: [Hires.ipynb](http://nbviewer.jupyter.org/github/JuliaDiffEq/DiffEqBenchmarks.jl/blob/master/StiffODE/Hires.ipynb)
 """
-prob_ode_hires = ODEProblem(
-    hires, [u0; p], (0.0, 321.8122), jac = true, eval_module = @__MODULE__)
+prob_ode_hires = ODEProblem(hires, u0, (0.0, 321.8122), p)
 
-@parameters p1 p2 p3
-@variables y1(t) y2(t) y3(t)
+## Orego Problem
 
-eqs = [D(y1) ~ p1 * (y2 + y1 * (1 - p2 * y1 - y2)),
-    D(y2) ~ (y3 - (1 + y1) * y2) / p1,
-    D(y3) ~ p3 * (y1 - y3)]
-orego = System(eqs, t; name = :orego) |> mtkcompile
+function orego(du, u, p, t)
+    y1, y2, y3 = u
+    p1, p2, p3 = p
+    
+    du[1] = p1 * (y2 + y1 * (1 - p2 * y1 - y2))
+    du[2] = (y3 - (1 + y1) * y2) / p1
+    du[3] = p3 * (y1 - y3)
+end
 
 """
 Orego Problem (Stiff)
@@ -430,6 +435,4 @@ where ``s=77.27``, ``w=0.161`` and ``q=8.375⋅10^{-6}``.
 Reference: [demoorego.pdf](http://www.radford.edu/~thompson/vodef90web/problems/demosnodislin/Demos_Pitagora/DemoOrego/demoorego.pdf)
 Notebook: [Orego.ipynb](http://nbviewer.jupyter.org/github/JuliaDiffEq/DiffEqBenchmarks.jl/blob/master/StiffODE/Orego.ipynb)
 """
-prob_ode_orego = ODEProblem(
-    orego, [[y1, y2, y3] .=> [1.0, 2.0, 3.0]; [p1, p2, p3] .=> [77.27, 8.375e-6, 0.161]],
-    (0.0, 30.0), jac = true, eval_module = @__MODULE__)
+prob_ode_orego = ODEProblem(orego, [1.0, 2.0, 3.0], (0.0, 30.0), [77.27, 8.375e-6, 0.161])