parametron file used for precompilation

src/DifferentialEquation.jl

@@ -35,7 +35,7 @@ Return the dependent variables of `diff_eom`.
 get_variables(diff_eom::DifferentialEquation) = collect(keys(diff_eom.equations))
 
 
-is_harmonic(diff_eom::DifferentialEquation, t::Num) = all([is_harmonic(eq, t) for eq in values(diff_eom.equations)])
+is_harmonic(diff_eom::DifferentialEquation, t::Num)::Bool = all([is_harmonic(eq, t) for eq in values(diff_eom.equations)])
 
 "Pretty printing of the newly defined types"
 function show_fields(object)

src/HarmonicBalance.jl

@@ -62,26 +62,7 @@ module HarmonicBalance
     include("modules/LimitCycles.jl")
     using .LimitCycles
 
-
-    @precompile_setup begin
-        # Putting some things in `setup` can reduce the size of the
-        # precompile file and potentially make loading faster.
-        #list = [OtherType("hello"), OtherType("world!")]
-
-        @variables Ω,γ,λ,F, x,θ,η,α, ω0, ω,t,T, ψ
-        @variables x(t)
-
-        natural_equation =  d(d(x,t),t) + γ*d(x,t) + Ω^2*(1-λ*cos(2*ω*t+ψ))*x + α * x^3 +η *d(x,t) * x^2
-        forces =  F*cos(ω*t+θ)
-
-        @precompile_all_calls begin
-            # all calls in this block will be precompiled, regardless of whether
-            # they belong to your package or not (on Julia 1.8 and higher)
-            dEOM = DifferentialEquation(natural_equation + forces, x)
-            add_harmonic!(dEOM, x, ω)
-            harmonic_eq = get_harmonic_equations(dEOM);
-        end
-    end
-
+    precomp_path = (@__DIR__) * "/../test/parametron.jl"
+    @precompile_all_calls include(precomp_path)
 
 end # module

src/Symbolics_customised.jl

@@ -95,7 +95,7 @@ exp_to_trig(x::Complex{Num}) = exp_to_trig(x.re)+im* exp_to_trig(x.im)
 
 # sometimes, expressions get stored as Complex{Num} with no way to decode what real(x) and imag(x)
 # this overloads the Num constructor to return a Num if x.re and x.im have similar arguments
-Num(x::Complex{Num}) = isequal(x.re.val.arguments, x.im.val.arguments) ? Num(first(x.re.val.arguments)) : error("Cannot convert Complex{Num} " * string(x) * " to Num")
+Num(x::Complex{Num})::Num = isequal(x.re.val.arguments, x.im.val.arguments) ? Num(first(x.re.val.arguments)) : error("Cannot convert Complex{Num} " * string(x) * " to Num")
 
 
 #=

test/firstplot_benchmark.jl

@@ -0,0 +1,12 @@
+using HarmonicBalance
+
+@variables α, ω, ω0, F, t, η, x(t) # declare constant variables and a function x(t)
+diff_eq = DifferentialEquation(d(x,t,2) + ω0^2*x + α*x^3 + η*d(x,t)*x^2 ~ F*cos(ω*t), x)
+add_harmonic!(diff_eq, x, ω) # specify the ansatz x = u(T) cos(ωt) + v(T) sin(ωt)
+
+# implement ansatz to get harmonic equations
+harmonic_eq = get_harmonic_equations(diff_eq)
+
+fixed = (α => 1., ω0 => 1.0, F => 0.01, η=>0.1)   # fixed parameters
+varied = ω => LinRange(0.9, 1.2, 100)           # range of parameter values
+result = get_steady_states(harmonic_eq, varied, fixed, show_progress=false);

test/parametron.jl

@@ -1,6 +1,6 @@
 using HarmonicBalance
 using Symbolics
-using Test
+#using Test # do not use Test as this file is used for precompilation
 
 @variables Ω,γ,λ,F, x,θ,η,α, ω0, ω,t,T, ψ
 @variables x(t)
@@ -15,7 +15,7 @@ p = HarmonicBalance.Problem(harmonic_eq);
 
 fixed = (Ω => 1.0,γ => 1E-2, λ => 5E-2, F => 1E-3,  α => 1.,  η=>0.3, θ => 0, ψ => 0)
 varied = ω => LinRange(0.9, 1.1, 100)
-res = get_steady_states(p, varied, fixed)
+res = get_steady_states(p, varied, fixed, show_progress=false)
 
 # save the result, try and load in the next step
 #current_path = @__DIR__
@@ -24,7 +24,7 @@ res = get_steady_states(p, varied, fixed)
 # try to run a 2D calculation
 fixed = (Ω => 1.0,γ => 1E-2, F => 1E-3,  α => 1.,  η=>0.3, θ => 0, ψ => 0)
 varied = (ω => LinRange(0.9, 1.1, 10), λ => LinRange(0.01, 0.05, 10))
-res = get_steady_states(p, varied, fixed)
+res = get_steady_states(p, varied, fixed, show_progress=false)
 
 
 ###
@@ -35,5 +35,5 @@ ref1 = (Ω^2)*u1 + F*cos(θ) + γ*Differential(T)(u1) + (3//4)*α*(u1^3) + γ*ω
 ref2 = γ*Differential(T)(v1) + (Ω^2)*v1 + (3//4)*α*(v1^3) + (3//4)*α*(u1^2)*v1 + (1//4)*η*(u1^2)*Differential(T)(v1) + (3//4)*η*(v1^2)*Differential(T)(v1) + (1//2)*λ*(Ω^2)*v1*cos(ψ) + (1//2)*η*u1*v1*Differential(T)(u1) + (1//2)*λ*(Ω^2)*u1*sin(ψ) - F*sin(θ) - (ω^2)*v1 - (2//1)*ω*Differential(T)(u1) - γ*ω*u1 - (1//4)*η*ω*(u1^3) - (1//4)*η*ω*(v1^2)*u1
 
 averaged = HarmonicBalance._remove_brackets(harmonic_eq)
-@test isequal(simplify(expand(averaged[1]-ref1)), 0)
-@test isequal(simplify(expand(averaged[2]-ref2)), 0)
+@assert isequal(simplify(expand(averaged[1]-ref1)), 0)
+@assert isequal(simplify(expand(averaged[2]-ref2)), 0)