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odesystem.jl
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using ModelingToolkit, StaticArrays, LinearAlgebra
using ModelingToolkit: get_metadata, MTKParameters
using SymbolicIndexingInterface
using OrdinaryDiffEq, Sundials
using DiffEqBase, SparseArrays
using StaticArrays
using Test
using SymbolicUtils: issym
using ForwardDiff
using ModelingToolkit: value
using ModelingToolkit: t_nounits as t, D_nounits as D
# Define some variables
@parameters σ ρ β
@constants κ = 1
@variables x(t) y(t) z(t)
@parameters k
# Define a differential equation
eqs = [D(x) ~ σ * (y - x),
D(y) ~ x * (ρ - z) - y,
D(z) ~ x * y - β * z * κ]
ModelingToolkit.toexpr.(eqs)[1]
@named de = ODESystem(eqs, t; defaults = Dict(x => 1))
subed = substitute(de, [σ => k])
ssort(eqs) = sort(eqs, by = string)
@test isequal(ssort(parameters(subed)), [k, β, ρ])
@test isequal(equations(subed),
[D(x) ~ k * (y - x)
D(y) ~ (ρ - z) * x - y
D(z) ~ x * y - β * κ * z])
@named des[1:3] = ODESystem(eqs, t)
@test length(unique(x -> ModelingToolkit.get_tag(x), des)) == 1
@test eval(toexpr(de)) == de
@test hash(deepcopy(de)) == hash(de)
generate_function(de)
function test_diffeq_inference(name, sys, iv, dvs, ps)
@testset "ODESystem construction: $name" begin
@test isequal(independent_variables(sys)[1], value(iv))
@test length(independent_variables(sys)) == 1
@test isempty(setdiff(Set(unknowns(sys)), Set(value.(dvs))))
@test isempty(setdiff(Set(parameters(sys)), Set(value.(ps))))
end
end
test_diffeq_inference("standard", de, t, [x, y, z], [ρ, σ, β])
generate_function(de, [x, y, z], [σ, ρ, β])
jac_expr = generate_jacobian(de)
jac = calculate_jacobian(de)
jacfun = eval(jac_expr[2])
de = complete(de)
for f in [
ODEFunction(de, [x, y, z], [σ, ρ, β], tgrad = true, jac = true),
eval(ODEFunctionExpr(de, [x, y, z], [σ, ρ, β], tgrad = true, jac = true))
]
# system
@test f.sys === de
# iip
du = zeros(3)
u = collect(1:3)
p = ModelingToolkit.MTKParameters(de, [σ, ρ, β] .=> 4.0:6.0)
f.f(du, u, p, 0.1)
@test du == [4, 0, -16]
# oop
du = @SArray zeros(3)
u = SVector(1:3...)
p = ModelingToolkit.MTKParameters(de, SVector{3}([σ, ρ, β] .=> 4.0:6.0))
@test f.f(u, p, 0.1) === @SArray [4.0, 0.0, -16.0]
# iip vs oop
du = zeros(3)
g = similar(du)
J = zeros(3, 3)
u = collect(1:3)
p = ModelingToolkit.MTKParameters(de, [σ, ρ, β] .=> 4.0:6.0)
f.f(du, u, p, 0.1)
@test du == f(u, p, 0.1)
f.tgrad(g, u, p, t)
@test g == f.tgrad(u, p, t)
f.jac(J, u, p, t)
@test J == f.jac(u, p, t)
end
#check iip_config
f = eval(ODEFunctionExpr(de, [x, y, z], [σ, ρ, β], iip_config = (false, true)))
du = zeros(3)
u = collect(1:3)
p = ModelingToolkit.MTKParameters(de, [σ, ρ, β] .=> 4.0:6.0)
f.f(du, u, p, 0.1)
@test du == [4, 0, -16]
@test_throws ArgumentError f.f(u, p, 0.1)
#check sparsity
f = eval(ODEFunctionExpr(de, [x, y, z], [σ, ρ, β], sparsity = true))
@test f.sparsity == ModelingToolkit.jacobian_sparsity(de)
f = eval(ODEFunctionExpr(de, [x, y, z], [σ, ρ, β], sparsity = false))
@test isnothing(f.sparsity)
eqs = [D(x) ~ σ * (y - x),
D(y) ~ x * (ρ - z) - y * t,
D(z) ~ x * y - β * z * κ]
@named de = ODESystem(eqs, t)
de = complete(de)
ModelingToolkit.calculate_tgrad(de)
tgrad_oop, tgrad_iip = eval.(ModelingToolkit.generate_tgrad(de))
u = SVector(1:3...)
p = ModelingToolkit.MTKParameters(de, SVector{3}([σ, ρ, β] .=> 4.0:6.0))
@test tgrad_oop(u, p, t) == [0.0, -u[2], 0.0]
du = zeros(3)
tgrad_iip(du, u, p, t)
@test du == [0.0, -u[2], 0.0]
@parameters σ′(t - 1)
eqs = [D(x) ~ σ′ * (y - x),
D(y) ~ x * (ρ - z) - y,
D(z) ~ x * y - β * z * κ]
@named de = ODESystem(eqs, t)
test_diffeq_inference("global iv-varying", de, t, (x, y, z), (σ′, ρ, β))
f = eval(generate_function(de, [x, y, z], [σ′, ρ, β])[2])
du = [0.0, 0.0, 0.0]
f(du, [1.0, 2.0, 3.0], [x -> x + 7, 2, 3], 5.0)
@test du ≈ [11, -3, -7]
@parameters σ(..)
eqs = [D(x) ~ σ(t - 1) * (y - x),
D(y) ~ x * (ρ - z) - y,
D(z) ~ x * y - β * z * κ]
@named de = ODESystem(eqs, t)
test_diffeq_inference("single internal iv-varying", de, t, (x, y, z), (σ, ρ, β))
f = eval(generate_function(de, [x, y, z], [σ, ρ, β])[2])
du = [0.0, 0.0, 0.0]
f(du, [1.0, 2.0, 3.0], [x -> x + 7, 2, 3], 5.0)
@test du ≈ [11, -3, -7]
eqs = [D(x) ~ x + 10σ(t - 1) + 100σ(t - 2) + 1000σ(t^2)]
@named de = ODESystem(eqs, t)
test_diffeq_inference("many internal iv-varying", de, t, (x,), (σ,))
f = eval(generate_function(de, [x], [σ])[2])
du = [0.0]
f(du, [1.0], [t -> t + 2], 5.0)
@test du ≈ [27561]
# Conversion to first-order ODEs #17
D3 = D^3
D2 = D^2
@variables u(t) uˍtt(t) uˍt(t) xˍt(t)
eqs = [D3(u) ~ 2(D2(u)) + D(u) + D(x) + 1
D2(x) ~ D(x) + 2]
@named de = ODESystem(eqs, t)
de1 = ode_order_lowering(de)
lowered_eqs = [D(uˍtt) ~ 2uˍtt + uˍt + xˍt + 1
D(xˍt) ~ xˍt + 2
D(uˍt) ~ uˍtt
D(u) ~ uˍt
D(x) ~ xˍt]
#@test de1 == ODESystem(lowered_eqs)
# issue #219
@test all(isequal.(
[ModelingToolkit.var_from_nested_derivative(eq.lhs)[1]
for eq in equations(de1)],
unknowns(@named lowered = ODESystem(lowered_eqs, t))))
test_diffeq_inference("first-order transform", de1, t, [uˍtt, xˍt, uˍt, u, x], [])
du = zeros(5)
ODEFunction(complete(de1), [uˍtt, xˍt, uˍt, u, x], [])(du, ones(5), nothing, 0.1)
@test du == [5.0, 3.0, 1.0, 1.0, 1.0]
# Internal calculations
@parameters σ
a = y - x
eqs = [D(x) ~ σ * a,
D(y) ~ x * (ρ - z) - y,
D(z) ~ x * y - β * z * κ]
@named de = ODESystem(eqs, t)
generate_function(de, [x, y, z], [σ, ρ, β])
jac = calculate_jacobian(de)
@test ModelingToolkit.jacobian_sparsity(de).colptr == sparse(jac).colptr
@test ModelingToolkit.jacobian_sparsity(de).rowval == sparse(jac).rowval
f = ODEFunction(complete(de), [x, y, z], [σ, ρ, β])
@parameters A B C
_x = y / C
eqs = [D(x) ~ -A * x,
D(y) ~ A * x - B * _x]
@named de = ODESystem(eqs, t)
@test begin
local f, du
f = eval(generate_function(de, [x, y], [A, B, C])[2])
du = [0.0, 0.0]
f(du, [1.0, 2.0], [1, 2, 3], 0.0)
du ≈ [-1, -1 / 3]
f = eval(generate_function(de, [x, y], [A, B, C])[1])
du ≈ f([1.0, 2.0], [1, 2, 3], 0.0)
end
function lotka(u, p, t)
x = u[1]
y = u[2]
[p[1] * x - p[2] * x * y,
-p[3] * y + p[4] * x * y]
end
prob = ODEProblem(ODEFunction{false}(lotka), [1.0, 1.0], (0.0, 1.0), [1.5, 1.0, 3.0, 1.0])
de = complete(modelingtoolkitize(prob))
ODEFunction(de)(similar(prob.u0), prob.u0, prob.p, 0.1)
function lotka(du, u, p, t)
x = u[1]
y = u[2]
du[1] = p[1] * x - p[2] * x * y
du[2] = -p[3] * y + p[4] * x * y
end
prob = ODEProblem(lotka, [1.0, 1.0], (0.0, 1.0), [1.5, 1.0, 3.0, 1.0])
de = complete(modelingtoolkitize(prob))
ODEFunction(de)(similar(prob.u0), prob.u0, prob.p, 0.1)
# automatic unknown detection for DAEs
@parameters k₁ k₂ k₃
@variables y₁(t) y₂(t) y₃(t)
# reorder the system just to be a little spicier
eqs = [D(y₁) ~ -k₁ * y₁ + k₃ * y₂ * y₃,
0 ~ y₁ + y₂ + y₃ - 1,
D(y₂) ~ k₁ * y₁ - k₂ * y₂^2 - k₃ * y₂ * y₃ * κ]
@named sys = ODESystem(eqs, t, defaults = [k₁ => 100, k₂ => 3e7, y₁ => 1.0])
sys = complete(sys)
u0 = Pair[]
push!(u0, y₂ => 0.0)
push!(u0, y₃ => 0.0)
p = [k₁ => 0.04,
k₃ => 1e4]
p2 = (k₁ => 0.04,
k₂ => 3e7,
k₃ => 1e4)
tspan = (0.0, 100000.0)
prob1 = ODEProblem(sys, u0, tspan, p)
@test prob1.f.sys == sys
prob12 = ODEProblem(sys, u0, tspan, [k₁ => 0.04, k₂ => 3e7, k₃ => 1e4])
prob13 = ODEProblem(sys, u0, tspan, (k₁ => 0.04, k₂ => 3e7, k₃ => 1e4))
prob14 = ODEProblem(sys, u0, tspan, p2)
for p in [prob1, prob14]
@test p.p == MTKParameters(sys, [k₁ => 0.04, k₂ => 3e7, k₃ => 1e4])
@test Set(Num.(unknowns(sys)) .=> p.u0) == Set([y₁ => 1, y₂ => 0, y₃ => 0])
end
# test remake with symbols
p3 = [k₁ => 0.05,
k₂ => 2e7,
k₃ => 1.1e4]
u01 = [y₁ => 1, y₂ => 1, y₃ => 1]
prob_pmap = remake(prob14; p = p3, u0 = u01)
prob_dpmap = remake(prob14; p = Dict(p3), u0 = Dict(u01))
for p in [prob_pmap, prob_dpmap]
@test p.p == MTKParameters(sys, [k₁ => 0.05, k₂ => 2e7, k₃ => 1.1e4])
@test Set(Num.(unknowns(sys)) .=> p.u0) == Set([y₁ => 1, y₂ => 1, y₃ => 1])
end
sol_pmap = solve(prob_pmap, Rodas5())
sol_dpmap = solve(prob_dpmap, Rodas5())
@test all(isequal(0.05), sol_pmap.(0:10:100, idxs = k₁))
@test sol_pmap.u ≈ sol_dpmap.u
@testset "symbolic remake with nested system" begin
function makesys(name)
@parameters a = 1.0
@variables x(t) = 0.0
ODESystem([D(x) ~ -a * x], t; name)
end
function makecombinedsys()
sys1 = makesys(:sys1)
sys2 = makesys(:sys2)
@parameters b = 1.0
complete(ODESystem(Equation[], t, [], [b]; systems = [sys1, sys2], name = :foo))
end
sys = makecombinedsys()
@unpack sys1, b = sys
prob = ODEProblem(sys, Pair[])
prob_new = SciMLBase.remake(prob, p = Dict(sys1.a => 3.0, b => 4.0),
u0 = Dict(sys1.x => 1.0))
@test prob_new.p == MTKParameters(sys, [b => 4.0, sys1.a => 3.0, sys.sys2.a => 1.0])
@test prob_new.u0 == [1.0, 0.0]
end
# test kwargs
prob2 = ODEProblem(sys, u0, tspan, p, jac = true)
prob3 = ODEProblem(sys, u0, tspan, p, jac = true, sparse = true) #SparseMatrixCSC need to handle
@test prob3.f.jac_prototype isa SparseMatrixCSC
prob3 = ODEProblem(sys, u0, tspan, p, jac = true, sparsity = true)
@test prob3.f.sparsity isa SparseMatrixCSC
@test_throws ArgumentError ODEProblem(sys, zeros(5), tspan, p)
for (prob, atol) in [(prob1, 1e-12), (prob2, 1e-12), (prob3, 1e-12)]
local sol
sol = solve(prob, Rodas5())
@test all(x -> ≈(sum(x), 1.0, atol = atol), sol.u)
end
du0 = [D(y₁) => -0.04
D(y₂) => 0.04
D(y₃) => 0.0]
prob4 = DAEProblem(sys, du0, u0, tspan, p2)
prob5 = eval(DAEProblemExpr(sys, du0, u0, tspan, p2))
for prob in [prob4, prob5]
local sol
@test prob.differential_vars == [true, true, false]
sol = solve(prob, IDA())
@test all(x -> ≈(sum(x), 1.0, atol = 1e-12), sol.u)
end
@parameters σ β
@variables x(t) y(t) z(t)
eqs = [D(x) ~ σ * (y - x),
D(y) ~ x - β * y,
x + z ~ y]
@named sys = ODESystem(eqs, t)
@test all(isequal.(unknowns(sys), [x, y, z]))
@test all(isequal.(parameters(sys), [σ, β]))
@test equations(sys) == eqs
@test ModelingToolkit.isautonomous(sys)
# issue 701
using ModelingToolkit
@parameters a
@variables x(t)
@named sys = ODESystem([D(x) ~ a], t)
@test issym(equations(sys)[1].rhs)
# issue 708
@parameters a
@variables x(t) y(t) z(t)
@named sys = ODESystem([D(x) ~ y, 0 ~ x + z, 0 ~ x - y], t, [z, y, x], [])
asys = add_accumulations(sys)
@variables accumulation_x(t) accumulation_y(t) accumulation_z(t)
eqs = [0 ~ x + z
0 ~ x - y
D(accumulation_x) ~ x
D(accumulation_y) ~ y
D(accumulation_z) ~ z
D(x) ~ y]
@test ssort(equations(asys)) == ssort(eqs)
@variables ac(t)
asys = add_accumulations(sys, [ac => (x + y)^2])
eqs = [0 ~ x + z
0 ~ x - y
D(ac) ~ (x + y)^2
D(x) ~ y]
@test ssort(equations(asys)) == ssort(eqs)
sys2 = ode_order_lowering(sys)
M = ModelingToolkit.calculate_massmatrix(sys2)
@test M == Diagonal([1, 0, 0])
# issue #609
@variables x1(t) x2(t)
eqs = [
D(x1) ~ -x1,
0 ~ x1 - x2
]
@named sys = ODESystem(eqs, t)
@test isequal(ModelingToolkit.get_iv(sys), t)
@test isequal(unknowns(sys), [x1, x2])
@test isempty(parameters(sys))
# one equation ODESystem test
@parameters r
@variables x(t)
eq = D(x) ~ r * x
@named ode = ODESystem(eq, t)
@test equations(ode) == [eq]
# issue #808
@testset "Combined system name collisions" begin
function makesys(name)
@parameters a
@variables x(t) f(t)
ODESystem([D(x) ~ -a * x + f], t; name)
end
function issue808()
sys1 = makesys(:sys1)
sys2 = makesys(:sys1)
@test_throws ArgumentError ODESystem([sys2.f ~ sys1.x, D(sys1.f) ~ 0], t,
systems = [sys1, sys2], name = :foo)
end
issue808()
end
#Issue 998
pars = []
vars = @variables((u1,))
eqs = [
D(u1) ~ 1
]
@test_throws ArgumentError ODESystem(eqs, t, vars, pars, name = :foo)
#Issue 1063/998
pars = [t]
vars = @variables((u1(t),))
@test_throws ArgumentError ODESystem(eqs, t, vars, pars, name = :foo)
@parameters w
der = Differential(w)
eqs = [
der(u1) ~ t
]
@test_throws ArgumentError ModelingToolkit.ODESystem(eqs, t, vars, pars, name = :foo)
@variables x(t)
@parameters M b k
eqs = [D(D(x)) ~ -b / M * D(x) - k / M * x]
ps = [M, b, k]
default_u0 = [D(x) => 0.0, x => 10.0]
default_p = [M => 1.0, b => 1.0, k => 1.0]
@named sys = ODESystem(eqs, t, [x], ps; defaults = [default_u0; default_p], tspan)
sys = ode_order_lowering(sys)
sys = complete(sys)
prob = ODEProblem(sys)
sol = solve(prob, Tsit5())
@test sol.t[end] == tspan[end]
@test sum(abs, sol.u[end]) < 1
prob = ODEProblem{false}(sys; u0_constructor = x -> SVector(x...))
@test prob.u0 isa SVector
# check_eqs_u0 kwarg test
@variables x1(t) x2(t)
eqs = [D(x1) ~ -x1]
@named sys = ODESystem(eqs, t, [x1, x2], [])
sys = complete(sys)
@test_throws ArgumentError ODEProblem(sys, [1.0, 1.0], (0.0, 1.0))
@test_nowarn ODEProblem(sys, [1.0, 1.0], (0.0, 1.0), check_length = false)
# check inputs
let
@parameters f k d
@variables x(t) ẋ(t)
δ = D
eqs = [δ(x) ~ ẋ, δ(ẋ) ~ f - k * x - d * ẋ]
@named sys = ODESystem(eqs, t, [x, ẋ], [f, d, k]; controls = [f])
calculate_control_jacobian(sys)
@test isequal(calculate_control_jacobian(sys),
reshape(Num[0, 1], 2, 1))
end
# issue 1109
let
@variables x(t)[1:3, 1:3]
@named sys = ODESystem(D.(x) .~ x, t)
@test_nowarn structural_simplify(sys)
end
# Array vars
using Symbolics: unwrap, wrap
using LinearAlgebra
sts = @variables x(t)[1:3]=[1, 2, 3.0] y(t)=1.0
ps = @parameters p[1:3] = [1, 2, 3]
eqs = [collect(D.(x) .~ x)
D(y) ~ norm(collect(x)) * y - x[1]]
@named sys = ODESystem(eqs, t, sts, ps)
sys = structural_simplify(sys)
@test isequal(@nonamespace(sys.x), x)
@test isequal(@nonamespace(sys.y), y)
@test isequal(@nonamespace(sys.p), p)
@test_nowarn sys.x, sys.y, sys.p
@test all(x -> x isa Symbolics.Arr, (sys.x, sys.p))
@test all(x -> x isa Symbolics.Arr, @nonamespace (sys.x, sys.p))
@test ModelingToolkit.isvariable(Symbolics.unwrap(x[1]))
prob = ODEProblem(sys, [], (0, 1.0))
sol = solve(prob, Tsit5())
@test sol[2x[1] + 3x[3] + norm(x)] ≈
2sol[x[1]] + 3sol[x[3]] + sol[norm(x)]
@test sol[x .+ [y, 2y, 3y]] ≈ map((x...) -> [x...],
map((x, y) -> x[1] .+ y, sol[x], sol[y]),
map((x, y) -> x[2] .+ 2y, sol[x], sol[y]),
map((x, y) -> x[3] .+ 3y, sol[x], sol[y]))
using ModelingToolkit
function submodel(; name)
@variables y(t)
@parameters A[1:5]
A = collect(A)
ODESystem(D(y) ~ sum(A) * y, t; name = name)
end
# Build system
@named sys1 = submodel()
@named sys2 = submodel()
@named sys = ODESystem([0 ~ sys1.y + sys2.y], t; systems = [sys1, sys2])
# DelayDiffEq
using ModelingToolkit: hist
@variables x(t) y(t)
xₜ₋₁ = hist(x, t - 1)
eqs = [D(x) ~ x * y
D(y) ~ y * x - xₜ₋₁]
@named sys = ODESystem(eqs, t)
# register
using StaticArrays
using SymbolicUtils: term
using SymbolicUtils.Code
using Symbolics: unwrap, wrap, @register_symbolic
foo(a, ms::AbstractVector) = a + sum(ms)
@register_symbolic foo(a, ms::AbstractVector)
@variables x(t) ms(t)[1:3]
eqs = [D(x) ~ foo(x, ms); D(ms) ~ ones(3)]
@named sys = ODESystem(eqs, t, [x; ms], [])
@named emptysys = ODESystem(Equation[], t)
@mtkbuild outersys = compose(emptysys, sys)
prob = ODEProblem(
outersys, [outersys.sys.x => 1.0; collect(outersys.sys.ms .=> 1:3)], (0, 1.0))
@test_nowarn solve(prob, Tsit5())
# array equations
bar(x, p) = p * x
@register_array_symbolic bar(x::AbstractVector, p::AbstractMatrix) begin
size = size(x)
eltype = promote_type(eltype(x), eltype(p))
end
@parameters p[1:3, 1:3]
eqs = [D(x) ~ foo(x, ms); D(ms) ~ bar(ms, p)]
@named sys = ODESystem(eqs, t)
@named emptysys = ODESystem(Equation[], t)
@mtkbuild outersys = compose(emptysys, sys)
prob = ODEProblem(
outersys, [sys.x => 1.0, sys.ms => 1:3], (0.0, 1.0), [sys.p => ones(3, 3)])
@test_nowarn solve(prob, Tsit5())
obsfn = ModelingToolkit.build_explicit_observed_function(
outersys, bar(3outersys.sys.ms, 3outersys.sys.p))
@test_nowarn obsfn(sol.u[1], prob.p, sol.t[1])
# x/x
@variables x(t)
@named sys = ODESystem([D(x) ~ x / x], t)
@test equations(alias_elimination(sys)) == [D(x) ~ 1]
# observed variable handling
@variables x(t) RHS(t)
@parameters τ
@named fol = ODESystem([D(x) ~ (1 - x) / τ], t; observed = [RHS ~ (1 - x) / τ])
@test isequal(RHS, @nonamespace fol.RHS)
RHS2 = RHS
@unpack RHS = fol
@test isequal(RHS, RHS2)
#1413 and 1389
@parameters α β
@variables x(t) y(t) z(t)
eqs = [
D(x) ~ 0.1x + 0.9y,
D(y) ~ 0.5x + 0.5y,
z ~ α * x - β * y
]
@named sys = ODESystem(eqs, t, [x, y, z], [α, β])
sys = complete(sys)
@test_throws Any ODEFunction(sys)
eqs = copy(eqs)
eqs[end] = D(D(z)) ~ α * x - β * y
@named sys = ODESystem(eqs, t, [x, y, z], [α, β])
sys = complete(sys)
@test_throws Any ODEFunction(sys)
@testset "Preface tests" begin
using OrdinaryDiffEq
using Symbolics
using DiffEqBase: isinplace
using ModelingToolkit
using SymbolicUtils.Code
using SymbolicUtils: Sym
c = [0]
function f(c, du::AbstractVector{Float64}, u::AbstractVector{Float64}, p, t::Float64)
c .= [c[1] + 1]
du .= randn(length(u))
nothing
end
dummy_identity(x, _) = x
@register_symbolic dummy_identity(x, y)
u0 = ones(5)
p0 = Float64[]
syms = [Symbol(:a, i) for i in 1:5]
syms_p = Symbol[]
@assert isinplace(f, 5)
wf = let buffer = similar(u0), u = similar(u0), p = similar(p0), c = c
t -> (f(c, buffer, u, p, t); buffer)
end
num = hash(f) ⊻ length(u0) ⊻ length(p0)
buffername = Symbol(:fmi_buffer_, num)
D = Differential(t)
us = map(s -> (@variables $s(t))[1], syms)
ps = map(s -> (@variables $s(t))[1], syms_p)
buffer, = @variables $buffername[1:length(u0)]
dummy_var = Sym{Any}(:_) # this is safe because _ cannot be a rvalue in Julia
ss = Iterators.flatten((us, ps))
vv = Iterators.flatten((u0, p0))
defs = Dict{Any, Any}(s => v for (s, v) in zip(ss, vv))
preface = [Assignment(dummy_var, SetArray(true, term(getfield, wf, Meta.quot(:u)), us))
Assignment(dummy_var, SetArray(true, term(getfield, wf, Meta.quot(:p)), ps))
Assignment(buffer, term(wf, t))]
eqs = map(1:length(us)) do i
D(us[i]) ~ dummy_identity(buffer[i], us[i])
end
@named sys = ODESystem(eqs, t, us, ps; defaults = defs, preface = preface)
sys = complete(sys)
prob = ODEProblem(sys, [], (0.0, 1.0))
sol = solve(prob, Euler(); dt = 0.1)
@test c[1] == length(sol)
end
let
x = map(xx -> xx(t), Symbolics.variables(:x, 1:2, T = SymbolicUtils.FnType))
@variables y(t) = 0
@parameters k = 1
eqs = [D(x[1]) ~ x[2]
D(x[2]) ~ -x[1] - 0.5 * x[2] + k
y ~ 0.9 * x[1] + x[2]]
@named sys = ODESystem(eqs, t, vcat(x, [y]), [k], defaults = Dict(x .=> 0))
sys = structural_simplify(sys)
u0 = [0.5, 0]
du0 = 0 .* copy(u0)
prob = DAEProblem(sys, du0, u0, (0, 50))
@test prob.u0 ≈ u0
@test prob.du0 ≈ du0
@test vcat(prob.p...) ≈ [1]
sol = solve(prob, IDA())
@test sol[y] ≈ 0.9 * sol[x[1]] + sol[x[2]]
@test isapprox(sol[x[1]][end], 1, atol = 1e-3)
prob = DAEProblem(sys, [D(y) => 0, D(x[1]) => 0, D(x[2]) => 0], Pair[x[1] => 0.5],
(0, 50))
@test prob.u0 ≈ [0.5, 0]
@test prob.du0 ≈ [0, 0]
@test vcat(prob.p...) ≈ [1]
sol = solve(prob, IDA())
@test isapprox(sol[x[1]][end], 1, atol = 1e-3)
prob = DAEProblem(sys, [D(y) => 0, D(x[1]) => 0, D(x[2]) => 0], Pair[x[1] => 0.5],
(0, 50), [k => 2])
@test prob.u0 ≈ [0.5, 0]
@test prob.du0 ≈ [0, 0]
@test vcat(prob.p...) ≈ [2]
sol = solve(prob, IDA())
@test isapprox(sol[x[1]][end], 2, atol = 1e-3)
# no initial conditions for D(x[1]) and D(x[2]) provided
@test_throws ModelingToolkit.MissingVariablesError prob=DAEProblem(
sys, Pair[], Pair[], (0, 50))
prob = ODEProblem(sys, Pair[x[1] => 0], (0, 50))
sol = solve(prob, Rosenbrock23())
@test isapprox(sol[x[1]][end], 1, atol = 1e-3)
end
#issue 1475 (mixed numeric type for parameters)
let
@parameters k1 k2::Int
@variables A(t)
eqs = [D(A) ~ -k1 * k2 * A]
@named sys = ODESystem(eqs, t)
sys = complete(sys)
u0map = [A => 1.0]
pmap = (k1 => 1.0, k2 => 1)
tspan = (0.0, 1.0)
prob = ODEProblem(sys, u0map, tspan, pmap; tofloat = false)
@test (prob.p...,) == ([1], [1.0]) || (prob.p...,) == ([1.0], [1])
prob = ODEProblem(sys, u0map, tspan, pmap)
@test vcat(prob.p...) isa Vector{Float64}
pmap = [k1 => 1, k2 => 1]
tspan = (0.0, 1.0)
prob = ODEProblem(sys, u0map, tspan, pmap)
@test eltype(vcat(prob.p...)) === Float64
prob = ODEProblem(sys, u0map, tspan, pmap)
@test vcat(prob.p...) isa Vector{Float64}
# No longer supported, Tuple used instead
# pmap = Pair{Any, Union{Int, Float64}}[k1 => 1, k2 => 1.0]
# tspan = (0.0, 1.0)
# prob = ODEProblem(sys, u0map, tspan, pmap, use_union = true)
# @test eltype(prob.p) === Union{Float64, Int}
end
let
@parameters C L R
@variables q(t) p(t) F(t)
eqs = [D(q) ~ -p / L - F
D(p) ~ q / C
0 ~ q / C - R * F]
@named sys = ODESystem(eqs, t)
@test length(equations(structural_simplify(sys))) == 2
end
let
eq_to_lhs(eq) = eq.lhs - eq.rhs ~ 0
eqs_to_lhs(eqs) = eq_to_lhs.(eqs)
@parameters σ=10 ρ=28 β=8 / 3 sigma rho beta
@variables x(t)=1 y(t)=0 z(t)=0 x2(t)=1 y2(t)=0 z2(t)=0 u(t)[1:3]
eqs = [D(x) ~ σ * (y - x),
D(y) ~ x * (ρ - z) - y,
D(z) ~ x * y - β * z]
eqs2 = [
D(y2) ~ x2 * (rho - z2) - y2,
D(x2) ~ sigma * (y2 - x2),
D(z2) ~ x2 * y2 - beta * z2
]
# array u
eqs3 = [D(u[1]) ~ sigma * (u[2] - u[1]),
D(u[2]) ~ u[1] * (rho - u[3]) - u[2],
D(u[3]) ~ u[1] * u[2] - beta * u[3]]
eqs3 = eqs_to_lhs(eqs3)
eqs4 = [
D(y2) ~ x2 * (rho - z2) - y2,
D(x2) ~ sigma * (y2 - x2),
D(z2) ~ y2 - beta * z2 # missing x2 term
]
@named sys1 = ODESystem(eqs, t)
@named sys2 = ODESystem(eqs2, t)
@named sys3 = ODESystem(eqs3, t)
ssys3 = structural_simplify(sys3)
@named sys4 = ODESystem(eqs4, t)
@test ModelingToolkit.isisomorphic(sys1, sys2)
@test !ModelingToolkit.isisomorphic(sys1, sys3)
@test ModelingToolkit.isisomorphic(sys1, ssys3) # I don't call structural_simplify in isisomorphic
@test !ModelingToolkit.isisomorphic(sys1, sys4)
# 1281
iv2 = only(independent_variables(sys2))
@test isequal(only(independent_variables(convert_system(ODESystem, sys1, iv2))), iv2)
end
let
vars = @variables sP(t) spP(t) spm(t) sph(t)
pars = @parameters a b
eqs = [sP ~ 1
spP ~ sP
spm ~ a
sph ~ b
spm ~ 0
sph ~ a]
@named sys = ODESystem(eqs, t, vars, pars)
@test_throws ModelingToolkit.ExtraEquationsSystemException structural_simplify(sys)
end
# 1561
let
vars = @variables x y
arr = ModelingToolkit.varmap_to_vars([x => 0.0, y => [0.0, 1.0]], vars) #error
sol = Union{Float64, Vector{Float64}}[0.0, [0.0, 1.0]]
@test arr == sol
@test typeof(arr) == typeof(sol)
end
let
u = collect(first(@variables u(t)[1:4]))
Dt = D
eqs = [Differential(t)(u[2]) - 1.1u[1] ~ 0
Differential(t)(u[3]) - 1.1u[2] ~ 0
u[1] ~ 0.0
u[4] ~ 0.0]
ps = []
@named sys = ODESystem(eqs, t, u, ps)
@test_nowarn simpsys = structural_simplify(sys)
sys = structural_simplify(sys)
u0 = ModelingToolkit.missing_variable_defaults(sys)
u0_expected = Pair[s => 0.0 for s in unknowns(sys)]
@test string(u0) == string(u0_expected)
u0 = ModelingToolkit.missing_variable_defaults(sys, [1, 2])
u0_expected = Pair[s => i for (i, s) in enumerate(unknowns(sys))]
@test string(u0) == string(u0_expected)
@test_nowarn ODEProblem(sys, u0, (0, 1))
end
# https://github.com/SciML/ModelingToolkit.jl/issues/1583
let
@parameters k
@variables A(t)
eqs = [D(A) ~ -k * A]
@named osys = ODESystem(eqs, t)
osys = complete(osys)
oprob = ODEProblem(osys, [A => 1.0], (0.0, 10.0), [k => 1.0]; check_length = false)
@test_nowarn sol = solve(oprob, Tsit5())
end
let
function sys1(; name)
vars = @variables x(t)=0.0 dx(t)=0.0
ODESystem([D(x) ~ dx], t, vars, []; name, defaults = [D(x) => x])
end
function sys2(; name)
@named s1 = sys1()
ODESystem(Equation[], t, [], []; systems = [s1], name)
end
s1′ = sys1(; name = :s1)
@named s2 = sys2()
@unpack s1 = s2
@test isequal(s1, s1′)
defs = Dict(s1.dx => 0.0, D(s1.x) => s1.x, s1.x => 0.0)
@test isequal(ModelingToolkit.defaults(s2), defs)
end
# https://github.com/SciML/ModelingToolkit.jl/issues/1705
let
x0 = 0.0
v0 = 1.0
kx = -1.0
kv = -1.0
tf = 10.0
## controller
function pd_ctrl(; name)
@parameters kx kv
@variables u(t) x(t) v(t)
eqs = [u ~ kx * x + kv * v]
ODESystem(eqs, t; name)
end
@named ctrl = pd_ctrl()
## double integrator
function double_int(; name)
@variables u(t) x(t) v(t)
eqs = [D(x) ~ v, D(v) ~ u]
ODESystem(eqs, t; name)
end
@named sys = double_int()
## connections
connections = [sys.u ~ ctrl.u, ctrl.x ~ sys.x, ctrl.v ~ sys.v]
@named connected = ODESystem(connections, t)
@named sys_con = compose(connected, sys, ctrl)
sys_simp = structural_simplify(sys_con)
true_eqs = [D(sys.x) ~ sys.v
D(sys.v) ~ ctrl.kv * sys.v + ctrl.kx * sys.x]
@test isequal(full_equations(sys_simp), true_eqs)
end
let
@variables x(t) = 1
@variables y(t) = 1
@parameters pp = -1
@named sys4 = ODESystem([D(x) ~ -y; D(y) ~ 1 + pp * y + x], t)
sys4s = structural_simplify(sys4)
prob = ODEProblem(sys4s, [x => 1.0, D(x) => 1.0], (0, 1.0))
@test string.(unknowns(prob.f.sys)) == ["x(t)", "y(t)"]
@test string.(parameters(prob.f.sys)) == ["pp"]
@test string.(independent_variables(prob.f.sys)) == ["t"]
end
let
@parameters P(t) Q(t)
∂t = D
eqs = [∂t(Q) ~ 0.2P
∂t(P) ~ -80.0sin(Q)]
@test_throws ArgumentError @named sys = ODESystem(eqs, t)
end
@parameters C L R
@variables q(t) p(t) F(t)
eqs = [D(q) ~ -p / L - F
D(p) ~ q / C
0 ~ q / C - R * F]
testdict = Dict([:name => "test"])
@named sys = ODESystem(eqs, t, metadata = testdict)
@test get_metadata(sys) == testdict
@variables P(t)=0 Q(t)=2
∂t = D
eqs = [∂t(Q) ~ 1 / sin(P)
∂t(P) ~ log(-cos(Q))]
@named sys = ODESystem(eqs, t, [P, Q], [])
sys = complete(debug_system(sys));
prob = ODEProblem(sys, [], (0, 1.0));
du = zero(prob.u0);
if VERSION < v"1.8"
@test_throws DomainError prob.f(du, [1, 0], prob.p, 0.0)
@test_throws DomainError prob.f(du, [0, 2], prob.p, 0.0)
else
@test_throws "-cos(Q(t))" prob.f(du, [1, 0], prob.p, 0.0)
@test_throws "sin(P(t))" prob.f(du, [0, 2], prob.p, 0.0)
end
let
@variables x(t) = 1
@variables y(t) = 1
@parameters pp = -1
der = Differential(t)
@named sys4 = ODESystem([der(x) ~ -y; der(y) ~ 1 + pp * y + x], t)
sys4s = structural_simplify(sys4)
prob = ODEProblem(sys4s, [x => 1.0, D(x) => 1.0], (0, 1.0))
@test !isnothing(prob.f.sys)
end
# SYS 1:
vars_sub1 = @variables s1(t)
@named sub = ODESystem(Equation[], t, vars_sub1, [])
vars1 = @variables x1(t)
@named sys1 = ODESystem(Equation[], t, vars1, [], systems = [sub])
@named sys2 = ODESystem(Equation[], t, vars1, [], systems = [sys1, sub])
# SYS 2: Extension to SYS 1
vars_sub2 = @variables s2(t)
@named partial_sub = ODESystem(Equation[], t, vars_sub2, [])
@named sub = extend(partial_sub, sub)
# no warnings for systems without events
new_sys2 = @test_nowarn complete(substitute(sys2, Dict(:sub => sub)))
Set(unknowns(new_sys2)) == Set([new_sys2.x1, new_sys2.sys1.x1,
new_sys2.sys1.sub.s1, new_sys2.sys1.sub.s2,
new_sys2.sub.s1, new_sys2.sub.s2])
let # Issue https://github.com/SciML/ModelingToolkit.jl/issues/2322
@parameters a=10 b=a / 10 c=a / 20
Dt = D
@variables x(t)=1 z(t)
eqs = [Dt(x) ~ -b * (x - z),
0 ~ z - c * x]
sys = ODESystem(eqs, t; name = :kjshdf)
sys_simp = structural_simplify(sys)
@test a ∈ keys(ModelingToolkit.defaults(sys_simp))
tspan = (0.0, 1)
prob = ODEProblem(sys_simp, [], tspan)
sol = solve(prob, Rodas4())
@test sol(1)[]≈0.6065307685451087 rtol=1e-4