Clean up generate_initializesystem()

src/systems/nonlinear/initializesystem.jl

@@ -5,109 +5,81 @@ Generate `NonlinearSystem` which initializes an ODE problem from specified initi
 """
 function generate_initializesystem(sys::ODESystem;
         u0map = Dict(),
-        name = nameof(sys),
-        guesses = Dict(), check_defguess = false,
-        default_dd_value = 0.0,
-        algebraic_only = false,
         initialization_eqs = [],
-        check_units = true,
-        kwargs...)
-    sts, eqs = unknowns(sys), equations(sys)
+        guesses = Dict(),
+        default_dd_guess = 0.0,
+        algebraic_only = false,
+        check_units = true, check_defguess = false,
+        name = nameof(sys), kwargs...)
+    vars = unique([unknowns(sys); getfield.((observed(sys)), :lhs)])
+    vars_set = Set(vars) # for efficient in-lookup
+
+    eqs = equations(sys)
     idxs_diff = isdiffeq.(eqs)
     idxs_alge = .!idxs_diff
-    num_alge = sum(idxs_alge)
-
-    # Start the equations list with algebraic equations
-    eqs_ics = eqs[idxs_alge]
-    u0 = Vector{Pair}(undef, 0)
 
+    # prepare map for dummy derivative substitution
     eqs_diff = eqs[idxs_diff]
-    diffmap = Dict(getfield.(eqs_diff, :lhs) .=> getfield.(eqs_diff, :rhs))
-    observed_diffmap = Dict(Differential(get_iv(sys)).(getfield.((observed(sys)), :lhs)) .=>
-        Differential(get_iv(sys)).(getfield.((observed(sys)), :rhs)))
-    full_diffmap = merge(diffmap, observed_diffmap)
+    D = Differential(get_iv(sys))
+    diffmap = merge(
+        Dict(eq.lhs => eq.rhs for eq in eqs_diff),
+        Dict(D(eq.lhs) => D(eq.rhs) for eq in observed(sys))
+    )
 
-    full_states = unique([sts; getfield.((observed(sys)), :lhs)])
-    set_full_states = Set(full_states)
+    # 1) process dummy derivatives and u0map into initialization system
+    eqs_ics = eqs[idxs_alge] # start equation list with algebraic equations
+    defs = copy(defaults(sys)) # copy so we don't modify sys.defaults
     guesses = merge(get_guesses(sys), todict(guesses))
     schedule = getfield(sys, :schedule)
-
-    if schedule !== nothing
-        guessmap = [x[1] => get(guesses, x[1], default_dd_value)
-                    for x in schedule.dummy_sub]
-        dd_guess = Dict(filter(x -> !isnothing(x[1]), guessmap))
-        if u0map === nothing || isempty(u0map)
-            filtered_u0 = u0map
-        else
-            filtered_u0 = Pair[]
-            for x in u0map
-                y = get(schedule.dummy_sub, x[1], x[1])
-                y = ModelingToolkit.fixpoint_sub(y, full_diffmap)
-
-                if y ∈ set_full_states
-                    # defer initialization until defaults are merged below
-                    push!(filtered_u0, y => x[2])
-                elseif y isa Symbolics.Arr
-                    # scalarize array # TODO: don't scalarize arrays
-                    _y = collect(y)
-                    for i in eachindex(_y)
-                        push!(filtered_u0, _y[i] => x[2][i])
-                    end
-                elseif y isa Symbolics.BasicSymbolic
-                    # y is a derivative expression expanded
-                    # add to the initialization equations
-                    push!(eqs_ics, y ~ x[2])
-                else
-                    error("Initialization expression $y is currently not supported. If its a higher order derivative expression, then only the dummy derivative expressions are supported.")
-                end
+    if !isnothing(schedule)
+        for x in filter(x -> !isnothing(x[1]), schedule.dummy_sub)
+            # set dummy derivatives to default_dd_guess unless specified
+            push!(defs, x[1] => get(guesses, x[1], default_dd_guess))
+        end
+        for (y, x) in u0map
+            y = get(schedule.dummy_sub, y, y)
+            y = fixpoint_sub(y, diffmap)
+            if y ∈ vars_set
+                # variables specified in u0 overrides defaults
+                push!(defs, y => x)
+            elseif y isa Symbolics.Arr
+                # TODO: don't scalarize arrays
+                merge!(defs, Dict(scalarize(y .=> x)))
+            elseif y isa Symbolics.BasicSymbolic
+                # y is a derivative expression expanded; add it to the initialization equations
+                push!(eqs_ics, y ~ x)
+            else
+                error("Initialization expression $y is currently not supported. If its a higher order derivative expression, then only the dummy derivative expressions are supported.")
             end
-            filtered_u0 = todict(filtered_u0)
         end
-    else
-        dd_guess = Dict()
-        filtered_u0 = todict(u0map)
     end
 
-    defs = merge(defaults(sys), filtered_u0)
-
-    for st in full_states
-        if st ∈ keys(defs)
-            def = defs[st]
-
-            if def isa Equation
-                st ∉ keys(guesses) && check_defguess &&
-                    error("Invalid setup: unknown $(st) has an initial condition equation with no guess.")
-                push!(eqs_ics, def)
-                push!(u0, st => guesses[st])
-            else
-                push!(eqs_ics, st ~ def)
-                push!(u0, st => def)
-            end
-        elseif st ∈ keys(guesses)
-            push!(u0, st => guesses[st])
+    # 2) process other variables
+    for var in vars
+        if var ∈ keys(defs)
+            push!(eqs_ics, var ~ defs[var])
+        elseif var ∈ keys(guesses)
+            push!(defs, var => guesses[var])
         elseif check_defguess
-            error("Invalid setup: unknown $(st) has no default value or initial guess")
+            error("Invalid setup: variable $(var) has no default value or initial guess")
         end
     end
 
+    # 3) process explicitly provided initialization equations
     if !algebraic_only
-        for eq in [get_initialization_eqs(sys); initialization_eqs]
-            _eq = ModelingToolkit.fixpoint_sub(eq, full_diffmap)
-            push!(eqs_ics, _eq)
+        initialization_eqs = [get_initialization_eqs(sys); initialization_eqs]
+        for eq in initialization_eqs
+            eq = fixpoint_sub(eq, diffmap) # expand dummy derivatives
+            push!(eqs_ics, eq)
         end
     end
 
-    pars = [parameters(sys); get_iv(sys)]
-    nleqs = [eqs_ics; observed(sys)]
-
-    sys_nl = NonlinearSystem(nleqs,
-        full_states,
-        pars;
-        defaults = merge(ModelingToolkit.defaults(sys), todict(u0), dd_guess),
-        parameter_dependencies = parameter_dependencies(sys),
+    pars = [parameters(sys); get_iv(sys)] # include independent variable as pseudo-parameter
+    eqs_ics = [eqs_ics; observed(sys)]
+    return NonlinearSystem(
+        eqs_ics, vars, pars;
+        defaults = defs, parameter_dependencies = parameter_dependencies(sys),
         checks = check_units,
-        name,
-        kwargs...)
-
-    return sys_nl
+        name, kwargs...
+    )
 end

src/systems/nonlinear/nonlinearsystem.jl

@@ -126,25 +126,23 @@ function NonlinearSystem(eqs, unknowns, ps;
         throw(ArgumentError("NonlinearSystem does not accept `continuous_events`, you provided $continuous_events"))
     discrete_events === nothing || isempty(discrete_events) ||
         throw(ArgumentError("NonlinearSystem does not accept `discrete_events`, you provided $discrete_events"))
-
     name === nothing &&
         throw(ArgumentError("The `name` keyword must be provided. Please consider using the `@named` macro"))
-    # Move things over, but do not touch array expressions
-    #
-    # # we cannot scalarize in the loop because `eqs` itself might require
-    # scalarization
-    eqs = [x.lhs isa Union{Symbolic, Number} ? 0 ~ x.rhs - x.lhs : x
-           for x in scalarize(eqs)]
-
-    if !(isempty(default_u0) && isempty(default_p))
+    length(unique(nameof.(systems))) == length(systems) ||
+        throw(ArgumentError("System names must be unique."))
+    (isempty(default_u0) && isempty(default_p)) ||
         Base.depwarn(
             "`default_u0` and `default_p` are deprecated. Use `defaults` instead.",
             :NonlinearSystem, force = true)
+
+    # Accept a single (scalar/vector) equation, but make array for consistent internal handling
+    if !(eqs isa AbstractArray)
+        eqs = [eqs]
     end
-    sysnames = nameof.(systems)
-    if length(unique(sysnames)) != length(sysnames)
-        throw(ArgumentError("System names must be unique."))
-    end
+
+    # Copy equations to canonical form, but do not touch array expressions
+    eqs = [wrap(eq.lhs) isa Symbolics.Arr ? eq : 0 ~ eq.rhs - eq.lhs for eq in eqs]
+
     jac = RefValue{Any}(EMPTY_JAC)
     defaults = todict(defaults)
     defaults = Dict{Any, Any}(value(k) => value(v)

test/initializationsystem.jl

@@ -567,3 +567,12 @@ oprob_2nd_order_2 = ODEProblem(sys_2nd_order, u0_2nd_order_2, tspan, ps)
 sol = solve(oprob_2nd_order_2, Rosenbrock23()) # retcode: Success
 @test sol[Y][1] == 2.0
 @test sol[D(Y)][1] == 0.5
+
+@testset "Vector in initial conditions" begin
+    @variables x(t)[1:5] y(t)[1:5]
+    @named sys = ODESystem([D(x) ~ x, D(y) ~ y], t; initialization_eqs = [y ~ -x])
+    sys = structural_simplify(sys)
+    prob = ODEProblem(sys, [sys.x => ones(5)], (0.0, 1.0), [])
+    sol = solve(prob, Tsit5(), reltol = 1e-4)
+    @test all(sol(1.0, idxs = sys.x) .≈ +exp(1)) && all(sol(1.0, idxs = sys.y) .≈ -exp(1))
+end

test/nonlinearsystem.jl

@@ -327,6 +327,20 @@ end
     @test_nowarn solve(prob)
 end
 
+@testset "System of linear equations with vector variable" begin
+    # 1st example in https://en.wikipedia.org/w/index.php?title=System_of_linear_equations&oldid=1247697953
+    @variables x[1:3]
+    A = [3 2 -1
+         2 -2 4
+         -1 1/2 -1]
+    b = [1, -2, 0]
+    @named sys = NonlinearSystem(A * x ~ b, [x], [])
+    sys = structural_simplify(sys)
+    prob = NonlinearProblem(sys, unknowns(sys) .=> 0.0)
+    sol = solve(prob)
+    @test all(sol[x] .≈ A \ b)
+end
+
 @testset "resid_prototype when system has no unknowns and an equation" begin
     @variables x
     @parameters p

test/reduction.jl

@@ -178,6 +178,7 @@ A = reshape(1:(N^2), N, N)
 eqs = xs ~ A * xs
 @named sys′ = NonlinearSystem(eqs, [xs], [])
 sys = structural_simplify(sys′)
+@test length(equations(sys)) == 3 && length(observed(sys)) == 2
 
 # issue 958
 @parameters k₁ k₂ k₋₁ E₀