feat: add cycle detection in initial conditions

src/remake.jl

@@ -509,6 +509,21 @@ function varmap_get(varmap, var, default = nothing)
     return default
 end
 
+"""
+    $(TYPEDSIGNATURES)
+
+Check if `varmap::Dict{Any, Any}` contains cyclic values for any symbolic variables in
+`syms`. Falls back on the basis of `symbolic_container(indp)`. Returns `false` by default.
+"""
+function detect_cycles(indp, varmap, syms)
+    if hasmethod(symbolic_container, Tuple{typeof(indp)}) &&
+       (sc = symbolic_container(indp)) != indp
+        return detect_cycles(sc, varmap, syms)
+    else
+        return false
+    end
+end
+
 anydict(d::Dict{Any, Any}) = d
 anydict(d) = Dict{Any, Any}(d)
 anydict() = Dict{Any, Any}()
@@ -560,14 +575,24 @@ function _updated_u0_p_internal(
 end
 
 function fill_u0(prob, u0; defs = nothing, use_defaults = false)
-    vsyms = variable_symbols(prob)
-    idx_to_vsym = anydict(variable_index(prob, sym) => sym for sym in vsyms)
+    fill_vars(prob, u0; defs, use_defaults, allsyms = variable_symbols(prob),
+        index_function = variable_index)
+end
+
+function fill_p(prob, p; defs = nothing, use_defaults = false)
+    fill_vars(prob, p; defs, use_defaults, allsyms = parameter_symbols(prob),
+        index_function = parameter_index)
+end
+
+function fill_vars(
+        prob, varmap; defs = nothing, use_defaults = false, allsyms, index_function)
+    idx_to_vsym = anydict(index_function(prob, sym) => sym for sym in allsyms)
     sym_to_idx = anydict()
     idx_to_sym = anydict()
     idx_to_val = anydict()
-    for (k, v) in u0
+    for (k, v) in varmap
         v === nothing && continue
-        idx = variable_index(prob, k)
+        idx = index_function(prob, k)
         idx === nothing && continue
         if !(idx isa AbstractArray) || symbolic_type(k) != ArraySymbolic()
             idx = (idx,)
@@ -582,9 +607,9 @@ function fill_u0(prob, u0; defs = nothing, use_defaults = false)
             idx_to_val[ii] = vv
         end
     end
-    for sym in vsyms
+    for sym in allsyms
         haskey(sym_to_idx, sym) && continue
-        idx = variable_index(prob, sym)
+        idx = index_function(prob, sym)
         haskey(idx_to_val, idx) && continue
         sym_to_idx[sym] = idx
         idx_to_sym[idx] = sym
@@ -593,72 +618,40 @@ function fill_u0(prob, u0; defs = nothing, use_defaults = false)
                              (symbolic_type(defval) != NotSymbolic() || use_defaults)
             defval
         else
-            getu(prob, sym)(prob)
+            getsym(prob, sym)(prob)
         end
     end
     newvals = anydict()
     for (idx, val) in idx_to_val
         newvals[idx_to_sym[idx]] = val
     end
-    for (k, v) in u0
+    for (k, v) in varmap
         haskey(sym_to_idx, k) && continue
         newvals[k] = v
     end
     return newvals
 end
 
-function fill_p(prob, p; defs = nothing, use_defaults = false)
-    psyms = parameter_symbols(prob)
-    idx_to_psym = anydict(parameter_index(prob, sym) => sym for sym in psyms)
-    sym_to_idx = anydict()
-    idx_to_sym = anydict()
-    idx_to_val = anydict()
-    for (k, v) in p
-        v === nothing && continue
-        idx = parameter_index(prob, k)
-        idx === nothing && continue
-        if !(idx isa AbstractArray) || symbolic_type(k) != ArraySymbolic()
-            idx = (idx,)
-            k = (k,)
-            v = (v,)
-        end
-        for (kk, vv, ii) in zip(k, v, idx)
-            sym_to_idx[kk] = ii
-            kk = idx_to_psym[ii]
-            sym_to_idx[kk] = ii
-            idx_to_sym[ii] = kk
-            idx_to_val[ii] = vv
-        end
-    end
-    for sym in psyms
-        haskey(sym_to_idx, sym) && continue
-        idx = parameter_index(prob, sym)
-        haskey(idx_to_val, idx) && continue
-        sym_to_idx[sym] = idx
-        idx_to_sym[idx] = sym
-        idx_to_val[idx] = if defs !== nothing &&
-                             (defval = varmap_get(defs, sym)) !== nothing &&
-                             (symbolic_type(defval) != NotSymbolic() || use_defaults)
-            defval
-        else
-            getp(prob, sym)(prob)
-        end
-    end
-    newvals = anydict()
-    for (idx, val) in idx_to_val
-        newvals[idx_to_sym[idx]] = val
-    end
-    for (k, v) in p
-        haskey(sym_to_idx, k) && continue
-        newvals[k] = v
+struct CyclicDependencyError <: Exception
+    varmap::Dict{Any, Any}
+    vars::Any
+end
+
+function Base.showerror(io::IO, err::CyclicDependencyError)
+    println(io, "Detected cyclic dependency in initial values:")
+    for (k, v) in err.varmap
+        println(io, k, " => ", "v")
     end
-    return newvals
+    println(io, "While trying to solve for variables: ", err.vars)
 end
 
 function _updated_u0_p_symmap(prob, u0, ::Val{true}, p, ::Val{false}, t0)
     isdep = any(symbolic_type(v) !== NotSymbolic() for (_, v) in u0)
     isdep || return remake_buffer(prob, state_values(prob), keys(u0), values(u0)), p
 
+    if detect_cycles(prob, u0, variable_symbols(prob))
+        throw(CyclicDependencyError(u0, variable_symbols(prob)))
+    end
     for (k, v) in u0
         u0[k] = symbolic_type(v) === NotSymbolic() ? v : symbolic_evaluate(v, u0)
     end
@@ -680,6 +673,9 @@ function _updated_u0_p_symmap(prob, u0, ::Val{false}, p, ::Val{true}, t0)
     isdep = any(symbolic_type(v) !== NotSymbolic() for (_, v) in p)
     isdep || return u0, remake_buffer(prob, parameter_values(prob), keys(p), values(p))
 
+    if detect_cycles(prob, p, parameter_symbols(prob))
+        throw(CyclicDependencyError(p, parameter_symbols(prob)))
+    end
     for (k, v) in p
         p[k] = symbolic_type(v) === NotSymbolic() ? v : symbolic_evaluate(v, p)
     end
@@ -707,6 +703,10 @@ function _updated_u0_p_symmap(prob, u0, ::Val{true}, p, ::Val{true}, t0)
     end
 
     varmap = merge(u0, p)
+    allsyms = [variable_symbols(prob); parameter_symbols(prob)]
+    if detect_cycles(prob, varmap, allsyms)
+        throw(CyclicDependencyError(varmap, allsyms))
+    end
     if is_time_dependent(prob)
         varmap[only(independent_variable_symbols(prob))] = t0
     end

src/solutions/solution_interface.jl

@@ -209,7 +209,7 @@ indices that can be plotted as continuous variables. This is useful for systems
 that store auxiliary variables in the state vector which are not meant to be
 used for plotting.
 """
-plottable_indices(x:: AbstractArray) = 1:length(x)
+plottable_indices(x::AbstractArray) = 1:length(x)
 plottable_indices(x::Number) = 1
 
 @recipe function f(sol::AbstractTimeseriesSolution;

test/downstream/modelingtoolkit_remake.jl

@@ -248,3 +248,29 @@ end
     prob2 = remake(prob; u0 = [x => t + 3.0])
     @test prob2[x] ≈ 3.0
 end
+
+@static if length(methods(SciMLBase.detect_cycles)) == 1
+    function SciMLBase.detect_cycles(
+            ::ModelingToolkit.AbstractSystem, varmap::Dict{Any, Any}, vars)
+        for sym in vars
+            if symbolic_type(ModelingToolkit.fixpoint_sub(sym, varmap; maxiters = 10)) !=
+               NotSymbolic()
+                return true
+            end
+        end
+        return false
+    end
+end
+
+@testset "Cycle detection" begin
+    @variables x(t) y(t)
+    @parameters p q
+    @mtkbuild sys = ODESystem([D(x) ~ x * p, D(y) ~ y * q], t)
+
+    prob = ODEProblem(sys, [x => 1.0, y => 1.0], (0.0, 1.0), [p => 1.0, q => 1.0])
+    @test_throws SciMLBase.CyclicDependencyError remake(
+        prob; u0 = [x => 2y + 3, y => 2x + 1])
+    @test_throws SciMLBase.CyclicDependencyError remake(prob; p = [p => 2q + 1, q => p + 3])
+    @test_throws SciMLBase.CyclicDependencyError remake(
+        prob; u0 = [x => 2y + p, y => q + 3], p = [p => x + y, q => p + 3])
+end