feat: add simple CSE for array scalarization case

Author: AayushSabharwal

src/structural_transformation/symbolics_tearing.jl

@@ -584,6 +584,16 @@ function tearing_reassemble(state::TearingState, var_eq_matching,
     end
     @set! sys.unknowns = unknowns
 
+    # HACK: Since we don't support array equations, any equation of the sort
+    # `x[1:n] ~ f(...)[1:n]` gets turned into `x[1] ~ f(...)[1], x[2] ~ f(...)[2]`. Repeatedly
+    # calling `f` gets _very_ expensive. this hack performs a limited form of CSE specifically
+    # for this case to avoid the unnecessary cost.
+    # This and the below hack are implemented simultaneously
+
+    # mapping of rhs to temporary CSE variable
+    # `f(...) => tmpvar` in above example
+    rhs_to_tempvar = Dict()
+
     # HACK: Add equations for array observed variables. If `p[i] ~ (...)`
     # are equations, add an equation `p ~ [p[1], p[2], ...]`
     # allow topsort to reorder them
@@ -597,9 +607,44 @@ function tearing_reassemble(state::TearingState, var_eq_matching,
     arr_obs_occurrences = Dict()
     # to check if array variables occur in unscalarized form anywhere
     all_vars = Set()
-    for eq in obs
-        vars!(all_vars, eq.rhs)
+    for (i, eq) in enumerate(obs)
         lhs = eq.lhs
+        rhs = eq.rhs
+        vars!(all_vars, rhs)
+
+        # HACK 1
+        if iscall(rhs) && operation(rhs) === getindex &&
+           Symbolics.shape(rhs) != Symbolics.Unknown()
+            rhs_arr = arguments(rhs)[1]
+            if !haskey(rhs_to_tempvar, rhs_arr)
+                tempvar = gensym(Symbol(lhs))
+                N = length(rhs_arr)
+                tempvar = unwrap(Symbolics.variable(
+                    tempvar; T = Symbolics.symtype(rhs_arr)))
+                tempvar = setmetadata(
+                    tempvar, Symbolics.ArrayShapeCtx, Symbolics.shape(rhs_arr))
+                tempeq = tempvar ~ rhs_arr
+                rhs_to_tempvar[rhs_arr] = tempvar
+                # ideally we would like to do this:
+                push!(obs, tempeq)
+                push!(subeqs, tempeq)
+                # and let topsort_equations handle it, but that treats `x` and `x[1]`
+                # as different variables and thus doesn
+            end
+
+            # getindex_wrapper is used because `observed2graph` treats `x` and `x[i]` as different,
+            # so it doesn't find a dependency between this equation and `tempvar ~ rhs_arr`
+            # which fails the topological sort
+            neweq = lhs ~ getindex_wrapper(
+                rhs_to_tempvar[rhs_arr], Tuple(arguments(rhs)[2:end]))
+            obs[i] = neweq
+            subeqi = findfirst(isequal(eq), subeqs)
+            if subeqi !== nothing
+                subeqs[subeqi] = neweq
+            end
+        end
+        # end HACK 1
+
         iscall(lhs) || continue
         operation(lhs) === getindex || continue
         Symbolics.shape(lhs) != Symbolics.Unknown() || continue
@@ -640,6 +685,7 @@ function tearing_reassemble(state::TearingState, var_eq_matching,
     end
     append!(obs, obs_arr_eqs)
     append!(subeqs, obs_arr_eqs)
+
     # need to re-sort subeqs
     subeqs = ModelingToolkit.topsort_equations(subeqs, [eq.lhs for eq in subeqs])
 
@@ -659,6 +705,12 @@ function tearing_reassemble(state::TearingState, var_eq_matching,
     return invalidate_cache!(sys)
 end
 
+# PART OF HACK 1
+getindex_wrapper(x, i) = x[i...]
+
+@register_symbolic getindex_wrapper(x::AbstractArray, i::Tuple{Vararg{Int}})
+
+# PART OF HACK 2
 function change_origin(origin, arr)
     return origin(arr)
 end

test/structural_transformation/utils.jl

@@ -48,9 +48,25 @@ end
     @mtkbuild sys = ODESystem(
         [D(x) ~ z[1] + z[2] + foo(z)[1], y[1] ~ 2t, y[2] ~ 3t, z ~ foo(y)], t)
     @test length(equations(sys)) == 1
-    @test length(observed(sys)) == 6
+    @test length(observed(sys)) == 7
     @test any(eq -> isequal(eq.lhs, y), observed(sys))
     @test any(eq -> isequal(eq.lhs, z), observed(sys))
     prob = ODEProblem(sys, [x => 1.0], (0.0, 1.0), [foo => _tmp_fn])
     @test_nowarn prob.f(prob.u0, prob.p, 0.0)
 end
+
+@testset "scalarized array observed calling same function multiple times" begin
+    @variables x(t) y(t)[1:2]
+    @parameters foo(::Real)[1:2]
+    val = Ref(0)
+    function _tmp_fn2(x)
+        val[] += 1
+        return [x, 2x]
+    end
+    @mtkbuild sys = ODESystem([D(x) ~ y[1] + y[2], y ~ foo(x)], t)
+    @test length(equations(sys)) == 1
+    @test length(observed(sys)) == 3
+    prob = ODEProblem(sys, [x => 1.0], (0.0, 1.0), [foo => _tmp_fn2])
+    @test_nowarn prob.f(prob.u0, prob.p, 0.0)
+    @test val[] == 1
+end