No elimination -- no worry

benchmarking/IdentifiableFunctions/new_tide.jl

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+using StructuralIdentifiability, StatsBase
+using Logging
+
+# macro taken from here
+# https://discourse.julialang.org/t/help-writing-a-timeout-macro/16591/7
+macro timeout(seconds, expr, fail)
+    quote
+        tsk = @task $(esc(expr))
+        schedule(tsk)
+        Timer($(esc(seconds))) do timer
+            istaskdone(tsk) || Base.throwto(tsk, InterruptException())
+        end
+        try
+            fetch(tsk)
+        catch _
+            $(esc(fail))
+        end
+    end
+end
+
+function simplify(genset)
+    rff = StructuralIdentifiability.RationalFunctionField(genset)
+    genset = StructuralIdentifiability.simplified_generating_set(rff, simplify=:weak)
+    genset
+end
+
+function iterative_lie(
+        ode::StructuralIdentifiability.ODE{P};
+        initial_genset=nothing,
+        tides=2,
+        percentile=20,
+        wait_for=20) where {P}
+    genset = Vector()
+    if initial_genset === nothing
+        for y in ode.y_vars
+            append!(genset, StructuralIdentifiability.extract_coefficients_ratfunc(ode.y_equations[y], ode.u_vars))
+        end
+    else
+        genset = map(gen -> StructuralIdentifiability.parent_ring_change(gen, parent(ode)), initial_genset)
+    end
+
+    genset = simplify(genset)
+
+    dense_id = frac -> length(numerator(frac)) * length(denominator(frac))
+    dense_elems = empty(genset)
+    new_elems = empty(genset)
+    wave = 1
+    while true
+        @warn "Wave $wave" genset
+        println(replace("$genset", "(t)" => ""))
+
+        for gen in genset
+            append!(new_elems, StructuralIdentifiability.extract_coefficients_ratfunc(
+                StructuralIdentifiability.lie_derivative(gen, ode), ode.u_vars))
+        end
+
+        for tide in 1:tides
+            @warn "The tide is coming: also computing derivatives of derivatives"
+            new_new_elems = empty(new_elems)
+            for gens in new_elems
+                append!(new_new_elems, StructuralIdentifiability.extract_coefficients_ratfunc(
+                    StructuralIdentifiability.lie_derivative(gens, ode), ode.u_vars))
+            end
+            append!(new_elems, new_new_elems)
+        end
+        filter!(!StructuralIdentifiability.is_rational_func_const, new_elems)
+
+        @warn "Finding the simplest among $(length(new_elems)) new elems and $(length(dense_elems)) dense elems"
+        new_elems = vcat(new_elems, dense_elems)
+        sort!(new_elems, by=dense_id)
+        containment = StructuralIdentifiability.field_contains(
+            StructuralIdentifiability.RationalFunctionField(genset), new_elems, 0.99)
+        @warn "Containment:" length(containment) count(iszero, containment)
+
+        perm = filter(i -> containment[i] == 0, 1:length(containment))
+        new_elems = new_elems[perm]
+        n = length(new_elems)
+
+        @warn "Densities:\n$(map(dense_id, new_elems))"
+        if n == 0
+            break
+        end
+
+        threshold = StatsBase.percentile(map(dense_id, new_elems), percentile)
+        threshold_idx = findlast(map(dense_id, new_elems) .<= threshold)
+        @warn """Simplifying elements 1:$threshold_idx ($percentile% percentile). 
+                 Putting elems at $(threshold_idx+1)..$n back to dense list"""
+        dense_elems = new_elems[threshold_idx+1:end]
+        new_elems = new_elems[1:threshold_idx]
+
+        new_genset = vcat(genset, new_elems)
+        new_genset = @timeout wait_for begin 
+            simplify(new_genset) 
+        end Set()
+        if isempty(new_genset)
+            @warn "Interrupted by timeout"
+            break
+        end
+        genset = new_genset
+        wave += 1
+    end
+
+    return genset
+end
+
+TumorPillis2007 = StructuralIdentifiability.@ODEmodel(
+            T'(t) =
+                a * T(t) * (1 - b * T(t)) - c1 * N(t) * T(t) - D(t) * T(t) -
+                KT * M(t) * T(t), #tumor cells
+            L'(t) =
+                -m * L(t) - q * L(t) * T(t) - ucte * L(t)^2 +
+                r2 * C(t) * T(t) +
+                pI * L(t) * I(t) / (gI + I(t)) +
+                u1(t) - KL * M(t) * L(t), # tumor-specific effector cells, T-celss
+            N'(t) =
+                alpha1 - f * N(t) + g * T(t) * N(t) / (h + T(t)) - p * N(t) * T(t) -
+                KN * M(t) * N(t), # non-specific effector cells, NK cells
+            C'(t) = alpha2 - beta * C(t) - KC * M(t) * C(t), #circulating lymphocytes
+            I'(t) =
+                pt * T(t) * L(t) / (gt + T(t)) + w * L(t) * I(t) - muI * I(t) + u2(t), # IL-2, VI = u2 aplicación directa, terapia de IL2
+            M'(t) = -gamma * M(t) + u1(t), #chemotherapy drug, terapia/aplicación de quimio, u1 = VM
+            y1(t) = L(t),
+            y2(t) = N(t),
+            y3(t) = M(t)
+        )
+
+
+ode = TumorPillis2007
+
+#find_ioequations(ode; loglevel=Logging.Debug)
+
+genset = iterative_lie(ode, tides=2, percentile=20, wait_for=2)
+println(genset)
+