feat: add benchmark for effect of CSE on jacobian computation/compilation

benchmarks/Symbolics/BCR.jmd

@@ -0,0 +1,244 @@
+---
+title: BCR Symbolic Jacobian
+author: Aayush Sabharwal, Bowen Zhu, Chris Rackauckas
+---
+
+The following benchmark is of 1122 ODEs with 24388 terms that describe a stiff
+chemical reaction network modeling the BCR signaling network from [Barua et
+al.](https://doi.org/10.4049/jimmunol.1102003). We use
+[`ReactionNetworkImporters`](https://github.com/isaacsas/ReactionNetworkImporters.jl)
+to load the BioNetGen model files as a
+[Catalyst](https://github.com/SciML/Catalyst.jl) model, and then use
+[ModelingToolkit](https://github.com/SciML/ModelingToolkit.jl) to convert the
+Catalyst network model to ODEs.
+
+The resultant large model is used to benchmark the time taken to compute a symbolic
+jacobian, generate a function to calculate it and call the function.
+
+
+```julia
+using Catalyst, ReactionNetworkImporters,
+    TimerOutputs, LinearAlgebra, ModelingToolkit, Chairmarks,
+    LinearSolve, Symbolics, SymbolicUtils, SymbolicUtils.Code, SparseArrays, CairoMakie,
+    PrettyTables
+
+using Pkg
+Pkg.add(Pkg.PackageSpec(; name = "SymbolicUtils", rev="9d52810c547276a60c0aae502ffee7f93ff99143"))
+
+datadir  = joinpath(dirname(pathof(ReactionNetworkImporters)),"../data/bcr")
+const to = TimerOutput()
+tf       = 100000.0
+
+# generate ModelingToolkit ODEs
+prnbng = loadrxnetwork(BNGNetwork(), joinpath(datadir, "bcr.net"))
+show(to)
+rn    = complete(prnbng.rn; split = false)
+obs = [eq.lhs for eq in observed(rn)]
+osys = convert(ODESystem, rn)
+
+rhs = [eq.rhs for eq in full_equations(osys)]
+vars = unknowns(osys)
+pars = parameters(osys)
+```
+
+The `sparsejacobian` function in Symbolics.jl is optimized for hashconsing and caching, and as such
+performs very poorly without either of those features. We use the old implementation, optimized without
+hashconsing, to benchmark performance without hashconsing and without caching to avoid biasing the results.
+
+```julia
+include("old_sparse_jacobian.jl")
+```
+
+```julia
+SymbolicUtils.ENABLE_HASHCONSING[] = false
+@timeit to "Calculate jacobian - without hashconsing" jac_nohc = old_sparsejacobian(rhs, vars);
+SymbolicUtils.ENABLE_HASHCONSING[] = true
+Symbolics.toggle_derivative_caching!(false)
+Symbolics.clear_derivative_caches!()
+@timeit to "Calculate jacobian - hashconsing, without caching" jac_hc_nocache = old_sparsejacobian(rhs, vars);
+Symbolics.toggle_derivative_caching!(true)
+for fn in Symbolics.cached_derivative_functions()
+    stats = SymbolicUtils.get_stats(fn)
+    @assert stats.hits == stats.misses == 0
+end
+Symbolics.clear_derivative_caches!()
+@timeit to "Calculate jacobian - hashconsing and caching" jac_hc_cache = Symbolics.sparsejacobian(rhs, vars);
+
+@assert isequal(jac_nohc, jac_hc_nocache)
+@assert isequal(jac_hc_nocache, jac_hc_cache)
+
+jac = jac_hc_cache
+args = (vars, pars, ModelingToolkit.get_iv(osys))
+# out of place versions run into an error saying the expression is too large
+# due to the `SymbolicUtils.Code.create_array` call. `iip_config` prevents it
+# from trying to build the function.
+kwargs = (; iip_config = (false, true), expression = Val{true})
+@timeit to "Build jacobian - no CSE" _, jac_nocse_iip = build_function(jac, args...; cse = false, kwargs...);
+@timeit to "Build jacobian - CSE" _, jac_cse_iip = build_function(jac, args...; cse = true, kwargs...);
+
+jac_nocse_iip = eval(jac_nocse_iip)
+jac_cse_iip = eval(jac_cse_iip)
+
+defs = defaults(osys)
+u = Float64[Symbolics.fixpoint_sub(var, defs) for var in vars]
+buffer_cse = similar(jac, Float64)
+buffer_nocse = similar(jac, Float64)
+p = Float64[Symbolics.fixpoint_sub(par, defs) for par in pars]
+tt = 0.0
+
+@timeit to "Compile jacobian - CSE" jac_cse_iip(buffer_cse, u, p, tt)
+@timeit to "Compute jacobian - CSE" jac_cse_iip(buffer_cse, u, p, tt)
+
+@timeit to "Compile jacobian - no CSE" jac_nocse_iip(buffer_nocse, u, p, tt)
+@timeit to "Compute jacobian - no CSE" jac_nocse_iip(buffer_nocse, u, p, tt)
+
+@assert isapprox(buffer_cse, buffer_nocse, rtol = 1e-10)
+
+show(to)
+```
+
+We'll also measure scaling.
+
+
+```julia
+function run_and_time_construct!(rhs, vars, pars, iv, N, i, jac_times, jac_allocs, build_times, functions)
+    outputs = rhs[1:N]
+    SymbolicUtils.ENABLE_HASHCONSING[] = false
+    jac_result = @be old_sparsejacobian(outputs, vars)
+    jac_times[1][i] = minimum(x -> x.time, jac_result.samples)
+    jac_allocs[1][i] = minimum(x -> x.bytes, jac_result.samples)
+
+    SymbolicUtils.ENABLE_HASHCONSING[] = true
+    jac_result = @be (Symbolics.clear_derivative_caches!(); Symbolics.sparsejacobian(outputs, vars))
+    jac_times[2][i] = minimum(x -> x.time, jac_result.samples)
+    jac_allocs[2][i] = minimum(x -> x.bytes, jac_result.samples)
+
+    jac = Symbolics.sparsejacobian(outputs, vars)
+    args = (vars, pars, iv)
+    kwargs = (; iip_config = (false, true), expression = Val{true})
+
+    build_result = @be build_function(jac, args...; cse = false, kwargs...);
+    build_times[1][i] = minimum(x -> x.time, build_result.samples)
+    jacfn_nocse = eval(build_function(jac, args...; cse = false, kwargs...)[2])
+
+    build_result = @be build_function(jac, args...; cse = true, kwargs...);
+    build_times[2][i] = minimum(x -> x.time, build_result.samples)
+    jacfn_cse = eval(build_function(jac, args...; cse = true, kwargs...)[2])
+
+    functions[1][i] = let buffer = similar(jac, Float64), fn = jacfn_nocse
+        function nocse(u, p, t)
+            fn(buffer, u, p, t)
+            buffer
+        end
+    end
+    functions[2][i] = let buffer = similar(jac, Float64), fn = jacfn_cse
+        function cse(u, p, t)
+            fn(buffer, u, p, t)
+            buffer
+        end
+    end
+
+    return nothing
+end
+
+function run_and_time_call!(i, u, p, tt, functions, first_call_times, second_call_times)
+    jacfn_nocse = functions[1][i]
+    jacfn_cse = functions[2][i]
+
+    call_result = @timed jacfn_nocse(u, p, tt)
+    first_call_times[1][i] = call_result.time
+    call_result = @timed jacfn_cse(u, p, tt)
+    first_call_times[2][i] = call_result.time
+
+    call_result = @be jacfn_nocse(u, p, tt)
+    second_call_times[1][i] = minimum(x -> x.time, call_result.samples)
+    call_result = @be jacfn_cse(u, p, tt)
+    second_call_times[2][i] = minimum(x -> x.time, call_result.samples)
+end
+```
+
+# Run benchmark
+
+```julia
+Chairmarks.DEFAULTS.seconds = 15.0
+N = [10, 20, 40, 80, 160, 320]
+jacobian_times = [zeros(Float64, length(N)), zeros(Float64, length(N))]
+jacobian_allocs = copy.(jacobian_times)
+functions = [Vector{Any}(undef, length(N)), Vector{Any}(undef, length(N))]
+# [without_cse_times, with_cse_times]
+build_times = copy.(jacobian_times)
+first_call_times = copy.(jacobian_times)
+second_call_times = copy.(jacobian_times)
+
+iv = ModelingToolkit.get_iv(osys)
+run_and_time_construct!(rhs, vars, pars, iv, 10, 1, jacobian_times, jacobian_allocs, build_times, functions)
+run_and_time_call!(1, u, p, tt, functions, first_call_times, second_call_times)
+for (i, n) in enumerate(N)
+    @info i n
+    run_and_time_construct!(rhs, vars, pars, iv, n, i, jacobian_times, jacobian_allocs, build_times, functions)
+end
+for (i, n) in enumerate(N)
+    @info i n
+    run_and_time_call!(i, u, p, tt, functions, first_call_times, second_call_times)
+end
+```
+
+# Plot figures
+
+```julia
+tabledata = hcat(N, jacobian_times..., jacobian_allocs..., build_times..., first_call_times..., second_call_times...)
+header = ["N", "Jacobian time (no hashconsing)", "Jacobian time (hashconsing)", "Jacobian allocated memory (no hashconsing) (B)", "Jacobian allocated memory (hashconsing) (B)", "`build_function` time (no CSE)", "`build_function` time (CSE)", "First call time (no CSE)", "First call time (CSE)", "Second call time (no CSE)", "Second call time (CSE)"]
+pretty_table(tabledata; header, backend = Val(:html))
+```
+
+```julia
+f = Figure(size = (750, 400))
+titles = [
+    "Jacobian symbolic computation", "Jacobian symbolic computation", "Code generation",
+    "Numerical function compilation", "Numerical function evaluation"]
+labels = ["Time (seconds)", "Allocated memory (bytes)",
+    "Time (seconds)", "Time (seconds)", "Time (seconds)"]
+times = [jacobian_times, jacobian_allocs, build_times, first_call_times, second_call_times]
+axes = Axis[]
+for i in 1:2
+    label = labels[i]
+    data = times[i]
+    ax = Axis(f[1, i], xscale = log10, yscale = log10, xlabel = "model size",
+        xlabelsize = 10, ylabel = label, ylabelsize = 10, xticks = N,
+        title = titles[i], titlesize = 12, xticklabelsize = 10, yticklabelsize = 10)
+    push!(axes, ax)
+    l1 = scatterlines!(ax, N, data[1], label = "without hashconsing")
+    l2 = scatterlines!(ax, N, data[2], label = "with hashconsing")
+end
+Legend(f[1, 3], axes[1], "Methods", tellwidth = false, labelsize = 12, titlesize = 15)
+axes2 = Axis[]
+# make equal y-axis unit length
+mn3, mx3 = extrema(reduce(vcat, times[3]))
+xn3 = log10(mx3 / mn3)
+mn4, mx4 = extrema(reduce(vcat, times[4]))
+xn4 = log10(mx4 / mn4)
+mn5, mx5 = extrema(reduce(vcat, times[5]))
+xn5 = log10(mx5 / mn5)
+xn = max(xn3, xn4, xn5)
+xn += 0.2
+hxn = xn / 2
+hxn3 = (log10(mx3) + log10(mn3)) / 2
+hxn4 = (log10(mx4) + log10(mn4)) / 2
+hxn5 = (log10(mx5) + log10(mn5)) / 2
+ylims = [(exp10(hxn3 - hxn), exp10(hxn3 + hxn)), (exp10(hxn4 - hxn), exp10(hxn4 + hxn)),
+    (exp10(hxn5 - hxn), exp10(hxn5 + hxn))]
+for i in 1:3
+    ir = i + 2
+    label = labels[ir]
+    data = times[ir]
+    ax = Axis(f[2, i], xscale = log10, yscale = log10, xlabel = "model size",
+        xlabelsize = 10, ylabel = label, ylabelsize = 10, xticks = N,
+        title = titles[ir], titlesize = 12, xticklabelsize = 10, yticklabelsize = 10)
+    ylims!(ax, ylims[i]...)
+    push!(axes2, ax)
+    l1 = scatterlines!(ax, N, data[1], label = "without hashconsing")
+    l2 = scatterlines!(ax, N, data[2], label = "with hashconsing")
+end
+save("bcr.pdf", f)
+f
+```

benchmarks/Symbolics/Project.toml

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+[deps]
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
+Catalyst = "479239e8-5488-4da2-87a7-35f2df7eef83"
+Chairmarks = "0ca39b1e-fe0b-4e98-acfc-b1656634c4de"
+DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
+ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
+OrderedCollections = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
+OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+Polynomials = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
+PrettyTables = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
+ReactionNetworkImporters = "b4db0fb7-de2a-5028-82bf-5021f5cfa881"
+SciMLBenchmarks = "31c91b34-3c75-11e9-0341-95557aab0344"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
+Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
+TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
+XSteam = "95ff35a0-be81-11e9-2ca3-5b4e338e8476"
+
+[compat]
+ModelingToolkit = "9"
+SymbolicUtils = "3.26"
+Symbolics = "6.34"