Automatic Conversion of Julia Code to C Functions

Since Symbolics.jl can trace Julia code into Symbolics IR that can be built and compiled via build_function to C, this gives us a nifty way to automatically generate C functions from Julia code! To see this in action, let's start with the Lotka-Volterra equations:

using Symbolics
function lotka_volterra!(du, u, p, t)
  x, y = u
  α, β, δ, γ = p
  du[1] = dx = α*x - β*x*y
  du[2] = dy = -δ*y + γ*x*y
lotka_volterra! (generic function with 1 method)

Now we trace this into Symbolics:

@variables t du[1:2] u[1:2] p[1:4]
du = collect(du)
lotka_volterra!(du, u, p, t)

\[ \begin{equation} \left[ \begin{array}{c} p_1 u_1 - p_2 u_1 u_2 \\ - p_3 u_2 + p_4 u_1 u_2 \\ \end{array} \right] \end{equation} \]

and then we build the function:

build_function(du, u, p, t, target=Symbolics.CTarget())
"#include <math.h>\nvoid diffeqf(double* du, const double* RHS1, const double* RHS2, const double RHS3) {\n  du[0] = RHS2[0] * RHS1[0] + -1 * RHS2[1] * RHS1[0] * RHS1[1];\n  du[1] = -1 * RHS2[2] * RHS1[1] + RHS2[3] * RHS1[0] * RHS1[1];\n}\n"

If we want to compile this, we do expression=Val{false}:

f = build_function(du, u, p, t, target=Symbolics.CTarget(), expression=Val{false})
RuntimeGeneratedFunction(#=in Symbolics=#, #=using Symbolics=#, :((du, u, p, t)->begin
          #= /home/runner/work/Symbolics.jl/Symbolics.jl/src/build_function.jl:809 =#
          ccall(("diffeqf", "/tmp/jl_0rIxsjsvmj"), Cvoid, (Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Float64), du, u, p, t)

now we check it computes the same thing:

du = rand(2); du2 = rand(2)
u = rand(2)
p = rand(4)
t = rand()
f(du, u, p, t)
lotka_volterra!(du2, u, p, t)
du == du2 # true!