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
end

Now we trace this into Symbolics:

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

which gives:

du = Num[p₁ * u₁ - (p₂ * u₁) * u₂, -p₃ * u₂ + (p₄ * u₁) * u₂]

Since Lotka-Volterra equations are differential equations with respect of to time t, we define derivative D with respect to this variable.

D = Differential(t)

Now we build the equations we want to solve:

eqs = @. D(u) ~ du

2-element Array{Equation,1}:
 Equation(derivative(u₁, t), p₁ * u₁ - (p₂ * u₁) * u₂)
 Equation(derivative(u₂, t), -p₃ * u₂ + (p₄ * u₁) * u₂)

and then we build the function:

build_function(eqs, u, p, t, target=Symbolics.CTarget())

void diffeqf(double* du, double* RHS1, double* RHS2, double RHS3) {
  du[0] = RHS2[0] * RHS1[0] - (RHS2[1] * RHS1[0]) * RHS1[1];
  du[1] = -(RHS2[2]) * RHS1[1] + (RHS2[3] * RHS1[0]) * RHS1[1];
}

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

f = build_function(eqs, u, p, t, target=Symbolics.CTarget(), expression=Val{false})

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!