MethodError when solving SDE in DifferentialEquations.jl

New to Julia
,
1

Hi,

Apologies for not having a more informative title. I’m having a little trouble solving a 2-dimensional SDE in DifferentialEquations.jl. My current code is

using DifferentialEquations, ForwardDiff

# Solve Chemical Langevin Equation SDE
# dX = α(X) dt + √β(x) dW

S = [ 1 -1 0; 0 1 -1]

function h(x, c)
    return h = [ c[1] * x[1]; c[2] * x[1] * x[2]; c[3] * x[2]]
end

function α(x, c)
    return dx = S * h(x, c)
end

function β(x, c)
    return σx = S * Diagonal(h(x, c)) * transpose(S)
end

function sqrtβ(x, c)
    return sqrt(β(x, c))
end

x0 = [ 70 ; 80 ]

tspan = (0.0, 50.0)

c = [ 1.0, 0.005, 0.6 ]

lotvol_CLE_SDE = SDEProblem(α, sqrtβ, x0, tspan, c)
CLE_sol = solve(lotvol_CLE_SDE)

which, upon running the final line, returns the error

> MethodError: no method matching α(::Array{Float64,1}, ::Array{Float64, 1}, ::Float64)

and I can’t totally make sense of this. Is the issue to do with e.g.

  • how I’ve written the drift function
  • how I’ve passed the drift function to the SDE problem
  • how I’ve passed the parameters c to the problem

or something else entirely?

Separately, the SDE in question has a multiplicative, non-diagonal noise structure. I’m not sure whether this is causing the problem (the error I’m receiving doesn’t seem to suggest so), but I wanted to get a sanity check on whether I’ve written it sensibly. The examples here were useful, but are phrased in slightly different terms to what I’m used to.

2

there is no two argument syntax. See the examples in https://diffeq.sciml.ai/stable/tutorials/sde_example/

1 Like
3

Ah, of course! Thank you. I have changed the functions to

function α(dx, x, c, t)
    return dx = S * h(x, c)
end

function β(x, c)
    return σx = S * Diagonal(h(x, c)) * transpose(S)
end

function sqrtβ(dx, x, c, t)
    return sqrt(β(x, c))
end

and the code runs now. I seem to be getting a slightly weird solution for the SDE itself (constant?), but I’ll try to work that out in my own time. Thanks!

4

dx .= S * h(x, c) you’re creating new arrays, but you need to mutate like that.

1 Like
5

Thanks, I’m getting much more sensible outputs now.