Zero cost abstraction Maruyama solver

solver.jl

using StaticArrays
struct EulerMaruyama!
end


"""
    tangent!(du, u, dz, P)


"""
function tangent!
end

function zero_tangent(x, P) # euclidian fallback
    zero(x) # check false*similar
end
function zero_tangent(u::Tuple, P) # euclidian fallback
    ntuple(length(u)) do i
        false*u[i]
    end
end

function zero_integrator(Z, P)
    tozero!(deepcopy(Z[1]), P)
end

tozero!(x::Union{Number,SArray}, _) = false*x
tozero!(x::Array, _) = Base.fill!(x, false)
function tozero!(u::Tuple, P)
    ntuple(length(u)) do i
        tozero!(u[i], P)
    end
end


function exponential_map!(x::Array, dx, P)
    x .+= dx
end
function exponential_map!(x::Union{SArray,Number}, dx, P)
    x + dx
end

saveit!(uu, u, P) = push!(uu, deepcopy(u))
saveit!(::Nothing, u, P) = nothing

endcondition(uu, u, Z, P) = u[1] >= Z[end][1]

endpoint!(u, _) = u
function solve!(solver::EulerMaruyama!, uu, u, Z, P)
    du = zero_tangent(u, P)
    dz = zero_integrator(Z, P)
    uu, u = solve_inner!(solver, uu, u, du, Z, dz, P)
    u = endpoint!(u, P)
    saveit!(uu, u, P) 
    uu, u
end
function solve_inner!(solver::EulerMaruyama!, uu, u, du, Z, dz, P)   
    while true
        saveit!(uu, u, P) 
        dz = dZ!(u, dz, Z, P)
        du = tangent!(du, u, dz, P)
        u = exponential_map!(u, du, P)
        endcondition(uu, u, Z, P) && break
    end
    uu, u
end
function dZ!(u, dz, Z, P) 
    i = u[1]
    dw = dz[3]
    @. dw = Z[i+1][3] -  Z[i][3]
    (Z[i+1][1] - Z[i][1], Z[i+1][2] - Z[i][2], dw)
end    
function tangent!(du, u, dz, P)
    @. du[3] = -u[3]*dz[2] +  u[3][]*dz[3]
    (dz[1], dz[2], du[3])
end
function exponential_map!(u::Tuple{Int64, Float64, Vector{Float64}}, du::Tuple, P)
    x = u[3]
    @. x += du[3]
    (u[1] + du[1], u[2] + du[2], x)
end

n = 10000
t = 0:1/n:1.0
Z = collect(zip(1:n, t, [[w] for w in [0; sqrt(1/n)*cumsum(randn(n))]]))
u = (1, 0.0, [1.0])
dz = (0, 0.0, [0.0])
du = (0, 0.0, [0.0])

solve!(EulerMaruyama!(), nothing, u, Z, ())
@time solve!(EulerMaruyama!(), nothing, u, Z, ())

@code_warntype solve!(EulerMaruyama!(), nothing, u, Z, ())

uu, uT = solve!(EulerMaruyama!(), typeof(u)[], u, Z, ())

• lines 87 and 88 are redundant, right?
• the drift and diffusivity go into tangent!, right?

1.) Yes, just thought I show how they look

2.) Let me decifer

# u = (i, t, x)
# dz = (1, dt, dW)
# du = (Δi, dt, dX) 
function tangent!(du, u, dz, P)
    @. du[3] = -u[3]*dz[2] +  u[3][]*dz[3] # dX .= -X dt .+ X dW inplace
    (dz[1], dz[2], du[3]) # (1, dt, dX)
end

You mean “dz = “dloglik, dt, dW’ I guess.

…

On 4 May 2021, at 19:46, Moritz Schauer ***@***.***> wrote: @mschauer commented on this gist. 1.) Yes, just thought I show how they look 2.) Let me decifer # u = (i, t, x) # dz = (1, dt, dW) # du = (Δi, dt, dX) function tangent!(du, u, dz, P) @. du[3] = -u[3]*dz[2] + u[3][]*dz[3] # dX .= -X dt .+ X dW inplace (dz[1], dz[2], du[3]) # (1, dt, dX) end — You are receiving this because you commented. Reply to this email directly, view it on GitHub <https://urldefense.proofpoint.com/v2/url?u=https-3A__gist.github.com_da7bddafa958e674f666df3201c3375e-23gistcomment-2D3731359&d=DwMFaQ&c=XYzUhXBD2cD-CornpT4QE19xOJBbRy-TBPLK0X9U2o8&r=7iF-JNHl-g2k0SDAFdfpFNwTGT5g4T8E90C3u4ODfF8&m=l_WQ5UzDCVpJP2VKo38iWywFWyFuiO3YWuCScqXhobI&s=XF3ylBaP-HFnyzftR6Hs_4vui60z6MaOmEqrW9wjNhk&e=>, or unsubscribe <https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_notifications_unsubscribe-2Dauth_AJTTG32VQV4CAHAOFBRZB7LTMAXIRANCNFSM44DD2LLQ&d=DwMFaQ&c=XYzUhXBD2cD-CornpT4QE19xOJBbRy-TBPLK0X9U2o8&r=7iF-JNHl-g2k0SDAFdfpFNwTGT5g4T8E90C3u4ODfF8&m=l_WQ5UzDCVpJP2VKo38iWywFWyFuiO3YWuCScqXhobI&s=iVauK7zWM3C_LRimuqGFhqmxt5vBwDlAZ-5A_PL2rGU&e=>.

--- Frank van der Meulen Delft University of Technology http://dutiosb.twi.tudelft.nl/~meulen/

In my example case, u = (i, t, x) the first entry is an iteration counter so Δi = 1. But you can of course extend to u = (i, t, x, l)` with also a log-likelihood.