sde_problems.jl

struct StandardSDEProblem end

struct SDEProblem{uType,tType,isinplace,NP,F,G,C,MM,ND} <: AbstractSDEProblem{uType,tType,isinplace,ND}
  f::F
  g::G
  u0::uType
  tspan::Tuple{tType,tType}
  noise::NP
  callback::C
  mass_matrix::MM
  noise_rate_prototype::ND
  seed::UInt64
  function SDEProblem{iip}(f,g,u0,tspan,problem_type=StandardSDEProblem();
          noise_rate_prototype = nothing,
          noise= nothing, seed = UInt64(0),
          callback = nothing,mass_matrix=I) where {iip}

    if mass_matrix == I && typeof(f) <: Tuple
      _mm = ((I for i in 1:length(f))...)
    else
      _mm = mass_matrix
    end

    new{typeof(u0),promote_type(map(typeof,tspan)...),
        iip,typeof(noise),typeof(f),typeof(g),
        typeof(callback),typeof(_mm),
        typeof(noise_rate_prototype)}(
        f,g,u0,tspan,noise,callback,_mm,
        noise_rate_prototype,seed)
  end
end

function SDEProblem(f,g,u0,tspan;kwargs...)
  iip = typeof(f)<: Tuple ? isinplace(f[2],3) : isinplace(f,3)
  SDEProblem{iip}(f,g,u0,tspan;kwargs...)
end

abstract type AbstractSplitSDEProblem end
struct SplitSDEProblem{iip} <: AbstractSplitSDEProblem end
# u' = Au + f
function SplitSDEProblem(f1,f2,g,u0,tspan;kwargs...)
  iip = isinplace(f2,3)
  SplitSDEProblem{iip}(f1,f2,g,u0,tspan;kwargs...)
end
function SplitSDEProblem{iip}(f1,f2,g,u0,tspan;
                                     func_cache=nothing,kwargs...) where iip
  iip ? _func_cache = similar(u0) : _func_cache = nothing
  SDEProblem{iip}(SplitFunction{iip}(f1,f2,_func_cache),g,u0,tspan,SplitSDEProblem{iip}();kwargs...)
end