From 30d09705a6fc5d65650cead4eb1f42d5c7e06041 Mon Sep 17 00:00:00 2001 From: oameye Date: Thu, 25 Jul 2024 00:12:18 +0200 Subject: [PATCH 01/38] add coupledSDEs type --- .gitignore | 3 +- Project.toml | 2 + src/DynamicalSystemsBase.jl | 1 + src/core_systems/continuous_time_sde.jl | 245 ++++++++++++++++++++++++ test/Project.toml | 1 + test/runtests.jl | 1 + test/stochastic.jl | 70 +++++++ test/test_system_function.jl | 7 +- 8 files changed, 327 insertions(+), 3 deletions(-) create mode 100644 src/core_systems/continuous_time_sde.jl create mode 100644 test/stochastic.jl diff --git a/.gitignore b/.gitignore index d96c3c11..6d9b112f 100644 --- a/.gitignore +++ b/.gitignore @@ -6,4 +6,5 @@ deps/build.log Manifest.toml *style.jl *.scss -*.css \ No newline at end of file +*.css +.vscode \ No newline at end of file diff --git a/Project.toml b/Project.toml index 6695a2d7..29d0d58d 100644 --- a/Project.toml +++ b/Project.toml @@ -13,6 +13,7 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" StateSpaceSets = "40b095a5-5852-4c12-98c7-d43bf788e795" Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" +StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0" SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5" [compat] @@ -23,5 +24,6 @@ Roots = "1, 2" SciMLBase = "1.19.5, 2" StateSpaceSets = "1" Statistics = "1" +StochasticDiffEq = "6.66.0" SymbolicIndexingInterface = "0.3.4" julia = "1.9" diff --git a/src/DynamicalSystemsBase.jl b/src/DynamicalSystemsBase.jl index 07c4474f..a8eed1eb 100644 --- a/src/DynamicalSystemsBase.jl +++ b/src/DynamicalSystemsBase.jl @@ -22,6 +22,7 @@ include("core/pretty_printing.jl") include("core_systems/discrete_time_map.jl") include("core_systems/continuous_time_ode.jl") +include("core_systems/continuous_time_sde.jl") include("core_systems/arbitrary_steppable.jl") include("core_systems/additional_supertypes.jl") include("core_systems/jacobian.jl") diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl new file mode 100644 index 00000000..17feb072 --- /dev/null +++ b/src/core_systems/continuous_time_sde.jl @@ -0,0 +1,245 @@ +using SciMLBase: SDEProblem, AbstractSDEIntegrator, __init, SDEFunction +using StochasticDiffEq: SOSRA +export CoupledSDEs + +########################################################################################### +# DiffEq options +########################################################################################### +const DEFAULT_SDE_SOLVER = SOSRA() # default recommendation for additive noise +const DEFAULT_STOCH_DIFFEQ = (alg=DEFAULT_SDE_SOLVER, DEFAULT_DIFFEQ_KWARGS...) + +# Function from user `@xlxs4`, see +# https://github.com/JuliaDynamics/jl/pull/153 +function _decompose_into_sde_solver_and_remaining(diffeq) + if haskey(diffeq, :alg) + return (diffeq[:alg], _delete(diffeq, :alg)) + else + return (DEFAULT_SDE_SOLVER, diffeq) + end +end + +########################################################################################### +# Type +########################################################################################### + +# Define CoupledSDEs +""" + CoupledSDEs <: ContinuousTimeDynamicalSystem + CoupledSDEs(f, g, u0 [, p, σ]; kwargs...) + +A stochastic continuous time dynamical system defined by a set of +coupled ordinary differential equations as follows: +```math +d\\vec{u} = \\vec{f}(\\vec{u}, p, t) dt + \\vec{g}(\\vec{u}, p, t) dW_t +``` + +Optionally provide the overall noise strength `σ`, the parameter container `p` and initial time as keyword `t0`. If `σ` is provided, the diffusion function `g` is multiplied by `σ`. + +For construction instructions regarding `f, u0` see the [DynamicalSystems.jl tutorial](https://juliadynamics.github.io/DynamicalSystems.jl/latest/tutorial/#CoupledODEs). + +The stochastic part of the differential equation is defined by the function `g` and the keyword arguments `noise_rate_prototype` and `noise`. `noise` indicates the noise process applied during generation and defaults to Gaussian white noise. For details on defining various noise processes, refer to the noise process documentation page. `noise_rate_prototype` indicates the prototype type instance for the noise rates, i.e., the output of `g`. It can be any type which overloads `A_mul_B!` with itself being the middle argument. Commonly, this is a matrix or sparse matrix. If this is not given, it defaults to `nothing`, which means the problem should be interpreted as having diagonal noise. + +## DifferentialEquations.jl interfacing + +The ODEs are evolved via the solvers of DifferentialEquations.jl. +When initializing a `CoupledODEs`, you can specify the solver that will integrate +`f` in time, along with any other integration options, using the `diffeq` keyword. +For example you could use `diffeq = (abstol = 1e-9, reltol = 1e-9)`. +If you want to specify a solver, do so by using the keyword `alg`, e.g.: +`diffeq = (alg = Tsit5(), reltol = 1e-6)`. This requires you to have been first +`using OrdinaryDiffEq` to access the solvers. The default `diffeq` is: + +```julia +$(DEFAULT_STOCH_DIFFEQ) +``` + +`diffeq` keywords can also include `callback` for [event handling +](https://docs.sciml.ai/DiffEqDocs/stable/features/callback_functions/). + +Dev note: `CoupledSDEs` is a light wrapper of `StochasticDiffEq.SDEIntegrator` from DifferentialEquations.jl. +The integrator is available as the field `integ`, and the `SDEProblem` is `integ.sol.prob`. +The convenience syntax `SDEProblem(ds::CoupledSDEs, tspan = (t0, Inf))` is available +to extract the problem. +""" +struct CoupledSDEs{IIP,D,I,P,S} <: ContinuousTimeDynamicalSystem + # D parametrised by length of u0 + # S indicated if the noise strength has been added to the diffusion function + integ::I + # things we can't recover from `integ` + p0::P + noise_strength + diffeq # isn't parameterized because it is only used for display +end + +function CoupledSDEs( + f, + g, + u0, + p=SciMLBase.NullParameters(), + noise_strength=1.0; + t0=0.0, + diffeq=DEFAULT_STOCH_DIFFEQ, + noise_rate_prototype=nothing, + noise=nothing, + seed=UInt64(0), +) + IIP = isinplace(f, 4) # from SciMLBase + @assert IIP == isinplace(g, 4) "f and g must both be in-place or out-of-place" + + s = correct_state(Val{IIP}(), u0) + T = eltype(s) + prob = SDEProblem{IIP}( + f, + g, + s, + (T(t0), T(Inf)), + p; + noise_rate_prototype=noise_rate_prototype, + noise=noise, + seed=seed, + ) + return CoupledSDEs(prob, diffeq, noise_strength) +end + +function CoupledSDEs( + prob::SDEProblem, diffeq=DEFAULT_STOCH_DIFFEQ, noise_strength=1.0; special_kwargs... + ) + if haskey(special_kwargs, :diffeq) + throw(ArgumentError("`diffeq` is given as positional argument when an ODEProblem is provided.")) + end + IIP = isinplace(prob) # from SciMLBase + D = length(prob.u0) + P = typeof(prob.p) + if prob.tspan === (nothing, nothing) + # If the problem was made via MTK, it is possible to not have a default timespan. + U = eltype(prob.u0) + prob = SciMLBase.remake(prob; tspan=(U(0), U(Inf))) + end + sde_function = SDEFunction(prob.f, add_noise_strength(noise_strength, prob.g, IIP)) + prob = SciMLBase.remake(prob; f=sde_function) + + solver, remaining = _decompose_into_sde_solver_and_remaining(diffeq) + integ = __init( + prob, + solver; + remaining..., + # Integrators are used exclusively iteratively. There is no reason to save anything. + save_start=false, + save_end=false, + save_everystep=false, + # DynamicalSystems.jl operates on integrators and `step!` exclusively, + # so there is no reason to limit the maximum time evolution + maxiters=Inf, + ) + return CoupledSDEs{IIP,D,typeof(integ),P,true}( + integ, deepcopy(prob.p), noise_strength, diffeq + ) +end + +""" + CoupledSDEs(ds::CoupledODEs, g, p [, σ]; kwargs...) + +Converts a [`CoupledODEs`](https://juliadynamics.github.io/DynamicalSystems.jl/stable/tutorial/#CoupledODEs) +system into a [`CoupledSDEs`](@ref). +""" +function CoupledSDEs( + ds::CoupledODEs, + g, + p, # the parameter is likely changed as the diffusion function g is added. + noise_strength=1.0; + diffeq=DEFAULT_STOCH_DIFFEQ, + noise_rate_prototype=nothing, + noise=nothing, + seed=UInt64(0), +) + return CoupledSDEs( + dynamic_rule(ds), + g, + current_state(ds), + p, + noise_strength; + diffeq=diffeq, + noise_rate_prototype=noise_rate_prototype, + noise=noise, + seed=seed, + ) +end + +""" + CoupledODEs(ds::CoupledSDEs; kwargs...) + +Converts a [`CoupledSDEs`](@ref) into [`CoupledODEs`](@ref). +""" +function CoupledODEs( + sys::CoupledSDEs; diffeq=DEFAULT_STOCH_DIFFEQ, t0=0.0 +) + return CoupledODEs( + sys.integ.f, SVector{length(sys.integ.u)}(sys.integ.u), sys.p0; diffeq=diffeq, t0=t0 + ) +end + +# Pretty print +function additional_details(ds::CoupledSDEs) + solver, remaining = _decompose_into_sde_solver_and_remaining(ds.diffeq) + return [ + "Noise strength" => ds.noise_strength, + "SDE solver" => string(nameof(typeof(solver))), + "SDE kwargs" => remaining, + ] +end + +########################################################################################### +# API - obtaining information from the system +########################################################################################### + +SciMLBase.isinplace(::CoupledSDEs{IIP}) where {IIP} = IIP +StateSpaceSets.dimension(::CoupledSDEs{IIP,D}) where {IIP,D} = D +current_state(ds::CoupledSDEs) = current_state(ds.integ) +isdeterministic(ds::CoupledSDEs) = false + +function dynamic_rule(sys::CoupledSDEs) + f = sys.integ.f + while hasfield(typeof(f), :f) + f = f.f + end + return f +end + +# so that `ds` is printed +set_state!(ds::CoupledSDEs, u::AbstractArray) = (set_state!(ds.integ, u); ds) +SciMLBase.step!(ds::CoupledSDEs, args...) = (step!(ds.integ, args...); ds) + +function successful_step(integ::AbstractSDEIntegrator) + rcode = integ.sol.retcode + return rcode == SciMLBase.ReturnCode.Default || rcode == SciMLBase.ReturnCode.Success +end + +# This is here to ensure that `u_modified!` is called +function set_parameter!(ds::CoupledSDEs, args...) + _set_parameter!(ds, args...) + u_modified!(ds.integ, true) + return nothing +end + +referrenced_sciml_prob(ds::CoupledSDEs) = ds.integ.sol.prob + +########################################################################################### +# Utilities +########################################################################################### + +function σg(σ, g) + return (u, p, t) -> σ .* g(u, p, t) +end + +function σg!(σ, g!) + function (du, u, p, t) + g!(du, u, p, t) + du .*= σ + return nothing + end +end + +function add_noise_strength(σ, g, IIP) + newg = IIP ? σg!(σ, g) : σg(σ, g) + return newg +end diff --git a/test/Project.toml b/test/Project.toml index 38a2779c..460f5153 100644 --- a/test/Project.toml +++ b/test/Project.toml @@ -4,6 +4,7 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78" OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" +StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [compat] diff --git a/test/runtests.jl b/test/runtests.jl index 3084f88f..051862c1 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -7,6 +7,7 @@ testfile(file, testname=defaultname(file)) = @testset "$testname" begin; include @testset "DynamicalSystemsBase" begin testfile("discrete.jl") testfile("continuous.jl") + testfile("stochastic.jl") testfile("arbitrarysteppable.jl") testfile("stroboscopic.jl") testfile("parallel.jl") diff --git a/test/stochastic.jl b/test/stochastic.jl new file mode 100644 index 00000000..412de95d --- /dev/null +++ b/test/stochastic.jl @@ -0,0 +1,70 @@ +using DynamicalSystemsBase, Test +using StochasticDiffEq: SDEProblem, SRA, SRI, SOSRA + +include("test_system_function.jl") + +# Creation of lorenz +@inbounds function lorenz_rule(u, p, t) + σ = p[1]; ρ = p[2]; β = p[3] + du1 = σ*(u[2]-u[1]) + du2 = u[1]*(ρ-u[3]) - u[2] + du3 = u[1]*u[2] - β*u[3] + return SVector{3}(du1, du2, du3) +end +@inbounds function lorenz_rule_iip(du, u, p, t) + σ = p[1]; ρ = p[2]; β = p[3] + du[1] = σ*(u[2]-u[1]) + du[2] = u[1]*(ρ-u[3]) - u[2] + du[3] = u[1]*u[2] - β*u[3] + return nothing +end + +σ = 0.1 +function diagonal_noise!(σ) + function (du, u, p, t) + du .= σ .* ones(length(u)) + return nothing + end +end +diagonal_noise(σ) = (u, p, t) -> SVector{3}(σ, σ, σ) + +u0 = [0, 10.0, 0] +p0 = [10, 28, 8/3] + +# diagonal additive noise +lorenz_oop = CoupledSDEs(lorenz_rule, diagonal_noise(σ), u0, p0) +lorenz_iip = CoupledSDEs(SDEProblem(lorenz_rule_iip, diagonal_noise!(σ), copy(u0), (0.0, Inf), p0)) +lorenz_SRA = CoupledSDEs(lorenz_rule, diagonal_noise(σ), u0, p0; + diffeq = (alg = SRA(), abstol = 1e-6, reltol = 1e-6) +) + +for (ds, iip) in zip((lorenz_oop, lorenz_iip, lorenz_SRA), (false, true, false)) + + name = (ds === lorenz_SRA) ? "lorSRA" : "lorenz" + @testset "$(name) IIP=$(iip)" begin + @test dynamic_rule(ds) == (iip ? lorenz_rule_iip : lorenz_rule) + test_dynamical_system(ds, u0, p0; idt = false, iip) + end +end + +@testset "correct SDE propagation" begin + lorenz_oop = CoupledSDEs(lorenz_rule, diagonal_noise(σ), u0, p0) + @test lorenz_oop.integ.alg isa SOSRA + + lorenz_SRA = CoupledSDEs(lorenz_rule, diagonal_noise(σ), u0, p0; + diffeq = (alg = SRA(), abstol = 1e-6, reltol = 1e-6, verbose=false) + ) + @test lorenz_SRA.integ.alg isa SRA + @test lorenz_SRA.integ.opts.verbose == false + + # # also test SDEproblem creation + prob = lorenz_SRA.integ.sol.prob + + ds = CoupledSDEs(prob, (alg=SRI(), abstol=0.0, reltol=1e-6, verbose=false)) + + @test ds.integ.alg isa SRI + @test ds.integ.opts.verbose == false + + @test_throws ArgumentError CoupledSDEs(prob; diffeq = (alg=SRI(), )) + +end diff --git a/test/test_system_function.jl b/test/test_system_function.jl index 1c1017a0..3e93b5d1 100644 --- a/test/test_system_function.jl +++ b/test/test_system_function.jl @@ -14,7 +14,11 @@ function test_dynamical_system(ds, u0, p0; idt, iip, @test current_time(ds) == 0 @test initial_time(ds) == 0 @test isinplace(ds) == iip - @test isdeterministic(ds) == true + if ds isa DynamicalSystemsBase.CoupledSDEs + @test isdeterministic(ds) == false + else + @test isdeterministic(ds) == true + end @test isdiscretetime(ds) == idt @test ds(0) == u0 end @@ -138,4 +142,3 @@ function test_dynamical_system(ds, u0, p0; idt, iip, end end - From a11ba2c4c383a8604d941502e814db9be77b9674 Mon Sep 17 00:00:00 2001 From: oameye Date: Sun, 28 Jul 2024 10:08:45 +0200 Subject: [PATCH 02/38] add CoupledSDEs docs --- docs/src/CoupledSDEs.md | 152 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 152 insertions(+) create mode 100644 docs/src/CoupledSDEs.md diff --git a/docs/src/CoupledSDEs.md b/docs/src/CoupledSDEs.md new file mode 100644 index 00000000..51ac2c06 --- /dev/null +++ b/docs/src/CoupledSDEs.md @@ -0,0 +1,152 @@ +# Define a CoupledSDEs system + +A `CoupledSDEs` defines a stochastic dynamical system of the form + +```math +\text{d}\vec x = f(\vec x(t); \ p) \text{d}t + \sigma g(\vec x(t); \ p) \, \text{d}\mathcal{W} \ , +``` +where $\vec x \in \mathbb{R}^\text{D}$, $\sigma > 0$ is the noise strength, $\text{d}\mathcal{W}=\Gamma \cdot \text{d}\mathcal{N}$, and $\mathcal N$ denotes a stochastic process. The (positive definite) noise covariance matrix is $\Sigma = \Gamma \Gamma^\top \in \mathbb R^{N\times N}$. + +The function $f$ is the deterministic part of the system and follows the syntax of a `ContinuousTimeDynamicalSystem` in [DynamicalSystems.jl](https://juliadynamics.github.io/DynamicalSystems.jl/latest/tutorial/), i.e., `f(u, p, t)` for out-of-place (oop) and `f!(du, u, p, t)` for in-place (iip). The function $g$ allows to specify the stochastic dynamics of the system along with the [noise process](#noise-process) $\mathcal{W}$. It should be of the same type (iip or oop) as $f$. + +By combining $\sigma$, $g$ and $\mathcal{W}$, you can define different type of stochastic systems. Examples of different types of stochastic systems can be found on the [StochasticDiffEq.jl tutorial page](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example/). A quick overview of common types of stochastic systems can be found [below](#Type-of-stochastic-system). + +!!! info + Note that nonlinear mixings of the Noise Process $\mathcal{W}$ fall into the class of random ordinary differential equations (RODEs) and is not supported in DynamicalSystems.jl at the moment. See [DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/rode_example/) for an implementation. + +```@docs +CoupledSDEs +``` + +## Converting between `CoupledSDEs` and `CoupledODEs` + +!!! tip "Analyzing deterministic dynamics with DynamicalSystems.jl" + The deterministic part of a [`CoupledSDEs`](@ref) system can easily be extracted as a + [`CoupledODEs`](https://juliadynamics.github.io/DynamicalSystems.jl/dev/tutorial/#DynamicalSystemsBase.CoupledODEs), a common subtype of a `ContinuousTimeDynamicalSystem` in DynamicalSystems.jl. + +- `CoupledODEs(sde::CoupledSDEs)` extracts the deterministic part of `sde` as a `CoupledODEs` +- `CoupledSDEs(ode::CoupledODEs, g)`, with `g` the noise function, turns `ode` into a `CoupledSDEs` + +```@docs +CoupledODEs +``` +For example, the +Lyapunov spectrum of a `CoupledSDEs` in the absence of noise, here exemplified by the +FitzHugh-Nagumo model, can be computed by typing: + +```julia +using CriticalTransitions +using DynamicalSystems: lyapunovspectrum + +function fitzhugh_nagumo(u, p, t) + x, y = u + ϵ, β, α, γ, κ, I = p + + dx = (-α * x^3 + γ * x - κ * y + I) / ϵ + dy = -β * y + x + + return SA[dx, dy] +end + +sys = CoupledSDEs(fitzhugh_nagumo, idfunc, zeros(2), [1.,3.,1.,1.,1.,0.], 0.1) +ls = lyapunovspectrum(CoupledODEs(sys), 10000) +``` + +## Defining stochastic dynamics +Let's look at some examples of the different types of stochastic systems that can be defined. + +For simplicity, we choose a slow exponential growth in 2 dimensions as the deterministic dynamics `f`: +```@example type +using CriticalTransitions, Plots +import Random # hide +Random.seed!(10) # hide +f!(du, u, p, t) = du .= 1.01u # deterministic part +σ = 0.25 # noise strength +``` +### Additive noise +When `g \, \text{d}\mathcal{W}` is independent of the state variables `u`, the noise is called additive. + +#### Diagonal noise +A system of diagonal noise is the most common type of noise. It is defined by a vector of random numbers `dW` whose size matches the output of `g` where the noise is applied element-wise, i.e. `g.*dW`. +```@example type +t0 = 0.0; W0 = zeros(2); +W = WienerProcess(t0, W0, 0.0) +sde = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise=W) +``` +or equivalently +```@example type +sde = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ) +``` +where we used the helper function +```@docs +idfunc! +idfunc +``` +The vector `dW` is by default zero mean white gaussian noise $\mathcal{N}(0, \text{d}t)$ where the variance is the timestep $\text{d}t$ unit variance (Wiener Process). +```@example type +sol = simulate(sde, 1.0, dt=0.01, alg=SOSRA()) +plot(sol) +``` + +#### Scalar noise +Scalar noise is where a single random variable is applied to all dependent variables. To do this, one has to give the noise process to the `noise` keyword of the `CoupledSDEs` constructor. A common example is the Wiener process starting at `W0=0.0` at time `t0=0.0`. + +```@example type +t0 = 0.0; W0 = 0.0; +noise = WienerProcess(t0, W0, 0.0) +sde = CoupledSDEs(f!, idfunc!, rand(2)./10, nothing, σ; noise=noise) +sol = simulate(sde, 1.0, dt=0.01, alg=SOSRA()) +plot(sol) +``` +### Multiplicative noise +Multiplicative Noise is when $g_i(t, u)=a_i u$ +```@example type +function g(du, u, p, t) + du[1] = σ*u[1] + du[2] = σ*u[2] + return nothing +end +sde = CoupledSDEs(f!, g, rand(2)./10) +sol = simulate(sde, 1.0, dt=0.01, alg=SOSRI()) +plot(sol) +``` +### Correlated noise +```@example type +ρ = 0.3 +Σ = [1 ρ; ρ 1] +t0 = 0.0; W0 = zeros(2); Z0 = zeros(2); +W = CorrelatedWienerProcess(Σ, t0, W0, Z0) +sde = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise=W) +sol = simulate(sde, 1.0, dt=0.01, alg=SOSRA()) +plot(sol) +``` + +#### More complex Non-diagonal noise +Non-diagonal noise allows for the terms to linearly mixed via `g` being a matrix. Suppose we have two Wiener processes and two dependent random variables such that the output of `g` is a 2x2 matrix. Therefore, we have +```math +du_1 = f_1(u,p,t)dt + g_{11}(u,p,t)dW_1 + g_{12}(u,p,t)dW_2 \\ +du_2 = f_2(u,p,t)dt + g_{21}(u,p,t)dW_1 + g_{22}(u,p,t)dW_2 +``` +To indicate the structure that `g` should have, we can use the `noise_rate_prototype` keyword. Let us define a special type of non-diagonal noise called commutative noise. For this we can utilize the `RKMilCommute` algorithm which is designed to utilise the structure of commutative noise. + +```@example type +function g(du, u, p, t) + du[1,1] = σ*u[1] + du[2,1] = σ*u[2] + du[1,2] = σ*u[1] + du[2,2] = σ*u[2] + return nothing +end +sde = CoupledSDEs(f!, g, rand(2)./10, noise_rate_prototype = zeros(2, 2)) +sol = simulate(sde, 1.0, dt=0.01, alg=RKMilCommute()) +plot(sol) +``` + +!!! warning + Non-diagonal problems need specific type of solvers. See the [SciML recommendations](https://docs.sciml.ai/DiffEqDocs/stable/solvers/sde_solve/#sde_solve). + +## Available noise processes +We provide the noise processes $\mathcal{W}$ that can be used in the stochastic simulations through the [DiffEqNoiseProcess.jl](https://docs.sciml.ai/DiffEqNoiseProcess/stable) package. A complete list of the available processes can be found [here](https://docs.sciml.ai/DiffEqNoiseProcess/stable/noise_processes/). +``` + + From 62c5e7ec4587d37981b6f436b80ce5a4850034df Mon Sep 17 00:00:00 2001 From: oameye Date: Sun, 28 Jul 2024 11:08:39 +0200 Subject: [PATCH 03/38] apply suggested format changes --- src/core_systems/continuous_time_sde.jl | 37 ++++++++++++++++--------- 1 file changed, 24 insertions(+), 13 deletions(-) diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index 17feb072..60032f9f 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -21,8 +21,6 @@ end ########################################################################################### # Type ########################################################################################### - -# Define CoupledSDEs """ CoupledSDEs <: ContinuousTimeDynamicalSystem CoupledSDEs(f, g, u0 [, p, σ]; kwargs...) @@ -30,14 +28,24 @@ end A stochastic continuous time dynamical system defined by a set of coupled ordinary differential equations as follows: ```math -d\\vec{u} = \\vec{f}(\\vec{u}, p, t) dt + \\vec{g}(\\vec{u}, p, t) dW_t +d\\vec{u} = \\vec{f}(\\vec{u}, p, t) dt + σ \\vec{g}(\\vec{u}, p, t) dW_t ``` -Optionally provide the overall noise strength `σ`, the parameter container `p` and initial time as keyword `t0`. If `σ` is provided, the diffusion function `g` is multiplied by `σ`. +Optionally provide the overall noise strength `σ`, the parameter container `p` +and initial time as keyword `t0`. By defualt `σ=1` and `t0=0`. -For construction instructions regarding `f, u0` see the [DynamicalSystems.jl tutorial](https://juliadynamics.github.io/DynamicalSystems.jl/latest/tutorial/#CoupledODEs). +For construction instructions regarding `f, u0` see the [DynamicalSystems.jl tutorial +](https://juliadynamics.github.io/DynamicalSystemsDocs.jl/dynamicalsystems/dev/tutorial/). -The stochastic part of the differential equation is defined by the function `g` and the keyword arguments `noise_rate_prototype` and `noise`. `noise` indicates the noise process applied during generation and defaults to Gaussian white noise. For details on defining various noise processes, refer to the noise process documentation page. `noise_rate_prototype` indicates the prototype type instance for the noise rates, i.e., the output of `g`. It can be any type which overloads `A_mul_B!` with itself being the middle argument. Commonly, this is a matrix or sparse matrix. If this is not given, it defaults to `nothing`, which means the problem should be interpreted as having diagonal noise. +The stochastic part of the differential equation is defined by the function `g` and +the keyword arguments `noise_rate_prototype` and `noise`. `noise` indicates +the noise process applied and defaults to Gaussian white noise (Wiener process). +For details on defining various noise processes, refer to [DiffEqNoiseProcess.jl +](https://docs.sciml.ai/DiffEqNoiseProcess/stable/). +`noise_rate_prototype` indicates the prototype type instance for the noise rates, i.e., +the output of `g`. It can be any type which overloads `A_mul_B!` with itself being the +middle argument. Commonly, this is a matrix or sparse matrix. If this is not given, it +defaults to `nothing`, which means the `g` should be interpreted as being diagonal. ## DifferentialEquations.jl interfacing @@ -56,7 +64,7 @@ $(DEFAULT_STOCH_DIFFEQ) `diffeq` keywords can also include `callback` for [event handling ](https://docs.sciml.ai/DiffEqDocs/stable/features/callback_functions/). -Dev note: `CoupledSDEs` is a light wrapper of `StochasticDiffEq.SDEIntegrator` from DifferentialEquations.jl. +Dev note: `CoupledSDEs` is a light wrapper of `SDEIntegrator` from StochasticDiffEq.jl. The integrator is available as the field `integ`, and the `SDEProblem` is `integ.sol.prob`. The convenience syntax `SDEProblem(ds::CoupledSDEs, tspan = (t0, Inf))` is available to extract the problem. @@ -103,9 +111,13 @@ end function CoupledSDEs( prob::SDEProblem, diffeq=DEFAULT_STOCH_DIFFEQ, noise_strength=1.0; special_kwargs... - ) +) if haskey(special_kwargs, :diffeq) - throw(ArgumentError("`diffeq` is given as positional argument when an ODEProblem is provided.")) + throw( + ArgumentError( + "`diffeq` is given as positional argument when an ODEProblem is provided." + ), + ) end IIP = isinplace(prob) # from SciMLBase D = length(prob.u0) @@ -139,7 +151,8 @@ end """ CoupledSDEs(ds::CoupledODEs, g, p [, σ]; kwargs...) -Converts a [`CoupledODEs`](https://juliadynamics.github.io/DynamicalSystems.jl/stable/tutorial/#CoupledODEs) +Converts a [`CoupledODEs` +](https://juliadynamics.github.io/DynamicalSystems.jl/stable/tutorial/#CoupledODEs) system into a [`CoupledSDEs`](@ref). """ function CoupledSDEs( @@ -170,9 +183,7 @@ end Converts a [`CoupledSDEs`](@ref) into [`CoupledODEs`](@ref). """ -function CoupledODEs( - sys::CoupledSDEs; diffeq=DEFAULT_STOCH_DIFFEQ, t0=0.0 -) +function CoupledODEs(sys::CoupledSDEs; diffeq=DEFAULT_STOCH_DIFFEQ, t0=0.0) return CoupledODEs( sys.integ.f, SVector{length(sys.integ.u)}(sys.integ.u), sys.p0; diffeq=diffeq, t0=t0 ) From 89225a48238d4b80082b7da52574648d14fa738f Mon Sep 17 00:00:00 2001 From: oameye Date: Sun, 28 Jul 2024 11:26:23 +0200 Subject: [PATCH 04/38] add idfunc --- src/core_systems/continuous_time_sde.jl | 21 +++++++++++++++++++++ 1 file changed, 21 insertions(+) diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index 60032f9f..8424ee65 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -254,3 +254,24 @@ function add_noise_strength(σ, g, IIP) newg = IIP ? σg!(σ, g) : σg(σ, g) return newg end + +""" + idfunc(u, p, t) + +Identity function for a diffusion function `g` of `CoupledSDEs` (out-of-place). +Equivalent to `(u, p, t) -> ones(length(u))`, +""" +function idfunc(u, p, t) + return typeof(u)(ones(eltype(u), length(u))) +end; + +""" + idfunc!(du, u, p, t) + +Identity function for a diffusion function `g` of `CoupledSDEs` (in-place). +Equivalent to `idfunc!(du, u, p, t) = (du .= ones(length(u)); return nothing)` +""" +function idfunc!(du, u, p, t) + du .= ones(eltype(u), length(u)) + return nothing +end; From f169386c93752784b113f9333201444980aadbc8 Mon Sep 17 00:00:00 2001 From: oameye Date: Sun, 28 Jul 2024 17:06:29 +0200 Subject: [PATCH 05/38] Fix docs? --- docs/make.jl | 1 + docs/src/CoupledSDEs.md | 98 +---------------------------------------- 2 files changed, 3 insertions(+), 96 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index 22ab6ef3..09cb2926 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -4,6 +4,7 @@ using DynamicalSystemsBase pages = [ "index.md", + "CoupledSDEs.md", ] using DynamicalSystemsBase.SciMLBase diff --git a/docs/src/CoupledSDEs.md b/docs/src/CoupledSDEs.md index 51ac2c06..eedc85a4 100644 --- a/docs/src/CoupledSDEs.md +++ b/docs/src/CoupledSDEs.md @@ -9,7 +9,7 @@ where $\vec x \in \mathbb{R}^\text{D}$, $\sigma > 0$ is the noise strength, $\te The function $f$ is the deterministic part of the system and follows the syntax of a `ContinuousTimeDynamicalSystem` in [DynamicalSystems.jl](https://juliadynamics.github.io/DynamicalSystems.jl/latest/tutorial/), i.e., `f(u, p, t)` for out-of-place (oop) and `f!(du, u, p, t)` for in-place (iip). The function $g$ allows to specify the stochastic dynamics of the system along with the [noise process](#noise-process) $\mathcal{W}$. It should be of the same type (iip or oop) as $f$. -By combining $\sigma$, $g$ and $\mathcal{W}$, you can define different type of stochastic systems. Examples of different types of stochastic systems can be found on the [StochasticDiffEq.jl tutorial page](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example/). A quick overview of common types of stochastic systems can be found [below](#Type-of-stochastic-system). +By combining $\sigma$, $g$ and $\mathcal{W}$, you can define different type of stochastic systems. Examples of different types of stochastic systems can be found on the [StochasticDiffEq.jl tutorial page](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example/). A quick overview of common types of stochastic systems can be found [below](#Defining-stochastic-dynamics). !!! info Note that nonlinear mixings of the Noise Process $\mathcal{W}$ fall into the class of random ordinary differential equations (RODEs) and is not supported in DynamicalSystems.jl at the moment. See [DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/rode_example/) for an implementation. @@ -35,8 +35,7 @@ Lyapunov spectrum of a `CoupledSDEs` in the absence of noise, here exemplified b FitzHugh-Nagumo model, can be computed by typing: ```julia -using CriticalTransitions -using DynamicalSystems: lyapunovspectrum +using DynamicalSystems function fitzhugh_nagumo(u, p, t) x, y = u @@ -52,99 +51,6 @@ sys = CoupledSDEs(fitzhugh_nagumo, idfunc, zeros(2), [1.,3.,1.,1.,1.,0.], 0.1) ls = lyapunovspectrum(CoupledODEs(sys), 10000) ``` -## Defining stochastic dynamics -Let's look at some examples of the different types of stochastic systems that can be defined. - -For simplicity, we choose a slow exponential growth in 2 dimensions as the deterministic dynamics `f`: -```@example type -using CriticalTransitions, Plots -import Random # hide -Random.seed!(10) # hide -f!(du, u, p, t) = du .= 1.01u # deterministic part -σ = 0.25 # noise strength -``` -### Additive noise -When `g \, \text{d}\mathcal{W}` is independent of the state variables `u`, the noise is called additive. - -#### Diagonal noise -A system of diagonal noise is the most common type of noise. It is defined by a vector of random numbers `dW` whose size matches the output of `g` where the noise is applied element-wise, i.e. `g.*dW`. -```@example type -t0 = 0.0; W0 = zeros(2); -W = WienerProcess(t0, W0, 0.0) -sde = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise=W) -``` -or equivalently -```@example type -sde = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ) -``` -where we used the helper function -```@docs -idfunc! -idfunc -``` -The vector `dW` is by default zero mean white gaussian noise $\mathcal{N}(0, \text{d}t)$ where the variance is the timestep $\text{d}t$ unit variance (Wiener Process). -```@example type -sol = simulate(sde, 1.0, dt=0.01, alg=SOSRA()) -plot(sol) -``` - -#### Scalar noise -Scalar noise is where a single random variable is applied to all dependent variables. To do this, one has to give the noise process to the `noise` keyword of the `CoupledSDEs` constructor. A common example is the Wiener process starting at `W0=0.0` at time `t0=0.0`. - -```@example type -t0 = 0.0; W0 = 0.0; -noise = WienerProcess(t0, W0, 0.0) -sde = CoupledSDEs(f!, idfunc!, rand(2)./10, nothing, σ; noise=noise) -sol = simulate(sde, 1.0, dt=0.01, alg=SOSRA()) -plot(sol) -``` -### Multiplicative noise -Multiplicative Noise is when $g_i(t, u)=a_i u$ -```@example type -function g(du, u, p, t) - du[1] = σ*u[1] - du[2] = σ*u[2] - return nothing -end -sde = CoupledSDEs(f!, g, rand(2)./10) -sol = simulate(sde, 1.0, dt=0.01, alg=SOSRI()) -plot(sol) -``` -### Correlated noise -```@example type -ρ = 0.3 -Σ = [1 ρ; ρ 1] -t0 = 0.0; W0 = zeros(2); Z0 = zeros(2); -W = CorrelatedWienerProcess(Σ, t0, W0, Z0) -sde = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise=W) -sol = simulate(sde, 1.0, dt=0.01, alg=SOSRA()) -plot(sol) -``` - -#### More complex Non-diagonal noise -Non-diagonal noise allows for the terms to linearly mixed via `g` being a matrix. Suppose we have two Wiener processes and two dependent random variables such that the output of `g` is a 2x2 matrix. Therefore, we have -```math -du_1 = f_1(u,p,t)dt + g_{11}(u,p,t)dW_1 + g_{12}(u,p,t)dW_2 \\ -du_2 = f_2(u,p,t)dt + g_{21}(u,p,t)dW_1 + g_{22}(u,p,t)dW_2 -``` -To indicate the structure that `g` should have, we can use the `noise_rate_prototype` keyword. Let us define a special type of non-diagonal noise called commutative noise. For this we can utilize the `RKMilCommute` algorithm which is designed to utilise the structure of commutative noise. - -```@example type -function g(du, u, p, t) - du[1,1] = σ*u[1] - du[2,1] = σ*u[2] - du[1,2] = σ*u[1] - du[2,2] = σ*u[2] - return nothing -end -sde = CoupledSDEs(f!, g, rand(2)./10, noise_rate_prototype = zeros(2, 2)) -sol = simulate(sde, 1.0, dt=0.01, alg=RKMilCommute()) -plot(sol) -``` - -!!! warning - Non-diagonal problems need specific type of solvers. See the [SciML recommendations](https://docs.sciml.ai/DiffEqDocs/stable/solvers/sde_solve/#sde_solve). - ## Available noise processes We provide the noise processes $\mathcal{W}$ that can be used in the stochastic simulations through the [DiffEqNoiseProcess.jl](https://docs.sciml.ai/DiffEqNoiseProcess/stable) package. A complete list of the available processes can be found [here](https://docs.sciml.ai/DiffEqNoiseProcess/stable/noise_processes/). ``` From 43ad5e9e3229710ccceadef37a2da8e01df2f28e Mon Sep 17 00:00:00 2001 From: oameye Date: Sun, 28 Jul 2024 18:04:01 +0200 Subject: [PATCH 06/38] change coupled sde example to use trajectory --- docs/src/CoupledSDEs.md | 7 ++++--- src/core_systems/continuous_time_sde.jl | 4 ++-- 2 files changed, 6 insertions(+), 5 deletions(-) diff --git a/docs/src/CoupledSDEs.md b/docs/src/CoupledSDEs.md index eedc85a4..a4da7df3 100644 --- a/docs/src/CoupledSDEs.md +++ b/docs/src/CoupledSDEs.md @@ -35,7 +35,8 @@ Lyapunov spectrum of a `CoupledSDEs` in the absence of noise, here exemplified b FitzHugh-Nagumo model, can be computed by typing: ```julia -using DynamicalSystems +using DynamicalSystemsBase, StaticArrays +using DynamicalSystemsBase: idfunc function fitzhugh_nagumo(u, p, t) x, y = u @@ -47,8 +48,8 @@ function fitzhugh_nagumo(u, p, t) return SA[dx, dy] end -sys = CoupledSDEs(fitzhugh_nagumo, idfunc, zeros(2), [1.,3.,1.,1.,1.,0.], 0.1) -ls = lyapunovspectrum(CoupledODEs(sys), 10000) +sde = CoupledSDEs(fitzhugh_nagumo, idfunc, zeros(2), [1.,3.,1.,1.,1.,0.], 0.1) +tr = trajectory(sde, 10) ``` ## Available noise processes diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index 8424ee65..cefe8b84 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -183,7 +183,7 @@ end Converts a [`CoupledSDEs`](@ref) into [`CoupledODEs`](@ref). """ -function CoupledODEs(sys::CoupledSDEs; diffeq=DEFAULT_STOCH_DIFFEQ, t0=0.0) +function CoupledODEs(sys::CoupledSDEs; diffeq=DEFAULT_DIFFEQ, t0=0.0) return CoupledODEs( sys.integ.f, SVector{length(sys.integ.u)}(sys.integ.u), sys.p0; diffeq=diffeq, t0=t0 ) @@ -262,7 +262,7 @@ Identity function for a diffusion function `g` of `CoupledSDEs` (out-of-place). Equivalent to `(u, p, t) -> ones(length(u))`, """ function idfunc(u, p, t) - return typeof(u)(ones(eltype(u), length(u))) + return SVector{length(u)}(ones(eltype(u), length(u))) end; """ From 8de87b8abab9f51416f613467e8922ecdc28ed72 Mon Sep 17 00:00:00 2001 From: oameye Date: Sun, 28 Jul 2024 19:31:58 +0200 Subject: [PATCH 07/38] specify which CoupledODEs docstring --- docs/src/CoupledSDEs.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/src/CoupledSDEs.md b/docs/src/CoupledSDEs.md index a4da7df3..85be9a86 100644 --- a/docs/src/CoupledSDEs.md +++ b/docs/src/CoupledSDEs.md @@ -28,7 +28,7 @@ CoupledSDEs - `CoupledSDEs(ode::CoupledODEs, g)`, with `g` the noise function, turns `ode` into a `CoupledSDEs` ```@docs -CoupledODEs +CoupledODEs(::CoupledSDEs; kwargs...) ``` For example, the Lyapunov spectrum of a `CoupledSDEs` in the absence of noise, here exemplified by the From 023ff0c3b0c7865bc73dfbe5aa3d2c6d4243605f Mon Sep 17 00:00:00 2001 From: oameye Date: Sun, 28 Jul 2024 19:47:24 +0200 Subject: [PATCH 08/38] change to SciML default tolerances --- src/core_systems/continuous_time_sde.jl | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index cefe8b84..5c910516 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -6,7 +6,8 @@ export CoupledSDEs # DiffEq options ########################################################################################### const DEFAULT_SDE_SOLVER = SOSRA() # default recommendation for additive noise -const DEFAULT_STOCH_DIFFEQ = (alg=DEFAULT_SDE_SOLVER, DEFAULT_DIFFEQ_KWARGS...) +const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol = 1e-2, reltol = 1e-2) +const DEFAULT_STOCH_DIFFEQ = (alg=DEFAULT_SDE_SOLVER, DEFAULT_STOCH_DIFFEQ_KWARGS...) # Function from user `@xlxs4`, see # https://github.com/JuliaDynamics/jl/pull/153 From f6a400e2e98ca354a4672cbec486f364b923b3c7 Mon Sep 17 00:00:00 2001 From: oameye Date: Mon, 29 Jul 2024 11:15:05 +0200 Subject: [PATCH 09/38] classify noise --- src/DynamicalSystemsBase.jl | 1 + src/core_systems/characterise_sde.jl | 81 +++++++++++++++++++++++++ src/core_systems/continuous_time_sde.jl | 9 ++- test/Project.toml | 3 +- test/runtests.jl | 1 + test/stochastic.jl | 4 +- test/stochastic_characterisation.jl | 65 ++++++++++++++++++++ 7 files changed, 158 insertions(+), 6 deletions(-) create mode 100644 src/core_systems/characterise_sde.jl create mode 100644 test/stochastic_characterisation.jl diff --git a/src/DynamicalSystemsBase.jl b/src/DynamicalSystemsBase.jl index a8eed1eb..96042bd0 100644 --- a/src/DynamicalSystemsBase.jl +++ b/src/DynamicalSystemsBase.jl @@ -22,6 +22,7 @@ include("core/pretty_printing.jl") include("core_systems/discrete_time_map.jl") include("core_systems/continuous_time_ode.jl") +include("core_systems/characterise_sde.jl") include("core_systems/continuous_time_sde.jl") include("core_systems/arbitrary_steppable.jl") include("core_systems/additional_supertypes.jl") diff --git a/src/core_systems/characterise_sde.jl b/src/core_systems/characterise_sde.jl new file mode 100644 index 00000000..c381e7d4 --- /dev/null +++ b/src/core_systems/characterise_sde.jl @@ -0,0 +1,81 @@ +using StochasticDiffEq: WienerProcess, CorrelatedWienerProcess, EM, SDEProblem +using LinearAlgebra + +function is_state_independent(g, u, p, t) + rdm_states = [rand(eltype(u), length(u)) for _ in 1:10] + val = map(u -> g(u, p, t), rdm_states) + length(unique(val)) == 1 +end +function is_time_independent(g, u, p) + trange = 0:0.1:1 + val = map(t -> g(u, p, t), trange) |> unique |> length == 1 + length(unique(val)) == 1 +end +# isinvertible(x) = applicable(inv, x) && isone(inv(x) * x) +isinvertible(x) = issuccess(lu(x, check = false)) + +function is_linear(f, x, y, c) + check1 = f(x + y) == f(x) + f(y) + check2 = f(c * x) == c * f(x) + return check1 && check2 +end + +function find_noise_type(prob::SDEProblem, IIP) + noise = prob.noise + noise_rate_prototype = prob.noise_rate_prototype + noise_rate_size = isnothing(noise_rate_prototype) ? nothing : size(noise_rate_prototype) + covariance = isnothing(noise) ? nothing : noise.covariance + param = prob.p + u0 = prob.u0 + D = length(u0) + + properties = Symbol[] + + function g(u, p, t) + if IIP + du = deepcopy(isnothing(noise_rate_prototype) ? u : noise_rate_prototype) + prob.g(du, u, p, t) + return du + else + return prob.g(u, p, t) + end + end + time_independent = is_time_independent(g, rand(D), param) + state_independent = is_state_independent(g, u0, param, 1.0) + + # additive noise is equal to state independent noise + push!(properties, state_independent ? :additive : :multiplicative) + push!(properties, time_independent ? :autonomous : :non_autonomous) + if !state_independent + linear = is_linear(u -> g(u, param, 1.0), rand(D), rand(D), 2.0) + push!(properties, linear ? :linear : :non_linear) + else + push!(properties, :linear) + end + + if time_independent && state_independent + if noise_rate_size == (D, D) && !isnothing(covariance) + error( + "The diffusion function `g` acts as an covariance matrix but + the noise process W also has a covariance matrix. This is ambiguous.") + elseif noise_rate_size == (D, D) && isnothing(covariance) + covariance = g(zeros(D), param, 0.0) + if !isinvertible(covariance) + push!(properties, :non_invertiable) + else + push!(properties, :invertiable) + end + elseif !isnothing(covariance) && !isinvertible(covariance) + push!(properties, :non_invertiable) + elseif !isnothing(noise_rate_size) && noise_rate_size != (D, D) + push!(properties, :non_invertiable) + else + push!(properties, :invertiable) + end + end + + if !isnothing(noise) && D != length(noise.dW) && length(noise.dW) == 1 + push!(properties, :scalar) + end + return properties +end # function diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index 5c910516..d825d101 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -1,11 +1,11 @@ using SciMLBase: SDEProblem, AbstractSDEIntegrator, __init, SDEFunction -using StochasticDiffEq: SOSRA +using StochasticDiffEq: SOSRI export CoupledSDEs ########################################################################################### # DiffEq options ########################################################################################### -const DEFAULT_SDE_SOLVER = SOSRA() # default recommendation for additive noise +const DEFAULT_SDE_SOLVER = SOSRI() # default sciml solver const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol = 1e-2, reltol = 1e-2) const DEFAULT_STOCH_DIFFEQ = (alg=DEFAULT_SDE_SOLVER, DEFAULT_STOCH_DIFFEQ_KWARGS...) @@ -78,6 +78,7 @@ struct CoupledSDEs{IIP,D,I,P,S} <: ContinuousTimeDynamicalSystem p0::P noise_strength diffeq # isn't parameterized because it is only used for display + noise_type::Vector{Symbol} end function CoupledSDEs( @@ -130,6 +131,7 @@ function CoupledSDEs( end sde_function = SDEFunction(prob.f, add_noise_strength(noise_strength, prob.g, IIP)) prob = SciMLBase.remake(prob; f=sde_function) + noise_type = find_noise_type(prob, IIP) solver, remaining = _decompose_into_sde_solver_and_remaining(diffeq) integ = __init( @@ -145,7 +147,7 @@ function CoupledSDEs( maxiters=Inf, ) return CoupledSDEs{IIP,D,typeof(integ),P,true}( - integ, deepcopy(prob.p), noise_strength, diffeq + integ, deepcopy(prob.p), noise_strength, diffeq, noise_type ) end @@ -197,6 +199,7 @@ function additional_details(ds::CoupledSDEs) "Noise strength" => ds.noise_strength, "SDE solver" => string(nameof(typeof(solver))), "SDE kwargs" => remaining, + "Noise type" => ds.noise_type, ] end diff --git a/test/Project.toml b/test/Project.toml index 460f5153..90f1118d 100644 --- a/test/Project.toml +++ b/test/Project.toml @@ -1,4 +1,5 @@ [deps] +DiffEqNoiseProcess = "77a26b50-5914-5dd7-bc55-306e6241c503" DynamicalSystemsBase = "6e36e845-645a-534a-86f2-f5d4aa5a06b4" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78" @@ -8,4 +9,4 @@ StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [compat] -ModelingToolkit = "9" \ No newline at end of file +ModelingToolkit = "9" diff --git a/test/runtests.jl b/test/runtests.jl index 051862c1..118a58ba 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -8,6 +8,7 @@ testfile(file, testname=defaultname(file)) = @testset "$testname" begin; include testfile("discrete.jl") testfile("continuous.jl") testfile("stochastic.jl") + testfile("stochastic_characterisation.jl") testfile("arbitrarysteppable.jl") testfile("stroboscopic.jl") testfile("parallel.jl") diff --git a/test/stochastic.jl b/test/stochastic.jl index 412de95d..b4aac0e0 100644 --- a/test/stochastic.jl +++ b/test/stochastic.jl @@ -1,5 +1,5 @@ using DynamicalSystemsBase, Test -using StochasticDiffEq: SDEProblem, SRA, SRI, SOSRA +using StochasticDiffEq: SDEProblem, SRA, SRI, SOSRI include("test_system_function.jl") @@ -49,7 +49,7 @@ end @testset "correct SDE propagation" begin lorenz_oop = CoupledSDEs(lorenz_rule, diagonal_noise(σ), u0, p0) - @test lorenz_oop.integ.alg isa SOSRA + @test lorenz_oop.integ.alg isa SOSRI lorenz_SRA = CoupledSDEs(lorenz_rule, diagonal_noise(σ), u0, p0; diffeq = (alg = SRA(), abstol = 1e-6, reltol = 1e-6, verbose=false) diff --git a/test/stochastic_characterisation.jl b/test/stochastic_characterisation.jl new file mode 100644 index 00000000..117da3ac --- /dev/null +++ b/test/stochastic_characterisation.jl @@ -0,0 +1,65 @@ +using DynamicalSystemsBase, DiffEqNoiseProcess, Test, StochasticDiffEq +using DynamicalSystemsBase: find_noise_type, idfunc! +f!(du, u, p, t) = du .= 1.01u # deterministic part +σ = 0.25 # noise strength +get_prob(sde) = sde.integ.sol.prob +IIP = true + +# Additive Wiener noise +W = WienerProcess(0.0, zeros(2), zeros(2)) +addit_autom_inv = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) +types = addit_autom_inv.noise_type +@test issetequal(types, [:additive, :autonomous, :linear, :invertiable]) + +# Scalar Wiener noise +W = WienerProcess(0.0, 0.0, 0.0) +scalar_a = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) +types = scalar_a.noise_type +@test issetequal(types, [:scalar, :additive, :autonomous, :linear, :invertiable]) + +# invertiable correlated Wiener noise +W = CorrelatedWienerProcess([1 0.3; 0.3 1], 0.0, zeros(2), zeros(2)) +corr_a = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) +types = corr_a.noise_type +@test issetequal(types, [:additive, :autonomous, :linear, :invertiable]) + +# invertiable correlated Wiener noise +g!(du, u, p, t) = (du .= [1 0.3; 0.3 1]; return nothing) +corr_alt = CoupledSDEs( + f!, g!, zeros(2), nothing, σ, noise_rate_prototype = zeros(2, 2), + diffeq = (alg = EM(), dt = 0.1)) +types = corr_alt.noise_type +@test issetequal(types, [:additive, :autonomous, :linear, :invertiable]) + +# non-invertiable correlated Wiener noise +W = CorrelatedWienerProcess([1 2; 2 4], 0.0, zeros(2), zeros(2)) +corr_noninv = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) +types = corr_noninv.noise_type +@test issetequal(types, [:additive, :autonomous, :linear, :non_invertiable]) + +# non-invertiable correlated Wiener noise +g!(du, u, p, t) = (du .= [1 0.3 1; 0.3 1 1]; return nothing) +corr_alt = CoupledSDEs( + f!, g!, zeros(2), nothing, σ, noise_rate_prototype = zeros(2, 3), + diffeq = (alg = EM(), dt = 0.1)) +types = corr_alt.noise_type +@test issetequal(types, [:additive, :autonomous, :linear, :non_invertiable]) + +# multiplicative linear Wiener noise +g!(du, u, p, t) = (du .= u; return nothing) +linear_multipli = CoupledSDEs(f!, g!, rand(2) ./ 10, (), σ) +types = linear_multipli.noise_type +@test issetequal(types, [:multiplicative, :autonomous, :linear]) + +# non-diagonal multiplicative linear Wiener noise +lin_multipli_alt = CoupledSDEs( + f!, g!, rand(2), (), σ, noise_rate_prototype = zeros(2, 3), + diffeq = (alg = EM(), dt = 0.1)) +types = lin_multipli_alt.noise_type +@test issetequal(types, [:multiplicative, :autonomous, :linear]) + +# multiplicative nonlinear Wiener noise +g!(du, u, p, t) = (du .= u .^ 2; return nothing) +nonlinear_multiplicative = CoupledSDEs(f!, g!, rand(2), (), σ) +types = nonlinear_multiplicative.noise_type +@test issetequal(types, [:multiplicative, :autonomous, :non_linear]) From 5c5e6dc202bd71c76f4dd889ceace139834cfeb4 Mon Sep 17 00:00:00 2001 From: oameye Date: Mon, 29 Jul 2024 11:34:07 +0200 Subject: [PATCH 10/38] correct spelling of invertible --- src/core_systems/characterise_sde.jl | 10 +++++----- test/stochastic_characterisation.jl | 20 ++++++++++---------- 2 files changed, 15 insertions(+), 15 deletions(-) diff --git a/src/core_systems/characterise_sde.jl b/src/core_systems/characterise_sde.jl index c381e7d4..de2ced44 100644 --- a/src/core_systems/characterise_sde.jl +++ b/src/core_systems/characterise_sde.jl @@ -61,16 +61,16 @@ function find_noise_type(prob::SDEProblem, IIP) elseif noise_rate_size == (D, D) && isnothing(covariance) covariance = g(zeros(D), param, 0.0) if !isinvertible(covariance) - push!(properties, :non_invertiable) + push!(properties, :non_invertible) else - push!(properties, :invertiable) + push!(properties, :invertible) end elseif !isnothing(covariance) && !isinvertible(covariance) - push!(properties, :non_invertiable) + push!(properties, :non_invertible) elseif !isnothing(noise_rate_size) && noise_rate_size != (D, D) - push!(properties, :non_invertiable) + push!(properties, :non_invertible) else - push!(properties, :invertiable) + push!(properties, :invertible) end end diff --git a/test/stochastic_characterisation.jl b/test/stochastic_characterisation.jl index 117da3ac..9fcad641 100644 --- a/test/stochastic_characterisation.jl +++ b/test/stochastic_characterisation.jl @@ -9,41 +9,41 @@ IIP = true W = WienerProcess(0.0, zeros(2), zeros(2)) addit_autom_inv = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) types = addit_autom_inv.noise_type -@test issetequal(types, [:additive, :autonomous, :linear, :invertiable]) +@test issetequal(types, [:additive, :autonomous, :linear, :invertible]) # Scalar Wiener noise W = WienerProcess(0.0, 0.0, 0.0) scalar_a = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) types = scalar_a.noise_type -@test issetequal(types, [:scalar, :additive, :autonomous, :linear, :invertiable]) +@test issetequal(types, [:scalar, :additive, :autonomous, :linear, :invertible]) -# invertiable correlated Wiener noise +# invertible correlated Wiener noise W = CorrelatedWienerProcess([1 0.3; 0.3 1], 0.0, zeros(2), zeros(2)) corr_a = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) types = corr_a.noise_type -@test issetequal(types, [:additive, :autonomous, :linear, :invertiable]) +@test issetequal(types, [:additive, :autonomous, :linear, :invertible]) -# invertiable correlated Wiener noise +# invertible correlated Wiener noise g!(du, u, p, t) = (du .= [1 0.3; 0.3 1]; return nothing) corr_alt = CoupledSDEs( f!, g!, zeros(2), nothing, σ, noise_rate_prototype = zeros(2, 2), diffeq = (alg = EM(), dt = 0.1)) types = corr_alt.noise_type -@test issetequal(types, [:additive, :autonomous, :linear, :invertiable]) +@test issetequal(types, [:additive, :autonomous, :linear, :invertible]) -# non-invertiable correlated Wiener noise +# non-invertible correlated Wiener noise W = CorrelatedWienerProcess([1 2; 2 4], 0.0, zeros(2), zeros(2)) corr_noninv = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) types = corr_noninv.noise_type -@test issetequal(types, [:additive, :autonomous, :linear, :non_invertiable]) +@test issetequal(types, [:additive, :autonomous, :linear, :non_invertible]) -# non-invertiable correlated Wiener noise +# non-invertible correlated Wiener noise g!(du, u, p, t) = (du .= [1 0.3 1; 0.3 1 1]; return nothing) corr_alt = CoupledSDEs( f!, g!, zeros(2), nothing, σ, noise_rate_prototype = zeros(2, 3), diffeq = (alg = EM(), dt = 0.1)) types = corr_alt.noise_type -@test issetequal(types, [:additive, :autonomous, :linear, :non_invertiable]) +@test issetequal(types, [:additive, :autonomous, :linear, :non_invertible]) # multiplicative linear Wiener noise g!(du, u, p, t) = (du .= u; return nothing) From ce7a03e36bfed04edaffed222f9ac2b9562e149d Mon Sep 17 00:00:00 2001 From: oameye Date: Tue, 30 Jul 2024 19:18:01 +0200 Subject: [PATCH 11/38] make noisetype field a namedtuple --- src/core_systems/characterise_sde.jl | 42 +++++++++---------------- src/core_systems/continuous_time_sde.jl | 2 +- test/stochastic_characterisation.jl | 18 +++++------ 3 files changed, 25 insertions(+), 37 deletions(-) diff --git a/src/core_systems/characterise_sde.jl b/src/core_systems/characterise_sde.jl index de2ced44..891ed788 100644 --- a/src/core_systems/characterise_sde.jl +++ b/src/core_systems/characterise_sde.jl @@ -11,8 +11,7 @@ function is_time_independent(g, u, p) val = map(t -> g(u, p, t), trange) |> unique |> length == 1 length(unique(val)) == 1 end -# isinvertible(x) = applicable(inv, x) && isone(inv(x) * x) -isinvertible(x) = issuccess(lu(x, check = false)) +is_invertible(x) = issuccess(lu(x, check = false)) function is_linear(f, x, y, c) check1 = f(x + y) == f(x) + f(y) @@ -29,7 +28,10 @@ function find_noise_type(prob::SDEProblem, IIP) u0 = prob.u0 D = length(u0) - properties = Symbol[] + isadditive = false + isautonomous = false + islinear = false + isinvertible = false function g(u, p, t) if IIP @@ -44,38 +46,24 @@ function find_noise_type(prob::SDEProblem, IIP) state_independent = is_state_independent(g, u0, param, 1.0) # additive noise is equal to state independent noise - push!(properties, state_independent ? :additive : :multiplicative) - push!(properties, time_independent ? :autonomous : :non_autonomous) - if !state_independent - linear = is_linear(u -> g(u, param, 1.0), rand(D), rand(D), 2.0) - push!(properties, linear ? :linear : :non_linear) - else - push!(properties, :linear) - end + isadditive = state_independent + isautonomous = time_independent + islinear = !state_independent ? + is_linear(u -> g(u, param, 1.0), rand(D), rand(D), 2.0) : true if time_independent && state_independent if noise_rate_size == (D, D) && !isnothing(covariance) - error( - "The diffusion function `g` acts as an covariance matrix but - the noise process W also has a covariance matrix. This is ambiguous.") + error("The diffusion function `g` acts as an covariance matrix but the noise process W also has a covariance matrix. This is ambiguous.") elseif noise_rate_size == (D, D) && isnothing(covariance) covariance = g(zeros(D), param, 0.0) - if !isinvertible(covariance) - push!(properties, :non_invertible) - else - push!(properties, :invertible) - end - elseif !isnothing(covariance) && !isinvertible(covariance) - push!(properties, :non_invertible) + isinvertible = is_invertible(covariance) elseif !isnothing(noise_rate_size) && noise_rate_size != (D, D) - push!(properties, :non_invertible) + isinvertible = false else - push!(properties, :invertible) + isinvertible = isnothing(covariance) || is_invertible(covariance) end end - if !isnothing(noise) && D != length(noise.dW) && length(noise.dW) == 1 - push!(properties, :scalar) - end - return properties + return (additive = isadditive, autonomous = isautonomous, + linear = islinear, invertible = isinvertible) end # function diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index d825d101..cf425b6c 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -78,7 +78,7 @@ struct CoupledSDEs{IIP,D,I,P,S} <: ContinuousTimeDynamicalSystem p0::P noise_strength diffeq # isn't parameterized because it is only used for display - noise_type::Vector{Symbol} + noise_type::NamedTuple end function CoupledSDEs( diff --git a/test/stochastic_characterisation.jl b/test/stochastic_characterisation.jl index 9fcad641..35ffec0a 100644 --- a/test/stochastic_characterisation.jl +++ b/test/stochastic_characterisation.jl @@ -9,19 +9,19 @@ IIP = true W = WienerProcess(0.0, zeros(2), zeros(2)) addit_autom_inv = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) types = addit_autom_inv.noise_type -@test issetequal(types, [:additive, :autonomous, :linear, :invertible]) +@test values(types) == (true, true, true, true) # Scalar Wiener noise W = WienerProcess(0.0, 0.0, 0.0) scalar_a = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) types = scalar_a.noise_type -@test issetequal(types, [:scalar, :additive, :autonomous, :linear, :invertible]) +@test values(types) == (true, true, true, true) # invertible correlated Wiener noise W = CorrelatedWienerProcess([1 0.3; 0.3 1], 0.0, zeros(2), zeros(2)) corr_a = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) types = corr_a.noise_type -@test issetequal(types, [:additive, :autonomous, :linear, :invertible]) +@test values(types) == (true, true, true, true) # invertible correlated Wiener noise g!(du, u, p, t) = (du .= [1 0.3; 0.3 1]; return nothing) @@ -29,13 +29,13 @@ corr_alt = CoupledSDEs( f!, g!, zeros(2), nothing, σ, noise_rate_prototype = zeros(2, 2), diffeq = (alg = EM(), dt = 0.1)) types = corr_alt.noise_type -@test issetequal(types, [:additive, :autonomous, :linear, :invertible]) +@test values(types) == (true, true, true, true) # non-invertible correlated Wiener noise W = CorrelatedWienerProcess([1 2; 2 4], 0.0, zeros(2), zeros(2)) corr_noninv = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) types = corr_noninv.noise_type -@test issetequal(types, [:additive, :autonomous, :linear, :non_invertible]) +@test values(types) == (true, true, true, false) # non-invertible correlated Wiener noise g!(du, u, p, t) = (du .= [1 0.3 1; 0.3 1 1]; return nothing) @@ -43,23 +43,23 @@ corr_alt = CoupledSDEs( f!, g!, zeros(2), nothing, σ, noise_rate_prototype = zeros(2, 3), diffeq = (alg = EM(), dt = 0.1)) types = corr_alt.noise_type -@test issetequal(types, [:additive, :autonomous, :linear, :non_invertible]) +@test values(types) == (true, true, true, false) # multiplicative linear Wiener noise g!(du, u, p, t) = (du .= u; return nothing) linear_multipli = CoupledSDEs(f!, g!, rand(2) ./ 10, (), σ) types = linear_multipli.noise_type -@test issetequal(types, [:multiplicative, :autonomous, :linear]) +@test values(types) == (false, true, true, false) # non-diagonal multiplicative linear Wiener noise lin_multipli_alt = CoupledSDEs( f!, g!, rand(2), (), σ, noise_rate_prototype = zeros(2, 3), diffeq = (alg = EM(), dt = 0.1)) types = lin_multipli_alt.noise_type -@test issetequal(types, [:multiplicative, :autonomous, :linear]) +@test values(types) == (false, true, true, false) # multiplicative nonlinear Wiener noise g!(du, u, p, t) = (du .= u .^ 2; return nothing) nonlinear_multiplicative = CoupledSDEs(f!, g!, rand(2), (), σ) types = nonlinear_multiplicative.noise_type -@test issetequal(types, [:multiplicative, :autonomous, :non_linear]) +@test values(types) == (false, true, false, false) From fba7327bbdb58656f627c06616a9d0aa345ae89a Mon Sep 17 00:00:00 2001 From: oameye Date: Wed, 31 Jul 2024 17:30:51 +0200 Subject: [PATCH 12/38] make coupledSDEs an extention --- Project.toml | 7 +- ext/StochasticSystemsBase.jl | 16 ++ ext/src/CoupledSDEs.jl | 202 ++++++++++++++++ .../src/classification.jl | 3 +- src/DynamicalSystemsBase.jl | 1 - src/core_systems/continuous_time_sde.jl | 223 +----------------- test/stochastic_characterisation.jl | 134 +++++++---- 7 files changed, 310 insertions(+), 276 deletions(-) create mode 100644 ext/StochasticSystemsBase.jl create mode 100644 ext/src/CoupledSDEs.jl rename src/core_systems/characterise_sde.jl => ext/src/classification.jl (94%) diff --git a/Project.toml b/Project.toml index 29d0d58d..67c46905 100644 --- a/Project.toml +++ b/Project.toml @@ -13,7 +13,6 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" StateSpaceSets = "40b095a5-5852-4c12-98c7-d43bf788e795" Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" -StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0" SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5" [compat] @@ -27,3 +26,9 @@ Statistics = "1" StochasticDiffEq = "6.66.0" SymbolicIndexingInterface = "0.3.4" julia = "1.9" + +[weakdeps] +StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0" + +[extensions] +StochasticSystemsBase = "StochasticDiffEq" \ No newline at end of file diff --git a/ext/StochasticSystemsBase.jl b/ext/StochasticSystemsBase.jl new file mode 100644 index 00000000..82131911 --- /dev/null +++ b/ext/StochasticSystemsBase.jl @@ -0,0 +1,16 @@ +module StochasticSystemsBase + +using DynamicalSystemsBase: DynamicalSystemsBase, SciMLBase, correct_state, CoupledODEs, + CoupledSDEs, StateSpaceSets, isinplace, _delete, set_parameter!, + set_state!, dynamic_rule, isdeterministic, current_state, + DynamicalSystemsBase, _set_parameter!, u_modified! +using SciMLBase: SDEProblem, AbstractSDEIntegrator, __init, SDEFunction, step! +using StochasticDiffEq: SOSRI +using LinearAlgebra + +include("src/CoupledSDEs.jl") +include("src/classification.jl") + +export CoupledSDEs + +end diff --git a/ext/src/CoupledSDEs.jl b/ext/src/CoupledSDEs.jl new file mode 100644 index 00000000..da6e4cfe --- /dev/null +++ b/ext/src/CoupledSDEs.jl @@ -0,0 +1,202 @@ +########################################################################################### +# DiffEq options +########################################################################################### + +const DEFAULT_SDE_SOLVER = SOSRI() # default sciml solver +const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol = 1e-2, reltol = 1e-2) +const DEFAULT_STOCH_DIFFEQ = (alg = DEFAULT_SDE_SOLVER, DEFAULT_STOCH_DIFFEQ_KWARGS...) + +# Function from user `@xlxs4`, see +# https://github.com/JuliaDynamics/jl/pull/153 +function _decompose_into_sde_solver_and_remaining(diffeq) + if haskey(diffeq, :alg) + return (diffeq[:alg], _delete(diffeq, :alg)) + else + return (DEFAULT_SDE_SOLVER, diffeq) + end +end + +########################################################################################### +# Constructor functions +########################################################################################### + +function DynamicalSystemsBase.CoupledSDEs( + f, + g, + u0, + p = SciMLBase.NullParameters(), + noise_strength = 1.0; + t0 = 0.0, + diffeq = DEFAULT_STOCH_DIFFEQ, + noise_rate_prototype = nothing, + noise = nothing, + seed = UInt64(0) +) + IIP = isinplace(f, 4) # from SciMLBase + @assert IIP==isinplace(g, 4) "f and g must both be in-place or out-of-place" + + s = correct_state(Val{IIP}(), u0) + T = eltype(s) + prob = SDEProblem{IIP}( + f, + g, + s, + (T(t0), T(Inf)), + p; + noise_rate_prototype = noise_rate_prototype, + noise = noise, + seed = seed + ) + return CoupledSDEs(prob, diffeq, noise_strength) +end + +function DynamicalSystemsBase.CoupledSDEs( + prob::SDEProblem, diffeq = DEFAULT_STOCH_DIFFEQ, noise_strength = 1.0; special_kwargs... +) + if haskey(special_kwargs, :diffeq) + throw( + ArgumentError( + "`diffeq` is given as positional argument when an ODEProblem is provided." + ), + ) + end + IIP = isinplace(prob) # from SciMLBase + D = length(prob.u0) + P = typeof(prob.p) + if prob.tspan === (nothing, nothing) + # If the problem was made via MTK, it is possible to not have a default timespan. + U = eltype(prob.u0) + prob = SciMLBase.remake(prob; tspan = (U(0), U(Inf))) + end + sde_function = SDEFunction(prob.f, add_noise_strength(noise_strength, prob.g, IIP)) + prob = SciMLBase.remake(prob; f = sde_function) + noise_type = find_noise_type(prob, IIP) + + solver, remaining = _decompose_into_sde_solver_and_remaining(diffeq) + integ = __init( + prob, + solver; + remaining..., + # Integrators are used exclusively iteratively. There is no reason to save anything. + save_start = false, + save_end = false, + save_everystep = false, + # DynamicalSystems.jl operates on integrators and `step!` exclusively, + # so there is no reason to limit the maximum time evolution + maxiters = Inf + ) + return CoupledSDEs{IIP, D, typeof(integ), P, true}( + integ, deepcopy(prob.p), noise_strength, diffeq, noise_type + ) +end + +""" + CoupledSDEs(ds::CoupledODEs, g, p [, σ]; kwargs...) + +Converts a [`CoupledODEs` +](https://juliadynamics.github.io/DynamicalSystems.jl/stable/tutorial/#CoupledODEs) +system into a [`CoupledSDEs`](@ref). +""" +function DynamicalSystemsBase.CoupledSDEs( + ds::CoupledODEs, + g, + p, # the parameter is likely changed as the diffusion function g is added. + noise_strength = 1.0; + diffeq = DEFAULT_STOCH_DIFFEQ, + noise_rate_prototype = nothing, + noise = nothing, + seed = UInt64(0) +) + return CoupledSDEs( + dynamic_rule(ds), + g, + current_state(ds), + p, + noise_strength; + diffeq = diffeq, + noise_rate_prototype = noise_rate_prototype, + noise = noise, + seed = seed + ) +end + +""" + CoupledODEs(ds::CoupledSDEs; kwargs...) + +Converts a [`CoupledSDEs`](@ref) into [`CoupledODEs`](@ref). +""" +function DynamicalSystemsBase.CoupledODEs( + sys::CoupledSDEs; diffeq = DEFAULT_DIFFEQ, t0 = 0.0) + return CoupledODEs( + sys.integ.f, SVector{length(sys.integ.u)}(sys.integ.u), sys.p0; diffeq = diffeq, t0 = t0 + ) +end + +# Pretty print +function additional_details(ds::CoupledSDEs) + solver, remaining = _decompose_into_sde_solver_and_remaining(ds.diffeq) + return [ + "Noise strength" => ds.noise_strength, + "SDE solver" => string(nameof(typeof(solver))), + "SDE kwargs" => remaining, + "Noise type" => ds.noise_type + ] +end + +########################################################################################### +# API - obtaining information from the system +########################################################################################### + +SciMLBase.isinplace(::CoupledSDEs{IIP}) where {IIP} = IIP +StateSpaceSets.dimension(::CoupledSDEs{IIP, D}) where {IIP, D} = D +DynamicalSystemsBase.current_state(ds::CoupledSDEs) = current_state(ds.integ) +DynamicalSystemsBase.isdeterministic(ds::CoupledSDEs) = false + +function DynamicalSystemsBase.dynamic_rule(sys::CoupledSDEs) + f = sys.integ.f + while hasfield(typeof(f), :f) + f = f.f + end + return f +end + +# so that `ds` is printed +function DynamicalSystemsBase.set_state!(ds::CoupledSDEs, u::AbstractArray) + (set_state!(ds.integ, u); ds) +end +SciMLBase.step!(ds::CoupledSDEs, args...) = (step!(ds.integ, args...); ds) + +function DynamicalSystemsBase.successful_step(integ::AbstractSDEIntegrator) + rcode = integ.sol.retcode + return rcode == SciMLBase.ReturnCode.Default || rcode == SciMLBase.ReturnCode.Success +end + +# This is here to ensure that `u_modified!` is called +function DynamicalSystemsBase.set_parameter!(ds::CoupledSDEs, args...) + _set_parameter!(ds, args...) + u_modified!(ds.integ, true) + return nothing +end + +referrenced_sciml_prob(ds::CoupledSDEs) = ds.integ.sol.prob + +########################################################################################### +# Utilities +########################################################################################### + +function σg(σ, g) + return (u, p, t) -> σ .* g(u, p, t) +end + +function σg!(σ, g!) + function (du, u, p, t) + g!(du, u, p, t) + du .*= σ + return nothing + end +end + +function add_noise_strength(σ, g, IIP) + newg = IIP ? σg!(σ, g) : σg(σ, g) + return newg +end diff --git a/src/core_systems/characterise_sde.jl b/ext/src/classification.jl similarity index 94% rename from src/core_systems/characterise_sde.jl rename to ext/src/classification.jl index 891ed788..e2cc224e 100644 --- a/src/core_systems/characterise_sde.jl +++ b/ext/src/classification.jl @@ -1,4 +1,3 @@ -using StochasticDiffEq: WienerProcess, CorrelatedWienerProcess, EM, SDEProblem using LinearAlgebra function is_state_independent(g, u, p, t) @@ -8,7 +7,7 @@ function is_state_independent(g, u, p, t) end function is_time_independent(g, u, p) trange = 0:0.1:1 - val = map(t -> g(u, p, t), trange) |> unique |> length == 1 + val = map(t -> g(u, p, t), trange) length(unique(val)) == 1 end is_invertible(x) = issuccess(lu(x, check = false)) diff --git a/src/DynamicalSystemsBase.jl b/src/DynamicalSystemsBase.jl index 96042bd0..a8eed1eb 100644 --- a/src/DynamicalSystemsBase.jl +++ b/src/DynamicalSystemsBase.jl @@ -22,7 +22,6 @@ include("core/pretty_printing.jl") include("core_systems/discrete_time_map.jl") include("core_systems/continuous_time_ode.jl") -include("core_systems/characterise_sde.jl") include("core_systems/continuous_time_sde.jl") include("core_systems/arbitrary_steppable.jl") include("core_systems/additional_supertypes.jl") diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index cf425b6c..26a6c71b 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -1,27 +1,5 @@ -using SciMLBase: SDEProblem, AbstractSDEIntegrator, __init, SDEFunction -using StochasticDiffEq: SOSRI export CoupledSDEs -########################################################################################### -# DiffEq options -########################################################################################### -const DEFAULT_SDE_SOLVER = SOSRI() # default sciml solver -const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol = 1e-2, reltol = 1e-2) -const DEFAULT_STOCH_DIFFEQ = (alg=DEFAULT_SDE_SOLVER, DEFAULT_STOCH_DIFFEQ_KWARGS...) - -# Function from user `@xlxs4`, see -# https://github.com/JuliaDynamics/jl/pull/153 -function _decompose_into_sde_solver_and_remaining(diffeq) - if haskey(diffeq, :alg) - return (diffeq[:alg], _delete(diffeq, :alg)) - else - return (DEFAULT_SDE_SOLVER, diffeq) - end -end - -########################################################################################### -# Type -########################################################################################### """ CoupledSDEs <: ContinuousTimeDynamicalSystem CoupledSDEs(f, g, u0 [, p, σ]; kwargs...) @@ -59,7 +37,7 @@ If you want to specify a solver, do so by using the keyword `alg`, e.g.: `using OrdinaryDiffEq` to access the solvers. The default `diffeq` is: ```julia -$(DEFAULT_STOCH_DIFFEQ) +(alg = SOSRI(), abstol = 1.0e-6, reltol = 1.0e-6) ``` `diffeq` keywords can also include `callback` for [event handling @@ -80,202 +58,3 @@ struct CoupledSDEs{IIP,D,I,P,S} <: ContinuousTimeDynamicalSystem diffeq # isn't parameterized because it is only used for display noise_type::NamedTuple end - -function CoupledSDEs( - f, - g, - u0, - p=SciMLBase.NullParameters(), - noise_strength=1.0; - t0=0.0, - diffeq=DEFAULT_STOCH_DIFFEQ, - noise_rate_prototype=nothing, - noise=nothing, - seed=UInt64(0), -) - IIP = isinplace(f, 4) # from SciMLBase - @assert IIP == isinplace(g, 4) "f and g must both be in-place or out-of-place" - - s = correct_state(Val{IIP}(), u0) - T = eltype(s) - prob = SDEProblem{IIP}( - f, - g, - s, - (T(t0), T(Inf)), - p; - noise_rate_prototype=noise_rate_prototype, - noise=noise, - seed=seed, - ) - return CoupledSDEs(prob, diffeq, noise_strength) -end - -function CoupledSDEs( - prob::SDEProblem, diffeq=DEFAULT_STOCH_DIFFEQ, noise_strength=1.0; special_kwargs... -) - if haskey(special_kwargs, :diffeq) - throw( - ArgumentError( - "`diffeq` is given as positional argument when an ODEProblem is provided." - ), - ) - end - IIP = isinplace(prob) # from SciMLBase - D = length(prob.u0) - P = typeof(prob.p) - if prob.tspan === (nothing, nothing) - # If the problem was made via MTK, it is possible to not have a default timespan. - U = eltype(prob.u0) - prob = SciMLBase.remake(prob; tspan=(U(0), U(Inf))) - end - sde_function = SDEFunction(prob.f, add_noise_strength(noise_strength, prob.g, IIP)) - prob = SciMLBase.remake(prob; f=sde_function) - noise_type = find_noise_type(prob, IIP) - - solver, remaining = _decompose_into_sde_solver_and_remaining(diffeq) - integ = __init( - prob, - solver; - remaining..., - # Integrators are used exclusively iteratively. There is no reason to save anything. - save_start=false, - save_end=false, - save_everystep=false, - # DynamicalSystems.jl operates on integrators and `step!` exclusively, - # so there is no reason to limit the maximum time evolution - maxiters=Inf, - ) - return CoupledSDEs{IIP,D,typeof(integ),P,true}( - integ, deepcopy(prob.p), noise_strength, diffeq, noise_type - ) -end - -""" - CoupledSDEs(ds::CoupledODEs, g, p [, σ]; kwargs...) - -Converts a [`CoupledODEs` -](https://juliadynamics.github.io/DynamicalSystems.jl/stable/tutorial/#CoupledODEs) -system into a [`CoupledSDEs`](@ref). -""" -function CoupledSDEs( - ds::CoupledODEs, - g, - p, # the parameter is likely changed as the diffusion function g is added. - noise_strength=1.0; - diffeq=DEFAULT_STOCH_DIFFEQ, - noise_rate_prototype=nothing, - noise=nothing, - seed=UInt64(0), -) - return CoupledSDEs( - dynamic_rule(ds), - g, - current_state(ds), - p, - noise_strength; - diffeq=diffeq, - noise_rate_prototype=noise_rate_prototype, - noise=noise, - seed=seed, - ) -end - -""" - CoupledODEs(ds::CoupledSDEs; kwargs...) - -Converts a [`CoupledSDEs`](@ref) into [`CoupledODEs`](@ref). -""" -function CoupledODEs(sys::CoupledSDEs; diffeq=DEFAULT_DIFFEQ, t0=0.0) - return CoupledODEs( - sys.integ.f, SVector{length(sys.integ.u)}(sys.integ.u), sys.p0; diffeq=diffeq, t0=t0 - ) -end - -# Pretty print -function additional_details(ds::CoupledSDEs) - solver, remaining = _decompose_into_sde_solver_and_remaining(ds.diffeq) - return [ - "Noise strength" => ds.noise_strength, - "SDE solver" => string(nameof(typeof(solver))), - "SDE kwargs" => remaining, - "Noise type" => ds.noise_type, - ] -end - -########################################################################################### -# API - obtaining information from the system -########################################################################################### - -SciMLBase.isinplace(::CoupledSDEs{IIP}) where {IIP} = IIP -StateSpaceSets.dimension(::CoupledSDEs{IIP,D}) where {IIP,D} = D -current_state(ds::CoupledSDEs) = current_state(ds.integ) -isdeterministic(ds::CoupledSDEs) = false - -function dynamic_rule(sys::CoupledSDEs) - f = sys.integ.f - while hasfield(typeof(f), :f) - f = f.f - end - return f -end - -# so that `ds` is printed -set_state!(ds::CoupledSDEs, u::AbstractArray) = (set_state!(ds.integ, u); ds) -SciMLBase.step!(ds::CoupledSDEs, args...) = (step!(ds.integ, args...); ds) - -function successful_step(integ::AbstractSDEIntegrator) - rcode = integ.sol.retcode - return rcode == SciMLBase.ReturnCode.Default || rcode == SciMLBase.ReturnCode.Success -end - -# This is here to ensure that `u_modified!` is called -function set_parameter!(ds::CoupledSDEs, args...) - _set_parameter!(ds, args...) - u_modified!(ds.integ, true) - return nothing -end - -referrenced_sciml_prob(ds::CoupledSDEs) = ds.integ.sol.prob - -########################################################################################### -# Utilities -########################################################################################### - -function σg(σ, g) - return (u, p, t) -> σ .* g(u, p, t) -end - -function σg!(σ, g!) - function (du, u, p, t) - g!(du, u, p, t) - du .*= σ - return nothing - end -end - -function add_noise_strength(σ, g, IIP) - newg = IIP ? σg!(σ, g) : σg(σ, g) - return newg -end - -""" - idfunc(u, p, t) - -Identity function for a diffusion function `g` of `CoupledSDEs` (out-of-place). -Equivalent to `(u, p, t) -> ones(length(u))`, -""" -function idfunc(u, p, t) - return SVector{length(u)}(ones(eltype(u), length(u))) -end; - -""" - idfunc!(du, u, p, t) - -Identity function for a diffusion function `g` of `CoupledSDEs` (in-place). -Equivalent to `idfunc!(du, u, p, t) = (du .= ones(length(u)); return nothing)` -""" -function idfunc!(du, u, p, t) - du .= ones(eltype(u), length(u)) - return nothing -end; diff --git a/test/stochastic_characterisation.jl b/test/stochastic_characterisation.jl index 35ffec0a..8c3e8290 100644 --- a/test/stochastic_characterisation.jl +++ b/test/stochastic_characterisation.jl @@ -5,61 +5,95 @@ f!(du, u, p, t) = du .= 1.01u # deterministic part get_prob(sde) = sde.integ.sol.prob IIP = true -# Additive Wiener noise -W = WienerProcess(0.0, zeros(2), zeros(2)) -addit_autom_inv = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) -types = addit_autom_inv.noise_type -@test values(types) == (true, true, true, true) +# function idfunc(u, p, t) +# return SVector{length(u)}(ones(eltype(u), length(u))) +# end; -# Scalar Wiener noise -W = WienerProcess(0.0, 0.0, 0.0) -scalar_a = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) -types = scalar_a.noise_type -@test values(types) == (true, true, true, true) +function idfunc!(du, u, p, t) + du .= ones(eltype(u), length(u)) + return nothing +end; -# invertible correlated Wiener noise -W = CorrelatedWienerProcess([1 0.3; 0.3 1], 0.0, zeros(2), zeros(2)) -corr_a = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) -types = corr_a.noise_type -@test values(types) == (true, true, true, true) +@testset "Additive" begin + # Additive Wiener noise + W = WienerProcess(0.0, zeros(2), zeros(2)) + addit_autom_inv = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) + types = addit_autom_inv.noise_type + @test values(types) == (true, true, true, true) -# invertible correlated Wiener noise -g!(du, u, p, t) = (du .= [1 0.3; 0.3 1]; return nothing) -corr_alt = CoupledSDEs( - f!, g!, zeros(2), nothing, σ, noise_rate_prototype = zeros(2, 2), - diffeq = (alg = EM(), dt = 0.1)) -types = corr_alt.noise_type -@test values(types) == (true, true, true, true) + # Scalar Wiener noise + W = WienerProcess(0.0, 0.0, 0.0) + scalar_a = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) + types = scalar_a.noise_type + @test values(types) == (true, true, true, true) -# non-invertible correlated Wiener noise -W = CorrelatedWienerProcess([1 2; 2 4], 0.0, zeros(2), zeros(2)) -corr_noninv = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) -types = corr_noninv.noise_type -@test values(types) == (true, true, true, false) + # invertible correlated Wiener noise + W = CorrelatedWienerProcess([1 0.3; 0.3 1], 0.0, zeros(2), zeros(2)) + corr_a = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) + types = corr_a.noise_type + @test values(types) == (true, true, true, true) -# non-invertible correlated Wiener noise -g!(du, u, p, t) = (du .= [1 0.3 1; 0.3 1 1]; return nothing) -corr_alt = CoupledSDEs( - f!, g!, zeros(2), nothing, σ, noise_rate_prototype = zeros(2, 3), - diffeq = (alg = EM(), dt = 0.1)) -types = corr_alt.noise_type -@test values(types) == (true, true, true, false) + # invertible correlated Wiener noise + g!(du, u, p, t) = (du .= [1 0.3; 0.3 1]; return nothing) + corr_alt = CoupledSDEs( + f!, g!, zeros(2), nothing, σ, noise_rate_prototype = zeros(2, 2), + diffeq = (alg = EM(), dt = 0.1)) + types = corr_alt.noise_type + @test values(types) == (true, true, true, true) -# multiplicative linear Wiener noise -g!(du, u, p, t) = (du .= u; return nothing) -linear_multipli = CoupledSDEs(f!, g!, rand(2) ./ 10, (), σ) -types = linear_multipli.noise_type -@test values(types) == (false, true, true, false) + # non-invertible correlated Wiener noise + W = CorrelatedWienerProcess([1 2; 2 4], 0.0, zeros(2), zeros(2)) + corr_noninv = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) + types = corr_noninv.noise_type + @test values(types) == (true, true, true, false) -# non-diagonal multiplicative linear Wiener noise -lin_multipli_alt = CoupledSDEs( - f!, g!, rand(2), (), σ, noise_rate_prototype = zeros(2, 3), - diffeq = (alg = EM(), dt = 0.1)) -types = lin_multipli_alt.noise_type -@test values(types) == (false, true, true, false) + # non-invertible correlated Wiener noise + g!(du, u, p, t) = (du .= [1 0.3 1; 0.3 1 1]; return nothing) + corr_alt = CoupledSDEs( + f!, g!, zeros(2), nothing, σ, noise_rate_prototype = zeros(2, 3), + diffeq = (alg = EM(), dt = 0.1)) + types = corr_alt.noise_type + @test values(types) == (true, true, true, false) -# multiplicative nonlinear Wiener noise -g!(du, u, p, t) = (du .= u .^ 2; return nothing) -nonlinear_multiplicative = CoupledSDEs(f!, g!, rand(2), (), σ) -types = nonlinear_multiplicative.noise_type -@test values(types) == (false, true, false, false) + # non-autonomous Wiener noise + g!(du, u, p, t) = (du .= 1 / (1 + t); return nothing) + W = WienerProcess(0.0, zeros(2), zeros(2)) + addit_non_autom = CoupledSDEs(f!, g!, zeros(2), nothing, σ; noise = W) + types = addit_non_autom.noise_type + @test values(types) == (true, false, true, false) +end + +@testset "Multiplicative" begin + # multiplicative linear Wiener noise + g!(du, u, p, t) = (du .= u; return nothing) + linear_multipli = CoupledSDEs(f!, g!, rand(2) ./ 10, (), σ) + types = linear_multipli.noise_type + @test values(types) == (false, true, true, false) + + # non-diagonal multiplicative linear Wiener noise + lin_multipli_alt = CoupledSDEs( + f!, g!, rand(2), (), σ, noise_rate_prototype = zeros(2, 3), + diffeq = (alg = EM(), dt = 0.1)) + types = lin_multipli_alt.noise_type + @test values(types) == (false, true, true, false) + + # multiplicative nonlinear Wiener noise + g!(du, u, p, t) = (du .= u .^ 2; return nothing) + nonlinear_multiplicative = CoupledSDEs(f!, g!, rand(2), (), σ) + types = nonlinear_multiplicative.noise_type + @test values(types) == (false, true, false, false) + + # non-autonomous linear multiplicative Wiener noise + g!(du, u, p, t) = (du .= u ./ (1 + t); return nothing) + W = WienerProcess(0.0, zeros(2), zeros(2)) + addit_non_autom = CoupledSDEs(f!, g!, zeros(2), nothing, σ; noise = W) + types = addit_non_autom.noise_type + @test values(types) == (false, false, true, false) + + # non-autonomous nonlinear multiplicative Wiener noise + g!(du, u, p, t) = (du .= u.^2 ./ (1 + t); return nothing) + W = WienerProcess(0.0, zeros(2), zeros(2)) + addit_non_autom = CoupledSDEs(f!, g!, zeros(2), nothing, σ; noise = W) + types = addit_non_autom.noise_type + @test values(types) == (false, false, false, false) +end From c875b5efa8eb8f8bc5b91c37bb410ff20e4a02fe Mon Sep 17 00:00:00 2001 From: oameye Date: Wed, 31 Jul 2024 17:35:12 +0200 Subject: [PATCH 13/38] export pretty print add extentention to docs clean up test file --- docs/Project.toml | 1 + docs/make.jl | 3 ++- ext/StochasticSystemsBase.jl | 3 ++- ext/src/CoupledSDEs.jl | 6 +++--- test/stochastic_characterisation.jl | 8 +------- 5 files changed, 9 insertions(+), 12 deletions(-) diff --git a/docs/Project.toml b/docs/Project.toml index d2759d5c..9426585b 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -5,3 +5,4 @@ DocumenterTools = "35a29f4d-8980-5a13-9543-d66fff28ecb8" DynamicalSystemsBase = "6e36e845-645a-534a-86f2-f5d4aa5a06b4" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" StateSpaceSets = "40b095a5-5852-4c12-98c7-d43bf788e795" +StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0" diff --git a/docs/make.jl b/docs/make.jl index 09cb2926..441e62b1 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -1,6 +1,7 @@ cd(@__DIR__) using DynamicalSystemsBase +using StochasticDiffEq # for extention pages = [ "index.md", @@ -16,5 +17,5 @@ Downloads.download( include("build_docs_with_style.jl") build_docs_with_style(pages, - DynamicalSystemsBase, SciMLBase, StateSpaceSets; + DynamicalSystemsBase, SciMLBase, StateSpaceSets, StochasticDiffEq; ) diff --git a/ext/StochasticSystemsBase.jl b/ext/StochasticSystemsBase.jl index 82131911..5f6cbc53 100644 --- a/ext/StochasticSystemsBase.jl +++ b/ext/StochasticSystemsBase.jl @@ -3,7 +3,8 @@ module StochasticSystemsBase using DynamicalSystemsBase: DynamicalSystemsBase, SciMLBase, correct_state, CoupledODEs, CoupledSDEs, StateSpaceSets, isinplace, _delete, set_parameter!, set_state!, dynamic_rule, isdeterministic, current_state, - DynamicalSystemsBase, _set_parameter!, u_modified! + DynamicalSystemsBase, _set_parameter!, u_modified!, + additional_details, referrenced_sciml_prob using SciMLBase: SDEProblem, AbstractSDEIntegrator, __init, SDEFunction, step! using StochasticDiffEq: SOSRI using LinearAlgebra diff --git a/ext/src/CoupledSDEs.jl b/ext/src/CoupledSDEs.jl index da6e4cfe..c8514a13 100644 --- a/ext/src/CoupledSDEs.jl +++ b/ext/src/CoupledSDEs.jl @@ -3,7 +3,7 @@ ########################################################################################### const DEFAULT_SDE_SOLVER = SOSRI() # default sciml solver -const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol = 1e-2, reltol = 1e-2) +const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol = 1e-2, reltol = 1e-2) # default sciml tol const DEFAULT_STOCH_DIFFEQ = (alg = DEFAULT_SDE_SOLVER, DEFAULT_STOCH_DIFFEQ_KWARGS...) # Function from user `@xlxs4`, see @@ -133,7 +133,7 @@ function DynamicalSystemsBase.CoupledODEs( end # Pretty print -function additional_details(ds::CoupledSDEs) +function DynamicalSystemsBase.additional_details(ds::CoupledSDEs) solver, remaining = _decompose_into_sde_solver_and_remaining(ds.diffeq) return [ "Noise strength" => ds.noise_strength, @@ -178,7 +178,7 @@ function DynamicalSystemsBase.set_parameter!(ds::CoupledSDEs, args...) return nothing end -referrenced_sciml_prob(ds::CoupledSDEs) = ds.integ.sol.prob +DynamicalSystemsBase.referrenced_sciml_prob(ds::CoupledSDEs) = ds.integ.sol.prob ########################################################################################### # Utilities diff --git a/test/stochastic_characterisation.jl b/test/stochastic_characterisation.jl index 8c3e8290..508369d2 100644 --- a/test/stochastic_characterisation.jl +++ b/test/stochastic_characterisation.jl @@ -1,13 +1,7 @@ using DynamicalSystemsBase, DiffEqNoiseProcess, Test, StochasticDiffEq -using DynamicalSystemsBase: find_noise_type, idfunc! + f!(du, u, p, t) = du .= 1.01u # deterministic part σ = 0.25 # noise strength -get_prob(sde) = sde.integ.sol.prob -IIP = true - -# function idfunc(u, p, t) -# return SVector{length(u)}(ones(eltype(u), length(u))) -# end; function idfunc!(du, u, p, t) du .= ones(eltype(u), length(u)) From b3ccb26c02b0c04594d14c02c92866739c919ee3 Mon Sep 17 00:00:00 2001 From: oameye Date: Wed, 31 Jul 2024 18:33:01 +0200 Subject: [PATCH 14/38] export CoupledODEs --- ext/StochasticSystemsBase.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/ext/StochasticSystemsBase.jl b/ext/StochasticSystemsBase.jl index 5f6cbc53..fb06d37e 100644 --- a/ext/StochasticSystemsBase.jl +++ b/ext/StochasticSystemsBase.jl @@ -12,6 +12,6 @@ using LinearAlgebra include("src/CoupledSDEs.jl") include("src/classification.jl") -export CoupledSDEs +export CoupledSDEs, CoupledODEs end From b08fd7cdcecb74ab44e8bd8823524a6df29c9490 Mon Sep 17 00:00:00 2001 From: oameye Date: Thu, 1 Aug 2024 09:10:09 +0200 Subject: [PATCH 15/38] add CoupledODEs <-> CoupledSDEs tests --- ext/StochasticSystemsBase.jl | 8 ++++---- ext/src/CoupledSDEs.jl | 12 +++--------- src/core_systems/continuous_time_ode.jl | 12 ++++++++++-- test/continuous.jl | 4 ++-- test/stochastic.jl | 16 +++++++++++++--- 5 files changed, 32 insertions(+), 20 deletions(-) diff --git a/ext/StochasticSystemsBase.jl b/ext/StochasticSystemsBase.jl index fb06d37e..8c581d90 100644 --- a/ext/StochasticSystemsBase.jl +++ b/ext/StochasticSystemsBase.jl @@ -1,10 +1,10 @@ module StochasticSystemsBase using DynamicalSystemsBase: DynamicalSystemsBase, SciMLBase, correct_state, CoupledODEs, - CoupledSDEs, StateSpaceSets, isinplace, _delete, set_parameter!, - set_state!, dynamic_rule, isdeterministic, current_state, - DynamicalSystemsBase, _set_parameter!, u_modified!, - additional_details, referrenced_sciml_prob + CoupledSDEs, StateSpaceSets, isinplace, _delete, set_parameter!, + set_state!, dynamic_rule, isdeterministic, current_state, + DynamicalSystemsBase, _set_parameter!, u_modified!, + additional_details, referrenced_sciml_prob, DEFAULT_DIFFEQ, SVector using SciMLBase: SDEProblem, AbstractSDEIntegrator, __init, SDEFunction, step! using StochasticDiffEq: SOSRI using LinearAlgebra diff --git a/ext/src/CoupledSDEs.jl b/ext/src/CoupledSDEs.jl index c8514a13..bcdaf428 100644 --- a/ext/src/CoupledSDEs.jl +++ b/ext/src/CoupledSDEs.jl @@ -128,7 +128,8 @@ Converts a [`CoupledSDEs`](@ref) into [`CoupledODEs`](@ref). function DynamicalSystemsBase.CoupledODEs( sys::CoupledSDEs; diffeq = DEFAULT_DIFFEQ, t0 = 0.0) return CoupledODEs( - sys.integ.f, SVector{length(sys.integ.u)}(sys.integ.u), sys.p0; diffeq = diffeq, t0 = t0 + dynamic_rule(sys), SVector{length(sys.integ.u)}(sys.integ.u), sys.p0; + diffeq = diffeq, t0 = t0 ) end @@ -152,20 +153,13 @@ StateSpaceSets.dimension(::CoupledSDEs{IIP, D}) where {IIP, D} = D DynamicalSystemsBase.current_state(ds::CoupledSDEs) = current_state(ds.integ) DynamicalSystemsBase.isdeterministic(ds::CoupledSDEs) = false -function DynamicalSystemsBase.dynamic_rule(sys::CoupledSDEs) - f = sys.integ.f - while hasfield(typeof(f), :f) - f = f.f - end - return f -end - # so that `ds` is printed function DynamicalSystemsBase.set_state!(ds::CoupledSDEs, u::AbstractArray) (set_state!(ds.integ, u); ds) end SciMLBase.step!(ds::CoupledSDEs, args...) = (step!(ds.integ, args...); ds) +# TODO We have to check if for SDEIntegrators a different step interruption is possible. function DynamicalSystemsBase.successful_step(integ::AbstractSDEIntegrator) rcode = integ.sol.retcode return rcode == SciMLBase.ReturnCode.Default || rcode == SciMLBase.ReturnCode.Success diff --git a/src/core_systems/continuous_time_ode.jl b/src/core_systems/continuous_time_ode.jl index 20d2a32a..e9a0a7cf 100644 --- a/src/core_systems/continuous_time_ode.jl +++ b/src/core_systems/continuous_time_ode.jl @@ -150,7 +150,15 @@ function SciMLBase.reinit!(ds::ContinuousTimeDynamicalSystem, u::AbstractArray = end # `DEIntegrator` stuff -dynamic_rule(integ::DEIntegrator) = integ.f.f +function dynamic_rule(integ::DEIntegrator) + # with remake it can happen that we have nested ODEFunctions + # sciml integrator deals with this internally well + f = integ.f + while hasfield(typeof(f), :f) + f = f.f + end + return f +end current_parameters(integ::DEIntegrator) = integ.p initial_state(integ::DEIntegrator) = integ.sol.prob.u0 current_state(ds::CoupledODEs) = current_state(ds.integ) @@ -189,4 +197,4 @@ function set_parameter!(ds::CoupledODEs, args...) return end -referrenced_sciml_prob(ds::CoupledODEs) = ds.integ.sol.prob \ No newline at end of file +referrenced_sciml_prob(ds::CoupledODEs) = ds.integ.sol.prob diff --git a/test/continuous.jl b/test/continuous.jl index 16b1a69d..d66dfd38 100644 --- a/test/continuous.jl +++ b/test/continuous.jl @@ -34,7 +34,7 @@ for (ds, iip) in zip((lorenz_oop, lorenz_iip, lorenz_vern), (false, true, false) name = (ds === lorenz_vern) ? "lorvern" : "lorenz" @testset "$(name) IIP=$(iip)" begin @test dynamic_rule(ds) == (iip ? lorenz_rule_iip : lorenz_rule) - test_dynamical_system(ds, u0, p0; idt = false, iip) + test_dynamical_system(ds, u0, p0; idt = false, iip=iip) end end @@ -58,4 +58,4 @@ end @test_throws ArgumentError CoupledODEs(prob; diffeq = (alg=Rodas5(autodiff=false), )) -end \ No newline at end of file +end diff --git a/test/stochastic.jl b/test/stochastic.jl index b4aac0e0..1693cdea 100644 --- a/test/stochastic.jl +++ b/test/stochastic.jl @@ -1,4 +1,5 @@ using DynamicalSystemsBase, Test +using OrdinaryDiffEq: Tsit5 using StochasticDiffEq: SDEProblem, SRA, SRI, SOSRI include("test_system_function.jl") @@ -43,7 +44,7 @@ for (ds, iip) in zip((lorenz_oop, lorenz_iip, lorenz_SRA), (false, true, false)) name = (ds === lorenz_SRA) ? "lorSRA" : "lorenz" @testset "$(name) IIP=$(iip)" begin @test dynamic_rule(ds) == (iip ? lorenz_rule_iip : lorenz_rule) - test_dynamical_system(ds, u0, p0; idt = false, iip) + test_dynamical_system(ds, u0, p0; idt = false, iip=iip) end end @@ -52,12 +53,12 @@ end @test lorenz_oop.integ.alg isa SOSRI lorenz_SRA = CoupledSDEs(lorenz_rule, diagonal_noise(σ), u0, p0; - diffeq = (alg = SRA(), abstol = 1e-6, reltol = 1e-6, verbose=false) + diffeq = (alg = SRA(), abstol = 1e-3, reltol = 1e-3, verbose=false) ) @test lorenz_SRA.integ.alg isa SRA @test lorenz_SRA.integ.opts.verbose == false - # # also test SDEproblem creation + # also test SDEproblem creation prob = lorenz_SRA.integ.sol.prob ds = CoupledSDEs(prob, (alg=SRI(), abstol=0.0, reltol=1e-6, verbose=false)) @@ -67,4 +68,13 @@ end @test_throws ArgumentError CoupledSDEs(prob; diffeq = (alg=SRI(), )) + # CoupledODEs creation + ds = CoupledODEs(lorenz_oop) + @test dynamic_rule(ds) == lorenz_rule + @test ds.integ.alg isa Tsit5 + test_dynamical_system(ds, u0, p0; idt = false, iip=false) + # and back + sde = CoupledSDEs(ds, diagonal_noise(σ), p0) + @test dynamic_rule(sde) == lorenz_rule + @test sde.integ.alg isa SOSRI end From dfc3053ea20f69ad1a2b0d85b71670b8ef21d490 Mon Sep 17 00:00:00 2001 From: oameye Date: Thu, 1 Aug 2024 09:10:43 +0200 Subject: [PATCH 16/38] add extention to modules in makedocs --- docs/make.jl | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/docs/make.jl b/docs/make.jl index 441e62b1..3bb3c46c 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -2,6 +2,7 @@ cd(@__DIR__) using DynamicalSystemsBase using StochasticDiffEq # for extention +StochasticSystemsBase = Base.get_extension(DynamicalSystemsBase, :StochasticSystemsBase) pages = [ "index.md", @@ -17,5 +18,5 @@ Downloads.download( include("build_docs_with_style.jl") build_docs_with_style(pages, - DynamicalSystemsBase, SciMLBase, StateSpaceSets, StochasticDiffEq; + DynamicalSystemsBase, SciMLBase, StateSpaceSets, StochasticSystemsBase; ) From daca4a7b029fd8a1724efb1526093d52381d5149 Mon Sep 17 00:00:00 2001 From: oameye Date: Thu, 1 Aug 2024 10:26:22 +0200 Subject: [PATCH 17/38] define dynamics rule sde specific --- ext/src/CoupledSDEs.jl | 10 ++++++++++ src/core_systems/continuous_time_ode.jl | 10 +--------- 2 files changed, 11 insertions(+), 9 deletions(-) diff --git a/ext/src/CoupledSDEs.jl b/ext/src/CoupledSDEs.jl index bcdaf428..02d249f4 100644 --- a/ext/src/CoupledSDEs.jl +++ b/ext/src/CoupledSDEs.jl @@ -153,6 +153,16 @@ StateSpaceSets.dimension(::CoupledSDEs{IIP, D}) where {IIP, D} = D DynamicalSystemsBase.current_state(ds::CoupledSDEs) = current_state(ds.integ) DynamicalSystemsBase.isdeterministic(ds::CoupledSDEs) = false +function DynamicalSystemsBase.dynamic_rule(ds::CoupledSDEs) + # with remake it can happen that we have nested SDEFunctions + # sciml integrator deals with this internally well + f = ds.integ.f + while hasfield(typeof(f), :f) + f = f.f + end + return f +end + # so that `ds` is printed function DynamicalSystemsBase.set_state!(ds::CoupledSDEs, u::AbstractArray) (set_state!(ds.integ, u); ds) diff --git a/src/core_systems/continuous_time_ode.jl b/src/core_systems/continuous_time_ode.jl index e9a0a7cf..95fce626 100644 --- a/src/core_systems/continuous_time_ode.jl +++ b/src/core_systems/continuous_time_ode.jl @@ -150,15 +150,7 @@ function SciMLBase.reinit!(ds::ContinuousTimeDynamicalSystem, u::AbstractArray = end # `DEIntegrator` stuff -function dynamic_rule(integ::DEIntegrator) - # with remake it can happen that we have nested ODEFunctions - # sciml integrator deals with this internally well - f = integ.f - while hasfield(typeof(f), :f) - f = f.f - end - return f -end +dynamic_rule(integ::DEIntegrator) = integ.f.f current_parameters(integ::DEIntegrator) = integ.p initial_state(integ::DEIntegrator) = integ.sol.prob.u0 current_state(ds::CoupledODEs) = current_state(ds.integ) From 73af9902252dd6b31057fc46a6b96d5c8afd6563 Mon Sep 17 00:00:00 2001 From: Datseris Date: Thu, 1 Aug 2024 14:57:03 +0200 Subject: [PATCH 18/38] port docs into the docstring --- docs/juliadynamics-dark.scss | 51 ++++++++++++++------- docs/juliadynamics-darkdefs.scss | 51 ++++++++++++++------- docs/make.jl | 3 +- docs/src/CoupledSDEs.md | 47 ++++--------------- docs/src/assets/themes/documenter-dark.css | 4 +- docs/src/assets/themes/documenter-light.css | 2 +- src/core_systems/continuous_time_sde.jl | 44 ++++++++++++++---- 7 files changed, 118 insertions(+), 84 deletions(-) diff --git a/docs/juliadynamics-dark.scss b/docs/juliadynamics-dark.scss index e06171fd..cd2afc22 100644 --- a/docs/juliadynamics-dark.scss +++ b/docs/juliadynamics-dark.scss @@ -70,6 +70,7 @@ $code-background: $codebg; // for inline code $pre-background: $codebg; // for code blocks $documenter-docstring-header-background: lighten-color($body-background-color, 0.5); + // Sidebar $documenter-sidebar-background: darken-color($maincolor, 1.2); //background color for sidebar $documenter-sidebar-color: $text; //font color for sidebar @@ -86,22 +87,8 @@ $input-focus-border-color: $mainwhite; $documenter-docstring-shadow: 3px 3px 4px invert($shadow-color); - - -// Admonition stuff -$admbg: lighten-color($body-background-color, 0.5); -$admonition-background: ( - 'default': $admbg, 'info': $admbg, 'success': $admbg, 'warning': $admbg, - 'danger': $admbg, 'compat': $admbg -); -$admonition-header-background: ( - 'default': #ba3f1f, 'warning': #a88b17, 'danger': #c7524c, - 'success': #42ac68, 'info': #28c); - -// Deprecations -$admonition-body-color: null; -$admonition-body-color: null; -$admonition-header-color: null; +// This line is required after https://github.com/JuliaDocs/Documenter.jl/pull/2499 +$admonition-default: $darkbg; // All secondary themes have to be nested in a theme--$(themename) class. When Documenter // switches themes, it applies this class to and then disables the primary @@ -157,4 +144,36 @@ html.theme--#{$themename} { .hljs-subst { color: #f8f8f2; } + + + + // fix for the settings/modal panel + .modal-card-head { + background-color: darken($darkbg,5); + } + .modal-card-body { + background-color: darken($darkbg,5); + } + .modal-card-foot { + background-color: darken($darkbg,5); + } + .select { + > select { + background-color: darken($darkbg,5); + } + } + + // fix for the search panel + .input { + background-color: darken($darkbg,5); + } + .search-result-title { + color: white + } + + // match the size of the light theme (additional rule + // that is dark-theme specific and messing around + // with the size of elements, making the size be 0,75em + // only for the dark theme, no idea why) + font-size: unset !important; } diff --git a/docs/juliadynamics-darkdefs.scss b/docs/juliadynamics-darkdefs.scss index 5c0847dc..eb1c4f31 100644 --- a/docs/juliadynamics-darkdefs.scss +++ b/docs/juliadynamics-darkdefs.scss @@ -24,6 +24,7 @@ $code-background: $codebg; // for inline code $pre-background: $codebg; // for code blocks $documenter-docstring-header-background: lighten-color($body-background-color, 0.5); + // Sidebar $documenter-sidebar-background: darken-color($maincolor, 1.2); //background color for sidebar $documenter-sidebar-color: $text; //font color for sidebar @@ -40,22 +41,8 @@ $input-focus-border-color: $mainwhite; $documenter-docstring-shadow: 3px 3px 4px invert($shadow-color); - - -// Admonition stuff -$admbg: lighten-color($body-background-color, 0.5); -$admonition-background: ( - 'default': $admbg, 'info': $admbg, 'success': $admbg, 'warning': $admbg, - 'danger': $admbg, 'compat': $admbg -); -$admonition-header-background: ( - 'default': #ba3f1f, 'warning': #a88b17, 'danger': #c7524c, - 'success': #42ac68, 'info': #28c); - -// Deprecations -$admonition-body-color: null; -$admonition-body-color: null; -$admonition-header-color: null; +// This line is required after https://github.com/JuliaDocs/Documenter.jl/pull/2499 +$admonition-default: $darkbg; // All secondary themes have to be nested in a theme--$(themename) class. When Documenter // switches themes, it applies this class to and then disables the primary @@ -111,4 +98,36 @@ html.theme--#{$themename} { .hljs-subst { color: #f8f8f2; } + + + + // fix for the settings/modal panel + .modal-card-head { + background-color: darken($darkbg,5); + } + .modal-card-body { + background-color: darken($darkbg,5); + } + .modal-card-foot { + background-color: darken($darkbg,5); + } + .select { + > select { + background-color: darken($darkbg,5); + } + } + + // fix for the search panel + .input { + background-color: darken($darkbg,5); + } + .search-result-title { + color: white + } + + // match the size of the light theme (additional rule + // that is dark-theme specific and messing around + // with the size of elements, making the size be 0,75em + // only for the dark theme, no idea why) + font-size: unset !important; } diff --git a/docs/make.jl b/docs/make.jl index 3bb3c46c..6e3458b9 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -1,7 +1,8 @@ cd(@__DIR__) using DynamicalSystemsBase -using StochasticDiffEq # for extention +using StochasticDiffEq # to enable extention +# We need this because Documenter doesn't know where to get the docstring from otherwise StochasticSystemsBase = Base.get_extension(DynamicalSystemsBase, :StochasticSystemsBase) pages = [ diff --git a/docs/src/CoupledSDEs.md b/docs/src/CoupledSDEs.md index 85be9a86..4d803282 100644 --- a/docs/src/CoupledSDEs.md +++ b/docs/src/CoupledSDEs.md @@ -1,4 +1,9 @@ -# Define a CoupledSDEs system +# `CoupledSDEs` + +```@docs +CoupledSDEs +``` + A `CoupledSDEs` defines a stochastic dynamical system of the form @@ -18,42 +23,6 @@ By combining $\sigma$, $g$ and $\mathcal{W}$, you can define different type of s CoupledSDEs ``` -## Converting between `CoupledSDEs` and `CoupledODEs` - -!!! tip "Analyzing deterministic dynamics with DynamicalSystems.jl" - The deterministic part of a [`CoupledSDEs`](@ref) system can easily be extracted as a - [`CoupledODEs`](https://juliadynamics.github.io/DynamicalSystems.jl/dev/tutorial/#DynamicalSystemsBase.CoupledODEs), a common subtype of a `ContinuousTimeDynamicalSystem` in DynamicalSystems.jl. - -- `CoupledODEs(sde::CoupledSDEs)` extracts the deterministic part of `sde` as a `CoupledODEs` -- `CoupledSDEs(ode::CoupledODEs, g)`, with `g` the noise function, turns `ode` into a `CoupledSDEs` - -```@docs -CoupledODEs(::CoupledSDEs; kwargs...) -``` -For example, the -Lyapunov spectrum of a `CoupledSDEs` in the absence of noise, here exemplified by the -FitzHugh-Nagumo model, can be computed by typing: - -```julia -using DynamicalSystemsBase, StaticArrays -using DynamicalSystemsBase: idfunc - -function fitzhugh_nagumo(u, p, t) - x, y = u - ϵ, β, α, γ, κ, I = p - - dx = (-α * x^3 + γ * x - κ * y + I) / ϵ - dy = -β * y + x - - return SA[dx, dy] -end - -sde = CoupledSDEs(fitzhugh_nagumo, idfunc, zeros(2), [1.,3.,1.,1.,1.,0.], 0.1) -tr = trajectory(sde, 10) -``` - -## Available noise processes -We provide the noise processes $\mathcal{W}$ that can be used in the stochastic simulations through the [DiffEqNoiseProcess.jl](https://docs.sciml.ai/DiffEqNoiseProcess/stable) package. A complete list of the available processes can be found [here](https://docs.sciml.ai/DiffEqNoiseProcess/stable/noise_processes/). -``` - +## [Examples defining stochastic dynamics](@id defining-stochastic-dynamics) +TODO? diff --git a/docs/src/assets/themes/documenter-dark.css b/docs/src/assets/themes/documenter-dark.css index 85986a64..ccc66895 100644 --- a/docs/src/assets/themes/documenter-dark.css +++ b/docs/src/assets/themes/documenter-dark.css @@ -1,7 +1,7 @@ -html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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!important}html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark 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rgba(244,199,47,0.25)}html.theme--documenter-dark .button.is-warning:active,html.theme--documenter-dark .button.is-warning.is-active{background-color:#f3c017;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#f4c72f;border-color:#f4c72f;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#f4c72f;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-outlined.is-focused{background-color:#f4c72f;border-color:#f4c72f;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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.button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar 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.button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark 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1.5rem}}html.theme--documenter-dark .columns.is-variable.is-7{--columnGap: 1.75rem}@media screen and (max-width: 768px){html.theme--documenter-dark .columns.is-variable.is-7-mobile{--columnGap: 1.75rem}}@media screen and (min-width: 769px),print{html.theme--documenter-dark .columns.is-variable.is-7-tablet{--columnGap: 1.75rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-7-tablet-only{--columnGap: 1.75rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-7-touch{--columnGap: 1.75rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-7-desktop{--columnGap: 1.75rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-7-desktop-only{--columnGap: 1.75rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-7-widescreen{--columnGap: 1.75rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark .columns.is-variable.is-7-widescreen-only{--columnGap: 1.75rem}}@media screen and (min-width: 1408px){html.theme--documenter-dark .columns.is-variable.is-7-fullhd{--columnGap: 1.75rem}}html.theme--documenter-dark .columns.is-variable.is-8{--columnGap: 2rem}@media screen and (max-width: 768px){html.theme--documenter-dark .columns.is-variable.is-8-mobile{--columnGap: 2rem}}@media screen and (min-width: 769px),print{html.theme--documenter-dark .columns.is-variable.is-8-tablet{--columnGap: 2rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-8-tablet-only{--columnGap: 2rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-8-touch{--columnGap: 2rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-8-desktop{--columnGap: 2rem}}@media screen and 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!important}html.theme--documenter-dark .tile.is-parent{padding:.75rem}html.theme--documenter-dark .tile.is-vertical{flex-direction:column}html.theme--documenter-dark .tile.is-vertical>.tile.is-child:not(:last-child){margin-bottom:1.5rem !important}@media screen and (min-width: 769px),print{html.theme--documenter-dark .tile:not(.is-child){display:flex}html.theme--documenter-dark .tile.is-1{flex:none;width:8.33333337%}html.theme--documenter-dark .tile.is-2{flex:none;width:16.66666674%}html.theme--documenter-dark .tile.is-3{flex:none;width:25%}html.theme--documenter-dark .tile.is-4{flex:none;width:33.33333337%}html.theme--documenter-dark .tile.is-5{flex:none;width:41.66666674%}html.theme--documenter-dark .tile.is-6{flex:none;width:50%}html.theme--documenter-dark .tile.is-7{flex:none;width:58.33333337%}html.theme--documenter-dark .tile.is-8{flex:none;width:66.66666674%}html.theme--documenter-dark .tile.is-9{flex:none;width:75%}html.theme--documenter-dark 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body{color:#fbfbfb;font-size:1em;font-weight:400;line-height:1.5}html.theme--documenter-dark a{color:#2ad7e6;cursor:pointer;text-decoration:none}html.theme--documenter-dark a strong{color:currentColor}html.theme--documenter-dark a:hover{color:#97ebf3}html.theme--documenter-dark code{background-color:#312550;color:#fff;font-size:.875em;font-weight:normal;padding:.1em}html.theme--documenter-dark hr{background-color:#f5f5f5;border:none;display:block;height:2px;margin:1.5rem 0}html.theme--documenter-dark img{height:auto;max-width:100%}html.theme--documenter-dark input[type="checkbox"],html.theme--documenter-dark input[type="radio"]{vertical-align:baseline}html.theme--documenter-dark small{font-size:.875em}html.theme--documenter-dark span{font-style:inherit;font-weight:inherit}html.theme--documenter-dark strong{color:#cdc3e3;font-weight:700}html.theme--documenter-dark fieldset{border:none}html.theme--documenter-dark pre{-webkit-overflow-scrolling:touch;background-color:#312550;color:#fbfbfb;font-size:.875em;overflow-x:auto;padding:1.25rem 1.5rem;white-space:pre;word-wrap:normal}html.theme--documenter-dark pre code{background-color:transparent;color:currentColor;font-size:1em;padding:0}html.theme--documenter-dark table td,html.theme--documenter-dark table th{vertical-align:top}html.theme--documenter-dark table td:not([align]),html.theme--documenter-dark table th:not([align]){text-align:inherit}html.theme--documenter-dark table th{color:#cdc3e3}html.theme--documenter-dark .box{background-color:#fff;border-radius:6px;box-shadow:#bbb;color:#fbfbfb;display:block;padding:1.25rem}html.theme--documenter-dark a.box:hover,html.theme--documenter-dark a.box:focus{box-shadow:0 0.5em 1em -0.125em rgba(10,10,10,0.1),0 0 0 1px #2ad7e6}html.theme--documenter-dark a.box:active{box-shadow:inset 0 1px 2px rgba(10,10,10,0.2),0 0 0 1px #2ad7e6}html.theme--documenter-dark 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.button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#292929;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:#363636;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark 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kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#4eb5de;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#43b1dc;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #cb3c33 #cb3c33 !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:2px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#fff;border-color:#dbdbdb;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#f5f5f5;border-color:#dbdbdb;color:#7a7a7a;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:2px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#cdc3e3;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#f5f5f5;border-left:5px solid #dbdbdb;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol:not([type]).is-lower-alpha{list-style-type:lower-alpha}html.theme--documenter-dark .content ol:not([type]).is-lower-roman{list-style-type:lower-roman}html.theme--documenter-dark .content ol:not([type]).is-upper-alpha{list-style-type:upper-alpha}html.theme--documenter-dark .content ol:not([type]).is-upper-roman{list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #dbdbdb;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#cdc3e3}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#cdc3e3}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#cdc3e3}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--documenter-dark .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--documenter-dark .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--documenter-dark div.icon-text{display:flex}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--documenter-dark .image.is-4by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--documenter-dark .image.is-3by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--documenter-dark .image.is-3by2 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--documenter-dark .image.is-5by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--documenter-dark .image.is-5by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--documenter-dark .image.is-16by9 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--documenter-dark .image.is-16by9 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--documenter-dark 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#documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--documenter-dark .image.is-2by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--documenter-dark .image.is-2by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--documenter-dark .image.is-3by5 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--documenter-dark .image.is-3by5 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--documenter-dark .image.is-9by16 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--documenter-dark .image.is-9by16 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--documenter-dark .image.is-1by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by2 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span.sgr107{background-color:#f5f5f5}code.language-julia-repl>span.hljs-meta{color:#066f00;font-weight:bolder}/*! Theme: Default Description: Original highlight.js style Author: (c) Ivan Sagalaev diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index 26a6c71b..64f2dc8c 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -5,36 +5,54 @@ export CoupledSDEs CoupledSDEs(f, g, u0 [, p, σ]; kwargs...) A stochastic continuous time dynamical system defined by a set of -coupled ordinary differential equations as follows: +coupled stochastic differential equations as follows: ```math d\\vec{u} = \\vec{f}(\\vec{u}, p, t) dt + σ \\vec{g}(\\vec{u}, p, t) dW_t ``` +where +``\\sigma > 0`` is the overall noise strength, +``\\text{d}\\mathcal{W} = \\Gamma \\cdot \\text{d}\\mathcal{N}``, +and ``\\mathcal N`` denotes a stochastic process. +The (positive definite) noise covariance matrix is +``\\Sigma = \\Gamma \\Gamma^\\top \\in \\mathbb R^{N\\times N}``. -Optionally provide the overall noise strength `σ`, the parameter container `p` -and initial time as keyword `t0`. By defualt `σ=1` and `t0=0`. +Optionally you can provide a paraemter container and the overall noise strength `σ`. +and initial time as keyword `t0`. By default `p = nothing`, `σ = 1` and `t0 = 0`. For construction instructions regarding `f, u0` see the [DynamicalSystems.jl tutorial ](https://juliadynamics.github.io/DynamicalSystemsDocs.jl/dynamicalsystems/dev/tutorial/). +`g` must follow the sae syntax, i.e., `g(u, p, t)` for out-of-place (oop) and +`g(du, u, p, t)` for in-place (iip). + +## Stochastic part The stochastic part of the differential equation is defined by the function `g` and the keyword arguments `noise_rate_prototype` and `noise`. `noise` indicates the noise process applied and defaults to Gaussian white noise (Wiener process). For details on defining various noise processes, refer to [DiffEqNoiseProcess.jl ](https://docs.sciml.ai/DiffEqNoiseProcess/stable/). + `noise_rate_prototype` indicates the prototype type instance for the noise rates, i.e., the output of `g`. It can be any type which overloads `A_mul_B!` with itself being the middle argument. Commonly, this is a matrix or sparse matrix. If this is not given, it defaults to `nothing`, which means the `g` should be interpreted as being diagonal. +By combining ``\\sigma g, \\mathcal{W}``, you can define different type of stochastic +systems. Examples of different types of stochastic systems can be found on the +[StochasticDiffEq.jl tutorial page](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example/). +A quick overview of common types of stochastic systems can also be +found in the [online docs for `CoupledSDEs`](@ref defining-stochastic-dynamics). + +The noise processes ``\\mathcal{W}`` that can be used in the stochastic simulations are +obtained from [DiffEqNoiseProcess.jl](https://docs.sciml.ai/DiffEqNoiseProcess/stable). +A complete list of the available processes can be found [here](https://docs.sciml.ai/DiffEqNoiseProcess/stable/noise_processes/). + ## DifferentialEquations.jl interfacing The ODEs are evolved via the solvers of DifferentialEquations.jl. -When initializing a `CoupledODEs`, you can specify the solver that will integrate -`f` in time, along with any other integration options, using the `diffeq` keyword. -For example you could use `diffeq = (abstol = 1e-9, reltol = 1e-9)`. -If you want to specify a solver, do so by using the keyword `alg`, e.g.: -`diffeq = (alg = Tsit5(), reltol = 1e-6)`. This requires you to have been first -`using OrdinaryDiffEq` to access the solvers. The default `diffeq` is: +If you want to specify a solver, do so by using the keyword `alg`, +which requires you to be using StochasticDiffEq.jl to access the solvers. +The default `diffeq` is: ```julia (alg = SOSRI(), abstol = 1.0e-6, reltol = 1.0e-6) @@ -47,6 +65,14 @@ Dev note: `CoupledSDEs` is a light wrapper of `SDEIntegrator` from StochasticDi The integrator is available as the field `integ`, and the `SDEProblem` is `integ.sol.prob`. The convenience syntax `SDEProblem(ds::CoupledSDEs, tspan = (t0, Inf))` is available to extract the problem. + +## Converting between `CoupledSDEs` and `CoupledODEs` + +You can convert to `CoupledODEs` to analyze the deterministic part via +the function `CoupledODEs(ds::CoupledSDEs; diffeq, t0)`. +Similarly, use `CoupledSDEs(ds::CoupledODEs, g; kw...)` to convert to a stochastic system. + + """ struct CoupledSDEs{IIP,D,I,P,S} <: ContinuousTimeDynamicalSystem # D parametrised by length of u0 From 92e33691c1ac394840ddeb41215e342f43264e95 Mon Sep 17 00:00:00 2001 From: Datseris Date: Thu, 1 Aug 2024 15:01:29 +0200 Subject: [PATCH 19/38] delete ported documentation --- docs/src/CoupledSDEs.md | 19 ------------------- 1 file changed, 19 deletions(-) diff --git a/docs/src/CoupledSDEs.md b/docs/src/CoupledSDEs.md index 4d803282..a29c1b98 100644 --- a/docs/src/CoupledSDEs.md +++ b/docs/src/CoupledSDEs.md @@ -4,25 +4,6 @@ CoupledSDEs ``` - -A `CoupledSDEs` defines a stochastic dynamical system of the form - -```math -\text{d}\vec x = f(\vec x(t); \ p) \text{d}t + \sigma g(\vec x(t); \ p) \, \text{d}\mathcal{W} \ , -``` -where $\vec x \in \mathbb{R}^\text{D}$, $\sigma > 0$ is the noise strength, $\text{d}\mathcal{W}=\Gamma \cdot \text{d}\mathcal{N}$, and $\mathcal N$ denotes a stochastic process. The (positive definite) noise covariance matrix is $\Sigma = \Gamma \Gamma^\top \in \mathbb R^{N\times N}$. - -The function $f$ is the deterministic part of the system and follows the syntax of a `ContinuousTimeDynamicalSystem` in [DynamicalSystems.jl](https://juliadynamics.github.io/DynamicalSystems.jl/latest/tutorial/), i.e., `f(u, p, t)` for out-of-place (oop) and `f!(du, u, p, t)` for in-place (iip). The function $g$ allows to specify the stochastic dynamics of the system along with the [noise process](#noise-process) $\mathcal{W}$. It should be of the same type (iip or oop) as $f$. - -By combining $\sigma$, $g$ and $\mathcal{W}$, you can define different type of stochastic systems. Examples of different types of stochastic systems can be found on the [StochasticDiffEq.jl tutorial page](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example/). A quick overview of common types of stochastic systems can be found [below](#Defining-stochastic-dynamics). - -!!! info - Note that nonlinear mixings of the Noise Process $\mathcal{W}$ fall into the class of random ordinary differential equations (RODEs) and is not supported in DynamicalSystems.jl at the moment. See [DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/rode_example/) for an implementation. - -```@docs -CoupledSDEs -``` - ## [Examples defining stochastic dynamics](@id defining-stochastic-dynamics) TODO? From 548130d6c0ef077ec8b8a83ff0aaa4e9eb2a2bac Mon Sep 17 00:00:00 2001 From: oameye Date: Thu, 1 Aug 2024 15:49:57 +0200 Subject: [PATCH 20/38] fix small typos in docstring --- src/core_systems/continuous_time_sde.jl | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index 64f2dc8c..6883ac79 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -16,7 +16,7 @@ and ``\\mathcal N`` denotes a stochastic process. The (positive definite) noise covariance matrix is ``\\Sigma = \\Gamma \\Gamma^\\top \\in \\mathbb R^{N\\times N}``. -Optionally you can provide a paraemter container and the overall noise strength `σ`. +Optionally you can provide a parameter container and the overall noise strength `σ`. and initial time as keyword `t0`. By default `p = nothing`, `σ = 1` and `t0 = 0`. For construction instructions regarding `f, u0` see the [DynamicalSystems.jl tutorial @@ -37,7 +37,7 @@ the output of `g`. It can be any type which overloads `A_mul_B!` with itself bei middle argument. Commonly, this is a matrix or sparse matrix. If this is not given, it defaults to `nothing`, which means the `g` should be interpreted as being diagonal. -By combining ``\\sigma g, \\mathcal{W}``, you can define different type of stochastic +By combining ``\\sigma, g, \\mathcal{W}``, you can define different type of stochastic systems. Examples of different types of stochastic systems can be found on the [StochasticDiffEq.jl tutorial page](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example/). A quick overview of common types of stochastic systems can also be @@ -45,11 +45,11 @@ found in the [online docs for `CoupledSDEs`](@ref defining-stochastic-dynamics). The noise processes ``\\mathcal{W}`` that can be used in the stochastic simulations are obtained from [DiffEqNoiseProcess.jl](https://docs.sciml.ai/DiffEqNoiseProcess/stable). -A complete list of the available processes can be found [here](https://docs.sciml.ai/DiffEqNoiseProcess/stable/noise_processes/). +A complete list of the pre-defined processes can be found [here](https://docs.sciml.ai/DiffEqNoiseProcess/stable/noise_processes/). Note that `DiffEqNoiseProcess.jl` also has an interface for defining custom noise processes. ## DifferentialEquations.jl interfacing -The ODEs are evolved via the solvers of DifferentialEquations.jl. +The SDEs are evolved via the solvers of DifferentialEquations.jl. If you want to specify a solver, do so by using the keyword `alg`, which requires you to be using StochasticDiffEq.jl to access the solvers. The default `diffeq` is: @@ -70,7 +70,7 @@ to extract the problem. You can convert to `CoupledODEs` to analyze the deterministic part via the function `CoupledODEs(ds::CoupledSDEs; diffeq, t0)`. -Similarly, use `CoupledSDEs(ds::CoupledODEs, g; kw...)` to convert to a stochastic system. +Similarly, use `CoupledSDEs(ds::CoupledODEs, g, p; kw...)` to convert to a stochastic system. """ From 1a0c884095c8f960c398556fbd348bcd0366757d Mon Sep 17 00:00:00 2001 From: oameye Date: Thu, 1 Aug 2024 19:38:59 +0200 Subject: [PATCH 21/38] add CoupledSDEs examples to docs --- docs/Project.toml | 1 + docs/make.jl | 2 +- docs/src/CoupledSDEs.md | 112 +++++++++++++++++++++++++++++++++++++++- 3 files changed, 113 insertions(+), 2 deletions(-) diff --git a/docs/Project.toml b/docs/Project.toml index 9426585b..43e71077 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -1,5 +1,6 @@ [deps] CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" +DiffEqNoiseProcess = "77a26b50-5914-5dd7-bc55-306e6241c503" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" DocumenterTools = "35a29f4d-8980-5a13-9543-d66fff28ecb8" DynamicalSystemsBase = "6e36e845-645a-534a-86f2-f5d4aa5a06b4" diff --git a/docs/make.jl b/docs/make.jl index 6e3458b9..132efeae 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -1,7 +1,7 @@ cd(@__DIR__) using DynamicalSystemsBase -using StochasticDiffEq # to enable extention +using StochasticDiffEq, DiffEqNoiseProcess # to enable extention # We need this because Documenter doesn't know where to get the docstring from otherwise StochasticSystemsBase = Base.get_extension(DynamicalSystemsBase, :StochasticSystemsBase) diff --git a/docs/src/CoupledSDEs.md b/docs/src/CoupledSDEs.md index a29c1b98..f415f8a1 100644 --- a/docs/src/CoupledSDEs.md +++ b/docs/src/CoupledSDEs.md @@ -6,4 +6,114 @@ CoupledSDEs ## [Examples defining stochastic dynamics](@id defining-stochastic-dynamics) -TODO? +Let's look at some examples of the different types of stochastic systems that can be defined. + +For simplicity, we choose a slow exponential growth in 2 dimensions as the deterministic dynamics `f`: +```@example type +using DynamicalSystemsBase, StochasticDiffEq, DiffEqNoiseProcess +using CairoMakie +import Random # hide +Random.seed!(10) # hide +f!(du, u, p, t) = du .= 1.01u # deterministic part +idfunc!(du, u, p, t) = (du .= ones(eltype(u), length(u)); return nothing) +σ = 0.25 # noise strength + +function plot_trajectory(Y, t) + fig = Figure() + ax = Axis(fig[1,1]; xlabel = "time", ylabel = "variable") + for var in columns(Y) + lines!(ax, t, var) + end + fig +end; +``` + +### Additive noise +When $g$ is independent of the state variables $u$, the noise is called additive, otherwise it is called multiplicative. The ladder is somewhat misleading, as it has come to signify the general case, despite seeming to suggest the limited case where $g(x) \propto x$. We can define a simple additive noise system as follows: +```@example type +t0 = 0.0; W0 = zeros(2); +W = WienerProcess(t0, W0, 0.0) +sde = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise=W) +``` +which is equivalent to +```@example type +sde = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ); +``` +We defined a vector of random numbers `dW`, whose size matches the output of `g`, with the noise applied element-wise, i.e., `g.*dW`. Specifically, `dW` is a vector of Gaussian noise processes whose size matches the output of `g`. The noise is applied element-wise, i.e., `g.*dW`. By default, the noise processes are uncorrelated, meaning the covariance matrix is diagonal. This type of noise is referred to as diagonal. The vector `dW` is by default zero mean white gaussian noise $\mathcal{N}(0, \text{d}t)$ where the variance is the timestep $\text{d}t$ unit variance (Wiener Process). We can sample a trajectory from this system using the `trajectory` also used for the deterministic systems: +```@example type +tr = trajectory(sde, 1.0) +plot_trajectory(tr...) +``` + +#### Correlated noise +Correlated noise is where the random number generated in `dW` are correlated. This can be done by specifying the covariance matrix $\Sigma$ for the noise processes and passing it to a `CorrelatedWienerProcess` of `DiffEqNoiseProcess.jl`.: +```@example type +ρ = 0.3 +Σ = [1 ρ; ρ 1] +t0 = 0.0; W0 = zeros(2); Z0 = zeros(2); +W = CorrelatedWienerProcess(Σ, t0, W0, Z0) +``` +Indeed, sampling 1_000 values from this process and plotting them shows the correlation: +```@example type +prob = NoiseProblem(W, (0.0, 1.0)) +sol = solve(prob; dt = 0.1) + +output_func = (sol, i) -> (sol.dW, false) +ensemble_prob = EnsembleProblem(prob, output_func = output_func) +values = Array(solve(ensemble_prob, dt = 0.1, trajectories = 10_000)) +scatter(values[1,:], values[2,:]) +``` +The CoupledSDEs can be defined by passing the `CorrelatedWienerProcess` to the `noise` keyword: +```@example type +sde = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise=W) +``` +The covariance matrix $\Sigma$ can be accessed via `sde.integ.covariance`. + +!!! warning + Another way to define correlated noise is to use the diffusion function $g$ to define the matrix $\Sigma$. However, this is in general not recommended as the solvers from StochasticDiffEq will assume that the problem is more complicated such that the fast additive solvers like `SOSRA` and `SOSRI` will not work. + +#### Scalar noise +Scalar noise is where a single random variable is applied to all dependent variables. To do this, one has to give an one dimensional noise process to the `noise` keyword of the `CoupledSDEs` constructor. +```@example type +t0 = 0.0; W0 = 0.0; +noise = WienerProcess(t0, W0, 0.0) +sde = CoupledSDEs(f!, idfunc!, rand(2)/10, nothing, σ; noise=noise) + +tr = trajectory(sde, 1.0) +plot_trajectory(tr...) +``` +We can see that noise applied to each variable is the same. + + +### Multiplicative and non-autonomous noise +Multiplicative noise in the SciML ecosystem is defined as when $g_i(t, u)=a_i u$. However, in the literature the name is sometimes used for when the noise is not-additive, including nonlinear. In general, we can make the noise time- and state-dependent in a similar fashion to the deterministic dynamics. For example, we can define a system with decreasing multiplicative noise as follows: +```@example type +function g!(du, u, p, t) + du .= u ./ (1+t) + return nothing +end +sde = CoupledSDEs(f!, g!, rand(2)./10, (), 1) +``` + +#### Non-diagonal noise +Non-diagonal noise allows for the terms to linearly mixed via `g` being a matrix. Suppose we have two Wiener processes and two dependent random variables such that the output of `g` is a 2x2 matrix. Therefore, we have +```math +du_1 = f_1(u,p,t)dt + g_{11}(u,p,t)dW_1 + g_{12}(u,p,t)dW_2 \\ +du_2 = f_2(u,p,t)dt + g_{21}(u,p,t)dW_1 + g_{22}(u,p,t)dW_2 +``` +To indicate the structure that `g` should have, we can use the `noise_rate_prototype` keyword. Let us define a special type of non-diagonal noise called commutative noise. For this we can utilize the `RKMilCommute` algorithm which is designed to utilise the structure of commutative noise. + +```@example type +function g(du, u, p, t) + du[1,1] = σ*u[1] + du[2,1] = σ*u[2] + du[1,2] = σ*u[1] + du[2,2] = σ*u[2] + return nothing +end +diffeq = (alg = RKMilCommute(), reltol = 1e-3, abstol = 1e-3) +sde = CoupledSDEs(f!, g, rand(2)./10, noise_rate_prototype = zeros(2, 2), diffeq = diffeq) +``` + +!!! warning + Non-diagonal problems need specific type of solvers. See the [SciML recommendations](https://docs.sciml.ai/DiffEqDocs/stable/solvers/sde_solve/#sde_solve). From 413a25adba56c80885a8b6a383c50aba73708ba0 Mon Sep 17 00:00:00 2001 From: oameye Date: Sat, 3 Aug 2024 20:05:05 +0200 Subject: [PATCH 22/38] remove noise strength --- ext/src/CoupledSDEs.jl | 111 +++++++++--------------- src/core_systems/continuous_time_sde.jl | 22 +++-- 2 files changed, 52 insertions(+), 81 deletions(-) diff --git a/ext/src/CoupledSDEs.jl b/ext/src/CoupledSDEs.jl index 02d249f4..57e070a0 100644 --- a/ext/src/CoupledSDEs.jl +++ b/ext/src/CoupledSDEs.jl @@ -3,8 +3,8 @@ ########################################################################################### const DEFAULT_SDE_SOLVER = SOSRI() # default sciml solver -const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol = 1e-2, reltol = 1e-2) # default sciml tol -const DEFAULT_STOCH_DIFFEQ = (alg = DEFAULT_SDE_SOLVER, DEFAULT_STOCH_DIFFEQ_KWARGS...) +const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol=1e-2, reltol=1e-2) # default sciml tol +const DEFAULT_STOCH_DIFFEQ = (alg=DEFAULT_SDE_SOLVER, DEFAULT_STOCH_DIFFEQ_KWARGS...) # Function from user `@xlxs4`, see # https://github.com/JuliaDynamics/jl/pull/153 @@ -21,19 +21,18 @@ end ########################################################################################### function DynamicalSystemsBase.CoupledSDEs( - f, - g, - u0, - p = SciMLBase.NullParameters(), - noise_strength = 1.0; - t0 = 0.0, - diffeq = DEFAULT_STOCH_DIFFEQ, - noise_rate_prototype = nothing, - noise = nothing, - seed = UInt64(0) + f, + g, + u0, + p=SciMLBase.NullParameters(); + t0=0.0, + diffeq=DEFAULT_STOCH_DIFFEQ, + noise_rate_prototype=nothing, + noise=nothing, + seed=UInt64(0) ) IIP = isinplace(f, 4) # from SciMLBase - @assert IIP==isinplace(g, 4) "f and g must both be in-place or out-of-place" + @assert IIP == isinplace(g, 4) "f and g must both be in-place or out-of-place" s = correct_state(Val{IIP}(), u0) T = eltype(s) @@ -43,21 +42,21 @@ function DynamicalSystemsBase.CoupledSDEs( s, (T(t0), T(Inf)), p; - noise_rate_prototype = noise_rate_prototype, - noise = noise, - seed = seed + noise_rate_prototype=noise_rate_prototype, + noise=noise, + seed=seed ) - return CoupledSDEs(prob, diffeq, noise_strength) + return CoupledSDEs(prob, diffeq) end function DynamicalSystemsBase.CoupledSDEs( - prob::SDEProblem, diffeq = DEFAULT_STOCH_DIFFEQ, noise_strength = 1.0; special_kwargs... + prob::SDEProblem, diffeq=DEFAULT_STOCH_DIFFEQ; special_kwargs... ) if haskey(special_kwargs, :diffeq) throw( ArgumentError( - "`diffeq` is given as positional argument when an ODEProblem is provided." - ), + "`diffeq` is given as positional argument when an ODEProblem is provided." + ), ) end IIP = isinplace(prob) # from SciMLBase @@ -66,10 +65,8 @@ function DynamicalSystemsBase.CoupledSDEs( if prob.tspan === (nothing, nothing) # If the problem was made via MTK, it is possible to not have a default timespan. U = eltype(prob.u0) - prob = SciMLBase.remake(prob; tspan = (U(0), U(Inf))) + prob = SciMLBase.remake(prob; tspan=(U(0), U(Inf))) end - sde_function = SDEFunction(prob.f, add_noise_strength(noise_strength, prob.g, IIP)) - prob = SciMLBase.remake(prob; f = sde_function) noise_type = find_noise_type(prob, IIP) solver, remaining = _decompose_into_sde_solver_and_remaining(diffeq) @@ -78,15 +75,15 @@ function DynamicalSystemsBase.CoupledSDEs( solver; remaining..., # Integrators are used exclusively iteratively. There is no reason to save anything. - save_start = false, - save_end = false, - save_everystep = false, + save_start=false, + save_end=false, + save_everystep=false, # DynamicalSystems.jl operates on integrators and `step!` exclusively, # so there is no reason to limit the maximum time evolution - maxiters = Inf + maxiters=Inf ) - return CoupledSDEs{IIP, D, typeof(integ), P, true}( - integ, deepcopy(prob.p), noise_strength, diffeq, noise_type + return CoupledSDEs{IIP,D,typeof(integ),P}( + integ, deepcopy(prob.p), diffeq, noise_type ) end @@ -98,25 +95,23 @@ Converts a [`CoupledODEs` system into a [`CoupledSDEs`](@ref). """ function DynamicalSystemsBase.CoupledSDEs( - ds::CoupledODEs, - g, - p, # the parameter is likely changed as the diffusion function g is added. - noise_strength = 1.0; - diffeq = DEFAULT_STOCH_DIFFEQ, - noise_rate_prototype = nothing, - noise = nothing, - seed = UInt64(0) + ds::CoupledODEs, + g, + p; # the parameter is likely changed as the diffusion function g is added. + diffeq=DEFAULT_STOCH_DIFFEQ, + noise_rate_prototype=nothing, + noise=nothing, + seed=UInt64(0) ) return CoupledSDEs( dynamic_rule(ds), g, current_state(ds), - p, - noise_strength; - diffeq = diffeq, - noise_rate_prototype = noise_rate_prototype, - noise = noise, - seed = seed + p; + diffeq=diffeq, + noise_rate_prototype=noise_rate_prototype, + noise=noise, + seed=seed ) end @@ -126,10 +121,10 @@ end Converts a [`CoupledSDEs`](@ref) into [`CoupledODEs`](@ref). """ function DynamicalSystemsBase.CoupledODEs( - sys::CoupledSDEs; diffeq = DEFAULT_DIFFEQ, t0 = 0.0) + sys::CoupledSDEs; diffeq=DEFAULT_DIFFEQ, t0=0.0) return CoupledODEs( dynamic_rule(sys), SVector{length(sys.integ.u)}(sys.integ.u), sys.p0; - diffeq = diffeq, t0 = t0 + diffeq=diffeq, t0=t0 ) end @@ -137,7 +132,6 @@ end function DynamicalSystemsBase.additional_details(ds::CoupledSDEs) solver, remaining = _decompose_into_sde_solver_and_remaining(ds.diffeq) return [ - "Noise strength" => ds.noise_strength, "SDE solver" => string(nameof(typeof(solver))), "SDE kwargs" => remaining, "Noise type" => ds.noise_type @@ -149,7 +143,7 @@ end ########################################################################################### SciMLBase.isinplace(::CoupledSDEs{IIP}) where {IIP} = IIP -StateSpaceSets.dimension(::CoupledSDEs{IIP, D}) where {IIP, D} = D +StateSpaceSets.dimension(::CoupledSDEs{IIP,D}) where {IIP,D} = D DynamicalSystemsBase.current_state(ds::CoupledSDEs) = current_state(ds.integ) DynamicalSystemsBase.isdeterministic(ds::CoupledSDEs) = false @@ -169,7 +163,7 @@ function DynamicalSystemsBase.set_state!(ds::CoupledSDEs, u::AbstractArray) end SciMLBase.step!(ds::CoupledSDEs, args...) = (step!(ds.integ, args...); ds) -# TODO We have to check if for SDEIntegrators a different step interruption is possible. +# TODO We have to check if for SDEIntegrators a different step ReturnCode is possible. function DynamicalSystemsBase.successful_step(integ::AbstractSDEIntegrator) rcode = integ.sol.retcode return rcode == SciMLBase.ReturnCode.Default || rcode == SciMLBase.ReturnCode.Success @@ -183,24 +177,3 @@ function DynamicalSystemsBase.set_parameter!(ds::CoupledSDEs, args...) end DynamicalSystemsBase.referrenced_sciml_prob(ds::CoupledSDEs) = ds.integ.sol.prob - -########################################################################################### -# Utilities -########################################################################################### - -function σg(σ, g) - return (u, p, t) -> σ .* g(u, p, t) -end - -function σg!(σ, g!) - function (du, u, p, t) - g!(du, u, p, t) - du .*= σ - return nothing - end -end - -function add_noise_strength(σ, g, IIP) - newg = IIP ? σg!(σ, g) : σg(σ, g) - return newg -end diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index 6883ac79..47577e76 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -2,22 +2,21 @@ export CoupledSDEs """ CoupledSDEs <: ContinuousTimeDynamicalSystem - CoupledSDEs(f, g, u0 [, p, σ]; kwargs...) + CoupledSDEs(f, g, u0 [, p]; kwargs...) A stochastic continuous time dynamical system defined by a set of coupled stochastic differential equations as follows: ```math -d\\vec{u} = \\vec{f}(\\vec{u}, p, t) dt + σ \\vec{g}(\\vec{u}, p, t) dW_t +d\\vec{u} = \\vec{f}(\\vec{u}, p, t) dt + \\vec{g}(\\vec{u}, p, t) dW_t ``` where -``\\sigma > 0`` is the overall noise strength, ``\\text{d}\\mathcal{W} = \\Gamma \\cdot \\text{d}\\mathcal{N}``, and ``\\mathcal N`` denotes a stochastic process. The (positive definite) noise covariance matrix is ``\\Sigma = \\Gamma \\Gamma^\\top \\in \\mathbb R^{N\\times N}``. -Optionally you can provide a parameter container and the overall noise strength `σ`. -and initial time as keyword `t0`. By default `p = nothing`, `σ = 1` and `t0 = 0`. +Optionally you can provide a parameter container and initial time as keyword `t0`. +By default `p = nothing`, and `t0 = 0`. For construction instructions regarding `f, u0` see the [DynamicalSystems.jl tutorial ](https://juliadynamics.github.io/DynamicalSystemsDocs.jl/dynamicalsystems/dev/tutorial/). @@ -37,15 +36,16 @@ the output of `g`. It can be any type which overloads `A_mul_B!` with itself bei middle argument. Commonly, this is a matrix or sparse matrix. If this is not given, it defaults to `nothing`, which means the `g` should be interpreted as being diagonal. -By combining ``\\sigma, g, \\mathcal{W}``, you can define different type of stochastic -systems. Examples of different types of stochastic systems can be found on the +By combining ``g`` and ``\\mathcal{W}``, you can define different type of stochastic systems. +Examples of different types of stochastic systems can be found on the [StochasticDiffEq.jl tutorial page](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example/). A quick overview of common types of stochastic systems can also be found in the [online docs for `CoupledSDEs`](@ref defining-stochastic-dynamics). The noise processes ``\\mathcal{W}`` that can be used in the stochastic simulations are obtained from [DiffEqNoiseProcess.jl](https://docs.sciml.ai/DiffEqNoiseProcess/stable). -A complete list of the pre-defined processes can be found [here](https://docs.sciml.ai/DiffEqNoiseProcess/stable/noise_processes/). Note that `DiffEqNoiseProcess.jl` also has an interface for defining custom noise processes. +A complete list of the pre-defined processes can be found [here](https://docs.sciml.ai/DiffEqNoiseProcess/stable/noise_processes/). +Note that `DiffEqNoiseProcess.jl` also has an interface for defining custom noise processes. ## DifferentialEquations.jl interfacing @@ -55,7 +55,7 @@ which requires you to be using StochasticDiffEq.jl to access the solvers. The default `diffeq` is: ```julia -(alg = SOSRI(), abstol = 1.0e-6, reltol = 1.0e-6) +(alg = SOSRI(), abstol = 1.0e-2, reltol = 1.0e-2) ``` `diffeq` keywords can also include `callback` for [event handling @@ -74,13 +74,11 @@ Similarly, use `CoupledSDEs(ds::CoupledODEs, g, p; kw...)` to convert to a stoch """ -struct CoupledSDEs{IIP,D,I,P,S} <: ContinuousTimeDynamicalSystem +struct CoupledSDEs{IIP,D,I,P} <: ContinuousTimeDynamicalSystem # D parametrised by length of u0 - # S indicated if the noise strength has been added to the diffusion function integ::I # things we can't recover from `integ` p0::P - noise_strength diffeq # isn't parameterized because it is only used for display noise_type::NamedTuple end From 381820f28703e108ce37a6979500bc739c0cbc5e Mon Sep 17 00:00:00 2001 From: oameye Date: Sun, 4 Aug 2024 08:43:26 +0200 Subject: [PATCH 23/38] update docs with no noise strength --- docs/src/CoupledSDEs.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/docs/src/CoupledSDEs.md b/docs/src/CoupledSDEs.md index f415f8a1..4d3a4d0c 100644 --- a/docs/src/CoupledSDEs.md +++ b/docs/src/CoupledSDEs.md @@ -33,11 +33,11 @@ When $g$ is independent of the state variables $u$, the noise is called additive ```@example type t0 = 0.0; W0 = zeros(2); W = WienerProcess(t0, W0, 0.0) -sde = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise=W) +sde = CoupledSDEs(f!, idfunc!, zeros(2); noise=W) ``` which is equivalent to ```@example type -sde = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ); +sde = CoupledSDEs(f!, idfunc!, zeros(2)); ``` We defined a vector of random numbers `dW`, whose size matches the output of `g`, with the noise applied element-wise, i.e., `g.*dW`. Specifically, `dW` is a vector of Gaussian noise processes whose size matches the output of `g`. The noise is applied element-wise, i.e., `g.*dW`. By default, the noise processes are uncorrelated, meaning the covariance matrix is diagonal. This type of noise is referred to as diagonal. The vector `dW` is by default zero mean white gaussian noise $\mathcal{N}(0, \text{d}t)$ where the variance is the timestep $\text{d}t$ unit variance (Wiener Process). We can sample a trajectory from this system using the `trajectory` also used for the deterministic systems: ```@example type @@ -65,7 +65,7 @@ scatter(values[1,:], values[2,:]) ``` The CoupledSDEs can be defined by passing the `CorrelatedWienerProcess` to the `noise` keyword: ```@example type -sde = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise=W) +sde = CoupledSDEs(f!, idfunc!, zeros(2); noise=W) ``` The covariance matrix $\Sigma$ can be accessed via `sde.integ.covariance`. @@ -77,7 +77,7 @@ Scalar noise is where a single random variable is applied to all dependent varia ```@example type t0 = 0.0; W0 = 0.0; noise = WienerProcess(t0, W0, 0.0) -sde = CoupledSDEs(f!, idfunc!, rand(2)/10, nothing, σ; noise=noise) +sde = CoupledSDEs(f!, idfunc!, rand(2)/10; noise=noise) tr = trajectory(sde, 1.0) plot_trajectory(tr...) @@ -92,7 +92,7 @@ function g!(du, u, p, t) du .= u ./ (1+t) return nothing end -sde = CoupledSDEs(f!, g!, rand(2)./10, (), 1) +sde = CoupledSDEs(f!, g!, rand(2)./10) ``` #### Non-diagonal noise @@ -112,7 +112,7 @@ function g(du, u, p, t) return nothing end diffeq = (alg = RKMilCommute(), reltol = 1e-3, abstol = 1e-3) -sde = CoupledSDEs(f!, g, rand(2)./10, noise_rate_prototype = zeros(2, 2), diffeq = diffeq) +sde = CoupledSDEs(f!, g, rand(2)./10; noise_rate_prototype = zeros(2, 2), diffeq = diffeq) ``` !!! warning From cb956e86b6fd69a2f73580456a26025441e3dafb Mon Sep 17 00:00:00 2001 From: oameye Date: Mon, 5 Aug 2024 11:19:36 +0200 Subject: [PATCH 24/38] add covariance kwarg and change g to kwarg --- ext/StochasticSystemsBase.jl | 11 +-- ext/src/CoupledSDEs.jl | 125 ++++++++++++++++++---------- ext/src/classification.jl | 95 ++++++++++++++------- test/stochastic.jl | 65 +++++++++++---- test/stochastic_characterisation.jl | 60 +++++++------ 5 files changed, 227 insertions(+), 129 deletions(-) diff --git a/ext/StochasticSystemsBase.jl b/ext/StochasticSystemsBase.jl index 8c581d90..6d56d2a7 100644 --- a/ext/StochasticSystemsBase.jl +++ b/ext/StochasticSystemsBase.jl @@ -1,12 +1,13 @@ module StochasticSystemsBase using DynamicalSystemsBase: DynamicalSystemsBase, SciMLBase, correct_state, CoupledODEs, - CoupledSDEs, StateSpaceSets, isinplace, _delete, set_parameter!, - set_state!, dynamic_rule, isdeterministic, current_state, - DynamicalSystemsBase, _set_parameter!, u_modified!, - additional_details, referrenced_sciml_prob, DEFAULT_DIFFEQ, SVector + CoupledSDEs, StateSpaceSets, isinplace, _delete, set_parameter!, + set_state!, dynamic_rule, isdeterministic, current_state, + DynamicalSystemsBase, _set_parameter!, u_modified!, + additional_details, referrenced_sciml_prob, DEFAULT_DIFFEQ, + SVector, SMatrix using SciMLBase: SDEProblem, AbstractSDEIntegrator, __init, SDEFunction, step! -using StochasticDiffEq: SOSRI +using StochasticDiffEq: SOSRA using LinearAlgebra include("src/CoupledSDEs.jl") diff --git a/ext/src/CoupledSDEs.jl b/ext/src/CoupledSDEs.jl index 57e070a0..5e8bfb77 100644 --- a/ext/src/CoupledSDEs.jl +++ b/ext/src/CoupledSDEs.jl @@ -1,10 +1,12 @@ +using LinearAlgebra: LinearAlgebra + ########################################################################################### # DiffEq options ########################################################################################### - -const DEFAULT_SDE_SOLVER = SOSRI() # default sciml solver -const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol=1e-2, reltol=1e-2) # default sciml tol -const DEFAULT_STOCH_DIFFEQ = (alg=DEFAULT_SDE_SOLVER, DEFAULT_STOCH_DIFFEQ_KWARGS...) +# SOSRI is only applicable for diagonal noise +const DEFAULT_SDE_SOLVER = SOSRA() # default sciml solver for adapitve non-diagonal noise +const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol = 1e-2, reltol = 1e-2) # default sciml tol +const DEFAULT_STOCH_DIFFEQ = (alg = DEFAULT_SDE_SOLVER, DEFAULT_STOCH_DIFFEQ_KWARGS...) # Function from user `@xlxs4`, see # https://github.com/JuliaDynamics/jl/pull/153 @@ -21,18 +23,25 @@ end ########################################################################################### function DynamicalSystemsBase.CoupledSDEs( - f, - g, - u0, - p=SciMLBase.NullParameters(); - t0=0.0, - diffeq=DEFAULT_STOCH_DIFFEQ, - noise_rate_prototype=nothing, - noise=nothing, - seed=UInt64(0) + f, + u0, + p = SciMLBase.NullParameters(); + g = nothing, + covariance = nothing, + t0 = 0.0, + diffeq = DEFAULT_STOCH_DIFFEQ, + noise_prototype = nothing, + noise = nothing, + seed = UInt64(0) ) IIP = isinplace(f, 4) # from SciMLBase - @assert IIP == isinplace(g, 4) "f and g must both be in-place or out-of-place" + if !isnothing(g) + @assert IIP==isinplace(g, 4) "f and g must both be in-place or out-of-place" + end + + noise_type, cov = find_noise_type(g, u0, p, t0, noise, covariance, noise_prototype, IIP) + g, noise_prototype = construct_diffusion_function( + g, cov, noise_prototype, length(u0), IIP) s = correct_state(Val{IIP}(), u0) T = eltype(s) @@ -42,21 +51,21 @@ function DynamicalSystemsBase.CoupledSDEs( s, (T(t0), T(Inf)), p; - noise_rate_prototype=noise_rate_prototype, - noise=noise, - seed=seed + noise_rate_prototype = noise_prototype, + noise = noise, + seed = seed ) - return CoupledSDEs(prob, diffeq) + return CoupledSDEs(prob, diffeq, noise_type) end function DynamicalSystemsBase.CoupledSDEs( - prob::SDEProblem, diffeq=DEFAULT_STOCH_DIFFEQ; special_kwargs... + prob::SDEProblem, diffeq = DEFAULT_STOCH_DIFFEQ, noise_type = nothing; special_kwargs... ) if haskey(special_kwargs, :diffeq) throw( ArgumentError( - "`diffeq` is given as positional argument when an ODEProblem is provided." - ), + "`diffeq` is given as positional argument when an ODEProblem is provided." + ), ) end IIP = isinplace(prob) # from SciMLBase @@ -65,9 +74,11 @@ function DynamicalSystemsBase.CoupledSDEs( if prob.tspan === (nothing, nothing) # If the problem was made via MTK, it is possible to not have a default timespan. U = eltype(prob.u0) - prob = SciMLBase.remake(prob; tspan=(U(0), U(Inf))) + prob = SciMLBase.remake(prob; tspan = (U(0), U(Inf))) + end + if isnothing(noise_type) + noise_type, _ = find_noise_type(prob, IIP) end - noise_type = find_noise_type(prob, IIP) solver, remaining = _decompose_into_sde_solver_and_remaining(diffeq) integ = __init( @@ -75,14 +86,14 @@ function DynamicalSystemsBase.CoupledSDEs( solver; remaining..., # Integrators are used exclusively iteratively. There is no reason to save anything. - save_start=false, - save_end=false, - save_everystep=false, + save_start = false, + save_end = false, + save_everystep = false, # DynamicalSystems.jl operates on integrators and `step!` exclusively, # so there is no reason to limit the maximum time evolution - maxiters=Inf + maxiters = Inf ) - return CoupledSDEs{IIP,D,typeof(integ),P}( + return CoupledSDEs{IIP, D, typeof(integ), P}( integ, deepcopy(prob.p), diffeq, noise_type ) end @@ -95,23 +106,25 @@ Converts a [`CoupledODEs` system into a [`CoupledSDEs`](@ref). """ function DynamicalSystemsBase.CoupledSDEs( - ds::CoupledODEs, - g, - p; # the parameter is likely changed as the diffusion function g is added. - diffeq=DEFAULT_STOCH_DIFFEQ, - noise_rate_prototype=nothing, - noise=nothing, - seed=UInt64(0) + ds::CoupledODEs, + p; # the parameter is likely changed as the diffusion function g is added. + g = nothing, + covariance = nothing, + diffeq = DEFAULT_STOCH_DIFFEQ, + noise_prototype = nothing, + noise = nothing, + seed = UInt64(0) ) return CoupledSDEs( dynamic_rule(ds), - g, current_state(ds), p; - diffeq=diffeq, - noise_rate_prototype=noise_rate_prototype, - noise=noise, - seed=seed + g = g, + covariance = covariance, + diffeq = diffeq, + noise_prototype = noise_prototype, + noise = noise, + seed = seed ) end @@ -121,10 +134,10 @@ end Converts a [`CoupledSDEs`](@ref) into [`CoupledODEs`](@ref). """ function DynamicalSystemsBase.CoupledODEs( - sys::CoupledSDEs; diffeq=DEFAULT_DIFFEQ, t0=0.0) + sys::CoupledSDEs; diffeq = DEFAULT_DIFFEQ, t0 = 0.0) return CoupledODEs( dynamic_rule(sys), SVector{length(sys.integ.u)}(sys.integ.u), sys.p0; - diffeq=diffeq, t0=t0 + diffeq = diffeq, t0 = t0 ) end @@ -138,12 +151,38 @@ function DynamicalSystemsBase.additional_details(ds::CoupledSDEs) ] end +""" +https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#The-uniform-scaling-operator +""" +function construct_diffusion_function(g, cov, noise_prototype, D, IIP) + if isnothing(g) # diagonal additive noise + cov = isnothing(cov) ? LinearAlgebra.I(D) : cov + if IIP + if isdiag(cov) + g = (du, u, p, t) -> du .= diag(cov) + else + g = (du, u, p, t) -> du .= cov + noise_prototype = zeros(size(cov)) + # ^ we could make this sparse to make it more performant + end + else + if isdiag(cov) + g = (u, p, t) -> SVector{length(diag(cov)), eltype(cov)}(diag(cov)) + else + g = (u, p, t) -> SMatrix{size(cov)..., eltype(cov)}(cov) + noise_prototype = zeros(size(cov)) + end + end + end + return g, noise_prototype +end + ########################################################################################### # API - obtaining information from the system ########################################################################################### SciMLBase.isinplace(::CoupledSDEs{IIP}) where {IIP} = IIP -StateSpaceSets.dimension(::CoupledSDEs{IIP,D}) where {IIP,D} = D +StateSpaceSets.dimension(::CoupledSDEs{IIP, D}) where {IIP, D} = D DynamicalSystemsBase.current_state(ds::CoupledSDEs) = current_state(ds.integ) DynamicalSystemsBase.isdeterministic(ds::CoupledSDEs) = false diff --git a/ext/src/classification.jl b/ext/src/classification.jl index e2cc224e..60af9932 100644 --- a/ext/src/classification.jl +++ b/ext/src/classification.jl @@ -5,8 +5,8 @@ function is_state_independent(g, u, p, t) val = map(u -> g(u, p, t), rdm_states) length(unique(val)) == 1 end -function is_time_independent(g, u, p) - trange = 0:0.1:1 +function is_time_independent(g, u, p, t0) + trange = t0:0.1:10 val = map(t -> g(u, p, t), trange) length(unique(val)) == 1 end @@ -18,51 +18,84 @@ function is_linear(f, x, y, c) return check1 && check2 end -function find_noise_type(prob::SDEProblem, IIP) - noise = prob.noise - noise_rate_prototype = prob.noise_rate_prototype - noise_rate_size = isnothing(noise_rate_prototype) ? nothing : size(noise_rate_prototype) - covariance = isnothing(noise) ? nothing : noise.covariance - param = prob.p - u0 = prob.u0 +""" +We classify the noise type of the CoupledSDEs based on the properties given by the user. +In doing this we also determine the covariance matrix + +""" +function find_noise_type(g, u0, p, t0, noise, covariance, noise_prototype, IIP) + noise_size = isnothing(noise_prototype) ? nothing : size(noise_prototype) + noise_cov = isnothing(noise) ? nothing : noise.covariance D = length(u0) + if !isnothing(noise_cov) + throw( + ArgumentError("CoupledSDEs does not support correlation between noise processes through DiffEqNoiseProcess.jl interface. Instead, use the `covariance` kwarg of `CoupledSDEs`.") + ) + end + isadditive = false isautonomous = false islinear = false isinvertible = false - function g(u, p, t) + function diffusion(u, p, t) if IIP - du = deepcopy(isnothing(noise_rate_prototype) ? u : noise_rate_prototype) - prob.g(du, u, p, t) + du = deepcopy(isnothing(noise_prototype) ? u : noise_prototype) + g(du, u, p, t) return du else - return prob.g(u, p, t) + return g(u, p, t) end end - time_independent = is_time_independent(g, rand(D), param) - state_independent = is_state_independent(g, u0, param, 1.0) - # additive noise is equal to state independent noise - isadditive = state_independent - isautonomous = time_independent - islinear = !state_independent ? - is_linear(u -> g(u, param, 1.0), rand(D), rand(D), 2.0) : true - - if time_independent && state_independent - if noise_rate_size == (D, D) && !isnothing(covariance) - error("The diffusion function `g` acts as an covariance matrix but the noise process W also has a covariance matrix. This is ambiguous.") - elseif noise_rate_size == (D, D) && isnothing(covariance) - covariance = g(zeros(D), param, 0.0) + if isnothing(g) + isadditive = true + isautonomous = true + islinear = true + if isnothing(covariance) + covariance = LinearAlgebra.I(D) + isinvertible = true + else isinvertible = is_invertible(covariance) - elseif !isnothing(noise_rate_size) && noise_rate_size != (D, D) - isinvertible = false + end + elseif !isnothing(covariance) + throw( + ArgumentError("Both `g` and `covariance` are provided. Instead opt to encode the covariance in the difussion function `g` with the `noise_prototype` kwarg.") + ) + else + time_independent = is_time_independent(diffusion, rand(D), p, t0) + state_independent = is_state_independent(diffusion, u0, p, t0) + + # additive noise is equal to state independent noise + isadditive = state_independent + isautonomous = time_independent + islinear = !state_independent ? + is_linear(u -> diffusion(u, p, t0), rand(D), rand(D), 2.0) : true + + if time_independent && state_independent + if !isnothing(noise_size) && isequal(noise_size...) + covariance = diffusion(zeros(D), p, 0.0) + isinvertible = is_invertible(covariance) + elseif !isnothing(noise_size) && !isequal(noise_size...) + isinvertible = false + covariance = nothing + else + isinvertible = true + covariance = LinearAlgebra.I(D) + end else - isinvertible = isnothing(covariance) || is_invertible(covariance) + covariance = nothing end end - return (additive = isadditive, autonomous = isautonomous, + noise_type = (additive = isadditive, autonomous = isautonomous, linear = islinear, invertible = isinvertible) -end # function + return noise_type, covariance +end + +function find_noise_type(prob::SDEProblem, IIP) + find_noise_type( + prob.g, prob.u0, prob.p, prob.tspan[1], prob.noise, + nothing, prob.noise_rate_prototype, IIP) +end diff --git a/test/stochastic.jl b/test/stochastic.jl index 1693cdea..2b6d677b 100644 --- a/test/stochastic.jl +++ b/test/stochastic.jl @@ -1,9 +1,10 @@ using DynamicalSystemsBase, Test using OrdinaryDiffEq: Tsit5 -using StochasticDiffEq: SDEProblem, SRA, SRI, SOSRI +using StochasticDiffEq: SDEProblem, SRA, SRA, SOSRA, CorrelatedWienerProcess include("test_system_function.jl") + # Creation of lorenz @inbounds function lorenz_rule(u, p, t) σ = p[1]; ρ = p[2]; β = p[3] @@ -30,30 +31,30 @@ end diagonal_noise(σ) = (u, p, t) -> SVector{3}(σ, σ, σ) u0 = [0, 10.0, 0] -p0 = [10, 28, 8/3] +p0 = [10, 28, 8 / 3] # diagonal additive noise -lorenz_oop = CoupledSDEs(lorenz_rule, diagonal_noise(σ), u0, p0) -lorenz_iip = CoupledSDEs(SDEProblem(lorenz_rule_iip, diagonal_noise!(σ), copy(u0), (0.0, Inf), p0)) -lorenz_SRA = CoupledSDEs(lorenz_rule, diagonal_noise(σ), u0, p0; - diffeq = (alg = SRA(), abstol = 1e-6, reltol = 1e-6) +lorenz_oop = CoupledSDEs(lorenz_rule, u0, p0) +lorenz_iip = CoupledSDEs(SDEProblem( + lorenz_rule_iip, diagonal_noise!(σ), copy(u0), (0.0, Inf), p0)) +lorenz_SRA = CoupledSDEs(lorenz_rule, u0, p0; + diffeq = (alg = SRA(), abstol = 1e-2, reltol = 1e-2) ) for (ds, iip) in zip((lorenz_oop, lorenz_iip, lorenz_SRA), (false, true, false)) - name = (ds === lorenz_SRA) ? "lorSRA" : "lorenz" @testset "$(name) IIP=$(iip)" begin @test dynamic_rule(ds) == (iip ? lorenz_rule_iip : lorenz_rule) - test_dynamical_system(ds, u0, p0; idt = false, iip=iip) + test_dynamical_system(ds, u0, p0; idt = false, iip = iip) end end @testset "correct SDE propagation" begin - lorenz_oop = CoupledSDEs(lorenz_rule, diagonal_noise(σ), u0, p0) - @test lorenz_oop.integ.alg isa SOSRI + lorenz_oop = CoupledSDEs(lorenz_rule, u0, p0) + @test lorenz_oop.integ.alg isa SOSRA - lorenz_SRA = CoupledSDEs(lorenz_rule, diagonal_noise(σ), u0, p0; - diffeq = (alg = SRA(), abstol = 1e-3, reltol = 1e-3, verbose=false) + lorenz_SRA = CoupledSDEs(lorenz_rule, u0, p0; + diffeq = (alg = SRA(), abstol = 1e-3, reltol = 1e-3, verbose = false) ) @test lorenz_SRA.integ.alg isa SRA @test lorenz_SRA.integ.opts.verbose == false @@ -61,20 +62,48 @@ end # also test SDEproblem creation prob = lorenz_SRA.integ.sol.prob - ds = CoupledSDEs(prob, (alg=SRI(), abstol=0.0, reltol=1e-6, verbose=false)) + ds = CoupledSDEs(prob, (alg = SRA(), abstol = 0.0, reltol = 1e-3, verbose = false)) - @test ds.integ.alg isa SRI + @test ds.integ.alg isa SRA @test ds.integ.opts.verbose == false - @test_throws ArgumentError CoupledSDEs(prob; diffeq = (alg=SRI(), )) + @test_throws ArgumentError CoupledSDEs(prob; diffeq = (alg = SRA(),)) # CoupledODEs creation ds = CoupledODEs(lorenz_oop) @test dynamic_rule(ds) == lorenz_rule @test ds.integ.alg isa Tsit5 - test_dynamical_system(ds, u0, p0; idt = false, iip=false) + test_dynamical_system(ds, u0, p0; idt = false, iip = false) # and back - sde = CoupledSDEs(ds, diagonal_noise(σ), p0) + sde = CoupledSDEs(ds, p0) @test dynamic_rule(sde) == lorenz_rule - @test sde.integ.alg isa SOSRI + @test sde.integ.alg isa SOSRA +end + +@testset "interface" begin + f(u, p, t) = 1.01u + f!(du, u, p, t) = du .= 1.01u + @testset "covariance" begin + g(u, p, t) = [1 0.3; 0.3 1] + corr = CoupledSDEs(f, zeros(2); covariance = [1 0.3; 0.3 1]) + corr_alt = CoupledSDEs(f, zeros(2); g = g, noise_prototype = zeros(2, 2)) + @test corr.noise_type == corr_alt.noise_type + @test all(corr.integ.g(zeros(2), (), 0.0) .== corr_alt.integ.g(zeros(2), (), 0.0)) + end + + @testset "ArgumentError" begin + W = CorrelatedWienerProcess([1 0.3; 0.3 1], 0.0, zeros(2), zeros(2)) + @test_throws ArgumentError CoupledSDEs(f!, zeros(2); noise = W) + + g!(du, u, p, t) = du .= u + @test_throws ArgumentError CoupledSDEs( + f!, zeros(2); g = g!, covariance = [1 0.3; 0.3 1]) + + g(u, p, t) = u + @test_throws AssertionError CoupledSDEs(f!, zeros(2); g = g) + + Csde = CoupledSDEs(f!, zeros(2)) + diffeq = (alg = SRA(), abstol = 1e-2, reltol = 1e-2) + @test_throws ArgumentError CoupledSDEs(Csde.integ.sol.prob; diffeq = diffeq) + end end diff --git a/test/stochastic_characterisation.jl b/test/stochastic_characterisation.jl index 508369d2..7553ac46 100644 --- a/test/stochastic_characterisation.jl +++ b/test/stochastic_characterisation.jl @@ -1,93 +1,89 @@ using DynamicalSystemsBase, DiffEqNoiseProcess, Test, StochasticDiffEq -f!(du, u, p, t) = du .= 1.01u # deterministic part -σ = 0.25 # noise strength - -function idfunc!(du, u, p, t) - du .= ones(eltype(u), length(u)) - return nothing -end; +sciml_prob(sde) = sde.integ.sol.prob +f!(du, u, p, t) = du .= 1.01u @testset "Additive" begin # Additive Wiener noise W = WienerProcess(0.0, zeros(2), zeros(2)) - addit_autom_inv = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) + addit_autom_inv = CoupledSDEs(f!, zeros(2); noise = W) types = addit_autom_inv.noise_type @test values(types) == (true, true, true, true) + @test CoupledSDEs(sciml_prob(addit_autom_inv)).noise_type == types # Scalar Wiener noise W = WienerProcess(0.0, 0.0, 0.0) - scalar_a = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) + scalar_a = CoupledSDEs(f!, zeros(2); noise = W) types = scalar_a.noise_type @test values(types) == (true, true, true, true) + @test CoupledSDEs(sciml_prob(scalar_a)).noise_type == types # invertible correlated Wiener noise - W = CorrelatedWienerProcess([1 0.3; 0.3 1], 0.0, zeros(2), zeros(2)) - corr_a = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) - types = corr_a.noise_type + corr = CoupledSDEs(f!, zeros(2); covariance = [1 0.3; 0.3 1]) + types = corr.noise_type @test values(types) == (true, true, true, true) + @test CoupledSDEs(sciml_prob(corr)).noise_type == types # invertible correlated Wiener noise g!(du, u, p, t) = (du .= [1 0.3; 0.3 1]; return nothing) - corr_alt = CoupledSDEs( - f!, g!, zeros(2), nothing, σ, noise_rate_prototype = zeros(2, 2), - diffeq = (alg = EM(), dt = 0.1)) + corr_alt = CoupledSDEs(f!, zeros(2); g = g!, noise_prototype = zeros(2, 2)) types = corr_alt.noise_type @test values(types) == (true, true, true, true) + @test CoupledSDEs(sciml_prob(corr_alt)).noise_type == types # non-invertible correlated Wiener noise - W = CorrelatedWienerProcess([1 2; 2 4], 0.0, zeros(2), zeros(2)) - corr_noninv = CoupledSDEs(f!, idfunc!, zeros(2), nothing, σ; noise = W) + corr_noninv = CoupledSDEs(f!, zeros(2); covariance = [1 2; 2 4]) types = corr_noninv.noise_type @test values(types) == (true, true, true, false) + @test CoupledSDEs(sciml_prob(corr_noninv)).noise_type == types # non-invertible correlated Wiener noise g!(du, u, p, t) = (du .= [1 0.3 1; 0.3 1 1]; return nothing) - corr_alt = CoupledSDEs( - f!, g!, zeros(2), nothing, σ, noise_rate_prototype = zeros(2, 3), - diffeq = (alg = EM(), dt = 0.1)) + corr_alt = CoupledSDEs(f!, zeros(2); g = g!, noise_prototype = zeros(2, 3)) types = corr_alt.noise_type @test values(types) == (true, true, true, false) + @test CoupledSDEs(sciml_prob(corr_alt)).noise_type == types # non-autonomous Wiener noise g!(du, u, p, t) = (du .= 1 / (1 + t); return nothing) - W = WienerProcess(0.0, zeros(2), zeros(2)) - addit_non_autom = CoupledSDEs(f!, g!, zeros(2), nothing, σ; noise = W) + addit_non_autom = CoupledSDEs(f!, zeros(2); g = g!) types = addit_non_autom.noise_type @test values(types) == (true, false, true, false) + @test CoupledSDEs(sciml_prob(addit_non_autom)).noise_type == types end @testset "Multiplicative" begin # multiplicative linear Wiener noise g!(du, u, p, t) = (du .= u; return nothing) - linear_multipli = CoupledSDEs(f!, g!, rand(2) ./ 10, (), σ) + linear_multipli = CoupledSDEs(f!, rand(2) ./ 10; g = g!) types = linear_multipli.noise_type @test values(types) == (false, true, true, false) + @test CoupledSDEs(sciml_prob(linear_multipli)).noise_type == types # non-diagonal multiplicative linear Wiener noise - lin_multipli_alt = CoupledSDEs( - f!, g!, rand(2), (), σ, noise_rate_prototype = zeros(2, 3), - diffeq = (alg = EM(), dt = 0.1)) + lin_multipli_alt = CoupledSDEs(f!, rand(2); g = g!, noise_prototype = zeros(2, 3)) types = lin_multipli_alt.noise_type @test values(types) == (false, true, true, false) + @test CoupledSDEs(sciml_prob(lin_multipli_alt)).noise_type == types # multiplicative nonlinear Wiener noise g!(du, u, p, t) = (du .= u .^ 2; return nothing) - nonlinear_multiplicative = CoupledSDEs(f!, g!, rand(2), (), σ) + nonlinear_multiplicative = CoupledSDEs(f!, rand(2); g = g!) types = nonlinear_multiplicative.noise_type @test values(types) == (false, true, false, false) + @test CoupledSDEs(sciml_prob(nonlinear_multiplicative)).noise_type == types # non-autonomous linear multiplicative Wiener noise g!(du, u, p, t) = (du .= u ./ (1 + t); return nothing) - W = WienerProcess(0.0, zeros(2), zeros(2)) - addit_non_autom = CoupledSDEs(f!, g!, zeros(2), nothing, σ; noise = W) + addit_non_autom = CoupledSDEs(f!, zeros(2); g = g!) types = addit_non_autom.noise_type @test values(types) == (false, false, true, false) + @test CoupledSDEs(sciml_prob(addit_non_autom)).noise_type == types # non-autonomous nonlinear multiplicative Wiener noise - g!(du, u, p, t) = (du .= u.^2 ./ (1 + t); return nothing) - W = WienerProcess(0.0, zeros(2), zeros(2)) - addit_non_autom = CoupledSDEs(f!, g!, zeros(2), nothing, σ; noise = W) + g!(du, u, p, t) = (du .= u .^ 2 ./ (1 + t); return nothing) + addit_non_autom = CoupledSDEs(f!, zeros(2); g = g!) types = addit_non_autom.noise_type @test values(types) == (false, false, false, false) + @test CoupledSDEs(sciml_prob(addit_non_autom)).noise_type == types end From 17cf5cb3d9b6e306ed4f195f9172e3be79c3ac20 Mon Sep 17 00:00:00 2001 From: oameye Date: Mon, 5 Aug 2024 11:55:30 +0200 Subject: [PATCH 25/38] update docs --- docs/src/CoupledSDEs.md | 46 +++++++++---------------- src/core_systems/continuous_time_sde.jl | 22 +++++++----- 2 files changed, 30 insertions(+), 38 deletions(-) diff --git a/docs/src/CoupledSDEs.md b/docs/src/CoupledSDEs.md index 4d3a4d0c..b3fd0465 100644 --- a/docs/src/CoupledSDEs.md +++ b/docs/src/CoupledSDEs.md @@ -15,8 +15,6 @@ using CairoMakie import Random # hide Random.seed!(10) # hide f!(du, u, p, t) = du .= 1.01u # deterministic part -idfunc!(du, u, p, t) = (du .= ones(eltype(u), length(u)); return nothing) -σ = 0.25 # noise strength function plot_trajectory(Y, t) fig = Figure() @@ -31,13 +29,13 @@ end; ### Additive noise When $g$ is independent of the state variables $u$, the noise is called additive, otherwise it is called multiplicative. The ladder is somewhat misleading, as it has come to signify the general case, despite seeming to suggest the limited case where $g(x) \propto x$. We can define a simple additive noise system as follows: ```@example type -t0 = 0.0; W0 = zeros(2); -W = WienerProcess(t0, W0, 0.0) -sde = CoupledSDEs(f!, idfunc!, zeros(2); noise=W) +sde = CoupledSDEs(f!, zeros(2)); ``` which is equivalent to ```@example type -sde = CoupledSDEs(f!, idfunc!, zeros(2)); +t0 = 0.0; W0 = zeros(2); +W = WienerProcess(t0, W0, 0.0) +sde = CoupledSDEs(f!, zeros(2); noise=W); ``` We defined a vector of random numbers `dW`, whose size matches the output of `g`, with the noise applied element-wise, i.e., `g.*dW`. Specifically, `dW` is a vector of Gaussian noise processes whose size matches the output of `g`. The noise is applied element-wise, i.e., `g.*dW`. By default, the noise processes are uncorrelated, meaning the covariance matrix is diagonal. This type of noise is referred to as diagonal. The vector `dW` is by default zero mean white gaussian noise $\mathcal{N}(0, \text{d}t)$ where the variance is the timestep $\text{d}t$ unit variance (Wiener Process). We can sample a trajectory from this system using the `trajectory` also used for the deterministic systems: ```@example type @@ -46,38 +44,25 @@ plot_trajectory(tr...) ``` #### Correlated noise -Correlated noise is where the random number generated in `dW` are correlated. This can be done by specifying the covariance matrix $\Sigma$ for the noise processes and passing it to a `CorrelatedWienerProcess` of `DiffEqNoiseProcess.jl`.: +Correlated noise is where the random number generated in `dW` are correlated. This can be done by specifying the covariance matrix $\Sigma$ to the `covariance` keyword: ```@example type ρ = 0.3 Σ = [1 ρ; ρ 1] -t0 = 0.0; W0 = zeros(2); Z0 = zeros(2); -W = CorrelatedWienerProcess(Σ, t0, W0, Z0) -``` -Indeed, sampling 1_000 values from this process and plotting them shows the correlation: -```@example type -prob = NoiseProblem(W, (0.0, 1.0)) -sol = solve(prob; dt = 0.1) - -output_func = (sol, i) -> (sol.dW, false) -ensemble_prob = EnsembleProblem(prob, output_func = output_func) -values = Array(solve(ensemble_prob, dt = 0.1, trajectories = 10_000)) -scatter(values[1,:], values[2,:]) +sde = CoupledSDEs(f!, zeros(2); covariance=Σ) ``` -The CoupledSDEs can be defined by passing the `CorrelatedWienerProcess` to the `noise` keyword: +Alternativly, we can parametrise the covariance matrix by defining the diffusion function $g$ ourselves: ```@example type -sde = CoupledSDEs(f!, idfunc!, zeros(2); noise=W) +g!(du, u, p, t) = (du .= [1 p[1]; p[1] 1]; return nothing) +sde = CoupledSDEs(f!, zeros(2), (ρ); g=g!, noise_prototype=zeros(2, 2)) ``` -The covariance matrix $\Sigma$ can be accessed via `sde.integ.covariance`. - -!!! warning - Another way to define correlated noise is to use the diffusion function $g$ to define the matrix $\Sigma$. However, this is in general not recommended as the solvers from StochasticDiffEq will assume that the problem is more complicated such that the fast additive solvers like `SOSRA` and `SOSRI` will not work. +Here, we had to provide a `noise_prototype` to indicate that the diffusion function `g` will output a 2x2 matrix. #### Scalar noise Scalar noise is where a single random variable is applied to all dependent variables. To do this, one has to give an one dimensional noise process to the `noise` keyword of the `CoupledSDEs` constructor. ```@example type t0 = 0.0; W0 = 0.0; noise = WienerProcess(t0, W0, 0.0) -sde = CoupledSDEs(f!, idfunc!, rand(2)/10; noise=noise) +sde = CoupledSDEs(f!, rand(2)/10; noise=noise) tr = trajectory(sde, 1.0) plot_trajectory(tr...) @@ -92,7 +77,7 @@ function g!(du, u, p, t) du .= u ./ (1+t) return nothing end -sde = CoupledSDEs(f!, g!, rand(2)./10) +sde = CoupledSDEs(f!, rand(2)./10; g=g!) ``` #### Non-diagonal noise @@ -101,10 +86,11 @@ Non-diagonal noise allows for the terms to linearly mixed via `g` being a matrix du_1 = f_1(u,p,t)dt + g_{11}(u,p,t)dW_1 + g_{12}(u,p,t)dW_2 \\ du_2 = f_2(u,p,t)dt + g_{21}(u,p,t)dW_1 + g_{22}(u,p,t)dW_2 ``` -To indicate the structure that `g` should have, we can use the `noise_rate_prototype` keyword. Let us define a special type of non-diagonal noise called commutative noise. For this we can utilize the `RKMilCommute` algorithm which is designed to utilise the structure of commutative noise. +To indicate the structure that `g` should have, we can use the `noise_prototype` keyword. Let us define a special type of non-diagonal noise called commutative noise. For this we can utilize the `RKMilCommute` algorithm which is designed to utilise the structure of commutative noise. ```@example type -function g(du, u, p, t) +σ = 0.25 # noise strength +function g!(du, u, p, t) du[1,1] = σ*u[1] du[2,1] = σ*u[2] du[1,2] = σ*u[1] @@ -112,7 +98,7 @@ function g(du, u, p, t) return nothing end diffeq = (alg = RKMilCommute(), reltol = 1e-3, abstol = 1e-3) -sde = CoupledSDEs(f!, g, rand(2)./10; noise_rate_prototype = zeros(2, 2), diffeq = diffeq) +sde = CoupledSDEs(f!, rand(2)./10; g=g!, noise_prototype = zeros(2, 2), diffeq = diffeq) ``` !!! warning diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index 47577e76..5c50286a 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -2,7 +2,7 @@ export CoupledSDEs """ CoupledSDEs <: ContinuousTimeDynamicalSystem - CoupledSDEs(f, g, u0 [, p]; kwargs...) + CoupledSDEs(f, u0 [, p]; kwargs...) A stochastic continuous time dynamical system defined by a set of coupled stochastic differential equations as follows: @@ -20,18 +20,24 @@ By default `p = nothing`, and `t0 = 0`. For construction instructions regarding `f, u0` see the [DynamicalSystems.jl tutorial ](https://juliadynamics.github.io/DynamicalSystemsDocs.jl/dynamicalsystems/dev/tutorial/). -`g` must follow the sae syntax, i.e., `g(u, p, t)` for out-of-place (oop) and +`g` must follow the same syntax, i.e., `g(u, p, t)` for out-of-place (oop) and `g(du, u, p, t)` for in-place (iip). ## Stochastic part -The stochastic part of the differential equation is defined by the function `g` and -the keyword arguments `noise_rate_prototype` and `noise`. `noise` indicates -the noise process applied and defaults to Gaussian white noise (Wiener process). +By default the stochastic part of the differential equation is additive diagional Wiener +noise applied to every variable. Alternativly, to correlate the noise procces can provide +a covariance matrix with the kwarg `covariance`. A more exotic stochastic process can be +defined by adding the keyword arguments `g`, `noise_prototype` and `noise`. + +`g` is the diffusion function of the CoupledSDEs and provides an interface to multiplicative +and non-autonomous noise processes. + +`noise` indicates the noise process applied and defaults to Gaussian white noise (Wiener process). For details on defining various noise processes, refer to [DiffEqNoiseProcess.jl ](https://docs.sciml.ai/DiffEqNoiseProcess/stable/). -`noise_rate_prototype` indicates the prototype type instance for the noise rates, i.e., +`noise_prototype` indicates the prototype type instance for the noise rates, i.e., the output of `g`. It can be any type which overloads `A_mul_B!` with itself being the middle argument. Commonly, this is a matrix or sparse matrix. If this is not given, it defaults to `nothing`, which means the `g` should be interpreted as being diagonal. @@ -55,7 +61,7 @@ which requires you to be using StochasticDiffEq.jl to access the solvers. The default `diffeq` is: ```julia -(alg = SOSRI(), abstol = 1.0e-2, reltol = 1.0e-2) +(alg = SOSRA(), abstol = 1.0e-2, reltol = 1.0e-2) ``` `diffeq` keywords can also include `callback` for [event handling @@ -70,7 +76,7 @@ to extract the problem. You can convert to `CoupledODEs` to analyze the deterministic part via the function `CoupledODEs(ds::CoupledSDEs; diffeq, t0)`. -Similarly, use `CoupledSDEs(ds::CoupledODEs, g, p; kw...)` to convert to a stochastic system. +Similarly, use `CoupledSDEs(ds::CoupledODEs, p; kw...)` to convert to a stochastic system. """ From ba148d9af39bb6c6918c651c6cb3aaf30efaf2b3 Mon Sep 17 00:00:00 2001 From: oameye Date: Wed, 7 Aug 2024 18:49:51 +0200 Subject: [PATCH 26/38] diffusion <-> covariance matrix --- ext/StochasticSystemsBase.jl | 2 +- ext/src/CoupledSDEs.jl | 83 +++++++++++++++++++++++++----------- ext/src/classification.jl | 25 +++++++---- test/stochastic.jl | 81 +++++++++++++++++++++++++++++------ 4 files changed, 142 insertions(+), 49 deletions(-) diff --git a/ext/StochasticSystemsBase.jl b/ext/StochasticSystemsBase.jl index 6d56d2a7..9a84eb3b 100644 --- a/ext/StochasticSystemsBase.jl +++ b/ext/StochasticSystemsBase.jl @@ -5,7 +5,7 @@ using DynamicalSystemsBase: DynamicalSystemsBase, SciMLBase, correct_state, Coup set_state!, dynamic_rule, isdeterministic, current_state, DynamicalSystemsBase, _set_parameter!, u_modified!, additional_details, referrenced_sciml_prob, DEFAULT_DIFFEQ, - SVector, SMatrix + SVector, SMatrix, current_parameters using SciMLBase: SDEProblem, AbstractSDEIntegrator, __init, SDEFunction, step! using StochasticDiffEq: SOSRA using LinearAlgebra diff --git a/ext/src/CoupledSDEs.jl b/ext/src/CoupledSDEs.jl index 5e8bfb77..41349cff 100644 --- a/ext/src/CoupledSDEs.jl +++ b/ext/src/CoupledSDEs.jl @@ -151,32 +151,6 @@ function DynamicalSystemsBase.additional_details(ds::CoupledSDEs) ] end -""" -https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#The-uniform-scaling-operator -""" -function construct_diffusion_function(g, cov, noise_prototype, D, IIP) - if isnothing(g) # diagonal additive noise - cov = isnothing(cov) ? LinearAlgebra.I(D) : cov - if IIP - if isdiag(cov) - g = (du, u, p, t) -> du .= diag(cov) - else - g = (du, u, p, t) -> du .= cov - noise_prototype = zeros(size(cov)) - # ^ we could make this sparse to make it more performant - end - else - if isdiag(cov) - g = (u, p, t) -> SVector{length(diag(cov)), eltype(cov)}(diag(cov)) - else - g = (u, p, t) -> SMatrix{size(cov)..., eltype(cov)}(cov) - noise_prototype = zeros(size(cov)) - end - end - end - return g, noise_prototype -end - ########################################################################################### # API - obtaining information from the system ########################################################################################### @@ -216,3 +190,60 @@ function DynamicalSystemsBase.set_parameter!(ds::CoupledSDEs, args...) end DynamicalSystemsBase.referrenced_sciml_prob(ds::CoupledSDEs) = ds.integ.sol.prob + +function covariance(ds::CoupledSDEs) + A = diffusion_matrix(ds) + A * A' +end + +function diffusion_matrix(ds::CoupledSDEs{IIP, D}) where {IIP, D} + if ds.noise_type[:invertible] + diffusion = diffusion_function(ds) + A = diffusion(zeros(D), current_parameters(ds), 0.0) + else + A = nothing + end + return A +end + +########################################################################################### +# Utilities +########################################################################################### + +""" +compute diffusion matrix given the covariance matrix of noise matrix. +""" +function diffusion_matrix(Γ::AbstractMatrix) + U, S, V = LinearAlgebra.svd(Γ) # A ≈ U * Diagonal(S) * V' + A = U * LinearAlgebra.Diagonal(sqrt.(S)) + return A +end + +""" +https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#The-uniform-scaling-operator +""" +function construct_diffusion_function(g, cov, noise_prototype, D, IIP) + if isnothing(g) # diagonal additive noise + cov = isnothing(cov) ? LinearAlgebra.I(D) : cov + size(cov)[1] != D && + throw(ArgumentError("covariance matrix must be of size $((D, D))")) + A = diffusion_matrix(cov) + if IIP + if isdiag(cov) + g = (du, u, p, t) -> du .= diag(A) + else + g = (du, u, p, t) -> du .= A + noise_prototype = zeros(size(A)) + # ^ we could make this sparse to make it more performant + end + else + if isdiag(cov) + g = (u, p, t) -> SVector{length(diag(A)), eltype(A)}(diag(A)) + else + g = (u, p, t) -> SMatrix{size(A)..., eltype(A)}(A) + noise_prototype = zeros(size(A)) + end + end + end + return g, noise_prototype +end diff --git a/ext/src/classification.jl b/ext/src/classification.jl index 60af9932..54ca92c3 100644 --- a/ext/src/classification.jl +++ b/ext/src/classification.jl @@ -18,6 +18,21 @@ function is_linear(f, x, y, c) return check1 && check2 end +function diffusion_function(g, IIP, noise_prototype) + function diffusion(u, p, t) + if IIP + du = deepcopy(isnothing(noise_prototype) ? u : noise_prototype) + g(du, u, p, t) + return du + else + return g(u, p, t) + end + end +end +function diffusion_function(ds::CoupledSDEs{IIP}) where {IIP} + diffusion_function(ds.integ.g, IIP, referrenced_sciml_prob(ds).noise_rate_prototype) +end + """ We classify the noise type of the CoupledSDEs based on the properties given by the user. In doing this we also determine the covariance matrix @@ -39,15 +54,7 @@ function find_noise_type(g, u0, p, t0, noise, covariance, noise_prototype, IIP) islinear = false isinvertible = false - function diffusion(u, p, t) - if IIP - du = deepcopy(isnothing(noise_prototype) ? u : noise_prototype) - g(du, u, p, t) - return du - else - return g(u, p, t) - end - end + diffusion = diffusion_function(g, IIP, noise_prototype) if isnothing(g) isadditive = true diff --git a/test/stochastic.jl b/test/stochastic.jl index 2b6d677b..61363845 100644 --- a/test/stochastic.jl +++ b/test/stochastic.jl @@ -1,23 +1,29 @@ using DynamicalSystemsBase, Test using OrdinaryDiffEq: Tsit5 -using StochasticDiffEq: SDEProblem, SRA, SRA, SOSRA, CorrelatedWienerProcess +using StochasticDiffEq: SDEProblem, SRA, SRA, SOSRA, CorrelatedWienerProcess, EM -include("test_system_function.jl") +StochasticSystemsBase = Base.get_extension(DynamicalSystemsBase, :StochasticSystemsBase) +diffusion_matrix = StochasticSystemsBase.diffusion_matrix +include("test_system_function.jl") # Creation of lorenz @inbounds function lorenz_rule(u, p, t) - σ = p[1]; ρ = p[2]; β = p[3] - du1 = σ*(u[2]-u[1]) - du2 = u[1]*(ρ-u[3]) - u[2] - du3 = u[1]*u[2] - β*u[3] + σ = p[1] + ρ = p[2] + β = p[3] + du1 = σ * (u[2] - u[1]) + du2 = u[1] * (ρ - u[3]) - u[2] + du3 = u[1] * u[2] - β * u[3] return SVector{3}(du1, du2, du3) end @inbounds function lorenz_rule_iip(du, u, p, t) - σ = p[1]; ρ = p[2]; β = p[3] - du[1] = σ*(u[2]-u[1]) - du[2] = u[1]*(ρ-u[3]) - u[2] - du[3] = u[1]*u[2] - β*u[3] + σ = p[1] + ρ = p[2] + β = p[3] + du[1] = σ * (u[2] - u[1]) + du[2] = u[1] * (ρ - u[3]) - u[2] + du[3] = u[1] * u[2] - β * u[3] return nothing end @@ -32,6 +38,7 @@ diagonal_noise(σ) = (u, p, t) -> SVector{3}(σ, σ, σ) u0 = [0, 10.0, 0] p0 = [10, 28, 8 / 3] +Γ = [1.0 0.3 0.0; 0.3 1 0.5; 0.0 0.5 1.0] # diagonal additive noise lorenz_oop = CoupledSDEs(lorenz_rule, u0, p0) @@ -41,13 +48,23 @@ lorenz_SRA = CoupledSDEs(lorenz_rule, u0, p0; diffeq = (alg = SRA(), abstol = 1e-2, reltol = 1e-2) ) -for (ds, iip) in zip((lorenz_oop, lorenz_iip, lorenz_SRA), (false, true, false)) - name = (ds === lorenz_SRA) ? "lorSRA" : "lorenz" +tr, t = trajectory(lorenz_oop, 1) +tr +# lorenz_oop_cov = CoupledSDEs(lorenz_rule, u0, p0; covariance = Γ, diffeq = (alg=EM(), dt=0.1)) +# trajectory(lorenz_oop_cov, 10) +# lorenz_oop_cov.integ.g(0,0,0) + +# lorenz_iip_cov = CoupledSDEs(lorenz_rule_iip, u0, p0; covariance = Γ) + +for (ds, iip) in zip( + (lorenz_oop, lorenz_iip, lorenz_SRA), (false, true, false, false, true)) + name = nameof(dynamic_rule(ds)) @testset "$(name) IIP=$(iip)" begin @test dynamic_rule(ds) == (iip ? lorenz_rule_iip : lorenz_rule) test_dynamical_system(ds, u0, p0; idt = false, iip = iip) end end +# trajectory(lorenz_oop, 10) @testset "correct SDE propagation" begin lorenz_oop = CoupledSDEs(lorenz_rule, u0, p0) @@ -84,7 +101,7 @@ end f(u, p, t) = 1.01u f!(du, u, p, t) = du .= 1.01u @testset "covariance" begin - g(u, p, t) = [1 0.3; 0.3 1] + g(u, p, t) = diffusion_matrix([1 0.3; 0.3 1]) corr = CoupledSDEs(f, zeros(2); covariance = [1 0.3; 0.3 1]) corr_alt = CoupledSDEs(f, zeros(2); g = g, noise_prototype = zeros(2, 2)) @test corr.noise_type == corr_alt.noise_type @@ -107,3 +124,41 @@ end @test_throws ArgumentError CoupledSDEs(Csde.integ.sol.prob; diffeq = diffeq) end end + +@testset "utilities" begin + StochasticSystemsBase = Base.get_extension(DynamicalSystemsBase, :StochasticSystemsBase) + diffusion_matrix = StochasticSystemsBase.diffusion_matrix + + Γ = [1.0 0.3 0.0; 0.3 1 0.5; 0.0 0.5 1.0] + A = diffusion_matrix(Γ) + lorenz_oop = CoupledSDEs(lorenz_rule, u0, p0, covariance = Γ) + @test A ≈ diffusion_matrix(lorenz_oop) + @test Γ ≈ A * A' + + @testset begin + Γ = [1.0 0.3; 0.3 1] + f(u, p, t) = [0.0, 0.0] + function diffusion(u, p, t) + Γ = [1.0 p[1]; p[1] 1.0] + diffusion_matrix(Γ) + end + diffeq = (alg = EM(), abstol = 1e-2, reltol = 1e-2, dt = 0.1) + ds = CoupledSDEs(f, zeros(2), [0.3]; g = diffusion, + noise_prototype = zeros(2, 2), diffeq = diffeq) + A = diffusion_matrix(ds) + @test Γ ≈ A * A' + set_parameter!(ds, 1, 0.5) + A = diffusion_matrix(ds) + A * A' ≈ [1.0 0.5; 0.5 1.0] + end + # trajectory(lorenz_oop, 10) + # trajectory(ds, 10) + # using StochasticDiffEq + # f(u, p, t) = [0.0,0.0] + # function g(u, p, t) + # Γ = [1.0 p[1]; p[1] 1.0] + # diffusion_matrix(Γ) + # end + # prob = SDEProblem{false}(f, g, ones(2), (0.0, 1.0), [0.3], noise_rate_prototype=zeros(2, 2)) + # solve(prob, EM(), dt=0.1) +end From eb8544b89d556eedab54ecf36ba518b2a9bd8a7b Mon Sep 17 00:00:00 2001 From: oameye Date: Wed, 7 Aug 2024 20:50:33 +0200 Subject: [PATCH 27/38] add noise_strength kwarg --- docs/src/CoupledSDEs.md | 4 +- ext/StochasticSystemsBase.jl | 2 +- ext/src/CoupledSDEs.jl | 28 ++++++------ test/stochastic.jl | 66 +++++++++++++---------------- test/stochastic_characterisation.jl | 4 +- 5 files changed, 50 insertions(+), 54 deletions(-) diff --git a/docs/src/CoupledSDEs.md b/docs/src/CoupledSDEs.md index b3fd0465..a155d804 100644 --- a/docs/src/CoupledSDEs.md +++ b/docs/src/CoupledSDEs.md @@ -35,7 +35,7 @@ which is equivalent to ```@example type t0 = 0.0; W0 = zeros(2); W = WienerProcess(t0, W0, 0.0) -sde = CoupledSDEs(f!, zeros(2); noise=W); +sde = CoupledSDEs(f!, zeros(2); noise_process=W); ``` We defined a vector of random numbers `dW`, whose size matches the output of `g`, with the noise applied element-wise, i.e., `g.*dW`. Specifically, `dW` is a vector of Gaussian noise processes whose size matches the output of `g`. The noise is applied element-wise, i.e., `g.*dW`. By default, the noise processes are uncorrelated, meaning the covariance matrix is diagonal. This type of noise is referred to as diagonal. The vector `dW` is by default zero mean white gaussian noise $\mathcal{N}(0, \text{d}t)$ where the variance is the timestep $\text{d}t$ unit variance (Wiener Process). We can sample a trajectory from this system using the `trajectory` also used for the deterministic systems: ```@example type @@ -62,7 +62,7 @@ Scalar noise is where a single random variable is applied to all dependent varia ```@example type t0 = 0.0; W0 = 0.0; noise = WienerProcess(t0, W0, 0.0) -sde = CoupledSDEs(f!, rand(2)/10; noise=noise) +sde = CoupledSDEs(f!, rand(2)/10; noise_process=noise) tr = trajectory(sde, 1.0) plot_trajectory(tr...) diff --git a/ext/StochasticSystemsBase.jl b/ext/StochasticSystemsBase.jl index 9a84eb3b..02add7f3 100644 --- a/ext/StochasticSystemsBase.jl +++ b/ext/StochasticSystemsBase.jl @@ -7,7 +7,7 @@ using DynamicalSystemsBase: DynamicalSystemsBase, SciMLBase, correct_state, Coup additional_details, referrenced_sciml_prob, DEFAULT_DIFFEQ, SVector, SMatrix, current_parameters using SciMLBase: SDEProblem, AbstractSDEIntegrator, __init, SDEFunction, step! -using StochasticDiffEq: SOSRA +using StochasticDiffEq: LambaEM using LinearAlgebra include("src/CoupledSDEs.jl") diff --git a/ext/src/CoupledSDEs.jl b/ext/src/CoupledSDEs.jl index 41349cff..d15cffec 100644 --- a/ext/src/CoupledSDEs.jl +++ b/ext/src/CoupledSDEs.jl @@ -4,7 +4,8 @@ using LinearAlgebra: LinearAlgebra # DiffEq options ########################################################################################### # SOSRI is only applicable for diagonal noise -const DEFAULT_SDE_SOLVER = SOSRA() # default sciml solver for adapitve non-diagonal noise +# SOSRA can only be used with CorrelatedWienerProcess +const DEFAULT_SDE_SOLVER = LambaEM() const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol = 1e-2, reltol = 1e-2) # default sciml tol const DEFAULT_STOCH_DIFFEQ = (alg = DEFAULT_SDE_SOLVER, DEFAULT_STOCH_DIFFEQ_KWARGS...) @@ -27,11 +28,12 @@ function DynamicalSystemsBase.CoupledSDEs( u0, p = SciMLBase.NullParameters(); g = nothing, + noise_strength = 1.0, covariance = nothing, t0 = 0.0, diffeq = DEFAULT_STOCH_DIFFEQ, noise_prototype = nothing, - noise = nothing, + noise_process = nothing, seed = UInt64(0) ) IIP = isinplace(f, 4) # from SciMLBase @@ -39,9 +41,9 @@ function DynamicalSystemsBase.CoupledSDEs( @assert IIP==isinplace(g, 4) "f and g must both be in-place or out-of-place" end - noise_type, cov = find_noise_type(g, u0, p, t0, noise, covariance, noise_prototype, IIP) + noise_type, cov = find_noise_type(g, u0, p, t0, noise_process, covariance, noise_prototype, IIP) g, noise_prototype = construct_diffusion_function( - g, cov, noise_prototype, length(u0), IIP) + g, cov, noise_prototype, noise_strength, length(u0), IIP) s = correct_state(Val{IIP}(), u0) T = eltype(s) @@ -52,7 +54,7 @@ function DynamicalSystemsBase.CoupledSDEs( (T(t0), T(Inf)), p; noise_rate_prototype = noise_prototype, - noise = noise, + noise = noise_process, seed = seed ) return CoupledSDEs(prob, diffeq, noise_type) @@ -109,10 +111,11 @@ function DynamicalSystemsBase.CoupledSDEs( ds::CoupledODEs, p; # the parameter is likely changed as the diffusion function g is added. g = nothing, + noise_strength = 1.0, covariance = nothing, diffeq = DEFAULT_STOCH_DIFFEQ, noise_prototype = nothing, - noise = nothing, + noise_process = nothing, seed = UInt64(0) ) return CoupledSDEs( @@ -120,10 +123,11 @@ function DynamicalSystemsBase.CoupledSDEs( current_state(ds), p; g = g, + noise_strength = noise_strength, covariance = covariance, diffeq = diffeq, noise_prototype = noise_prototype, - noise = noise, + noise_process = noise_process, seed = seed ) end @@ -222,7 +226,7 @@ end """ https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#The-uniform-scaling-operator """ -function construct_diffusion_function(g, cov, noise_prototype, D, IIP) +function construct_diffusion_function(g, cov, noise_prototype, σ, D, IIP) if isnothing(g) # diagonal additive noise cov = isnothing(cov) ? LinearAlgebra.I(D) : cov size(cov)[1] != D && @@ -230,17 +234,17 @@ function construct_diffusion_function(g, cov, noise_prototype, D, IIP) A = diffusion_matrix(cov) if IIP if isdiag(cov) - g = (du, u, p, t) -> du .= diag(A) + g = (du, u, p, t) -> du .= σ .* diag(A) else - g = (du, u, p, t) -> du .= A + g = (du, u, p, t) -> du .= σ .* A noise_prototype = zeros(size(A)) # ^ we could make this sparse to make it more performant end else if isdiag(cov) - g = (u, p, t) -> SVector{length(diag(A)), eltype(A)}(diag(A)) + g = (u, p, t) -> SVector{length(diag(A)), eltype(A)}(diag(σ .* A)) else - g = (u, p, t) -> SMatrix{size(A)..., eltype(A)}(A) + g = (u, p, t) -> SMatrix{size(A)..., eltype(A)}(σ .* A) noise_prototype = zeros(size(A)) end end diff --git a/test/stochastic.jl b/test/stochastic.jl index 61363845..7ccea77f 100644 --- a/test/stochastic.jl +++ b/test/stochastic.jl @@ -1,6 +1,6 @@ using DynamicalSystemsBase, Test using OrdinaryDiffEq: Tsit5 -using StochasticDiffEq: SDEProblem, SRA, SRA, SOSRA, CorrelatedWienerProcess, EM +using StochasticDiffEq: SDEProblem, SRA, LambaEM, CorrelatedWienerProcess StochasticSystemsBase = Base.get_extension(DynamicalSystemsBase, :StochasticSystemsBase) diffusion_matrix = StochasticSystemsBase.diffusion_matrix @@ -41,34 +41,28 @@ p0 = [10, 28, 8 / 3] Γ = [1.0 0.3 0.0; 0.3 1 0.5; 0.0 0.5 1.0] # diagonal additive noise -lorenz_oop = CoupledSDEs(lorenz_rule, u0, p0) -lorenz_iip = CoupledSDEs(SDEProblem( +lor_oop = CoupledSDEs(lorenz_rule, u0, p0) +lor_iip = CoupledSDEs(SDEProblem( lorenz_rule_iip, diagonal_noise!(σ), copy(u0), (0.0, Inf), p0)) -lorenz_SRA = CoupledSDEs(lorenz_rule, u0, p0; +lor_SRA = CoupledSDEs(lorenz_rule, u0, p0; diffeq = (alg = SRA(), abstol = 1e-2, reltol = 1e-2) ) -tr, t = trajectory(lorenz_oop, 1) -tr -# lorenz_oop_cov = CoupledSDEs(lorenz_rule, u0, p0; covariance = Γ, diffeq = (alg=EM(), dt=0.1)) -# trajectory(lorenz_oop_cov, 10) -# lorenz_oop_cov.integ.g(0,0,0) - -# lorenz_iip_cov = CoupledSDEs(lorenz_rule_iip, u0, p0; covariance = Γ) +lor_oop_cov = CoupledSDEs(lorenz_rule, u0, p0; covariance = Γ) +lor_iip_cov = CoupledSDEs(lorenz_rule_iip, u0, p0; covariance = Γ) for (ds, iip) in zip( - (lorenz_oop, lorenz_iip, lorenz_SRA), (false, true, false, false, true)) - name = nameof(dynamic_rule(ds)) + (lor_oop, lor_iip, lor_SRA, lor_oop_cov, lor_iip_cov), (false, true, false, false, true)) + name = (ds === lor_SRA) ? "lorvern" : "lorenz" @testset "$(name) IIP=$(iip)" begin @test dynamic_rule(ds) == (iip ? lorenz_rule_iip : lorenz_rule) test_dynamical_system(ds, u0, p0; idt = false, iip = iip) end end -# trajectory(lorenz_oop, 10) @testset "correct SDE propagation" begin lorenz_oop = CoupledSDEs(lorenz_rule, u0, p0) - @test lorenz_oop.integ.alg isa SOSRA + @test lorenz_oop.integ.alg isa LambaEM lorenz_SRA = CoupledSDEs(lorenz_rule, u0, p0; diffeq = (alg = SRA(), abstol = 1e-3, reltol = 1e-3, verbose = false) @@ -94,7 +88,7 @@ end # and back sde = CoupledSDEs(ds, p0) @test dynamic_rule(sde) == lorenz_rule - @test sde.integ.alg isa SOSRA + @test sde.integ.alg isa LambaEM end @testset "interface" begin @@ -110,7 +104,7 @@ end @testset "ArgumentError" begin W = CorrelatedWienerProcess([1 0.3; 0.3 1], 0.0, zeros(2), zeros(2)) - @test_throws ArgumentError CoupledSDEs(f!, zeros(2); noise = W) + @test_throws ArgumentError CoupledSDEs(f!, zeros(2); noise_process = W) g!(du, u, p, t) = du .= u @test_throws ArgumentError CoupledSDEs( @@ -129,36 +123,34 @@ end StochasticSystemsBase = Base.get_extension(DynamicalSystemsBase, :StochasticSystemsBase) diffusion_matrix = StochasticSystemsBase.diffusion_matrix - Γ = [1.0 0.3 0.0; 0.3 1 0.5; 0.0 0.5 1.0] - A = diffusion_matrix(Γ) - lorenz_oop = CoupledSDEs(lorenz_rule, u0, p0, covariance = Γ) - @test A ≈ diffusion_matrix(lorenz_oop) - @test Γ ≈ A * A' + @testset "diffusion_matrix" begin + Γ = [1.0 0.3 0.0; 0.3 1 0.5; 0.0 0.5 1.0] + A = diffusion_matrix(Γ) + lorenz_oop = CoupledSDEs(lorenz_rule, u0, p0, covariance = Γ) + @test A ≈ diffusion_matrix(lorenz_oop) + @test Γ ≈ A * A' + end - @testset begin + @testset "parametrize cov" begin Γ = [1.0 0.3; 0.3 1] f(u, p, t) = [0.0, 0.0] function diffusion(u, p, t) Γ = [1.0 p[1]; p[1] 1.0] diffusion_matrix(Γ) end - diffeq = (alg = EM(), abstol = 1e-2, reltol = 1e-2, dt = 0.1) - ds = CoupledSDEs(f, zeros(2), [0.3]; g = diffusion, - noise_prototype = zeros(2, 2), diffeq = diffeq) + ds = CoupledSDEs(f, zeros(2), [0.3]; g = diffusion, noise_prototype = zeros(2, 2)) A = diffusion_matrix(ds) @test Γ ≈ A * A' set_parameter!(ds, 1, 0.5) A = diffusion_matrix(ds) - A * A' ≈ [1.0 0.5; 0.5 1.0] + @test A * A' ≈ [1.0 0.5; 0.5 1.0] + end + @testset "approximate cov" begin + Γ = [1.0 0.3; 0.3 1] + f(u, p, t) = [0.0, 0.0] + ds = CoupledSDEs(f, zeros(2), (); covariance = Γ) + tr, _ = trajectory(ds, 1_000) + approx = cov(diff(reduce(hcat, tr.data), dims=2), dims=2) + @test approx ≈ Γ atol=1e-1 broken = true end - # trajectory(lorenz_oop, 10) - # trajectory(ds, 10) - # using StochasticDiffEq - # f(u, p, t) = [0.0,0.0] - # function g(u, p, t) - # Γ = [1.0 p[1]; p[1] 1.0] - # diffusion_matrix(Γ) - # end - # prob = SDEProblem{false}(f, g, ones(2), (0.0, 1.0), [0.3], noise_rate_prototype=zeros(2, 2)) - # solve(prob, EM(), dt=0.1) end diff --git a/test/stochastic_characterisation.jl b/test/stochastic_characterisation.jl index 7553ac46..6663b6e6 100644 --- a/test/stochastic_characterisation.jl +++ b/test/stochastic_characterisation.jl @@ -6,14 +6,14 @@ f!(du, u, p, t) = du .= 1.01u @testset "Additive" begin # Additive Wiener noise W = WienerProcess(0.0, zeros(2), zeros(2)) - addit_autom_inv = CoupledSDEs(f!, zeros(2); noise = W) + addit_autom_inv = CoupledSDEs(f!, zeros(2); noise_process = W) types = addit_autom_inv.noise_type @test values(types) == (true, true, true, true) @test CoupledSDEs(sciml_prob(addit_autom_inv)).noise_type == types # Scalar Wiener noise W = WienerProcess(0.0, 0.0, 0.0) - scalar_a = CoupledSDEs(f!, zeros(2); noise = W) + scalar_a = CoupledSDEs(f!, zeros(2); noise_process = W) types = scalar_a.noise_type @test values(types) == (true, true, true, true) @test CoupledSDEs(sciml_prob(scalar_a)).noise_type == types From e28b4dd6ad2787fe7ee20c932aac85b60820965f Mon Sep 17 00:00:00 2001 From: oameye Date: Wed, 7 Aug 2024 22:08:24 +0200 Subject: [PATCH 28/38] estimate invertiability with a tolerance --- ext/src/classification.jl | 9 +++++++-- 1 file changed, 7 insertions(+), 2 deletions(-) diff --git a/ext/src/classification.jl b/ext/src/classification.jl index 54ca92c3..a64ed0d7 100644 --- a/ext/src/classification.jl +++ b/ext/src/classification.jl @@ -10,7 +10,11 @@ function is_time_independent(g, u, p, t0) val = map(t -> g(u, p, t), trange) length(unique(val)) == 1 end -is_invertible(x) = issuccess(lu(x, check = false)) +function is_invertible(x; tol=1e-10) + F = lu(x, check = false) + det = abs(prod(diag(F.U))) + return det > tol +end function is_linear(f, x, y, c) check1 = f(x + y) == f(x) + f(y) @@ -82,7 +86,8 @@ function find_noise_type(g, u0, p, t0, noise, covariance, noise_prototype, IIP) if time_independent && state_independent if !isnothing(noise_size) && isequal(noise_size...) - covariance = diffusion(zeros(D), p, 0.0) + A = diffusion(zeros(D), p, 0.0) + covariance = A * A' isinvertible = is_invertible(covariance) elseif !isnothing(noise_size) && !isequal(noise_size...) isinvertible = false From 39057fbdf87b1548cfc80432dbc57e9c9f7411e9 Mon Sep 17 00:00:00 2001 From: Orjan Ameye Date: Tue, 10 Sep 2024 16:07:57 +0200 Subject: [PATCH 29/38] move to SOSRA with non-adaptive timesteps update docs to use LambdaEM when we have covariance remove accidently comitted JuliaFormatter fix tests Set default solver to EM --- docs/src/CoupledSDEs.md | 5 +++-- ext/StochasticSystemsBase.jl | 2 +- ext/src/CoupledSDEs.jl | 8 ++++---- test/stochastic.jl | 18 +++++++++--------- 4 files changed, 17 insertions(+), 16 deletions(-) diff --git a/docs/src/CoupledSDEs.md b/docs/src/CoupledSDEs.md index a155d804..090982cf 100644 --- a/docs/src/CoupledSDEs.md +++ b/docs/src/CoupledSDEs.md @@ -48,7 +48,8 @@ Correlated noise is where the random number generated in `dW` are correlated. Th ```@example type ρ = 0.3 Σ = [1 ρ; ρ 1] -sde = CoupledSDEs(f!, zeros(2); covariance=Σ) +diffeq = (alg = LambaEM(), dt=0.1) +sde = CoupledSDEs(f!, zeros(2); covariance=Σ, diffeq=diffeq) ``` Alternativly, we can parametrise the covariance matrix by defining the diffusion function $g$ ourselves: ```@example type @@ -97,7 +98,7 @@ function g!(du, u, p, t) du[2,2] = σ*u[2] return nothing end -diffeq = (alg = RKMilCommute(), reltol = 1e-3, abstol = 1e-3) +diffeq = (alg = RKMilCommute(), reltol = 1e-3, abstol = 1e-3, dt=0.1) sde = CoupledSDEs(f!, rand(2)./10; g=g!, noise_prototype = zeros(2, 2), diffeq = diffeq) ``` diff --git a/ext/StochasticSystemsBase.jl b/ext/StochasticSystemsBase.jl index 02add7f3..9a84eb3b 100644 --- a/ext/StochasticSystemsBase.jl +++ b/ext/StochasticSystemsBase.jl @@ -7,7 +7,7 @@ using DynamicalSystemsBase: DynamicalSystemsBase, SciMLBase, correct_state, Coup additional_details, referrenced_sciml_prob, DEFAULT_DIFFEQ, SVector, SMatrix, current_parameters using SciMLBase: SDEProblem, AbstractSDEIntegrator, __init, SDEFunction, step! -using StochasticDiffEq: LambaEM +using StochasticDiffEq: SOSRA using LinearAlgebra include("src/CoupledSDEs.jl") diff --git a/ext/src/CoupledSDEs.jl b/ext/src/CoupledSDEs.jl index d15cffec..eb789347 100644 --- a/ext/src/CoupledSDEs.jl +++ b/ext/src/CoupledSDEs.jl @@ -3,10 +3,10 @@ using LinearAlgebra: LinearAlgebra ########################################################################################### # DiffEq options ########################################################################################### -# SOSRI is only applicable for diagonal noise -# SOSRA can only be used with CorrelatedWienerProcess -const DEFAULT_SDE_SOLVER = LambaEM() -const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol = 1e-2, reltol = 1e-2) # default sciml tol +# SOSRA is only applicable for additive noise and must be adaptive + # default sciml tolerance is 1e-2 +const DEFAULT_SDE_SOLVER = SOSRA() +const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol = 1e-2, reltol = 1e-2, dt = 0.1) const DEFAULT_STOCH_DIFFEQ = (alg = DEFAULT_SDE_SOLVER, DEFAULT_STOCH_DIFFEQ_KWARGS...) # Function from user `@xlxs4`, see diff --git a/test/stochastic.jl b/test/stochastic.jl index 7ccea77f..6693cd76 100644 --- a/test/stochastic.jl +++ b/test/stochastic.jl @@ -1,12 +1,10 @@ using DynamicalSystemsBase, Test using OrdinaryDiffEq: Tsit5 -using StochasticDiffEq: SDEProblem, SRA, LambaEM, CorrelatedWienerProcess +using StochasticDiffEq: SDEProblem, SRA, SOSRA, LambaEM, CorrelatedWienerProcess StochasticSystemsBase = Base.get_extension(DynamicalSystemsBase, :StochasticSystemsBase) diffusion_matrix = StochasticSystemsBase.diffusion_matrix -include("test_system_function.jl") - # Creation of lorenz @inbounds function lorenz_rule(u, p, t) σ = p[1] @@ -48,8 +46,9 @@ lor_SRA = CoupledSDEs(lorenz_rule, u0, p0; diffeq = (alg = SRA(), abstol = 1e-2, reltol = 1e-2) ) -lor_oop_cov = CoupledSDEs(lorenz_rule, u0, p0; covariance = Γ) -lor_iip_cov = CoupledSDEs(lorenz_rule_iip, u0, p0; covariance = Γ) +diffeq_cov= (alg = LambaEM(), abstol = 1e-2, reltol = 1e-2, dt=0.1) +lor_oop_cov = CoupledSDEs(lorenz_rule, u0, p0; covariance = Γ, diffeq=diffeq_cov) +lor_iip_cov = CoupledSDEs(lorenz_rule_iip, u0, p0; covariance = Γ, diffeq=diffeq_cov) for (ds, iip) in zip( (lor_oop, lor_iip, lor_SRA, lor_oop_cov, lor_iip_cov), (false, true, false, false, true)) @@ -62,7 +61,7 @@ end @testset "correct SDE propagation" begin lorenz_oop = CoupledSDEs(lorenz_rule, u0, p0) - @test lorenz_oop.integ.alg isa LambaEM + @test lorenz_oop.integ.alg isa SOSRA lorenz_SRA = CoupledSDEs(lorenz_rule, u0, p0; diffeq = (alg = SRA(), abstol = 1e-3, reltol = 1e-3, verbose = false) @@ -88,7 +87,7 @@ end # and back sde = CoupledSDEs(ds, p0) @test dynamic_rule(sde) == lorenz_rule - @test sde.integ.alg isa LambaEM + @test sde.integ.alg isa SOSRA end @testset "interface" begin @@ -126,7 +125,7 @@ end @testset "diffusion_matrix" begin Γ = [1.0 0.3 0.0; 0.3 1 0.5; 0.0 0.5 1.0] A = diffusion_matrix(Γ) - lorenz_oop = CoupledSDEs(lorenz_rule, u0, p0, covariance = Γ) + lorenz_oop = CoupledSDEs(lorenz_rule, u0, p0, covariance = Γ, diffeq=diffeq_cov) @test A ≈ diffusion_matrix(lorenz_oop) @test Γ ≈ A * A' end @@ -148,9 +147,10 @@ end @testset "approximate cov" begin Γ = [1.0 0.3; 0.3 1] f(u, p, t) = [0.0, 0.0] - ds = CoupledSDEs(f, zeros(2), (); covariance = Γ) + ds = CoupledSDEs(f, zeros(2), (); covariance = Γ, diffeq=diffeq_cov) tr, _ = trajectory(ds, 1_000) approx = cov(diff(reduce(hcat, tr.data), dims=2), dims=2) @test approx ≈ Γ atol=1e-1 broken = true + # I think I understand something wromg here end end From 41c900b959b4b48d576fa544f54017d221ce4a97 Mon Sep 17 00:00:00 2001 From: Orjan Ameye Date: Mon, 23 Sep 2024 10:55:40 +0200 Subject: [PATCH 30/38] Reyk's comments --- ext/src/CoupledSDEs.jl | 99 +++++++++++++++++++-------------------- ext/src/classification.jl | 8 ++-- 2 files changed, 53 insertions(+), 54 deletions(-) diff --git a/ext/src/CoupledSDEs.jl b/ext/src/CoupledSDEs.jl index eb789347..39f8a60b 100644 --- a/ext/src/CoupledSDEs.jl +++ b/ext/src/CoupledSDEs.jl @@ -4,10 +4,10 @@ using LinearAlgebra: LinearAlgebra # DiffEq options ########################################################################################### # SOSRA is only applicable for additive noise and must be adaptive - # default sciml tolerance is 1e-2 +# default sciml tolerance is 1e-2 const DEFAULT_SDE_SOLVER = SOSRA() -const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol = 1e-2, reltol = 1e-2, dt = 0.1) -const DEFAULT_STOCH_DIFFEQ = (alg = DEFAULT_SDE_SOLVER, DEFAULT_STOCH_DIFFEQ_KWARGS...) +const DEFAULT_STOCH_DIFFEQ_KWARGS = (abstol=1e-2, reltol=1e-2, dt=0.1) +const DEFAULT_STOCH_DIFFEQ = (alg=DEFAULT_SDE_SOLVER, DEFAULT_STOCH_DIFFEQ_KWARGS...) # Function from user `@xlxs4`, see # https://github.com/JuliaDynamics/jl/pull/153 @@ -24,21 +24,21 @@ end ########################################################################################### function DynamicalSystemsBase.CoupledSDEs( - f, - u0, - p = SciMLBase.NullParameters(); - g = nothing, - noise_strength = 1.0, - covariance = nothing, - t0 = 0.0, - diffeq = DEFAULT_STOCH_DIFFEQ, - noise_prototype = nothing, - noise_process = nothing, - seed = UInt64(0) + f, + u0, + p=SciMLBase.NullParameters(); + g=nothing, + noise_strength=1.0, + covariance=nothing, + t0=0.0, + diffeq=DEFAULT_STOCH_DIFFEQ, + noise_prototype=nothing, + noise_process=nothing, + seed=UInt64(0) ) IIP = isinplace(f, 4) # from SciMLBase if !isnothing(g) - @assert IIP==isinplace(g, 4) "f and g must both be in-place or out-of-place" + @assert IIP == isinplace(g, 4) "f and g must both be in-place or out-of-place" end noise_type, cov = find_noise_type(g, u0, p, t0, noise_process, covariance, noise_prototype, IIP) @@ -53,21 +53,21 @@ function DynamicalSystemsBase.CoupledSDEs( s, (T(t0), T(Inf)), p; - noise_rate_prototype = noise_prototype, - noise = noise_process, - seed = seed + noise_rate_prototype=noise_prototype, + noise=noise_process, + seed=seed ) return CoupledSDEs(prob, diffeq, noise_type) end function DynamicalSystemsBase.CoupledSDEs( - prob::SDEProblem, diffeq = DEFAULT_STOCH_DIFFEQ, noise_type = nothing; special_kwargs... + prob::SDEProblem, diffeq=DEFAULT_STOCH_DIFFEQ, noise_type=nothing; special_kwargs... ) if haskey(special_kwargs, :diffeq) throw( ArgumentError( - "`diffeq` is given as positional argument when an ODEProblem is provided." - ), + "`diffeq` is given as positional argument when an SDEProblem is provided." + ), ) end IIP = isinplace(prob) # from SciMLBase @@ -76,7 +76,7 @@ function DynamicalSystemsBase.CoupledSDEs( if prob.tspan === (nothing, nothing) # If the problem was made via MTK, it is possible to not have a default timespan. U = eltype(prob.u0) - prob = SciMLBase.remake(prob; tspan = (U(0), U(Inf))) + prob = SciMLBase.remake(prob; tspan=(U(0), U(Inf))) end if isnothing(noise_type) noise_type, _ = find_noise_type(prob, IIP) @@ -88,14 +88,14 @@ function DynamicalSystemsBase.CoupledSDEs( solver; remaining..., # Integrators are used exclusively iteratively. There is no reason to save anything. - save_start = false, - save_end = false, - save_everystep = false, + save_start=false, + save_end=false, + save_everystep=false, # DynamicalSystems.jl operates on integrators and `step!` exclusively, # so there is no reason to limit the maximum time evolution - maxiters = Inf + maxiters=Inf ) - return CoupledSDEs{IIP, D, typeof(integ), P}( + return CoupledSDEs{IIP,D,typeof(integ),P}( integ, deepcopy(prob.p), diffeq, noise_type ) end @@ -108,27 +108,27 @@ Converts a [`CoupledODEs` system into a [`CoupledSDEs`](@ref). """ function DynamicalSystemsBase.CoupledSDEs( - ds::CoupledODEs, - p; # the parameter is likely changed as the diffusion function g is added. - g = nothing, - noise_strength = 1.0, - covariance = nothing, - diffeq = DEFAULT_STOCH_DIFFEQ, - noise_prototype = nothing, - noise_process = nothing, - seed = UInt64(0) + ds::CoupledODEs, + p; # the parameter is likely changed as the diffusion function g is added. + g=nothing, + noise_strength=1.0, + covariance=nothing, + diffeq=DEFAULT_STOCH_DIFFEQ, + noise_prototype=nothing, + noise_process=nothing, + seed=UInt64(0) ) return CoupledSDEs( dynamic_rule(ds), current_state(ds), p; - g = g, - noise_strength = noise_strength, - covariance = covariance, - diffeq = diffeq, - noise_prototype = noise_prototype, - noise_process = noise_process, - seed = seed + g=g, + noise_strength=noise_strength, + covariance=covariance, + diffeq=diffeq, + noise_prototype=noise_prototype, + noise_process=noise_process, + seed=seed ) end @@ -138,10 +138,10 @@ end Converts a [`CoupledSDEs`](@ref) into [`CoupledODEs`](@ref). """ function DynamicalSystemsBase.CoupledODEs( - sys::CoupledSDEs; diffeq = DEFAULT_DIFFEQ, t0 = 0.0) + sys::CoupledSDEs; diffeq=DEFAULT_DIFFEQ, t0=0.0) return CoupledODEs( dynamic_rule(sys), SVector{length(sys.integ.u)}(sys.integ.u), sys.p0; - diffeq = diffeq, t0 = t0 + diffeq=diffeq, t0=t0 ) end @@ -160,7 +160,7 @@ end ########################################################################################### SciMLBase.isinplace(::CoupledSDEs{IIP}) where {IIP} = IIP -StateSpaceSets.dimension(::CoupledSDEs{IIP, D}) where {IIP, D} = D +StateSpaceSets.dimension(::CoupledSDEs{IIP,D}) where {IIP,D} = D DynamicalSystemsBase.current_state(ds::CoupledSDEs) = current_state(ds.integ) DynamicalSystemsBase.isdeterministic(ds::CoupledSDEs) = false @@ -174,7 +174,6 @@ function DynamicalSystemsBase.dynamic_rule(ds::CoupledSDEs) return f end -# so that `ds` is printed function DynamicalSystemsBase.set_state!(ds::CoupledSDEs, u::AbstractArray) (set_state!(ds.integ, u); ds) end @@ -200,7 +199,7 @@ function covariance(ds::CoupledSDEs) A * A' end -function diffusion_matrix(ds::CoupledSDEs{IIP, D}) where {IIP, D} +function diffusion_matrix(ds::CoupledSDEs{IIP,D}) where {IIP,D} if ds.noise_type[:invertible] diffusion = diffusion_function(ds) A = diffusion(zeros(D), current_parameters(ds), 0.0) @@ -242,9 +241,9 @@ function construct_diffusion_function(g, cov, noise_prototype, σ, D, IIP) end else if isdiag(cov) - g = (u, p, t) -> SVector{length(diag(A)), eltype(A)}(diag(σ .* A)) + g = (u, p, t) -> SVector{length(diag(A)),eltype(A)}(diag(σ .* A)) else - g = (u, p, t) -> SMatrix{size(A)..., eltype(A)}(σ .* A) + g = (u, p, t) -> SMatrix{size(A)...,eltype(A)}(σ .* A) noise_prototype = zeros(size(A)) end end diff --git a/ext/src/classification.jl b/ext/src/classification.jl index a64ed0d7..fc6f6d52 100644 --- a/ext/src/classification.jl +++ b/ext/src/classification.jl @@ -11,7 +11,7 @@ function is_time_independent(g, u, p, t0) length(unique(val)) == 1 end function is_invertible(x; tol=1e-10) - F = lu(x, check = false) + F = lu(x, check=false) det = abs(prod(diag(F.U))) return det > tol end @@ -38,7 +38,7 @@ function diffusion_function(ds::CoupledSDEs{IIP}) where {IIP} end """ -We classify the noise type of the CoupledSDEs based on the properties given by the user. +We classify the noise type of the CoupledSDEs based on the system given by the user. In doing this we also determine the covariance matrix """ @@ -101,8 +101,8 @@ function find_noise_type(g, u0, p, t0, noise, covariance, noise_prototype, IIP) end end - noise_type = (additive = isadditive, autonomous = isautonomous, - linear = islinear, invertible = isinvertible) + noise_type = (additive=isadditive, autonomous=isautonomous, + linear=islinear, invertible=isinvertible) return noise_type, covariance end From e5bc61a0e182baf64ded2df683427e0de877e0cc Mon Sep 17 00:00:00 2001 From: reykboerner Date: Tue, 24 Sep 2024 12:46:37 +0100 Subject: [PATCH 31/38] implemented review comments - part 1 --- ext/src/CoupledSDEs.jl | 46 +++++++++++++++++++++++++-------------- ext/src/classification.jl | 11 ++++++++-- test/stochastic.jl | 8 +++---- 3 files changed, 43 insertions(+), 22 deletions(-) diff --git a/ext/src/CoupledSDEs.jl b/ext/src/CoupledSDEs.jl index 39f8a60b..11127c5b 100644 --- a/ext/src/CoupledSDEs.jl +++ b/ext/src/CoupledSDEs.jl @@ -194,43 +194,57 @@ end DynamicalSystemsBase.referrenced_sciml_prob(ds::CoupledSDEs) = ds.integ.sol.prob -function covariance(ds::CoupledSDEs) - A = diffusion_matrix(ds) - A * A' -end +""" + diffusion_matrix(ds::CoupledSDEs) +Returns the diffusion matrix of the stochastic term of the [`CoupledSDEs`](@ref) `ds`, +provided that the diffusion function `g` can be expressed as a constant invertible matrix. +If this is not the case, returns `nothing`. + +Note: The diffusion matrix ``Σ`` is the square root of the noise covariance matrix ``Q`` (see +[`covariance_matrix`](@ref)), defined via the Cholesky decomposition ``Q = Σ Σ^\\top``. +""" function diffusion_matrix(ds::CoupledSDEs{IIP,D}) where {IIP,D} if ds.noise_type[:invertible] diffusion = diffusion_function(ds) A = diffusion(zeros(D), current_parameters(ds), 0.0) else + @warn """ + The diffusion function of the `CoupledSDEs` cannot be expressed as a constant + invertible matrix. + """ A = nothing end return A end -########################################################################################### -# Utilities -########################################################################################### - """ -compute diffusion matrix given the covariance matrix of noise matrix. + covariance_matrix(ds::CoupledSDEs) + +Returns the covariance matrix of the stochastic term of the [`CoupledSDEs`](@ref) `ds`, +provided that the diffusion function `g` can be expressed as a constant invertible matrix. +If this is not the case, returns `nothing`. + +See also [`diffusion_matrix`](@ref). """ -function diffusion_matrix(Γ::AbstractMatrix) - U, S, V = LinearAlgebra.svd(Γ) # A ≈ U * Diagonal(S) * V' - A = U * LinearAlgebra.Diagonal(sqrt.(S)) - return A +function covariance_matrix(ds::CoupledSDEs) + A = diffusion_matrix(ds) + (A == nothing) ? nothing : A * A' end +########################################################################################### +# Utilities +########################################################################################### + """ https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#The-uniform-scaling-operator """ function construct_diffusion_function(g, cov, noise_prototype, σ, D, IIP) if isnothing(g) # diagonal additive noise cov = isnothing(cov) ? LinearAlgebra.I(D) : cov - size(cov)[1] != D && - throw(ArgumentError("covariance matrix must be of size $((D, D))")) - A = diffusion_matrix(cov) + size(cov) != (D,D) && + throw(ArgumentError("Covariance matrix must be of size $((D, D))")) + A = sqrt(cov) if IIP if isdiag(cov) g = (du, u, p, t) -> du .= σ .* diag(A) diff --git a/ext/src/classification.jl b/ext/src/classification.jl index fc6f6d52..472c7e2e 100644 --- a/ext/src/classification.jl +++ b/ext/src/classification.jl @@ -1,15 +1,17 @@ using LinearAlgebra function is_state_independent(g, u, p, t) - rdm_states = [rand(eltype(u), length(u)) for _ in 1:10] + rdm_states = [u .+ rand(eltype(u), length(u)) .- 0.5 for _ in 1:10] val = map(u -> g(u, p, t), rdm_states) length(unique(val)) == 1 end + function is_time_independent(g, u, p, t0) - trange = t0:0.1:10 + trange = t0 .+ [0, 0.101, 1.01, 10.1, 101.0] val = map(t -> g(u, p, t), trange) length(unique(val)) == 1 end + function is_invertible(x; tol=1e-10) F = lu(x, check=false) det = abs(prod(diag(F.U))) @@ -33,6 +35,7 @@ function diffusion_function(g, IIP, noise_prototype) end end end + function diffusion_function(ds::CoupledSDEs{IIP}) where {IIP} diffusion_function(ds.integ.g, IIP, referrenced_sciml_prob(ds).noise_rate_prototype) end @@ -111,3 +114,7 @@ function find_noise_type(prob::SDEProblem, IIP) prob.g, prob.u0, prob.p, prob.tspan[1], prob.noise, nothing, prob.noise_rate_prototype, IIP) end + +function noise_type(ds::CoupledSDEs; t0=0) + find_noise_type(SDEProblem(ds, tspan=(t0, Inf)), isinplace(ds)) +end diff --git a/test/stochastic.jl b/test/stochastic.jl index 6693cd76..c29dce8d 100644 --- a/test/stochastic.jl +++ b/test/stochastic.jl @@ -46,7 +46,7 @@ lor_SRA = CoupledSDEs(lorenz_rule, u0, p0; diffeq = (alg = SRA(), abstol = 1e-2, reltol = 1e-2) ) -diffeq_cov= (alg = LambaEM(), abstol = 1e-2, reltol = 1e-2, dt=0.1) +diffeq_cov = (alg = LambaEM(), abstol = 1e-2, reltol = 1e-2, dt=0.1) lor_oop_cov = CoupledSDEs(lorenz_rule, u0, p0; covariance = Γ, diffeq=diffeq_cov) lor_iip_cov = CoupledSDEs(lorenz_rule_iip, u0, p0; covariance = Γ, diffeq=diffeq_cov) @@ -94,7 +94,7 @@ end f(u, p, t) = 1.01u f!(du, u, p, t) = du .= 1.01u @testset "covariance" begin - g(u, p, t) = diffusion_matrix([1 0.3; 0.3 1]) + g(u, p, t) = sqrt([1 0.3; 0.3 1]) corr = CoupledSDEs(f, zeros(2); covariance = [1 0.3; 0.3 1]) corr_alt = CoupledSDEs(f, zeros(2); g = g, noise_prototype = zeros(2, 2)) @test corr.noise_type == corr_alt.noise_type @@ -124,7 +124,7 @@ end @testset "diffusion_matrix" begin Γ = [1.0 0.3 0.0; 0.3 1 0.5; 0.0 0.5 1.0] - A = diffusion_matrix(Γ) + A = sqrt(Γ) lorenz_oop = CoupledSDEs(lorenz_rule, u0, p0, covariance = Γ, diffeq=diffeq_cov) @test A ≈ diffusion_matrix(lorenz_oop) @test Γ ≈ A * A' @@ -135,7 +135,7 @@ end f(u, p, t) = [0.0, 0.0] function diffusion(u, p, t) Γ = [1.0 p[1]; p[1] 1.0] - diffusion_matrix(Γ) + sqrt(Γ) end ds = CoupledSDEs(f, zeros(2), [0.3]; g = diffusion, noise_prototype = zeros(2, 2)) A = diffusion_matrix(ds) From f907929690c1744cb9cb25b728e2f9256719d787 Mon Sep 17 00:00:00 2001 From: reykboerner Date: Thu, 26 Sep 2024 10:21:51 +0100 Subject: [PATCH 32/38] revised CoupledSDEs docstring --- src/core_systems/continuous_time_sde.jl | 105 +++++++++++++++--------- 1 file changed, 64 insertions(+), 41 deletions(-) diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index 5c50286a..0a090ddb 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -5,66 +5,90 @@ export CoupledSDEs CoupledSDEs(f, u0 [, p]; kwargs...) A stochastic continuous time dynamical system defined by a set of -coupled stochastic differential equations as follows: +coupled stochastic differential equations (SDEs) as follows: ```math -d\\vec{u} = \\vec{f}(\\vec{u}, p, t) dt + \\vec{g}(\\vec{u}, p, t) dW_t +\\text{d}\\mathbf{u} = \\mathbf{f}(\\mathbf{u}, p, t) \\text{d}t + \\mathbf{g}(\\mathbf{u}, p, t) \\text{d}\\mathcal{N}_t ``` where -``\\text{d}\\mathcal{W} = \\Gamma \\cdot \\text{d}\\mathcal{N}``, -and ``\\mathcal N`` denotes a stochastic process. -The (positive definite) noise covariance matrix is -``\\Sigma = \\Gamma \\Gamma^\\top \\in \\mathbb R^{N\\times N}``. - -Optionally you can provide a parameter container and initial time as keyword `t0`. -By default `p = nothing`, and `t0 = 0`. - -For construction instructions regarding `f, u0` see the [DynamicalSystems.jl tutorial +``\\mathbf{u}(t)`` is the state vector at time ``t``, ``\\mathbf{f}`` describes the +deterministic dynamics, and the noise term +``\\mathbf{g}(\\mathbf{u}, p, t) \\text{d}\\mathcal{N}_t`` describes +the stochastic forcing in terms of a noise function (or *diffusion function*) +``\\mathbf{g}`` and a noise process ``\\mathcal{N}_t``. The parameters of the functions +``\\mathcal{f}`` and ``\\mathcal{g}`` are contained in the vector ``p``. + +There are multiple ways to construct a `CoupledSDEs` depending on the type of stochastic +forcing. + +The only required positional arguments are the deterministic dynamic rule +`f(u, p, t)`, the initial state `u0`, and optinally the parameter container `p` +(by default `p = nothing`). For construction instructions regarding `f, u0` see the [DynamicalSystems.jl tutorial ](https://juliadynamics.github.io/DynamicalSystemsDocs.jl/dynamicalsystems/dev/tutorial/). -`g` must follow the same syntax, i.e., `g(u, p, t)` for out-of-place (oop) and -`g(du, u, p, t)` for in-place (iip). -## Stochastic part +By default, the noise term is standard Brownian motion, i.e. additive Gaussian white noise +with identity covariance matrix. To construct different noise structures, see +[below](@noise-term). + +## Noise term -By default the stochastic part of the differential equation is additive diagional Wiener -noise applied to every variable. Alternativly, to correlate the noise procces can provide -a covariance matrix with the kwarg `covariance`. A more exotic stochastic process can be -defined by adding the keyword arguments `g`, `noise_prototype` and `noise`. +The noise term can be specified via several keyword arguments. Based on these keyword +arguments, the noise function `g` is constructed behind the scenes unless explicitly given. -`g` is the diffusion function of the CoupledSDEs and provides an interface to multiplicative -and non-autonomous noise processes. +- The noise strength (i.e. the magnitude of the stochastic forcing) can be scaled with + `noise_strength` (defaults to `1.0`). This factor is multiplied with the whole noise term. +- For non-diagonal and correlated noise, a covariance matrix can be provided via + `covariance_matrix` (defaults to identity matrix of size `length(u0)`.) +- For more complicated noise structures, including state- and time-dependent noise, the + noise function `g` can be provided explicitly as a keyword argument (defaults to + `nothing`). For construction instructions, continue reading. -`noise` indicates the noise process applied and defaults to Gaussian white noise (Wiener process). -For details on defining various noise processes, refer to [DiffEqNoiseProcess.jl -](https://docs.sciml.ai/DiffEqNoiseProcess/stable/). +The function `g` interfaces to the diffusion function specified in an +[`SDEProblem`](https://docs.sciml.ai/DiffEqDocs/stable/types/sde_types/#SciMLBase.SDEProblem) +of DynamicalSystems.jl. `g` must follow the same syntax as `f`, i.e., `g(u, p, t)` +for out-of-place (oop) and `g!(du, u, p, t)` for in-place (iip). -`noise_prototype` indicates the prototype type instance for the noise rates, i.e., -the output of `g`. It can be any type which overloads `A_mul_B!` with itself being the -middle argument. Commonly, this is a matrix or sparse matrix. If this is not given, it +Unless `g` is of vector form and describes diagonal noise, a prototype type instance for the +output of `g` must be specified via the keyword argument `noise_prototype`. It can be of any +type that overloads `A_mul_B!` with itself being the middle argument. +Commonly, this is a matrix or sparse matrix. If this is not given, it defaults to `nothing`, which means the `g` should be interpreted as being diagonal. -By combining ``g`` and ``\\mathcal{W}``, you can define different type of stochastic systems. -Examples of different types of stochastic systems can be found on the +The noise process can be specified via `noise_process`. It defaults to a standard Wiener +process (Gaussian white noise). +For details on defining noise processes, see the docs of [DiffEqNoiseProcess.jl +](https://docs.sciml.ai/DiffEqNoiseProcess/stable/). A complete list of the pre-defined +processes can be found [here](https://docs.sciml.ai/DiffEqNoiseProcess/stable/noise_processes/). +Note that `DiffEqNoiseProcess.jl` also has an interface for defining custom noise processes. + +By combining `g` and `noise_process`, you can define different types of stochastic systems. +Examples of different types of stochastic systems are listed on the [StochasticDiffEq.jl tutorial page](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example/). A quick overview of common types of stochastic systems can also be found in the [online docs for `CoupledSDEs`](@ref defining-stochastic-dynamics). -The noise processes ``\\mathcal{W}`` that can be used in the stochastic simulations are -obtained from [DiffEqNoiseProcess.jl](https://docs.sciml.ai/DiffEqNoiseProcess/stable). -A complete list of the pre-defined processes can be found [here](https://docs.sciml.ai/DiffEqNoiseProcess/stable/noise_processes/). -Note that `DiffEqNoiseProcess.jl` also has an interface for defining custom noise processes. +## Keyword arguments + +- `g`: noise function (default `nothing`) +- `noise_strength`: scaling factor for noise strength (default `1.0`) +- `covariance_matrix`: noise covariance matrix (default `nothing`) +- `noise_prototype`: prototype instance for the output of `g` (default `nothing`) +- `noise_process`: stochastic process as provided by [DiffEqNoiseProcess.jl](https://docs.sciml.ai/DiffEqNoiseProcess/stable/) (default `nothing`, i.e. standard Wiener process) +- `t0`: initial time (default `0.0`) +- `diffeq`: DiffEq solver settings (see below) +- `seed`: random number seed (default `UInt64(0)`) ## DifferentialEquations.jl interfacing -The SDEs are evolved via the solvers of DifferentialEquations.jl. -If you want to specify a solver, do so by using the keyword `alg`, -which requires you to be using StochasticDiffEq.jl to access the solvers. +The `CoupledSDEs` is evolved using the solvers of DifferentialEquations.jl. +To specify a solver via the `diffeq` keyword argument, use the flag `alg`, which can be +accessed after loading StochasticDiffEq.jl (`using StochasticDiffEq`). The default `diffeq` is: ```julia (alg = SOSRA(), abstol = 1.0e-2, reltol = 1.0e-2) ``` -`diffeq` keywords can also include `callback` for [event handling +`diffeq` keywords can also include a `callback` for [event handling ](https://docs.sciml.ai/DiffEqDocs/stable/features/callback_functions/). Dev note: `CoupledSDEs` is a light wrapper of `SDEIntegrator` from StochasticDiffEq.jl. @@ -74,11 +98,10 @@ to extract the problem. ## Converting between `CoupledSDEs` and `CoupledODEs` -You can convert to `CoupledODEs` to analyze the deterministic part via -the function `CoupledODEs(ds::CoupledSDEs; diffeq, t0)`. -Similarly, use `CoupledSDEs(ds::CoupledODEs, p; kw...)` to convert to a stochastic system. - - +You can convert a `CoupledSDEs` system to `CoupledODEs` to analyze its deterministic part +using the function `CoupledODEs(ds::CoupledSDEs; diffeq, t0)`. +Similarly, use `CoupledSDEs(ds::CoupledODEs, p; kwargs...)` to convert a `CoupledODEs` into +a `CoupledSDEs`. """ struct CoupledSDEs{IIP,D,I,P} <: ContinuousTimeDynamicalSystem # D parametrised by length of u0 From 75996bebb25f6a6acaf53eb95f1041c1524a641a Mon Sep 17 00:00:00 2001 From: reykboerner Date: Thu, 26 Sep 2024 10:39:04 +0100 Subject: [PATCH 33/38] remove broken docs link --- src/core_systems/continuous_time_sde.jl | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index 0a090ddb..f447a366 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -26,8 +26,7 @@ The only required positional arguments are the deterministic dynamic rule ](https://juliadynamics.github.io/DynamicalSystemsDocs.jl/dynamicalsystems/dev/tutorial/). By default, the noise term is standard Brownian motion, i.e. additive Gaussian white noise -with identity covariance matrix. To construct different noise structures, see -[below](@noise-term). +with identity covariance matrix. To construct different noise structures, see below. ## Noise term @@ -37,7 +36,7 @@ arguments, the noise function `g` is constructed behind the scenes unless explic - The noise strength (i.e. the magnitude of the stochastic forcing) can be scaled with `noise_strength` (defaults to `1.0`). This factor is multiplied with the whole noise term. - For non-diagonal and correlated noise, a covariance matrix can be provided via - `covariance_matrix` (defaults to identity matrix of size `length(u0)`.) + `covariance` (defaults to identity matrix of size `length(u0)`.) - For more complicated noise structures, including state- and time-dependent noise, the noise function `g` can be provided explicitly as a keyword argument (defaults to `nothing`). For construction instructions, continue reading. @@ -70,7 +69,7 @@ found in the [online docs for `CoupledSDEs`](@ref defining-stochastic-dynamics). - `g`: noise function (default `nothing`) - `noise_strength`: scaling factor for noise strength (default `1.0`) -- `covariance_matrix`: noise covariance matrix (default `nothing`) +- `covariance`: noise covariance matrix (default `nothing`) - `noise_prototype`: prototype instance for the output of `g` (default `nothing`) - `noise_process`: stochastic process as provided by [DiffEqNoiseProcess.jl](https://docs.sciml.ai/DiffEqNoiseProcess/stable/) (default `nothing`, i.e. standard Wiener process) - `t0`: initial time (default `0.0`) From 7189029c5bea96e6ecba40c33380ab0ecd466942 Mon Sep 17 00:00:00 2001 From: reykboerner Date: Thu, 26 Sep 2024 12:23:43 +0100 Subject: [PATCH 34/38] implemented review comments - part 2 --- ext/src/CoupledSDEs.jl | 50 ++++++++++++++----------- ext/src/classification.jl | 41 ++++++++++++++------ src/core_systems/continuous_time_sde.jl | 6 ++- 3 files changed, 62 insertions(+), 35 deletions(-) diff --git a/ext/src/CoupledSDEs.jl b/ext/src/CoupledSDEs.jl index 11127c5b..ae8faa73 100644 --- a/ext/src/CoupledSDEs.jl +++ b/ext/src/CoupledSDEs.jl @@ -101,7 +101,7 @@ function DynamicalSystemsBase.CoupledSDEs( end """ - CoupledSDEs(ds::CoupledODEs, g, p [, σ]; kwargs...) + CoupledSDEs(ds::CoupledODEs, p; kwargs...) Converts a [`CoupledODEs` ](https://juliadynamics.github.io/DynamicalSystems.jl/stable/tutorial/#CoupledODEs) @@ -118,24 +118,15 @@ function DynamicalSystemsBase.CoupledSDEs( noise_process=nothing, seed=UInt64(0) ) - return CoupledSDEs( - dynamic_rule(ds), - current_state(ds), - p; - g=g, - noise_strength=noise_strength, - covariance=covariance, - diffeq=diffeq, - noise_prototype=noise_prototype, - noise_process=noise_process, - seed=seed - ) + return CoupledSDEs(dynamic_rule(ds), current_state(ds), p; + g, noise_strength, covariance, diffeq, noise_prototype, noise_process, seed) end """ CoupledODEs(ds::CoupledSDEs; kwargs...) -Converts a [`CoupledSDEs`](@ref) into [`CoupledODEs`](@ref). +Converts a [`CoupledSDEs`](@ref) into a [`CoupledODEs`](@ref) by extracting the +deterministic part of `ds`. """ function DynamicalSystemsBase.CoupledODEs( sys::CoupledSDEs; diffeq=DEFAULT_DIFFEQ, t0=0.0) @@ -237,30 +228,45 @@ end ########################################################################################### """ -https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#The-uniform-scaling-operator + construct_diffusion_function(g, covariance, noise_strength, noise_prototype, D, IIP) + +Constructs the noise function `g` based on the keyword arguments +`g`, `covariance`, `noise_strength`, and `noise_prototype` +specified by the user when defining a `CoupledSDEs`. + +Here `D` is the system dimension and `IIP` indicated whether the function `g` is in-place +(`IIP = true`) or out-of-place (`false`). + +Returns `g, noise_prototype`. """ -function construct_diffusion_function(g, cov, noise_prototype, σ, D, IIP) +function construct_diffusion_function( + g, covariance, noise_strength, noise_prototype, D, IIP + ) if isnothing(g) # diagonal additive noise - cov = isnothing(cov) ? LinearAlgebra.I(D) : cov + cov = isnothing(covariance) ? LinearAlgebra.I(D) : covariance size(cov) != (D,D) && throw(ArgumentError("Covariance matrix must be of size $((D, D))")) A = sqrt(cov) if IIP if isdiag(cov) - g = (du, u, p, t) -> du .= σ .* diag(A) + g = (du, u, p, t) -> du .= noise_strength .* diag(A) else - g = (du, u, p, t) -> du .= σ .* A + g = (du, u, p, t) -> du .= noise_strength .* A noise_prototype = zeros(size(A)) # ^ we could make this sparse to make it more performant end else if isdiag(cov) - g = (u, p, t) -> SVector{length(diag(A)),eltype(A)}(diag(σ .* A)) + g = (u, p, t) -> SVector{length(diag(A)),eltype(A)}( + diag(noise_strength .* A) + ) else - g = (u, p, t) -> SMatrix{size(A)...,eltype(A)}(σ .* A) + g = (u, p, t) -> SMatrix{size(A)...,eltype(A)}( + noise_strength .* A + ) noise_prototype = zeros(size(A)) end end end return g, noise_prototype -end +end \ No newline at end of file diff --git a/ext/src/classification.jl b/ext/src/classification.jl index 472c7e2e..548ee6d2 100644 --- a/ext/src/classification.jl +++ b/ext/src/classification.jl @@ -1,23 +1,36 @@ using LinearAlgebra +""" +Checks whether the function g depends on u based on 10 random points around the given u. +""" function is_state_independent(g, u, p, t) rdm_states = [u .+ rand(eltype(u), length(u)) .- 0.5 for _ in 1:10] val = map(u -> g(u, p, t), rdm_states) length(unique(val)) == 1 end +""" +Checks whether g depends explicitly on time for select points on the interval [t0, t0+101]. +""" function is_time_independent(g, u, p, t0) - trange = t0 .+ [0, 0.101, 1.01, 10.1, 101.0] + trange = t0 .+ [0.0, 0.101, 1.01, 10.1, 101.0] val = map(t -> g(u, p, t), trange) length(unique(val)) == 1 end +""" +Checks whether a matrix x is invertible by verifying that it has nonzero determinant. +""" function is_invertible(x; tol=1e-10) F = lu(x, check=false) det = abs(prod(diag(F.U))) return det > tol end +""" +Checks whether the function f is linear by checking additivity and scalar multiplication +for two points x and y. +""" function is_linear(f, x, y, c) check1 = f(x + y) == f(x) + f(y) check2 = f(c * x) == c * f(x) @@ -41,9 +54,8 @@ function diffusion_function(ds::CoupledSDEs{IIP}) where {IIP} end """ -We classify the noise type of the CoupledSDEs based on the system given by the user. -In doing this we also determine the covariance matrix - +Classifies the noise type of the CoupledSDEs given by the user. +Returns a named tuple of noise properties and the noise covariance matrix (if applicable). """ function find_noise_type(g, u0, p, t0, noise, covariance, noise_prototype, IIP) noise_size = isnothing(noise_prototype) ? nothing : size(noise_prototype) @@ -84,8 +96,19 @@ function find_noise_type(g, u0, p, t0, noise, covariance, noise_prototype, IIP) # additive noise is equal to state independent noise isadditive = state_independent isautonomous = time_independent - islinear = !state_independent ? - is_linear(u -> diffusion(u, p, t0), rand(D), rand(D), 2.0) : true + + islinear = true + if !state_independent + for i in 1:10 + check = is_linear(u -> diffusion(u, p, t0), + u0 + i .* rand(D), u0 + i .* rand(D), 2.0) + check ? nothing : islinear = false + end + end + + # Previous formulation: + #islinear = !state_independent ? + # is_linear(u -> diffusion(u, p, t0), rand(D), rand(D), 2.0) : true if time_independent && state_independent if !isnothing(noise_size) && isequal(noise_size...) @@ -113,8 +136,4 @@ function find_noise_type(prob::SDEProblem, IIP) find_noise_type( prob.g, prob.u0, prob.p, prob.tspan[1], prob.noise, nothing, prob.noise_rate_prototype, IIP) -end - -function noise_type(ds::CoupledSDEs; t0=0) - find_noise_type(SDEProblem(ds, tspan=(t0, Inf)), isinplace(ds)) -end +end \ No newline at end of file diff --git a/src/core_systems/continuous_time_sde.jl b/src/core_systems/continuous_time_sde.jl index f447a366..bcd9a789 100644 --- a/src/core_systems/continuous_time_sde.jl +++ b/src/core_systems/continuous_time_sde.jl @@ -48,7 +48,9 @@ for out-of-place (oop) and `g!(du, u, p, t)` for in-place (iip). Unless `g` is of vector form and describes diagonal noise, a prototype type instance for the output of `g` must be specified via the keyword argument `noise_prototype`. It can be of any -type that overloads `A_mul_B!` with itself being the middle argument. +type `A` that has the method +[`LinearAlgebra.mul!(Y, A, B) -> Y`](https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#LinearAlgebra.mul!) +defined. Commonly, this is a matrix or sparse matrix. If this is not given, it defaults to `nothing`, which means the `g` should be interpreted as being diagonal. @@ -109,4 +111,4 @@ struct CoupledSDEs{IIP,D,I,P} <: ContinuousTimeDynamicalSystem p0::P diffeq # isn't parameterized because it is only used for display noise_type::NamedTuple -end +end \ No newline at end of file From 109e7b4fd57473d34d38efd3b56c5937e1278c12 Mon Sep 17 00:00:00 2001 From: reykboerner Date: Thu, 26 Sep 2024 12:24:49 +0100 Subject: [PATCH 35/38] proofread and revised CoupledSDEs docs --- docs/src/CoupledSDEs.md | 31 +++++++++++++++++------------ test/stochastic.jl | 2 +- test/stochastic_characterisation.jl | 4 ++-- 3 files changed, 21 insertions(+), 16 deletions(-) diff --git a/docs/src/CoupledSDEs.md b/docs/src/CoupledSDEs.md index 090982cf..add9f3ce 100644 --- a/docs/src/CoupledSDEs.md +++ b/docs/src/CoupledSDEs.md @@ -27,7 +27,8 @@ end; ``` ### Additive noise -When $g$ is independent of the state variables $u$, the noise is called additive, otherwise it is called multiplicative. The ladder is somewhat misleading, as it has come to signify the general case, despite seeming to suggest the limited case where $g(x) \propto x$. We can define a simple additive noise system as follows: +When $g(u, p, t)$ is independent of the state $u$, the noise is called additive; otherwise, it is multiplicative. +We can define a simple additive noise system as follows: ```@example type sde = CoupledSDEs(f!, zeros(2)); ``` @@ -35,31 +36,36 @@ which is equivalent to ```@example type t0 = 0.0; W0 = zeros(2); W = WienerProcess(t0, W0, 0.0) -sde = CoupledSDEs(f!, zeros(2); noise_process=W); +sde = CoupledSDEs(f!, zeros(2); + noise_process=W, covariance=[1 0; 0 1], noise_strength=1.0 + ); ``` -We defined a vector of random numbers `dW`, whose size matches the output of `g`, with the noise applied element-wise, i.e., `g.*dW`. Specifically, `dW` is a vector of Gaussian noise processes whose size matches the output of `g`. The noise is applied element-wise, i.e., `g.*dW`. By default, the noise processes are uncorrelated, meaning the covariance matrix is diagonal. This type of noise is referred to as diagonal. The vector `dW` is by default zero mean white gaussian noise $\mathcal{N}(0, \text{d}t)$ where the variance is the timestep $\text{d}t$ unit variance (Wiener Process). We can sample a trajectory from this system using the `trajectory` also used for the deterministic systems: +We defined a Wiener process `W`, whose increments are vectors of normally distributed random numbers of length matching the output of `g`. The noise is applied element-wise, i.e., `g.*dW`. Since the noise processes are uncorrelated, meaning the covariance matrix is diagonal, this type of noise is referred to as diagonal. + +We can sample a trajectory from this system using the `trajectory` function also used for the deterministic systems: ```@example type tr = trajectory(sde, 1.0) plot_trajectory(tr...) ``` #### Correlated noise -Correlated noise is where the random number generated in `dW` are correlated. This can be done by specifying the covariance matrix $\Sigma$ to the `covariance` keyword: +In the case of correlated noise, the random numbers in a vector increment `dW` are correlated. This can be achieved by specifying the covariance matrix $\Sigma$ via the `covariance` keyword: ```@example type ρ = 0.3 Σ = [1 ρ; ρ 1] diffeq = (alg = LambaEM(), dt=0.1) sde = CoupledSDEs(f!, zeros(2); covariance=Σ, diffeq=diffeq) ``` -Alternativly, we can parametrise the covariance matrix by defining the diffusion function $g$ ourselves: +Alternatively, we can parametrise the covariance matrix by defining the diffusion function $g$ ourselves: ```@example type g!(du, u, p, t) = (du .= [1 p[1]; p[1] 1]; return nothing) sde = CoupledSDEs(f!, zeros(2), (ρ); g=g!, noise_prototype=zeros(2, 2)) ``` -Here, we had to provide a `noise_prototype` to indicate that the diffusion function `g` will output a 2x2 matrix. +Here, we had to provide `noise_prototype` to indicate that the diffusion function `g` will output a 2x2 matrix. #### Scalar noise -Scalar noise is where a single random variable is applied to all dependent variables. To do this, one has to give an one dimensional noise process to the `noise` keyword of the `CoupledSDEs` constructor. +If all state variables are forced by the same single random variable, we have scalar noise. +To define scalar noise, one has to give an one-dimensional noise process to the `noise_process` keyword of the `CoupledSDEs` constructor. ```@example type t0 = 0.0; W0 = 0.0; noise = WienerProcess(t0, W0, 0.0) @@ -70,9 +76,8 @@ plot_trajectory(tr...) ``` We can see that noise applied to each variable is the same. - -### Multiplicative and non-autonomous noise -Multiplicative noise in the SciML ecosystem is defined as when $g_i(t, u)=a_i u$. However, in the literature the name is sometimes used for when the noise is not-additive, including nonlinear. In general, we can make the noise time- and state-dependent in a similar fashion to the deterministic dynamics. For example, we can define a system with decreasing multiplicative noise as follows: +### Multiplicative and time-dependent noise +In the SciML ecosystem, multiplicative noise is defined through the condition $g_i(t, u)=a_i u$. However, in the literature the name is more broadly used for any situation where the noise is non-additive and depends on the state $u$, possibly also in a non-linear way. When defining a `CoupledSDEs`, we can make the noise term time- and state-dependent by specifying an explicit time- or state-dependence in the noise function `g`, just like we would define `f`. For example, we can define a system with temporally decreasing multiplicative noise as follows: ```@example type function g!(du, u, p, t) du .= u ./ (1+t) @@ -82,12 +87,12 @@ sde = CoupledSDEs(f!, rand(2)./10; g=g!) ``` #### Non-diagonal noise -Non-diagonal noise allows for the terms to linearly mixed via `g` being a matrix. Suppose we have two Wiener processes and two dependent random variables such that the output of `g` is a 2x2 matrix. Therefore, we have +Non-diagonal noise allows for the terms to be linearly mixed (correlated) via `g` being a matrix. Suppose we have two Wiener processes and two state variables such that the output of `g` is a 2x2 matrix. Therefore, we have ```math du_1 = f_1(u,p,t)dt + g_{11}(u,p,t)dW_1 + g_{12}(u,p,t)dW_2 \\ du_2 = f_2(u,p,t)dt + g_{21}(u,p,t)dW_1 + g_{22}(u,p,t)dW_2 ``` -To indicate the structure that `g` should have, we can use the `noise_prototype` keyword. Let us define a special type of non-diagonal noise called commutative noise. For this we can utilize the `RKMilCommute` algorithm which is designed to utilise the structure of commutative noise. +To indicate the structure that `g` should have, we must use the `noise_prototype` keyword. Let us define a special type of non-diagonal noise called commutative noise. For this we can utilize the `RKMilCommute` algorithm which is designed to utilize the structure of commutative noise. ```@example type σ = 0.25 # noise strength @@ -103,4 +108,4 @@ sde = CoupledSDEs(f!, rand(2)./10; g=g!, noise_prototype = zeros(2, 2), diffeq = ``` !!! warning - Non-diagonal problems need specific type of solvers. See the [SciML recommendations](https://docs.sciml.ai/DiffEqDocs/stable/solvers/sde_solve/#sde_solve). + Non-diagonal problems need specific solvers. See the [SciML recommendations](https://docs.sciml.ai/DiffEqDocs/stable/solvers/sde_solve/#sde_solve). \ No newline at end of file diff --git a/test/stochastic.jl b/test/stochastic.jl index c29dce8d..84cacbf1 100644 --- a/test/stochastic.jl +++ b/test/stochastic.jl @@ -153,4 +153,4 @@ end @test approx ≈ Γ atol=1e-1 broken = true # I think I understand something wromg here end -end +end \ No newline at end of file diff --git a/test/stochastic_characterisation.jl b/test/stochastic_characterisation.jl index 6663b6e6..7dcb1cf4 100644 --- a/test/stochastic_characterisation.jl +++ b/test/stochastic_characterisation.jl @@ -3,7 +3,7 @@ using DynamicalSystemsBase, DiffEqNoiseProcess, Test, StochasticDiffEq sciml_prob(sde) = sde.integ.sol.prob f!(du, u, p, t) = du .= 1.01u -@testset "Additive" begin +@testset "Additive noise" begin # Additive Wiener noise W = WienerProcess(0.0, zeros(2), zeros(2)) addit_autom_inv = CoupledSDEs(f!, zeros(2); noise_process = W) @@ -52,7 +52,7 @@ f!(du, u, p, t) = du .= 1.01u @test CoupledSDEs(sciml_prob(addit_non_autom)).noise_type == types end -@testset "Multiplicative" begin +@testset "Multiplicative noise" begin # multiplicative linear Wiener noise g!(du, u, p, t) = (du .= u; return nothing) linear_multipli = CoupledSDEs(f!, rand(2) ./ 10; g = g!) From 5df534a1daa6f76e8941a1eb0cae858f3d2525bd Mon Sep 17 00:00:00 2001 From: reykboerner Date: Thu, 26 Sep 2024 13:52:46 +0100 Subject: [PATCH 36/38] fixed bug that made tests fail --- ext/src/CoupledSDEs.jl | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/ext/src/CoupledSDEs.jl b/ext/src/CoupledSDEs.jl index ae8faa73..a8e73964 100644 --- a/ext/src/CoupledSDEs.jl +++ b/ext/src/CoupledSDEs.jl @@ -228,10 +228,10 @@ end ########################################################################################### """ - construct_diffusion_function(g, covariance, noise_strength, noise_prototype, D, IIP) + construct_diffusion_function(g, covariance, noise_prototype, noise_strength, D, IIP) Constructs the noise function `g` based on the keyword arguments -`g`, `covariance`, `noise_strength`, and `noise_prototype` +`g`, `covariance`, `noise_prototype`, and `noise_strength` specified by the user when defining a `CoupledSDEs`. Here `D` is the system dimension and `IIP` indicated whether the function `g` is in-place @@ -240,7 +240,7 @@ Here `D` is the system dimension and `IIP` indicated whether the function `g` is Returns `g, noise_prototype`. """ function construct_diffusion_function( - g, covariance, noise_strength, noise_prototype, D, IIP + g, covariance, noise_prototype, noise_strength, D, IIP ) if isnothing(g) # diagonal additive noise cov = isnothing(covariance) ? LinearAlgebra.I(D) : covariance From 78f25ee2009f75d9891738a54920325790a04a5c Mon Sep 17 00:00:00 2001 From: George Datseris Date: Mon, 30 Sep 2024 10:17:47 +0100 Subject: [PATCH 37/38] Update CHANGELOG.md --- CHANGELOG.md | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/CHANGELOG.md b/CHANGELOG.md index ec799380..cac7e740 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -1,3 +1,7 @@ +# v3.10.0 + +Brand new dynamical system `CoupledSDEs` that represents stochastic differential equations. It also comes with a dedicated documentation page. + # v3.9.0 A new function `jacobian` that generates Jacobian rule for any `ds<:CoreDynamicalSystem` via From de8258eaeac706d976d6defea7eba0716c59e10e Mon Sep 17 00:00:00 2001 From: George Datseris Date: Mon, 30 Sep 2024 10:19:19 +0100 Subject: [PATCH 38/38] Update Project.toml --- Project.toml | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Project.toml b/Project.toml index d1dadd43..e870a7a4 100644 --- a/Project.toml +++ b/Project.toml @@ -1,7 +1,7 @@ name = "DynamicalSystemsBase" uuid = "6e36e845-645a-534a-86f2-f5d4aa5a06b4" repo = "https://github.com/JuliaDynamics/DynamicalSystemsBase.jl.git" -version = "3.10.1" +version = "3.11.0" [deps] ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" @@ -31,4 +31,4 @@ julia = "1.9" StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0" [extensions] -StochasticSystemsBase = "StochasticDiffEq" \ No newline at end of file +StochasticSystemsBase = "StochasticDiffEq"