Transform functions to methods

docs/src/index.md

@@ -74,14 +74,14 @@ When ``\epsilon`` converges to zero, then, by homogenization theory, the process
 ```
 where ``K>0`` is a corrective constant that comes from the cell problem of the homogenization, see also [`K`](@ref). The task is to estimate the parameter ``\vartheta := \alpha K`` 
 through data that comes in form of a long trajectory of the process ``X_\epsilon`` with "small" ``\epsilon > 0``. We will use the [`MDE`](@ref) for the estimation. First, we generate synthetic
-data with the function [`Langevin_ϵ`](@ref). The plot of a trajectory, created with [`produce_trajectory`](@ref), looks like the following.
+data with the function [`Langevin`](@ref). The plot of a trajectory, created with [`produce_trajectory`](@ref), looks like the following.
 ```@example
 # quadratic potential V with sine oscillation p
 using MDEforM   # hide
 import Random   # hide
 Random.seed!(1111)  # hide
 T = 10
-trajectory = Langevin_ϵ(5.0, func_config=LDO(), α=2.0, σ=1.0, ϵ=0.1, T=T)
+trajectory = Langevin(5.0, 10.0, func_config=LDO(), α=2.0, σ=1.0, ϵ=0.1, T=T)
 fig = produce_trajectory(trajectory, T)
 ```
 
@@ -90,7 +90,7 @@ We now increase the time horizon ``T`` to obtain accurate estimates for ``\varth
 using MDEforM   # hide
 import Random   # hide
 Random.seed!(1111)  # hide
-data = Langevin_ϵ(5.0, func_config=LDO(), α=2.0, σ=1.0, ϵ=0.1, T=1000)[1]   # only slow process
+data = Langevin(5.0, 10.0, func_config=LDO(), α=2.0, σ=1.0, ϵ=0.1, T=1000)[1]   # only slow process
 nothing # hide
 ```
 Under this configuration the true parameter ``\vartheta`` is given by

docs/src/multiscale_limit_pairs.md

@@ -17,22 +17,16 @@ The majority of the following functions give realizations of the multiscale proc
 
 ## Functions
 ```@docs
-Fast_OU_ϵ
-Fast_OU_∞
+Fast_OU
 LDA
 NLDAM
 NSDP
-Langevin_ϵ
+Langevin
 K
-Langevin_∞
 LDO
 NLDO
-Langevin_ϵ_2D
-Langevin_∞_2D
-Burger_ϵ
-Burger_∞
-Fast_chaotic_ϵ
-Fast_chaotic_∞
+Burger
+Fast_chaotic
 produce_trajectory
 ```
 

src/MDE_functionals.jl

@@ -120,7 +120,7 @@ $ julia --threads 10 --project=. # start julia with 10 threads and activate proj
 ```julia-repl
 julia> Threads.nthreads()
 julia> using MDEforM
-julia> data = Langevin_ϵ(1.0, func_config=NLDO(), α=2.0, σ=1.0, ϵ=0.1, T=100)[1]
+julia> data = Langevin(1.0, 0.0, func_config=NLDO(), α=2.0, σ=1.0, ϵ=0.1, T=100)[1]
 julia> Δ(data, 1, 1, NLDO()[1])
 ```
 
@@ -163,7 +163,7 @@ See the main manuscript for details on this functional. It is the core object of
 # Examples
 ```julia-repl
 julia> using MDEforM
-julia> data = Langevin_ϵ(1.0, func_config=LDO(), α=2.0, σ=1.0, ϵ=0.1, T=100)[1]
+julia> data = Langevin(1.0, 0.0, func_config=LDO(), α=2.0, σ=1.0, ϵ=0.1, T=100)[1]
 julia> Δ_Gaussian1D(data, 1, 1)
 ```
 
@@ -239,7 +239,7 @@ and is given by the covariance matrix of the invariant Gaussian density, and ``\
 julia> using MDEforM
 julia> M=[4 2;2 3]
 julia> σ = 5.0  
-julia> data = Langevin_ϵ_2D([-5.0, -5.0], func_config=(x-> cos(x), x -> 1/2*cos(x)), M=M, σ=σ, ϵ=0.1, T=100.0)[1]
+julia> data = Langevin([-5.0, -5.0], [0.0, 0.0], func_config=(x-> cos(x), x -> 1/2*cos(x)), M=M, σ=σ, ϵ=0.1, T=100.0)[1]
 julia> CorrK = [K(x-> cos(x), σ) 0 ; 0 K(x -> 1/2*cos(x), σ)]
 julia> ϑ = CorrK*M
 julia> Σ = σ*CorrK

src/MDE_gradients.jl

@@ -88,7 +88,7 @@ $ julia --threads 10 --project=. # start julia with 10 threads and activate proj
 ```julia-repl
 julia> Threads.nthreads()
 julia> using MDEforM
-julia> data = Langevin_ϵ(1.0, func_config=NLDO(), α=2.0, σ=1.0, ϵ=0.1, T=100)[1]
+julia> data = Langevin(1.0, 0.0, func_config=NLDO(), α=2.0, σ=1.0, ϵ=0.1, T=100)[1]
 julia> Δ_grad_ϑ(data, 1, 1, NLDO()[1])
 ```
 
@@ -177,7 +177,7 @@ $ julia --threads 10 --project=. # start julia with 10 threads and activate proj
 ```julia-repl
 julia> Threads.nthreads()
 julia> using MDEforM
-julia> data = Langevin_ϵ(1.0, func_config=NLDO(), α=2.0, σ=1.0, ϵ=0.1, T=100)[1]
+julia> data = Langevin(1.0, 0.0, func_config=NLDO(), α=2.0, σ=1.0, ϵ=0.1, T=100)[1]
 julia> Δ_grad_Σ(data, 1, 1, NLDO()[1])
 ```
 
@@ -217,7 +217,7 @@ is implemented. Here, ``X_ϵ`` is a one-dimensional time series of length ``T``,
 # Examples
 ```julia-repl
 julia> using MDEforM
-julia> data = Langevin_ϵ(1.0, func_config=LDO(), α=2.0, σ=1.0, ϵ=0.1, T=100)[1]
+julia> data = Langevin(1.0, 0.0, func_config=LDO(), α=2.0, σ=1.0, ϵ=0.1, T=100)[1]
 julia> Δ_Gaussian1D_grad(data, 1, 1)
 ```
 

src/MDE_optimizers.jl

@@ -41,7 +41,7 @@ is, in the given case, quadratic, i.e. ``V(x)=x^2/2``.
 ```julia-repl
 julia> using MDEforM
 julia> limit_drift_parameter = 1.0
-julia> data = Fast_chaotic_ϵ([1.0, 1.0, 1.0, 1.0], A=-limit_drift_parameter, B=0.0, λ=2/45, ϵ=0.1, T=1000)
+julia> data = Fast_chaotic([1.0, 1.0, 1.0, 1.0], A=-limit_drift_parameter, B=0.0, λ=2/45, ϵ=0.1, T=1000)
 julia> MDE(data, "Fast Chaotic Noise", limit_drift_parameter, 10.0)
 ```
 
@@ -118,7 +118,7 @@ $ julia --threads 10 --project=. # start julia with 10 threads and activate proj
 ```julia-repl
 julia> using MDEforM
 julia> limit_drift_parameter = 1.0
-julia> data = Fast_chaotic_ϵ([1.0, 1.0, 1.0, 1.0], A=limit_drift_parameter, B=1.0, λ=2/45, ϵ=10^(-3/2), T=100)
+julia> data = Fast_chaotic([1.0, 1.0, 1.0, 1.0], A=limit_drift_parameter, B=1.0, λ=2/45, ϵ=10^(-3/2), T=100)
 julia> V = NLDO()[1]
 julia> MDE(data, "Fast Chaotic Noise", V, limit_drift_parameter, 0.8)
 ```
@@ -203,7 +203,7 @@ julia> p1_prime, p2_prime = (x-> cos(x), x -> 1/2*cos(x))
 julia> CorrK = [K(p1, σ) 0 ; 0 K(p2, σ)]
 julia> A = CorrK*M # true parameter; the parameter that ought to be estimated
 julia> Σ = σ*CorrK
-julia> data = Langevin_ϵ_2D([-5.0, -5.0], func_config=(p1_prime, p2_prime), M=M, σ=σ, ϵ=0.1, T=1000)[1]
+julia> data = Langevin([-5.0, -5.0], [0.0, 0.0], func_config=(p1_prime, p2_prime), M=M, σ=σ, ϵ=0.1, T=1000)[1]
 julia> ϑ_initial = [3.0 0.5*Σ[1]; 0.5*Σ[4] 6.0]
 julia> MDE(data, Σ, ϑ_initial)
 ```

src/MDEforM.jl

@@ -12,11 +12,10 @@ using NaNMath
 using QuadGK
 
 # main code
-export Fast_OU_ϵ, Fast_OU_∞, LDA, NLDAM, NSDP
-export Langevin_ϵ, Langevin_∞, K, LDO, NLDO
-export Langevin_ϵ_2D, Langevin_∞_2D
-export Burger_ϵ, Burger_∞
-export Fast_chaotic_ϵ, Fast_chaotic_∞
+export Fast_OU, LDA, NLDAM, NSDP
+export Langevin, K, LDO, NLDO
+export Burger
+export Fast_chaotic
 export produce_trajectory
 
 include("multiscale_limit_pairs.jl")