removed redundant code; added docs; adjused structure
Ruben Seitz
parent
5abce884d1
commit
f4ca3fb591
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@ -1,8 +1,8 @@
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# This file is machine-generated - editing it directly is not advised
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julia_version = "1.11.4"
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julia_version = "1.11.5"
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manifest_format = "2.0"
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project_hash = "0d147eaf78630b05e95b5317275a880443440272"
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project_hash = "ede42d5c0ee6ced5b877b9fea99444d4d8bea863"
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[[deps.ADTypes]]
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git-tree-sha1 = "e2478490447631aedba0823d4d7a80b2cc8cdb32"
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@ -15,6 +15,11 @@ weakdeps = ["ChainRulesCore", "ConstructionBase", "EnzymeCore"]
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ADTypesConstructionBaseExt = "ConstructionBase"
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ADTypesEnzymeCoreExt = "EnzymeCore"
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[[deps.ANSIColoredPrinters]]
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version = "0.0.1"
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[[deps.AbstractFFTs]]
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deps = ["LinearAlgebra"]
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git-tree-sha1 = "d92ad398961a3ed262d8bf04a1a2b8340f915fef"
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@ -300,6 +305,12 @@ git-tree-sha1 = "05ba0d07cd4fd8b7a39541e31a7b0254704ea581"
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[[deps.ColorBrewer]]
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git-tree-sha1 = "e771a63cc8b539eca78c85b0cabd9233d6c8f06f"
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@ -610,6 +621,12 @@ git-tree-sha1 = "e7b7e6f178525d17c720ab9c081e4ef04429f860"
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uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
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version = "0.9.4"
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[[deps.Documenter]]
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deps = ["ANSIColoredPrinters", "AbstractTrees", "Base64", "CodecZlib", "Dates", "DocStringExtensions", "Downloads", "Git", "IOCapture", "InteractiveUtils", "JSON", "Logging", "Markdown", "MarkdownAST", "Pkg", "PrecompileTools", "REPL", "RegistryInstances", "SHA", "TOML", "Test", "Unicode"]
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[[deps.Downloads]]
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@ -935,6 +952,18 @@ git-tree-sha1 = "6570366d757b50fabae9f4315ad74d2e40c0560a"
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[[deps.Git_jll]]
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deps = ["Artifacts", "Expat_jll", "JLLWrappers", "LibCURL_jll", "Libdl", "Libiconv_jll", "OpenSSL_jll", "PCRE2_jll", "Zlib_jll"]
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[[deps.Glib_jll]]
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deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"]
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git-tree-sha1 = "b0036b392358c80d2d2124746c2bf3d48d457938"
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@ -976,6 +1005,12 @@ git-tree-sha1 = "68c173f4f449de5b438ee67ed0c9c748dc31a2ec"
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uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
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version = "0.3.28"
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[[deps.IOCapture]]
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deps = ["Logging", "Random"]
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[[deps.IfElse]]
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git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
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uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
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@ -1189,6 +1224,11 @@ git-tree-sha1 = "a9eaadb366f5493a5654e843864c13d8b107548c"
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uuid = "10f19ff3-798f-405d-979b-55457f8fc047"
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[[deps.LazyArrays]]
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deps = ["ArrayLayouts", "FillArrays", "LinearAlgebra", "MacroTools", "SparseArrays"]
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git-tree-sha1 = "866ce84b15e54d758c11946aacd4e5df0e60b7a3"
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@ -1409,6 +1449,12 @@ deps = ["Base64"]
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uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
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version = "1.11.0"
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[[deps.MarkdownAST]]
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deps = ["AbstractTrees", "Markdown"]
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git-tree-sha1 = "465a70f0fc7d443a00dcdc3267a497397b8a3899"
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version = "0.1.2"
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[[deps.MathTeXEngine]]
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git-tree-sha1 = "f5a6805fb46c0285991009b526ec6fae43c6dec2"
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@ -1631,7 +1677,13 @@ version = "3.2.4+0"
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[[deps.OpenLibm_jll]]
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deps = ["Artifacts", "Libdl"]
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uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
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[[deps.OpenSSH_jll]]
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[[deps.OpenSSL_jll]]
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deps = ["Artifacts", "JLLWrappers", "Libdl"]
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@ -2109,6 +2161,12 @@ git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
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version = "0.1.0"
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git-tree-sha1 = "ffdaf70d81cf6ff22c2b6e733c900c3321cab864"
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@ -1,4 +1,5 @@
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[deps]
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DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
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Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
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GLMakie = "e9467ef8-e4e7-5192-8a1a-b1aee30e663a"
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Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
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14
model_fhn.jl
14
model_fhn.jl
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@ -1,14 +0,0 @@
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function fhn!(du, u, p::FHNParams, t)
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N, dx = p.N, p.dx
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u_mat = reshape(u[1:N^2], N, N)
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v_mat = reshape(u[N^2+1:end], N, N)
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Δu = laplacian(u_mat) / dx^2
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Δv = laplacian(v_mat) / dx^2
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fu = p.Du * Δu .+ u_mat .- u_mat .^ 3 ./ 3 .- v_mat
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fv = p.Dv * Δv .+ p.ε * (u_mat .+ p.a .- p.b .* v_mat)
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du .= vcat(vec(fu), vec(fv))
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end
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@ -2,9 +2,7 @@
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module AnimalFurFHN
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include("constants.jl")
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include("initial_conditions.jl")
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include("laplacian.jl")
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include("model_fhn.jl")
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include("solver.jl")
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export run_simulation # Make sure this is here!
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@ -1,9 +1,15 @@
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module Constants
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struct FHNParams
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N::Int
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dx::Float64
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dx::Float64 # grid spacing
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Du::Float64
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Dv::Float64
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ε::Float64
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ϵ::Float64
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a::Float64
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b::Float64
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end
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export FHNParams
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end # module Constants
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@ -1,8 +0,0 @@
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import Random
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function initial_conditions(N)
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Random.seed!(1234)
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u = 0.1 .+ 0.01 .* rand(N, N)
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v = 0.1 .+ 0.01 .* rand(N, N)
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return vec(u), vec(v)
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end
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@ -1,4 +1,19 @@
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"""
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laplacian(U::Matrix{Float64}, N::Int, h::Float64)
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Computes the discrete 2D Laplacian of a matrix `U` using a 5-point stencil
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and circular boundary conditions.
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# Arguments
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- `U::Matrix{Float64}`: The input 2D matrix representing the field or image.
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- `N::Int`: Integer
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- `h::Float64`: The spatial step size or grid spacing between points in the discretization.
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# Returns
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- `Vector{Float64}`: A flattened (vectorized) representation of the approximated Laplacian values for each element in `U`. The boundary conditions are handled circularly.
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"""
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function laplacian(U::Matrix{Float64}, N::Int, h::Float64)
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# shifts matrices and sums them up
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padded = circshift(U, (-1, 0)) .+ circshift(U, (1, 0)) .+
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circshift(U, (0, -1)) .+ circshift(U, (0, 1)) .- 4 .* U
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return vec(padded) ./ h^2
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@ -1,14 +0,0 @@
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function fhn!(du, u, p::FHNParams, t)
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N, dx = p.N, p.dx
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u_mat = reshape(u[1:N^2], N, N)
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v_mat = reshape(u[N^2+1:end], N, N)
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Δu = laplacian(u_mat) / dx^2
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Δv = laplacian(v_mat) / dx^2
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fu = p.Du * Δu .+ u_mat .- u_mat .^ 3 ./ 3 .- v_mat
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fv = p.Dv * Δv .+ p.ε * (u_mat .+ p.a .- p.b .* v_mat)
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du .= vcat(vec(fu), vec(fv))
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end
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@ -1,34 +1,48 @@
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using DifferentialEquations
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using Random
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using .Constants
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"""
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fhn(du, u, p:FHNParams, t:)
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Implements the spatial dynamics of FitzHugh-Nagumo (fhn). Designed to be
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within a larger numerical solver of partial differential equations.
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# Arguments
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- `du`: output argument which stores the calculated derivatives
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- `u`: input vector containing the current state of the system at time t
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- `p`: holds all the fixed parameters of the FHN model
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- `t`: current time
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# Returns
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- `du`: calculated derivatives put back into the du array
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"""
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function fhn!(du, u, p::FHNParams, t = 0)
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u_mat = reshape(u[1:N^2], N, N) # activation variable
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v_mat = reshape(u[N^2+1:end], N, N) # deactivation variable
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Δu = reshape(laplacian(u_mat, N, p.dx), N, N)
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Δv = reshape(laplacian(v_mat, N, p.dx), N, N)
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fu = p.Du * Δu .+ u_mat .- u_mat .^ 3 ./ 3 .- v_mat
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fv = p.Dv * Δv .+ p.ϵ * (u_mat .+ p.a .- p.b .* v_mat)
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du .= vcat(vec(fu), vec(fv))
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end
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function run_simulation(N::Int, tspan::Tuple{Float64,Float64})
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# Turing-spot parameters
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a = 0.1
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b = 0.5
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ϵ = 0.01
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Du = 1e-5
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Dv = 1e-3
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dx = 1.0 # grid spacing
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p = FHNParams(N, 1.0, 1e-5, 1e-3, 0.01, 0.1, 0.5)
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# Initial conditions (random noise)
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u0, v0 = initial_conditions(N)
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Random.seed!(1234)
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# Create two vectors with length N*N with numbers between 0.1 and 0.11
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u0 = vec(0.1 .+ 0.01 .* rand(N, N))
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v0 = vec(0.1 .+ 0.01 .* rand(N, N))
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y0 = vcat(u0, v0)
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function f!(du, u, p, t)
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u_mat = reshape(u[1:N^2], N, N)
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v_mat = reshape(u[N^2+1:end], N, N)
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Δu = reshape(laplacian(u_mat, N, dx), N, N)
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Δv = reshape(laplacian(v_mat, N, dx), N, N)
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fu = Du * Δu .+ u_mat .- u_mat .^ 3 ./ 3 .- v_mat
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fv = Dv * Δv .+ ϵ * (u_mat .+ a .- b .* v_mat)
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du .= vcat(vec(fu), vec(fv))
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end
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prob = ODEProblem(f!, y0, tspan)
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prob = ODEProblem(fhn!, y0, tspan, p)
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sol = solve(prob, BS3(), saveat=1.0) # You can try `Rosenbrock23()` too
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return sol
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