From 099745ebfe9107a753abba9be5d9e37b731e1241 Mon Sep 17 00:00:00 2001 From: schillic Date: Sat, 10 Feb 2024 13:19:40 +0100 Subject: [PATCH] experimental notebooks --- notebooks/test1.jl | 1116 +++++++++++++++++++++ notebooks/test2.jl | 2288 ++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 3404 insertions(+) create mode 100644 notebooks/test1.jl create mode 100644 notebooks/test2.jl diff --git a/notebooks/test1.jl b/notebooks/test1.jl new file mode 100644 index 0000000..3f1e4f0 --- /dev/null +++ b/notebooks/test1.jl @@ -0,0 +1,1116 @@ +### A Pluto.jl notebook ### +# v0.19.38 + +using Markdown +using InteractiveUtils + +# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error). +macro bind(def, element) + quote + local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end + local el = $(esc(element)) + global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) + el + end +end + +# ╔═╡ e70ff28c-8555-11ee-3655-8b281a850fb3 +using Plots + +# ╔═╡ 1a547eec-1829-4239-8f56-45fe8d2a1f98 +md"""## Reachability computation + +(The code is hidden for brevity.)""" + +# ╔═╡ 1dfc494b-4d5c-406f-82c0-c7fc5ab054bd +T = 5.0 + +# ╔═╡ e0d29d49-b78e-48fc-ad9b-8f9754cfdf98 +@bind α html"" + +# ╔═╡ 6057597d-de46-475c-8614-096ac1ff02df +md"Step size αT = $(α * T)" + +# ╔═╡ 038b5436-d021-42a2-909e-05a071786e2a +f(x) = α * T + 0.01 * x + +# ╔═╡ 84f05e80-a149-464b-85b3-8b07540cac17 +md"""## Results""" + +# ╔═╡ bbd4fee9-cdcc-4640-b69e-c2a7b2e07ee2 +plot(f, [0, 3]; ylims=(0.1, 0.5)) + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" + +[compat] +Plots = "~1.39.0" +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000002 +PLUTO_MANIFEST_TOML_CONTENTS = """ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.10.0" +manifest_format = 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"Libdl", "Ogg_jll", "Pkg"] +git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c" +uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" +version = "1.3.7+1" + +[[deps.mtdev_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11" +uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e" +version = "1.1.6+0" + +[[deps.nghttp2_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" +version = "1.52.0+1" + +[[deps.p7zip_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" +version = "17.4.0+2" + +[[deps.x264_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2" +uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" +version = "2021.5.5+0" + +[[deps.x265_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" +uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" +version = "3.5.0+0" + +[[deps.xkbcommon_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] +git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37" +uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" +version = "1.4.1+1" +""" + +# ╔═╡ Cell order: +# ╠═e70ff28c-8555-11ee-3655-8b281a850fb3 +# ╟─1a547eec-1829-4239-8f56-45fe8d2a1f98 +# ╠═1dfc494b-4d5c-406f-82c0-c7fc5ab054bd +# ╟─6057597d-de46-475c-8614-096ac1ff02df +# ╟─e0d29d49-b78e-48fc-ad9b-8f9754cfdf98 +# ╠═038b5436-d021-42a2-909e-05a071786e2a +# ╟─84f05e80-a149-464b-85b3-8b07540cac17 +# ╠═bbd4fee9-cdcc-4640-b69e-c2a7b2e07ee2 +# ╟─00000000-0000-0000-0000-000000000001 +# ╟─00000000-0000-0000-0000-000000000002 diff --git a/notebooks/test2.jl b/notebooks/test2.jl new file mode 100644 index 0000000..5c1fa12 --- /dev/null +++ b/notebooks/test2.jl @@ -0,0 +1,2288 @@ +### A Pluto.jl notebook ### +# v0.19.38 + +using Markdown +using InteractiveUtils + +# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error). +macro bind(def, element) + quote + local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end + local el = $(esc(element)) + global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) + el + end +end + +# ╔═╡ e70ff28c-8555-11ee-3655-8b281a850fb3 +using ReachabilityAnalysis, Plots + +# ╔═╡ bf31bfe5-041f-4f8d-a9d6-906754805463 +md"""## Introduction + +We consider as an illustrative example a simple harmonic oscillator system. +This is a single degree of freedom, second order problem given by the following equation: + +```math + u''(t) + ω^2 u(t) = 0, +``` +where $ω$ is a scalar and $u(t)$ is the unknown. + +This problem can be associated with a spring-mass system, where $u(t)$ is the +elongation of the spring at time $t$ and the mass and stiffness set a natural +frequency $ω$. In this case we consider $ω = 4π$. + +Let us introduce the state variable $v(t) := u'(t)$ and define the vector +$x(t) = [u(t), v(t)]^T$. Then we can rewrite the system in the following first order form + +```math + x'(t) = \begin{pmatrix} 0 & 1 \\ -\omega^2 & 0 \end{pmatrix} x(t) +``` +""" + +# ╔═╡ 1a547eec-1829-4239-8f56-45fe8d2a1f98 +md"""## Reachability computation + +(The code is hidden for brevity.)""" + +# ╔═╡ 5a5d78e6-76c7-4b6c-933a-a922effb11c2 +begin +# Source: https://github.com/JuliaReach/SetPropagation-FEM-Examples/tree/main/examples/SDOF + +# ### Equations of motion + +# Struct that holds a problem describing an harmonic oscillator with frequency ω: +# x''(t) + ω^2 x(t) = 0 +# +# solution x(t) = Acos(ωt + B), v(t) = -ωAsin(ωt + B) +# x(0) = Acos(B) +# v(0) = -ωAsin(B) +# +# special case: if x(0) = A, v(0) = 0 => x(t) = A cos ωt +struct SDOF{T, ST} + ivp::T + X0::ST + ω::Float64 + Ampl::Float64 + T::Float64 +end + +amplitude(p::SDOF) = p.Ampl +frequency(p::SDOF) = p.ω +period(p::SDOF) = p.T +MathematicalSystems.initial_state(p::SDOF) = p.X0 +MathematicalSystems.InitialValueProblem(p::SDOF) = p.ivp +MathematicalSystems.state_matrix(p::SDOF) = state_matrix(p.ivp) + +function analytic_solution(p::SDOF; A=p.Ampl, B=0.0, x0=nothing, v0=nothing) + @assert p.X0 isa Singleton "the analytic solution requires a singleton initial condition" + + ω = p.ω + if !isnothing(x0) && !isnothing(v0) + A = sqrt(x0^2 + v0^2 / ω^2) + B = atan(-v0 / (ω*x0)) + end + return t -> A * cos(ω * t + B) +end + +function analytic_derivative(p::SDOF; A=p.Ampl, B=0.0, x0=nothing, v0=nothing) + @assert p.X0 isa Singleton "the analytic solution requires a singleton initial condition" + + ω = p.ω + if !isnothing(x0) && !isnothing(v0) + A = sqrt(x0^2 + v0^2 / ω^2) + B = atan(-v0 / (ω*x0)) + end + return t -> -ω * A * sin(ω * t + B) +end + +function InitialValueProblem_quad(p::SDOF) + M = hcat(1.0) + ω = p.ω + K = hcat(ω^2) + C = zeros(1, 1) + R = zeros(1) + S = SecondOrderAffineContinuousSystem(M, C, K, R) + @assert p.X0 isa Singleton + x0 = element(p.X0) + U0 = [x0[1]] + U0dot = [x0[2]] + return IVP(S, (U0, U0dot)) +end + +function sdof(; T=0.5, # period + Ampl=1.0, # amplitude + X0 = Singleton([Ampl, 0.0])) # initial condition + ## frequency + ω = 2π / T + + ## cast as a first-order system: + ## x' = v + ## v' = -ω^2 * x + A = [ 0.0 1.0; + -ω^2 0.0] + + prob = @ivp(LinearContinuousSystem(A), X(0) ∈ X0) + return SDOF(prob, X0, ω, Ampl, T) +end + +nothing +end + +# ╔═╡ 3075126d-b7aa-43cd-b10f-256a99ffee38 +problem = sdof(); + +# ╔═╡ 955d9674-255a-45ee-9dd9-57c424ae3973 +T = problem.T + +# ╔═╡ e0d29d49-b78e-48fc-ad9b-8f9754cfdf98 +@bind α html"" + +# ╔═╡ 6057597d-de46-475c-8614-096ac1ff02df +md"Step size αT = $(α * T)" + +# ╔═╡ bbd4fee9-cdcc-4640-b69e-c2a7b2e07ee2 +begin +model = StepIntersect(setops=:concrete) + +# alg = VREP(δ=α*T, approx_model=model) +# solvrep = solve(prob, tspan=(0.0, tmax), alg=alg); + +alg = GLGM06(δ=α*T, approx_model=model) +solglg = solve(problem.ivp, tspan=(0.0, T), alg=alg); + +# alg = BOX(δ=α*T, approx_model=model) +# solbox = solve(prob, tspan=(0.0, tmax), alg=alg); + +# For plots: https://docs.juliaplots.org/stable/gallery/gr/generated/gr-ref016/#gr_ref016 + +nothing +end + +# ╔═╡ 84f05e80-a149-464b-85b3-8b07540cac17 +md"""## Results""" + +# ╔═╡ 0d99a847-c6af-4019-b955-ffa2f32492c8 +plot(solglg, vars=(0, 1), xlab="t", ylab="u(t)") + +# ╔═╡ 43d0a3f1-170d-4d58-9b6b-3201109d9677 +plot(solglg, vars=(0, 2), xlab="t", ylab="u'(t)") + +# ╔═╡ 1bd941f2-e1fa-446e-a489-4b1c87be97ed +plot(solglg, vars=(1, 2), xlab="u(t)", ylab="u'(t)") + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +ReachabilityAnalysis = "1e97bd63-91d1-579d-8e8d-501d2b57c93f" + +[compat] +Plots = "~1.39.0" +ReachabilityAnalysis = "~0.22.1" +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000002 +PLUTO_MANIFEST_TOML_CONTENTS = """ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.10.0" +manifest_format = "2.0" +project_hash = "32f9f254d0b0676d1d9dde2b45ed229c6cbeed99" 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