From e9e84ede326f16111c322558820ed4c2bf4fab04 Mon Sep 17 00:00:00 2001 From: schillic Date: Thu, 8 Feb 2024 21:44:33 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20JuliaRea?= =?UTF-8?q?ch/Notebooks@a3e84dcee64fb3fee60fb6724e3b17cfea301cdd=20?= =?UTF-8?q?=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .gitignore | 18 + LICENSE | 21 + Manifest.toml | 2175 ++++++++++++++++ Project.toml | 6 + README.md | 7 + index.md | 3 + notebooks/harmonic_oscillator.html | 16 + notebooks/harmonic_oscillator.jl | 2281 +++++++++++++++++ notebooks/harmonic_oscillator.plutostate | Bin 0 -> 18980 bytes notebooks/index.html | 23 + notebooks/pluto_export.json | 1 + ...Lm22IROUvVwt-h7lG4Uoybb9yIGKLSA.plutostate | Bin 0 -> 42623 bytes ...uLQz07oB9lk8F8GNYEff8yDAM1VlVPA.plutostate | Bin 0 -> 18980 bytes 13 files changed, 4551 insertions(+) create mode 100644 .gitignore create mode 100644 LICENSE create mode 100644 Manifest.toml create mode 100644 Project.toml create mode 100644 README.md create mode 100644 index.md create mode 100644 notebooks/harmonic_oscillator.html create mode 100644 notebooks/harmonic_oscillator.jl create mode 100644 notebooks/harmonic_oscillator.plutostate create mode 100644 notebooks/index.html create mode 100644 notebooks/pluto_export.json create mode 100644 pluto_state_cache/0_19_3846mhZHp3yQgBLm22IROUvVwt-h7lG4Uoybb9yIGKLSA.plutostate create mode 100644 pluto_state_cache/0_19_38k9p8n2d4c3uauLQz07oB9lk8F8GNYEff8yDAM1VlVPA.plutostate diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..e32cd21 --- /dev/null +++ b/.gitignore @@ -0,0 +1,18 @@ +# Files generated by invoking Julia with --code-coverage +*.jl.cov +*.jl.*.cov + +# Files generated by invoking Julia with --track-allocation +*.jl.mem + +# System-specific files and directories generated by the BinaryProvider and BinDeps packages +# They contain absolute paths specific to the host computer, and so should not be committed +deps/deps.jl +deps/build.log +deps/downloads/ +deps/usr/ +deps/src/ + +# Build artifacts for creating documentation generated by the Documenter package +docs/build/ +docs/site/ diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..f0ad8ea --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2023 JuliaReach + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/Manifest.toml b/Manifest.toml new file mode 100644 index 0000000..d2c04f7 --- /dev/null +++ b/Manifest.toml @@ -0,0 +1,2175 @@ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.10.0" +manifest_format = "2.0" +project_hash = "7c009ac6feea1bc0c119cc7d51cc8acbb85a9b3b" + +[[deps.ADTypes]] +git-tree-sha1 = "41c37aa88889c171f1300ceac1313c06e891d245" +uuid = "47edcb42-4c32-4615-8424-f2b9edc5f35b" +version = "0.2.6" + +[[deps.AbstractPlutoDingetjes]] +deps = ["Pkg"] +git-tree-sha1 = "c278dfab760520b8bb7e9511b968bf4ba38b7acc" +uuid = "6e696c72-6542-2067-7265-42206c756150" +version = "1.2.3" + +[[deps.Accessors]] +deps = ["CompositionsBase", "ConstructionBase", "Dates", 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"d8fb68d0-12a3-5cfd-a85a-d49703b185fd" +version = "1.4.1+1" diff --git a/Project.toml b/Project.toml new file mode 100644 index 0000000..0128bd3 --- /dev/null +++ b/Project.toml @@ -0,0 +1,6 @@ +[deps] +LazySets = "b4f0291d-fe17-52bc-9479-3d1a343d9043" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +Pluto = "c3e4b0f8-55cb-11ea-2926-15256bba5781" +PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" +ReachabilityAnalysis = "1e97bd63-91d1-579d-8e8d-501d2b57c93f" diff --git a/README.md b/README.md new file mode 100644 index 0000000..5365bfa --- /dev/null +++ b/README.md @@ -0,0 +1,7 @@ +# Notebooks + +Notebooks you can run on the web. + +Precomputed view: [![docs-dev](https://img.shields.io/badge/docs-latest-blue.svg)](https://juliareach.github.io/Notebooks/) + +1. [Harmonic oscillator](https://binder.plutojl.org/open?url=https%253A%252F%252Fraw.githubusercontent.com%252FJuliaReach%252FNotebooks%252Fmaster%252Fnotebooks%252Fharmonic_oscillator.jl) ([precomputed](https://juliareach.github.io/Notebooks/notebooks/harmonic_oscillator)) diff --git a/index.md b/index.md new file mode 100644 index 0000000..2bfea98 --- /dev/null +++ b/index.md @@ -0,0 +1,3 @@ +# Available notebooks + +* [Harmonic Oscillator](notebooks/harmonic_oscillator) diff --git a/notebooks/harmonic_oscillator.html b/notebooks/harmonic_oscillator.html new file mode 100644 index 0000000..b02352e --- /dev/null +++ b/notebooks/harmonic_oscillator.html @@ -0,0 +1,16 @@ + + + + + + +
\ No newline at end of file diff --git a/notebooks/harmonic_oscillator.jl b/notebooks/harmonic_oscillator.jl new file mode 100644 index 0000000..d3fa384 --- /dev/null +++ b/notebooks/harmonic_oscillator.jl @@ -0,0 +1,2281 @@ +### 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""" + +# ╔═╡ 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(X' = AX, X(0) ∈ X0) + return SDOF(prob, X0, ω, Ampl, T) +end + +problem = sdof() +T = problem.T + +nothing +end + +# ╔═╡ 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" + +[[deps.ADTypes]] +git-tree-sha1 = "41c37aa88889c171f1300ceac1313c06e891d245" +uuid = 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