From bd258c02fa522f3aa2fb417303abaecc399972dd Mon Sep 17 00:00:00 2001 From: Orjan Ameye Date: Thu, 21 Nov 2024 08:46:43 +0100 Subject: [PATCH 1/7] merge nav and sidebar --- docs/make.jl | 3 +- docs/pages.jl | 57 ++++---- docs/src/.vitepress/config.mts | 132 +++++++----------- docs/src/.vitepress/theme/VersionPicker.vue | 142 ++++++++++++++++++++ docs/src/.vitepress/theme/index.ts | 61 ++------- docs/src/.vitepress/theme/style.css | 73 ++++++---- docs/src/introduction/resources.md | 0 7 files changed, 283 insertions(+), 185 deletions(-) create mode 100644 docs/src/.vitepress/theme/VersionPicker.vue delete mode 100644 docs/src/introduction/resources.md diff --git a/docs/make.jl b/docs/make.jl index 08a90f6a..4598c9ce 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -26,7 +26,7 @@ include("make_md_examples.jl") makedocs(; sitename="HarmonicBalance.jl", - authors="Quest", + authors="Quest group", modules=[ HarmonicBalance, Base.get_extension(HarmonicBalance, :TimeEvolution), @@ -38,6 +38,7 @@ makedocs(; devbranch="master", devurl="dev", ), + pages = PAGES, source="src", build="build", draft=false, diff --git a/docs/pages.jl b/docs/pages.jl index ee3336cd..49b43773 100644 --- a/docs/pages.jl +++ b/docs/pages.jl @@ -1,26 +1,35 @@ #! format: off pages = [ - "Background" => Any[ - "background/harmonic_balance.md" - "background/stability_response.md" - "background/limit_cycles.md" - ], - "Examples" => Any[ - "examples/simple_Duffing.md" - "examples/linear_response.md" - "examples/time_dependent.md" - "examples/parametron.md" - "examples/limit_cycles.md" - ], - "Manual" => Any[ - "manual/entering_eom.md" - "manual/extracting_harmonics.md" - "manual/solving_harmonics.md" - "manual/Krylov-Bogoliubov_method.md" - "manual/plotting.md" - "manual/time_dependent.md" - "manual/linear_response.md" - "manual/saving.md" - ] - ] -#! format: on + "Home" => "index.md", + "Getting Started" => [ + "Brief Example" => "introduction/index.md", + "Citations" => "introduction/citation.md", + ], + "Theoretical Background" => [ + "Floquet expansions" => "background/harmonic_balance.md" + "Stability and Linear Response" => "background/stability_response.md" + "Limit Cycles" => "background/limit_cycles.md" + ], + "Tutorials" => [ + "Steady States" => "tutorials/steady_states.md" + "Classifying Solutions" => "tutorials/classification.md" + "Linear Response" => "tutorials/linear_response.md" + "Transient Dynamics" => "tutorials/time_dependent.md" + "Limit Cycles" => "tutorials/limit_cycles.md" + ], + "Examples" => [ + "Wave Mixing" => "examples/wave_mixing.md" + "Parametric Three Wave Mixing" => "examples/parametric_via_three_wave_mixing.md" + "Parametric Oscillator" => "examples/parametron.md" + ], + "Manual" => [ + "Entering Equations of Motion" => "manual/entering_eom.md" + "Computing Effective System" => "manual/extracting_harmonics.md" + "Computing Steady States" => "manual/methods.md" + "Krylov-Bogoliubov" => "manual/Krylov-Bogoliubov_method.md" + "Time Evolution" => "manual/time_dependent.md" + "Linear Response" => "manual/linear_response.md" + "Plotting" => "manual/plotting.md" + "Saving and Loading" => "manual/saving.md" + ] +] diff --git a/docs/src/.vitepress/config.mts b/docs/src/.vitepress/config.mts index 6fc8ed59..0fcbf175 100644 --- a/docs/src/.vitepress/config.mts +++ b/docs/src/.vitepress/config.mts @@ -4,16 +4,57 @@ import mathjax3 from "markdown-it-mathjax3"; import footnote from "markdown-it-footnote"; import { transformerMetaWordHighlight } from '@shikijs/transformers'; +const baseTemp = { + base: 'REPLACE_ME_DOCUMENTER_VITEPRESS',// TODO: replace this in makedocs! +} + +const navTemp = { + nav: 'REPLACE_ME_DOCUMENTER_VITEPRESS', +} + +const nav = [ + ...navTemp.nav, + { + component: 'VersionPicker' + } +] + // https://vitepress.dev/reference/site-config export default defineConfig({ - base: 'REPLACE_ME_DOCUMENTER_VITEPRESS', + base: baseTemp.base, title: 'REPLACE_ME_DOCUMENTER_VITEPRESS', description: 'REPLACE_ME_DOCUMENTER_VITEPRESS', cleanUrls: true, outDir: 'REPLACE_ME_DOCUMENTER_VITEPRESS', // This is required for MarkdownVitepress to work correctly... + head: [ + [ + "script", + { async: "", src: "https://www.googletagmanager.com/gtag/js?id=G-RE962QZ6DQ" }, + ], + [ + "script", + {}, + `window.dataLayer = window.dataLayer || []; + function gtag(){dataLayer.push(arguments);} + gtag('js', new Date()); + gtag('config', 'G-RE962QZ6DQ');`, + ], + ['link', { rel: 'icon', href: '/HarmonicBalance.jl/dev/favicon.ico' }], + ['link', { rel: 'icon', href: 'REPLACE_ME_DOCUMENTER_VITEPRESS_FAVICON' }], + ['link', { rel: 'manifest', href: '/site.webmanifest' }], + + ['script', { src: `/HarmonicBalance.jl/versions.js` }], + ['script', { src: `${baseTemp.base}siteinfo.js` }] + ], + ignoreDeadLinks: true, markdown: { math: true, + + // options for @mdit-vue/plugin-toc + // https://github.com/mdit-vue/mdit-vue/tree/main/packages/plugin-toc#options + toc: { level: [2, 3, 4] }, // for API page, triggered by: [[toc]] + config(md) { md.use(tabsMarkdownPlugin), md.use(mathjax3), @@ -22,30 +63,10 @@ export default defineConfig({ theme: { light: "github-light", dark: "github-dark" - }, - codeTransformers: [transformerMetaWordHighlight(),], + } }, - - head: [ - [ - "script", - { async: "", src: "https://www.googletagmanager.com/gtag/js?id=G-RE962QZ6DQ" }, - ], - [ - "script", - {}, - `window.dataLayer = window.dataLayer || []; - function gtag(){dataLayer.push(arguments);} - gtag('js', new Date()); - gtag('config', 'G-RE962QZ6DQ');`, - ], - ['link', { rel: 'icon', href: '/HarmonicBalance.jl/dev/favicon.ico' }], - ['link', { rel: 'manifest', href: '/site.webmanifest' }], - ], - themeConfig: { outline: 'deep', - // https://vitepress.dev/reference/default-theme-config logo: 'REPLACE_ME_DOCUMENTER_VITEPRESS', search: { provider: 'local', @@ -53,68 +74,9 @@ export default defineConfig({ detailedView: true } }, - - nav: [ - { text: 'Home', link: '/' }, - { text: 'Getting Started', link: '/introduction' }, - { text: 'Background', link: '/background/harmonic_balance' }, - { text: 'Tutorials', link: '/tutorials' }, - { text: 'Examples', link: '/examples' }, - { - text: 'Manual', items: [ - { text: 'Entering equations of motion', link: '/manual/entering_eom.md' }, - { text: 'Computing effective system', link: '/manual/extracting_harmonics' }, - { text: 'Computing steady states', link: '/manual/methods' }, - { text: 'Krylov-Bogoliubov', link: '/manual/Krylov-Bogoliubov_method' }, - { text: 'Time evolution', link: '/manual/time_dependent' }, - { text: 'Linear response', link: '/manual/linear_response' }, - { text: 'Plotting', link: '/manual/plotting' }, - { text: `Saving and loading`, link: '/manual/saving' }, - ] - }, - ], - - sidebar: { - "/introduction/": [ - { text: 'Introduction', link: '/index' }, - // { text: 'Overview', link: '/introduction/overview' }, - // { text: 'Tutorials', link: '/tutorials/index' }, - { text: 'Citation', link: '/introduction/citation' } - ], - "/background/": [ - { text: 'The method of Harmonic Balance', link: '/background/harmonic_balance.md' }, - { text: 'Stability and linear response', link: 'background/stability_response.md' }, - { text: 'Limit cycles', link: 'background/limit_cycles.md' } - ], - "/tutorials/": [ - { text: 'Steady states', link: '/tutorials/steady_states' }, - { text: 'Classifying solutions', link: '/tutorials/classification' }, - { text: 'Linear response', link: '/tutorials/linear_response' }, - { text: 'Transient dynamics', link: '/tutorials/time_dependent' }, - { text: 'Limit cycles', link: '/tutorials/limit_cycles' } - ], - "/examples/": [ - { text: 'Wave mixing', link: '/examples/wave_mixing' }, - { text: 'Parametric three wave mixing', link: '/examples/parametric_via_three_wave_mixing' }, - { text: 'Parametric oscillator', link: '/examples/parametron' } - ], - "/manual/": [ - { text: 'Entering equations of motion', link: '/manual/entering_eom.md' }, - { text: 'Computing effective system', link: '/manual/extracting_harmonics' }, - { text: 'Computing steady states', link: '/manual/methods' }, - { text: 'Krylov-Bogoliubov', link: '/manual/Krylov-Bogoliubov_method' }, - { text: 'Time evolution', link: '/manual/time_dependent' }, - { text: 'Linear response', link: '/manual/linear_response' }, - { text: 'Plotting', link: '/manual/plotting' }, - { text: `Saving and loading`, link: '/manual/saving' } - ], - "/api/": [] - }, - - editLink: { - pattern: 'https://github.com/NonlinearOscillations/HarmonicBalance.jl/edit/main/docs/src/:path', - text: 'Edit this page on GitHub' - }, + nav, + sidebar: 'REPLACE_ME_DOCUMENTER_VITEPRESS', + editLink: 'REPLACE_ME_DOCUMENTER_VITEPRESS', socialLinks: [ { icon: 'github', link: 'https://github.com/NonlinearOscillations/HarmonicBalance.jl' }, { icon: 'twitter', link: 'https://x.com/Zilberberg_Phys' }, @@ -125,4 +87,4 @@ export default defineConfig({ copyright: `© Copyright ${new Date().getUTCFullYear()}. Released under the MIT License.` }, } -}) +}) \ No newline at end of file diff --git a/docs/src/.vitepress/theme/VersionPicker.vue b/docs/src/.vitepress/theme/VersionPicker.vue new file mode 100644 index 00000000..759f36e0 --- /dev/null +++ b/docs/src/.vitepress/theme/VersionPicker.vue @@ -0,0 +1,142 @@ + + + + + + + \ No newline at end of file diff --git a/docs/src/.vitepress/theme/index.ts b/docs/src/.vitepress/theme/index.ts index 40d7b854..f8039085 100644 --- a/docs/src/.vitepress/theme/index.ts +++ b/docs/src/.vitepress/theme/index.ts @@ -1,58 +1,21 @@ // .vitepress/theme/index.ts -import { watch } from "vue"; +import { h } from 'vue' import type { Theme } from 'vitepress' import DefaultTheme from 'vitepress/theme' +import VersionPicker from "./VersionPicker.vue" import { enhanceAppWithTabs } from 'vitepress-plugin-tabs/client' import './style.css' -// taken from -// https://github.com/MakieOrg/Makie.jl/blob/master/docs/src/.vitepress/theme/index.ts - export default { - extends: DefaultTheme, - async enhanceApp({ app, router, siteData }) { - enhanceAppWithTabs(app); - // Only run this on the client. Not during build. - // this function replaces the version in the URL with the stable prefix whenever a - // new route is navigated to. VitePress does not support relative links all over the site, - // so urls will go to v0.XY even if we start at stable. This solution is not ideal as - // there is a noticeable delay between navigating to a new page and editing the url, but it's - // currently better than nothing, as users are bound to copy versioned links to the docs otherwise - // which will lead users to outdated docs in the future. - if (typeof window !== "undefined") { - function rewriteURL() { - // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE - // in siteinfo.js. - if ( - window.DOCUMENTER_NEWEST === undefined || - window.DOCUMENTER_CURRENT_VERSION === undefined || - window.DOCUMENTER_STABLE === undefined - ) { - return; - } - - // Current version is newest version, so we can rewrite the url - if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { - const rewritten_url = window.location.href.replace( - window.DOCUMENTER_CURRENT_VERSION, - window.DOCUMENTER_STABLE - ); - window.history.replaceState( - { additionalInformation: "URL rewritten to stable" }, - "DimensionalData", - rewritten_url - ); - return; - } - } - - // rewrite on router changes through vitepress - watch(() => router.route.data.relativePath, rewriteURL, { - immediate: true, - }); - // also rewrite at initial load - document.addEventListener("DOMContentLoaded", rewriteURL); + extends: DefaultTheme, + Layout() { + return h(DefaultTheme.Layout, null, { + // https://vitepress.dev/guide/extending-default-theme#layout-slots + }) + }, + enhanceApp({ app, router, siteData }) { + enhanceAppWithTabs(app); + app.component('VersionPicker', VersionPicker); } - }, -} satisfies Theme; \ No newline at end of file +} satisfies Theme \ No newline at end of file diff --git a/docs/src/.vitepress/theme/style.css b/docs/src/.vitepress/theme/style.css index 4dffba33..b5009c9e 100644 --- a/docs/src/.vitepress/theme/style.css +++ b/docs/src/.vitepress/theme/style.css @@ -32,25 +32,28 @@ https://github.com/vuejs/vitepress/blob/main/src/client/theme-default/styles/var } -.mono { - /* - Disable contextual alternates (kind of like ligatures but different) in monospace, - which turns `/>` to an up arrow and `|>` (the Julia pipe symbol) to an up arrow as well. - This is pretty bad for Julia folks reading even though copy+paste retains the same text. - */ - font-feature-settings: 'calt' 0; - - pre { - font-family: JuliaMono-Light; - } - - ; +/* +Disable contextual alternates (kind of like ligatures but different) in monospace, +which turns `/>` to an up arrow and `|>` (the Julia pipe symbol) to an up arrow as well. +This is pretty bad for Julia folks reading even though copy+paste retains the same text. +*/ +/* Target elements with class 'mono' */ +.mono-no-substitutions { + font-family: "JuliaMono-Light", monospace; + font-feature-settings: "calt" off; +} - code { - font-family: JuliaMono-Light; - } +/* Alternatively, you can use the following if you prefer: */ +.mono-no-substitutions-alt { + font-family: "JuliaMono-Light", monospace; + font-variant-ligatures: none; +} - ; +/* If you want to apply this globally to all monospace text: */ +pre, +code { + font-family: "JuliaMono-Light", monospace; + font-feature-settings: "calt" off; } /* Colors */ @@ -89,25 +92,28 @@ https://github.com/vuejs/vitepress/blob/main/src/client/theme-default/styles/var :root { --vp-home-hero-name-color: transparent; --vp-home-hero-name-background: -webkit-linear-gradient(120deg, - #9558B2 30%, - #CB3C33); + #9558B2 30%, + #CB3C33); + --vp-home-hero-image-background-image: none; /* remove the blur background */ + /* (default setting) --vp-home-hero-image-background-image: linear-gradient(-45deg, - #9558B2 30%, - #389826 30%, - #CB3C33); + #9558B2 30%, + #389826 30%, + #CB3C33); + */ --vp-home-hero-image-filter: blur(40px); } @media (min-width: 640px) { :root { - --vp-home-hero-image-filter: blur(56px); + --vp-home-hero-image-filter: blur(56px); } } @media (min-width: 960px) { :root { - --vp-home-hero-image-filter: blur(72px); + --vp-home-hero-image-filter: blur(72px); } } @@ -234,7 +240,7 @@ mjx-container>svg { @media (max-width: 960px) { .VPDoc { - padding-left: 25px !important; + padding-left: 25px !important; } } @@ -245,4 +251,19 @@ mjx-container>svg { overflow: hidden; white-space: nowrap; max-width: 200px; -} */ \ No newline at end of file +} */ + + +/* Component: Docstring Custom Block */ + +.jldocstring.custom-block { + border: 1px solid var(--vp-c-gray-2); + color: var(--vp-c-text-1) +} + +.jldocstring.custom-block summary { + font-weight: 700; + cursor: pointer; + user-select: none; + margin: 0 0 8px; +} \ No newline at end of file diff --git a/docs/src/introduction/resources.md b/docs/src/introduction/resources.md deleted file mode 100644 index e69de29b..00000000 From ce1011989eab1303050a229703b710911a30aaf5 Mon Sep 17 00:00:00 2001 From: Orjan Ameye Date: Thu, 21 Nov 2024 08:57:13 +0100 Subject: [PATCH 2/7] add pages to make file --- docs/make.jl | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index 4598c9ce..d4967da1 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -24,6 +24,8 @@ ENV["GKSwstype"] = "100" include("make_md_examples.jl") +include("pages.jl") + makedocs(; sitename="HarmonicBalance.jl", authors="Quest group", @@ -38,10 +40,10 @@ makedocs(; devbranch="master", devurl="dev", ), - pages = PAGES, + pages = pages, source="src", build="build", - draft=false, + draft=true, warnonly=true, doctest=false, # We test it in the CI, no need to run it here plugins=[bib], From 762bd45e46034e3ab35fc41b657f37db754838de Mon Sep 17 00:00:00 2001 From: Orjan Ameye Date: Thu, 21 Nov 2024 09:12:36 +0100 Subject: [PATCH 3/7] remove latex labels --- docs/make.jl | 2 +- docs/src/background/harmonic_balance.md | 20 ++++++++++---------- docs/src/background/stability_response.md | 2 +- docs/src/introduction/index.md | 2 +- docs/src/tutorials/limit_cycles.md | 4 ++-- 5 files changed, 15 insertions(+), 15 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index d4967da1..82d44e06 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -40,7 +40,7 @@ makedocs(; devbranch="master", devurl="dev", ), - pages = pages, + pages=pages, source="src", build="build", draft=true, diff --git a/docs/src/background/harmonic_balance.md b/docs/src/background/harmonic_balance.md index 10c818e3..ac2b2358 100644 --- a/docs/src/background/harmonic_balance.md +++ b/docs/src/background/harmonic_balance.md @@ -6,7 +6,7 @@ HarmonicBalance.jl focuses on harmonically-driven nonlinear systems, i.e., dynam governed by equations of motion where all explicitly time-dependent terms are harmonic. Let us take a general nonlinear system of $N$ second-order ODEs with real variables $x_i(t)$, $i = 1,2,\cdots,N$ and time $t$ as the independent variable, ```math -\begin{equation} \label{eq:ode} +\begin{equation} \ddot{\mathbf{x}}(t)+ \mathbf{F}(\mathbf{x}(t), t)=0\:. \end{equation} ``` @@ -29,7 +29,7 @@ Evidently, $\tilde{x}(\omega)$ is only nonvanishing for $\omega = \pm \omega_d$. The situation becomes more complex if nonlinear terms are present, as these cause _frequency conversion_. Suppose we add a quadratic nonlinearity $\beta x^2(t)$ to the equations of motion; an attempt to Fourier-transform gives ```math -\begin{equation} \label{eq:duffingFT} +\begin{equation} \text{FT}[x^2](\omega) = \int x^2(t) e^{-i\omega t} \: dt = \int_{-\infty}^{+\infty} \tilde{x}(\omega')\tilde{x}(\omega'') \delta(\omega''+\omega'-\omega) \: d\omega' \: d\omega'' \,, \end{equation} ``` @@ -46,14 +46,14 @@ x_i(t) = \sum_{j=1}^{M_i} u_{i,j} (T) \cos(\omega_{i,j} t)+ v_{i,j} (T) \sin(\ ``` Within this space, the system is described by a finite-dimensional vector ```math -\begin{equation} \label{eq:harmansatz} +\begin{equation} \mathbf{u}(T) = (u_{1,1}(T), v_{1,1}(T), \ldots u_{N, M_N}(T), v_{N, M_N}(T)) \end{equation} ``` -Under the assumption that $\mathbf{u}(T)$ evolves at much slower timescales than the oscillatory terms $\omega_{i,j} t$, we may neglect all of its higher order time derivatives. Notice that once ansatz \eqref{eq:harmansatz} is used in Eq. \eqref{eq:ode}, all terms become oscillatory - each prefactor of $\cos(\omega_{i,j} t)$ and $\sin(\omega_{i,j} t)$ thus generates a separate equation. Collecting these, we obtain a 1st order nonlinear ODEs, +Under the assumption that $\mathbf{u}(T)$ evolves at much slower timescales than the oscillatory terms $\omega_{i,j} t$, we may neglect all of its higher order time derivatives. Notice that once the ansatz is used in the equations of motion, all terms become oscillatory - each prefactor of $\cos(\omega_{i,j} t)$ and $\sin(\omega_{i,j} t)$ thus generates a separate equation. Collecting these, we obtain a 1st order nonlinear ODEs, ```math -\begin{equation} \label{eq:harmeq} +\begin{equation} \frac{d\mathbf{u}(T)}{dT} = \bar{\mathbf{F}} (\mathbf{u})\,, \end{equation} ``` @@ -73,7 +73,7 @@ As explained in [above](@ref prelude), for a periodic driving at frequency $\ome ### Single-frequency ansatz -We first attempt to describe the steady states of Eq. \eqref{eq:duffing} using only one harmonic, $\omega_d$. The starting point is the harmonic ansatz for $x$ +We first attempt to describe the steady states of the equations of motion using only one harmonic, $\omega_d$. The starting point is the harmonic ansatz for $x$ ```math \begin{equation} x(t) = u(T) \cos(\omega_d t) + v(T) \sin(\omega_d t)\:, @@ -82,14 +82,14 @@ We first attempt to describe the steady states of Eq. \eqref{eq:duffing} using o with the harmonic variables $u$ and $v$. The _slow time_ $T$ is, for now, equivalent to $t$. Substituting this ansatz into mechanical equations of motion results in ```math -\begin{align} \label{eq:ansatz1} +\begin{align} \left[\ddot{u} + 2 \omega_d \dot{v} + u \left(\omega_0^2 - \omega_d^2 \right) + \frac{3 \alpha \left(u^3 + uv^2\right)}{4} + F \cos{\theta}\right] &\cos(\omega_d t)& \\ + \left[\ddot{v} - 2 \omega_d \dot{u} + v \left(\omega_0^2 - \omega_d^2 \right) +\frac{3 \alpha \left(v^3 + u^2 v\right)}{4} - F \sin{\theta}\right] &\sin(\omega_d t)& \nonumber \\ + \frac{\alpha \left(u^3 - 3 u v^2\right)}{4} \cos(3 \omega_d t) + \frac{\alpha \left(3u^2 v - v^3\right)}{4} \sin(3 \omega_d t) &= 0. \nonumber \end{align} ``` -We see that the $x^3$ term has generated terms that oscillate at $3\omega_d$, describing the process of frequency upconversion. We now Fourier-transform both sides of Eq. \eqref{eq:ansatz1} with respect to $\omega_d$ to obtain the harmonic equations. This process is equivalent to extracting the respective coefficients of $\cos(\omega_d t)$ and $\sin(\omega_d t)$. Here the distinction between $t$ and $T$ becomes important: since the evolution of $u(T)$ and $v(T)$ is assumed to be slow, they are treated as constant for the purpose of the Fourier transformation. Since we are interested in steady states, we drop the higher-order derivatives and rearrange the resulting equation to +We see that the $x^3$ term has generated terms that oscillate at $3\omega_d$, describing the process of frequency upconversion. We now Fourier-transform both sides of the above equations with respect to $\omega_d$ to obtain the harmonic equations. This process is equivalent to extracting the respective coefficients of $\cos(\omega_d t)$ and $\sin(\omega_d t)$. Here the distinction between $t$ and $T$ becomes important: since the evolution of $u(T)$ and $v(T)$ is assumed to be slow, they are treated as constant for the purpose of the Fourier transformation. Since we are interested in steady states, we drop the higher-order derivatives and rearrange the resulting equation to ```math \begin{equation} \frac{d}{dT} \begin{pmatrix} u \\ v \end{pmatrix} = \frac{1}{8 \omega_d} \begin{pmatrix} 4 v \left(\omega_0^2-\omega_d^2 \right) + 3 \alpha \left(v^3 + u^2 v \right) - 4 F \sin{\theta} \\ 4 u \left(\omega_d^2-\omega_0^2 \right) - 3 \alpha \left(u^3 + u v^2 \right) - 4 F \cos{\theta} \end{pmatrix} \,. @@ -100,7 +100,7 @@ Steady states can now be found by setting the l.h.s. to zero, i.e., assuming $u( ### Sidenote: perturbative approach -The steady states describe a response that may be recast as $x_0(t) = X_0 \cos(\omega_d t + \phi)$, where $X_0=\sqrt{u^2+v^2}$ and $\phi=-\text{atan}(v/u)$. Frequency conversion from $\omega_d$ to $3 \omega_d$ can be found by setting $x(t) \equiv x_0(t) + \delta x(t)$ with $|\delta x(t)|\ll|x_0(t)|$ and expanding Eq. \eqref{eq:duffing} to first-order in $\delta x(t)$. The resulting equation +The steady states describe a response that may be recast as $x_0(t) = X_0 \cos(\omega_d t + \phi)$, where $X_0=\sqrt{u^2+v^2}$ and $\phi=-\text{atan}(v/u)$. Frequency conversion from $\omega_d$ to $3 \omega_d$ can be found by setting $x(t) \equiv x_0(t) + \delta x(t)$ with $|\delta x(t)|\ll|x_0(t)|$ and expanding the equations of motion to first-order in $\delta x(t)$. The resulting equation ```math \begin{equation} \delta \ddot{x}(t) + \left[\omega_0^2 + \frac{3 \alpha X_0^2}{4} \right]\delta x(t) = - \frac{\alpha X_0^3}{4} \cos(3 \omega_d t + 3 \phi)\,, @@ -116,7 +116,7 @@ An approach in the spirit of harmonic balance is to use both harmonics $\omega_d x(t) = u_1(T) \cos(\omega_d t) + v_1(T) \sin(\omega_d t) + u_2(T) \cos(3 \omega_d t) + v_2(T) \sin(3\omega_d t)\:, \end{equation} ``` -with $u_1, u_2, v_1, v_2$ being the harmonic variables. As before we substitute the ansatz into Eq. \eqref{eq:duffing}, drop second derivatives with respect to $T$ and Fourier-transform both sides. Now, the respective coefficients correspond to $\cos(\omega_d t)$, $\sin(\omega_d t)$, $\cos(3 \omega_d t)$ and $\sin(3\omega_d t)$. Rearranging, we obtain +with $u_1, u_2, v_1, v_2$ being the harmonic variables. As before we substitute the ansatz into the equations of motion, drop second derivatives with respect to $T$ and Fourier-transform both sides. Now, the respective coefficients correspond to $\cos(\omega_d t)$, $\sin(\omega_d t)$, $\cos(3 \omega_d t)$ and $\sin(3\omega_d t)$. Rearranging, we obtain ```math \begin{align} diff --git a/docs/src/background/stability_response.md b/docs/src/background/stability_response.md index 37278539..13f9e0a5 100644 --- a/docs/src/background/stability_response.md +++ b/docs/src/background/stability_response.md @@ -8,7 +8,7 @@ x_i(t) = \sum_{j=1}^{M_i} u_{i,j} (T) \cos(\omega_{i,j} t)+ v_{i,j} (T) \sin(\ ``` This means the system is now described using a discrete set of variables $u_{i,j}$ and $v_{i,j}$. Constructing the vector ```math -\begin{equation} \label{eq:harmvar} +\begin{equation} \mathbf{u}(T) = (u_{1,1}(T), v_{1,1}(T), \ldots u_{N,M_N}(T), v_{N, M_N}(T))\,, \end{equation} ``` diff --git a/docs/src/introduction/index.md b/docs/src/introduction/index.md index 2c61bdd9..8ab96f47 100644 --- a/docs/src/introduction/index.md +++ b/docs/src/introduction/index.md @@ -21,7 +21,7 @@ julia> status HarmonicBalance Let us find the steady states of an external driven Duffing oscillator with nonlinear damping. Its equation of motion is: ```math -\begin{equation} \label{eq:duffing} +\begin{equation} \underbrace{\ddot{x}(t) + \gamma \dot{x}(t) + \omega_0^2 x(t)}_{\text{damped harmonic oscillator}} + \underbrace{\alpha x(t)^3}_{\text{Duffing coefficient}} = \underbrace{F \cos(\omega t)}_{\text{periodic drive}} \end{equation} ``` diff --git a/docs/src/tutorials/limit_cycles.md b/docs/src/tutorials/limit_cycles.md index aa3face3..76af0023 100644 --- a/docs/src/tutorials/limit_cycles.md +++ b/docs/src/tutorials/limit_cycles.md @@ -42,12 +42,12 @@ plot(result, y="ω_lc", class="unique_cycle") ## Driven system - coupled Duffings So far, we have largely focused on finding and analysing steady states, i.e., fixed points of the harmonic equations, which satisfy ```math -\begin{equation} \label{eq:harmeqfull} +\begin{equation} \frac{d\mathbf{u}(T)}{dT} = \bar{\mathbf{F}} (\mathbf{u}) = 0\,. \end{equation} ``` -Fixed points are however merely a subset of possible solutions of Eq. \eqref{eq:harmeqfull} -- strictly speaking, solutions where $\mathbf{u}(T)$ remains time-dependent are allowed. These are quite unusual, since $\bar{\mathbf{F}} (\mathbf{u})$ [is by construction time-independent](@ref intro_hb) and Eq. \eqref{eq:harmeqfull} thus possesses _continuous time-translation symmetry_. The appearance of explicitly time-dependent solutions then constitutes spontaneous time-translation symmetry breaking. +Fixed points are however merely a subset of possible solutions of the slow-flow equations -- strictly speaking, solutions where $\mathbf{u}(T)$ remains time-dependent are allowed. These are quite unusual, since $\bar{\mathbf{F}} (\mathbf{u})$ [is by construction time-independent](@ref intro_hb) and the effective equations thus possesses _continuous time-translation symmetry_. The appearance of explicitly time-dependent solutions then constitutes spontaneous time-translation symmetry breaking. Such solutions, known as _limit cycles_, typically appear as closed periodic trajectories of the harmonic variables $\mathbf{u}(T)$. The simplest way to numerically characterise them is a time-dependent simulation, using a steady-state diagram as a guide. From c3a31948eba59a01f0fc523d9650b9c87df23ef8 Mon Sep 17 00:00:00 2001 From: Orjan Ameye Date: Thu, 21 Nov 2024 12:48:49 +0100 Subject: [PATCH 4/7] add API list --- docs/pages.jl | 49 +++++---- docs/src/manual/API.md | 103 +++++++++++++++++ docs/src/public/HB_thumbnail.png | Bin 0 -> 289553 bytes docs/src/public/favicon.ico | Bin 0 -> 278590 bytes docs/src/public/logo.png | Bin 0 -> 87023 bytes docs/src/public/logo.svg | 182 +++++++++++++++++++++++++++++++ docs/src/public/logo_dark.png | Bin 0 -> 87023 bytes docs/src/public/logo_light.png | Bin 0 -> 87023 bytes 8 files changed, 310 insertions(+), 24 deletions(-) create mode 100644 docs/src/manual/API.md create mode 100644 docs/src/public/HB_thumbnail.png create mode 100644 docs/src/public/favicon.ico create mode 100644 docs/src/public/logo.png create mode 100644 docs/src/public/logo.svg create mode 100644 docs/src/public/logo_dark.png create mode 100644 docs/src/public/logo_light.png diff --git a/docs/pages.jl b/docs/pages.jl index 49b43773..3ae476eb 100644 --- a/docs/pages.jl +++ b/docs/pages.jl @@ -1,35 +1,36 @@ #! format: off pages = [ "Home" => "index.md", - "Getting Started" => [ - "Brief Example" => "introduction/index.md", - "Citations" => "introduction/citation.md", - ], + "Getting Started" => "introduction/index.md", "Theoretical Background" => [ - "Floquet expansions" => "background/harmonic_balance.md" - "Stability and Linear Response" => "background/stability_response.md" - "Limit Cycles" => "background/limit_cycles.md" + "Floquet expansions" => "background/harmonic_balance.md", + "Stability and Linear Response" => "background/stability_response.md", + "Limit Cycles" => "background/limit_cycles.md", ], "Tutorials" => [ - "Steady States" => "tutorials/steady_states.md" - "Classifying Solutions" => "tutorials/classification.md" - "Linear Response" => "tutorials/linear_response.md" - "Transient Dynamics" => "tutorials/time_dependent.md" - "Limit Cycles" => "tutorials/limit_cycles.md" - ], - "Examples" => [ + "Steady States" => "tutorials/steady_states.md", + "Classifying Solutions" => "tutorials/classification.md", + "Linear Response" => "tutorials/linear_response.md", + "Transient Dynamics" => "tutorials/time_dependent.md", + "Limit Cycles" => "tutorials/limit_cycles.md", + "Examples" => [ "Wave Mixing" => "examples/wave_mixing.md" "Parametric Three Wave Mixing" => "examples/parametric_via_three_wave_mixing.md" "Parametric Oscillator" => "examples/parametron.md" + ], + ], + "Resources" => [ + "API" => "manual/API.md", + "Bibliography" => "introduction/citation.md", + "Manual" => [ + "Entering Equations of Motion" => "manual/entering_eom.md", + "Computing Effective System" => "manual/extracting_harmonics.md", + "Computing Steady States" => "manual/methods.md", + "Krylov-Bogoliubov" => "manual/Krylov-Bogoliubov_method.md", + "Time Evolution" => "manual/time_dependent.md", + "Linear Response" => "manual/linear_response.md", + "Plotting" => "manual/plotting.md", + "Saving and Loading" => "manual/saving.md", + ] ], - "Manual" => [ - "Entering Equations of Motion" => "manual/entering_eom.md" - "Computing Effective System" => "manual/extracting_harmonics.md" - "Computing Steady States" => "manual/methods.md" - "Krylov-Bogoliubov" => "manual/Krylov-Bogoliubov_method.md" - "Time Evolution" => "manual/time_dependent.md" - "Linear Response" => "manual/linear_response.md" - "Plotting" => "manual/plotting.md" - "Saving and Loading" => "manual/saving.md" - ] ] diff --git a/docs/src/manual/API.md b/docs/src/manual/API.md new file mode 100644 index 00000000..92eb5f7b --- /dev/null +++ b/docs/src/manual/API.md @@ -0,0 +1,103 @@ +```@meta +CurrentModule = HarmonicBalance +``` + +# [API](@id doc-API) + +**Table of contents** + +[[toc]] + +## System objects and types + +```@docs +DifferentialEquation +HarmonicVariable +HarmonicEquation +``` +```@docs +rearrange_standard +rearrange_standard! +first_order_transform! +is_rearranged_standard +get_equations +``` +```@docs +get_harmonic_equations +get_krylov_equations +add_harmonic! +``` +```@docs +get_independent_variables +get_variables +``` + +## Solving and transforming solutions + +```@docs +get_steady_states +``` + +### Methods +```@docs +WarmUp +TotalDegree +Polyhedral +``` + +### Access solutions +```@docs +get_single_solution +transform_solutions +``` + +### Classify +```@docs +classify_solutions! +get_class +``` + +### Plotting + +```@docs +plot +plot_phase_diagram +plot_spaghetti +``` + +## Limit cycles +```@docs +get_limit_cycles +get_cycle_variables +add_pairs! +``` + +## Linear Response + +```@docs +get_Jacobian +``` + +```@docs +plot_eigenvalues +plot_linear_response +plot_rotframe_jacobian_response +``` + +## Extentsions + +### OrdinaryDiffEq +```@docs +AdiabaticSweep +follow_branch +plot_1D_solutions_branch +``` + +### SteadyStateSweep +```@docs +steady_state_sweep +``` + +### ModelingToolkit +```@docs +``` diff --git a/docs/src/public/HB_thumbnail.png b/docs/src/public/HB_thumbnail.png 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zy>#5NRCyvufinLH_?CPcD`l3u7-#(v!{*MPl&e#=FgsnL(`a51EpYbg6UrSM&o^w# Rh6UJAvQmnYmExZR{~tF|-gp22 literal 0 HcmV?d00001 From 6a94a64266c7b28d2c81f22e18c4f0af64690e9d Mon Sep 17 00:00:00 2001 From: Orjan Ameye Date: Thu, 21 Nov 2024 13:26:04 +0100 Subject: [PATCH 5/7] restructure module folder and write missing public api docstrings --- ext/SteadyStateDiffEqExt.jl | 18 ++ src/DifferentialEquation.jl | 119 ++++++++++- src/HarmonicBalance.jl | 17 +- src/KrylovBogoliubov/KrylovBogoliubov.jl | 33 --- src/KrylovBogoliubov/KrylovEquation.jl | 169 --------------- src/KrylovBogoliubov/first_order_transform.jl | 70 ------ src/{ => modules}/ExprUtils/ExprUtils.jl | 0 .../ExprUtils/Symbolics_utils.jl | 0 src/{ => modules}/ExprUtils/drop_powers.jl | 0 src/{ => modules}/ExprUtils/exponentials.jl | 0 src/{ => modules}/ExprUtils/fourier.jl | 0 src/{ => modules}/FFTWExt.jl | 0 src/{ => modules}/HC_wrapper.jl | 0 src/modules/KrylovBogoliubov.jl | 200 ++++++++++++++++++ src/{ => modules}/LimitCycles/LimitCycles.jl | 0 src/{ => modules}/LimitCycles/analysis.jl | 0 src/{ => modules}/LimitCycles/gauge_fixing.jl | 0 .../LinearResponse/LinearResponse.jl | 0 .../LinearResponse/Lorentzian_spectrum.jl | 0 src/{ => modules}/LinearResponse/plotting.jl | 0 src/{ => modules}/LinearResponse/response.jl | 0 src/{ => modules}/LinearResponse/types.jl | 0 src/{ => modules}/LinearResponse/utils.jl | 0 test/code_quality.jl | 4 +- 24 files changed, 345 insertions(+), 285 deletions(-) delete mode 100644 src/KrylovBogoliubov/KrylovBogoliubov.jl delete mode 100644 src/KrylovBogoliubov/KrylovEquation.jl delete mode 100644 src/KrylovBogoliubov/first_order_transform.jl rename src/{ => modules}/ExprUtils/ExprUtils.jl (100%) rename src/{ => modules}/ExprUtils/Symbolics_utils.jl (100%) rename src/{ => modules}/ExprUtils/drop_powers.jl (100%) rename src/{ => modules}/ExprUtils/exponentials.jl (100%) rename src/{ => modules}/ExprUtils/fourier.jl (100%) rename src/{ => modules}/FFTWExt.jl (100%) rename src/{ => modules}/HC_wrapper.jl (100%) create mode 100644 src/modules/KrylovBogoliubov.jl rename src/{ => modules}/LimitCycles/LimitCycles.jl (100%) rename src/{ => modules}/LimitCycles/analysis.jl (100%) rename src/{ => modules}/LimitCycles/gauge_fixing.jl (100%) rename src/{ => modules}/LinearResponse/LinearResponse.jl (100%) rename src/{ => modules}/LinearResponse/Lorentzian_spectrum.jl (100%) rename src/{ => modules}/LinearResponse/plotting.jl (100%) rename src/{ => modules}/LinearResponse/response.jl (100%) rename src/{ => modules}/LinearResponse/types.jl (100%) rename src/{ => modules}/LinearResponse/utils.jl (100%) diff --git a/ext/SteadyStateDiffEqExt.jl b/ext/SteadyStateDiffEqExt.jl index 58ce4c69..f538d5f8 100644 --- a/ext/SteadyStateDiffEqExt.jl +++ b/ext/SteadyStateDiffEqExt.jl @@ -7,6 +7,15 @@ using SteadyStateDiffEq: solve, NonlinearProblem, SteadyStateProblem, DynamicSS, using LinearAlgebra: norm, eigvals using SteadyStateDiffEq.SciMLBase.SciMLStructures: Tunable, replace +""" + steady_state_sweep(prob::SteadyStateProblem, alg::DynamicSS; varied::Pair, kwargs...) + +Sweeps through a range of parameter values using a dynamic steady state solver `DynamicSS` +of the `SteadyStateDiffEq.jl` package. Given a steady state problem and a parameter to vary, +computes the steady state solution for each value in the sweep range. The solutions are +returned as a vector where each element corresponds to the steady state found at that +parameter value. +""" function HarmonicBalance.steady_state_sweep( prob::SteadyStateProblem, alg::DynamicSS; varied::Pair, kwargs... ) @@ -25,6 +34,15 @@ function HarmonicBalance.steady_state_sweep( return result end +""" + steady_state_sweep(prob_np::NonlinearProblem, prob_ss::SteadyStateProblem, + alg_np, alg_ss::DynamicSS; varied::Pair, kwargs...) + +Performs a parameter sweep by combining nonlinear root `alg_np` and steady state solvers `alg_ss`. +For each parameter value, it first attempts a direct nonlinear root solver and checks its +stability. If the solution is unstable or not found, it switches to a dynamic steady state solver. +This hybrid approach is much faster then only using a steady state solver. +""" function HarmonicBalance.steady_state_sweep( prob_np::NonlinearProblem, prob_ss::SteadyStateProblem, diff --git a/src/DifferentialEquation.jl b/src/DifferentialEquation.jl index 9cbf86be..ae6ea218 100644 --- a/src/DifferentialEquation.jl +++ b/src/DifferentialEquation.jl @@ -2,8 +2,8 @@ $(TYPEDEF) Holds differential equation(s) of motion and a set of harmonics to expand each variable. -This is the primary input for `HarmonicBalance.jl`. After inputting the equations, the harmonics -ansatz needs to be specified using `add_harmonic!`. +This is the primary input for `HarmonicBalance.jl`. After inputting the equations, +the harmonics ansatz needs to be specified using `add_harmonic!`. # Fields $(TYPEDFIELDS) @@ -96,7 +96,7 @@ Add the harmonic `ω` to the harmonic ansatz used to expand the variable `var` i ```julia-repl julia> @variables t, x(t), y(t), ω0, ω, F, k; julia> diff_eq = DifferentialEquation(d(x,t,2) + ω0^2 * x ~ F * cos(ω*t), x); -julia> add_harmonic!(diff_eq, x, ω) # expand x using ω +julia> add_harmonic!(diff_eq, x, ��) # expand x using ω System of 1 differential equations Variables: x(t) @@ -136,3 +136,116 @@ Return the independent dependent variables of `diff_eom`. function get_independent_variables(diff_eom::DifferentialEquation) return Num.(flatten(unique([x.val.arguments for x in keys(diff_eom.equations)]))) end + + +get_equations(eom::DifferentialEquation) = collect(values(eom.equations)) + +""" +$(TYPEDSIGNATURES) + +Checks if the differential equations in `eom` are arranged in standard form, where the highest +derivative of each variable appears isolated on the left-hand side. The default degree is 2, +corresponding to second-order differential equations. +""" +function is_rearranged_standard(eom::DifferentialEquation, degree=2) + tvar = get_independent_variables(eom)[1] + D = Differential(tvar)^degree + return isequal(getfield.(values(eom.equations), :lhs), D.(get_variables(eom))) +end + +""" +$(TYPEDSIGNATURES) + +Rearranges the differential equations in `eom` to standard form, where the highest derivative +of each variable (specified by `degree`, default 2) appears isolated on the left-hand side. +Modifies the equations in place. +""" +function rearrange_standard!(eom::DifferentialEquation, degree=2) + tvar = get_independent_variables(eom)[1] + D = Differential(tvar)^degree + dvars = D.(get_variables(eom)) + return rearrange!(eom, dvars) +end + +""" +$(TYPEDSIGNATURES) + +Rearranges the equations in `eom` such that the expressions in `new_lhs` appear isolated on +the left-hand sides. Uses symbolic linear solving to determine the right-hand sides. Modifies +the equations in place. +""" +function rearrange!(eom::DifferentialEquation, new_lhs::Vector{Num}) + soln = Symbolics.symbolic_linear_solve( + get_equations(eom), new_lhs; simplify=false, check=true + ) + eom.equations = OrderedDict(zip(get_variables_nums(new_lhs), new_lhs .~ soln)) + return nothing +end + +""" +$(TYPEDSIGNATURES) + +Creates a new differential equation system by rearranging the equations in `eom` such that +the expressions in `new_lhs` appear isolated on the left-hand sides. Similar to `rearrange!` +but returns a new system instead of modifying in place. +""" +function rearrange(eom::DifferentialEquation, new_lhs::Vector{Num}) + new_eom = deepcopy(eom) + rearrange!(new_eom, new_lhs) + return new_eom +end + +""" +$(TYPEDSIGNATURES) + +Transforms a higher-order differential equation system into an equivalent first-order system +by introducing additional variables. Modifies the system in place. The `time` parameter +specifies the independent variable used for differentiation. +""" +function first_order_transform!(diff_eom::DifferentialEquation, time) + eqs′, states′ = ode_order_lowering(diff_eom.equations, time, diff_eom.harmonics) + diff_eom.equations = eqs′ + diff_eom.harmonics = states′ + return nothing +end + +""" +$(TYPEDSIGNATURES) + +Helper function that performs the transformation of a higher-order differential equation system +into an equivalent first-order system. Returns a tuple of the transformed equations and the +corresponding harmonics dictionary for the new variables. Used internally by +`first_order_transform!`. +""" +function ode_order_lowering(equations, iv, harmonics) + states = unwrap.(collect(keys(harmonics))) + eqs = unwrap.(collect(values(equations))) + + var_order = OrderedDict{Any,Int}() + D = Differential(iv) + diff_eqs = empty(equations) + diff_vars = empty(harmonics) + + for (i, eq) in enumerate(eqs) + var, maxorder = var_from_nested_derivative(eq.lhs) + maxorder > get(var_order, var, 1) && (var_order[var] = maxorder) + + var′ = lower_varname(var, iv, maxorder - 1) + rhs′ = diff2term(eq.rhs) + + diff_vars[var′] = harmonics[var] + diff_eqs[var′] = D(var′) ~ rhs′ + end + + for (var, order) in var_order + for o in (order - 1):-1:1 + lvar = lower_varname(var, iv, o - 1) + rvar = lower_varname(var, iv, o) + + diff_vars[lvar] = harmonics[var] + diff_eqs[lvar] = D(lvar) ~ rvar + end + end + + return (diff_eqs, diff_vars) +end diff --git a/src/HarmonicBalance.jl b/src/HarmonicBalance.jl index d182bcc1..87b17dd2 100644 --- a/src/HarmonicBalance.jl +++ b/src/HarmonicBalance.jl @@ -32,10 +32,13 @@ using Symbolics: get_variables, Differential, unwrap, - wrap + wrap, + diff2term, + var_from_nested_derivative, + lower_varname using SymbolicUtils: SymbolicUtils -include("ExprUtils/ExprUtils.jl") +include("modules/ExprUtils/ExprUtils.jl") using .ExprUtils: is_harmonic, substitute_all, drop_powers, count_derivatives, is_identity # symbolics equations @@ -111,19 +114,19 @@ include("saving.jl") include("transform_solutions.jl") include("plotting_Plots.jl") -include("HC_wrapper.jl") +include("modules/HC_wrapper.jl") using .HC_wrapper -include("LinearResponse/LinearResponse.jl") +include("modules/LinearResponse/LinearResponse.jl") using .LinearResponse -include("LimitCycles/LimitCycles.jl") +include("modules/LimitCycles/LimitCycles.jl") using .LimitCycles -include("KrylovBogoliubov/KrylovBogoliubov.jl") +include("modules/KrylovBogoliubov.jl") using .KrylovBogoliubov -include("FFTWExt.jl") +include("modules/FFTWExt.jl") using .FFTWExt # Precompilation setup diff --git a/src/KrylovBogoliubov/KrylovBogoliubov.jl b/src/KrylovBogoliubov/KrylovBogoliubov.jl deleted file mode 100644 index e438e9cd..00000000 --- a/src/KrylovBogoliubov/KrylovBogoliubov.jl +++ /dev/null @@ -1,33 +0,0 @@ -module KrylovBogoliubov - -using DocStringExtensions -using OrderedCollections: OrderedDict - -using Symbolics -using Symbolics: unwrap, diff2term, var_from_nested_derivative, lower_varname -using SymbolicUtils: BasicSymbolic, isdiv - -using HarmonicBalance -using HarmonicBalance: - rearrange!, - flatten, - _create_harmonic_variable, - slow_flow, - _remove_brackets, - get_variables_nums - -using HarmonicBalance.ExprUtils: - get_all_terms, - substitute_all, - trig_reduce, - get_independent, - simplify_complex, - is_trig, - is_harmonic -include("first_order_transform.jl") -include("KrylovEquation.jl") - -export first_order_transform!, - is_rearranged_standard, rearrange_standard!, get_equations, get_krylov_equations - -end diff --git a/src/KrylovBogoliubov/KrylovEquation.jl b/src/KrylovBogoliubov/KrylovEquation.jl deleted file mode 100644 index b63f64b7..00000000 --- a/src/KrylovBogoliubov/KrylovEquation.jl +++ /dev/null @@ -1,169 +0,0 @@ -get_harmonic(var::HarmonicVariable) = var.ω -get_harmonics(eom::HarmonicEquation) = get_harmonic.(eom.variables) - -""" -$(TYPEDSIGNATURES) - -Apply the Krylov-Bogoliubov averaging method to a specific `order` to obtain a set of ODEs (the slow-flow equations) governing the harmonics of `diff_eom`. - -The harmonics evolve in `slow_time`, the oscillating terms themselves in `fast_time`. -If no input is used, a variable T is defined for `slow_time` and `fast_time` is taken as the independent variable -of `diff_eom`. - -Krylov-Bogoliubov averaging method can be applied up to `order = 2`. - -# Example -```julia-repl -julia> @variables t, x(t), ω0, ω, F; - -# enter the simple harmonic oscillator -julia> diff_eom = DifferentialEquation( d(x,t,2) + ω0^2 * x ~ F *cos(ω*t), x); - -# expand x in the harmonic ω -julia> add_harmonic!(diff_eom, x, ω); - -# get equations for the harmonics evolving in the slow time T to first order -julia> harmonic_eom = get_krylov_equations(diff_eom, order = 1) - -A set of 2 harmonic equations -Variables: u1(T), v1(T) -Parameters: ω, F, ω0 - -Harmonic ansatz: -xˍt(t) = -x(t) = u1(T)*cos(ωt) + v1(T)*sin(ωt) - -Harmonic equations: - -((1//2)*(ω^2)*v1(T) - (1//2)*(ω0^2)*v1(T)) / ω ~ Differential(T)(u1(T)) - -((1//2)*(ω0^2)*u1(T) - (1//2)*F - (1//2)*(ω^2)*u1(T)) / ω ~ Differential(T)(v1(T)) -``` - -""" -function get_krylov_equations( - diff_eom::DifferentialEquation; order, fast_time=nothing, slow_time=nothing -) - order < 1 && error("The order of the Krylov-Bogoliubov method must be at least 1!") - order > 2 && error("Krylov-Bogoliubov implementation only supports up to second order!") - - slow_time = isnothing(slow_time) ? (@variables T; T) : slow_time - fast_time = isnothing(fast_time) ? get_independent_variables(diff_eom)[1] : fast_time - - harmonics = values(diff_eom.harmonics) - all(isempty.(harmonics)) && error("No harmonics specified!") - any(isempty.(harmonics)) && - error("Krylov-Bogoliubov method needs all variables to have a single harmonic!") - any(length.(harmonics) .> 1) && - error("Krylov-Bogoliubov method only supports a single harmonic!") - - dEOM = deepcopy(diff_eom) - !is_rearranged_standard(dEOM) ? rearrange_standard!(dEOM) : nothing - first_order_transform!(dEOM, fast_time) - eom = van_der_Pol(dEOM, fast_time) - - eom = slow_flow(eom; fast_time=fast_time, slow_time=slow_time, degree=2) - - rearrange!(eom, d(get_variables(eom), slow_time)) - eom.equations = expand.(simplify.(eom.equations)) - eom.equations = expand.(simplify.(eom.equations)) - #^ need it two times to get it completely simplified due to some weird bug in Symbolics.jl - - if order == 1 - average!(eom, fast_time) - return eom - elseif order == 2 - vars_symb = get_variables(eom) - Fₜ = Num.(getfield.(eom.equations, :lhs)) - F₀ = Num.(getfield.(average(eom, fast_time), :lhs)) - Fₜ′ = substitute( - get_Jacobian(eom), Dict(zip(_remove_brackets.(vars_symb), vars_symb)) - ) - - Ḋ₁ = trig_reduce.(Fₜ - F₀) - D₁ = take_trig_integral.(Ḋ₁, get_harmonics(eom), fast_time) - D₁ = D₁ - average.(D₁, fast_time) - - Gₜ = trig_reduce.(Fₜ′ * D₁) - G₀ = average.(Gₜ, fast_time) - eom.equations = F₀ + G₀ .~ getfield.(eom.equations, :rhs) - end - - return eom -end - -function van_der_Pol(eom::DifferentialEquation, t::Num) - !is_harmonic(eom, t) && error("The differential equation is not harmonic in ", t, " !") - eqs = get_equations(eom) - rules, vars = Dict(), [] - - # keep count to label new variables - uv_idx = 1 - ω = first(flatten(unique(values(eom.harmonics)))) - nvars = get_variables(eom) - nvars = nvars[(length(nvars) ÷ 2 + 1):end] - - for nvar in nvars # sum over natural variables - rule_u, hvar_u = _create_harmonic_variable( - nvar, ω, t, "u"; new_symbol="u" * string(uv_idx) - ) - rule_v, hvar_v = _create_harmonic_variable( - nvar, ω, t, "v"; new_symbol="v" * string(uv_idx) - ) - rule = rule_u - rule_v - # ~ this is a choice, we use u*cos(ωt) + v*sin(ωt) as the ansatz - rules[nvar] = rule - - D = Differential(t) - nvar_t = diff2term(D(unwrap(nvar))) - vdP_rules = Dict(D(hvar_u.symbol) => 0, D(hvar_v.symbol) => 0) - rules[nvar_t] = Symbolics.substitute(expand_derivatives(D(rule)), vdP_rules) - - uv_idx += 1 - push!(vars, hvar_u, hvar_v) - end - eqs = expand_derivatives.(substitute_all(eqs, rules)) - return HarmonicEquation(eqs, Vector{HarmonicVariable}(vars), eom) -end - -function average!(eom::HarmonicEquation, t) - return eom.equations = average(eom, t) -end -function average(eom::HarmonicEquation, t) - eqs = similar(eom.equations) - for (i, eq) in pairs(eom.equations) - lhs = average(Num(eq.lhs), t) - rhs = average(Num(eq.rhs), t) - eqs[i] = lhs ~ rhs - end - return eqs -end -function average(x, t) - term = trig_reduce(x) - indep = get_independent(term, t) - ft = Num(simplify_complex(Symbolics.expand(indep))) - return Symbolics.expand(ft) -end - -function take_trig_integral(x::BasicSymbolic, ω, t) - if isdiv(x) - arg_num = arguments(x.num) - return simplify(expand(sum(take_trig_integral.(arg_num, ω, t)) * ω)) / (x.den * ω) - else - all_terms = get_all_terms(Num(x)) - trigs = filter(z -> is_trig(z), all_terms) - D = Differential(t) - - rules = [] - for trig in trigs - arg = first(arguments(trig.val)) - type = operation(trig.val) - - term = Num((type == cos ? sin(arg) : -cos(arg)) / expand_derivatives(D(arg))) - append!(rules, [trig => term]) - end - - return Symbolics.substitute(x, Dict(rules)) - end -end -take_trig_integral(x::Num, ω, t) = take_trig_integral(Symbolics.expand(unwrap(x)), ω, t) diff --git a/src/KrylovBogoliubov/first_order_transform.jl b/src/KrylovBogoliubov/first_order_transform.jl deleted file mode 100644 index 2e9873c6..00000000 --- a/src/KrylovBogoliubov/first_order_transform.jl +++ /dev/null @@ -1,70 +0,0 @@ -get_equations(eom::DifferentialEquation) = collect(values(eom.equations)) - -# TODO: check the degree of the eom -function is_rearranged_standard(eom::DifferentialEquation, degree=2) - tvar = get_independent_variables(eom)[1] - D = Differential(tvar)^degree - return isequal(getfield.(values(eom.equations), :lhs), D.(get_variables(eom))) -end - -function rearrange_standard!(eom::DifferentialEquation, degree=2) - tvar = get_independent_variables(eom)[1] - D = Differential(tvar)^degree - dvars = D.(get_variables(eom)) - return rearrange!(eom, dvars) -end - -function HarmonicBalance.rearrange!(eom::DifferentialEquation, new_lhs::Vector{Num}) - soln = Symbolics.symbolic_linear_solve( - get_equations(eom), new_lhs; simplify=false, check=true - ) - eom.equations = OrderedDict(zip(get_variables_nums(new_lhs), new_lhs .~ soln)) - return nothing -end - -function HarmonicBalance.rearrange(eom::DifferentialEquation, new_lhs::Vector{Num}) - new_eom = deepcopy(eom) - rearrange!(new_eom, new_lhs) - return new_eom -end - -function first_order_transform!(diff_eom::DifferentialEquation, time) - eqs′, states′ = ode_order_lowering(diff_eom.equations, time, diff_eom.harmonics) - diff_eom.equations = eqs′ - diff_eom.harmonics = states′ - return nothing -end - -# taken from ModelingToolkit.jl -function ode_order_lowering(equations, iv, harmonics) - states = unwrap.(collect(keys(harmonics))) - eqs = unwrap.(collect(values(equations))) - - var_order = OrderedDict{Any,Int}() - D = Differential(iv) - diff_eqs = empty(equations) - diff_vars = empty(harmonics) - - for (i, eq) in enumerate(eqs) - var, maxorder = var_from_nested_derivative(eq.lhs) - maxorder > get(var_order, var, 1) && (var_order[var] = maxorder) - - var′ = lower_varname(var, iv, maxorder - 1) - rhs′ = diff2term(eq.rhs) - - diff_vars[var′] = harmonics[var] - diff_eqs[var′] = D(var′) ~ rhs′ - end - - for (var, order) in var_order - for o in (order - 1):-1:1 - lvar = lower_varname(var, iv, o - 1) - rvar = lower_varname(var, iv, o) - - diff_vars[lvar] = harmonics[var] - diff_eqs[lvar] = D(lvar) ~ rvar - end - end - - return (diff_eqs, diff_vars) -end diff --git a/src/ExprUtils/ExprUtils.jl b/src/modules/ExprUtils/ExprUtils.jl similarity index 100% rename from src/ExprUtils/ExprUtils.jl rename to src/modules/ExprUtils/ExprUtils.jl diff --git a/src/ExprUtils/Symbolics_utils.jl b/src/modules/ExprUtils/Symbolics_utils.jl similarity index 100% rename from src/ExprUtils/Symbolics_utils.jl rename to src/modules/ExprUtils/Symbolics_utils.jl diff --git a/src/ExprUtils/drop_powers.jl b/src/modules/ExprUtils/drop_powers.jl similarity index 100% rename from src/ExprUtils/drop_powers.jl rename to src/modules/ExprUtils/drop_powers.jl diff --git a/src/ExprUtils/exponentials.jl b/src/modules/ExprUtils/exponentials.jl similarity index 100% rename from src/ExprUtils/exponentials.jl rename to src/modules/ExprUtils/exponentials.jl diff --git a/src/ExprUtils/fourier.jl b/src/modules/ExprUtils/fourier.jl similarity index 100% rename from src/ExprUtils/fourier.jl rename to src/modules/ExprUtils/fourier.jl diff --git a/src/FFTWExt.jl b/src/modules/FFTWExt.jl similarity index 100% rename from src/FFTWExt.jl rename to src/modules/FFTWExt.jl diff --git a/src/HC_wrapper.jl b/src/modules/HC_wrapper.jl similarity index 100% rename from src/HC_wrapper.jl rename to src/modules/HC_wrapper.jl diff --git a/src/modules/KrylovBogoliubov.jl b/src/modules/KrylovBogoliubov.jl new file mode 100644 index 00000000..8d830f34 --- /dev/null +++ b/src/modules/KrylovBogoliubov.jl @@ -0,0 +1,200 @@ +module KrylovBogoliubov + +using DocStringExtensions + +using Symbolics +using Symbolics: unwrap, diff2term +using SymbolicUtils: BasicSymbolic, isdiv + +using HarmonicBalance +using HarmonicBalance: + rearrange!, + flatten, + _create_harmonic_variable, + slow_flow, + _remove_brackets + +using HarmonicBalance.ExprUtils: + get_all_terms, + substitute_all, + trig_reduce, + get_independent, + simplify_complex, + is_trig, + is_harmonic + + get_harmonic(var::HarmonicVariable) = var.ω + get_harmonics(eom::HarmonicEquation) = get_harmonic.(eom.variables) + + """ + $(TYPEDSIGNATURES) + + Apply the Krylov-Bogoliubov averaging method to a specific `order` to obtain a set of ODEs (the slow-flow equations) governing the harmonics of `diff_eom`. + + The harmonics evolve in `slow_time`, the oscillating terms themselves in `fast_time`. + If no input is used, a variable T is defined for `slow_time` and `fast_time` is taken as the independent variable + of `diff_eom`. + + Krylov-Bogoliubov averaging method can be applied up to `order = 2`. + + # Example + ```julia-repl + julia> @variables t, x(t), ω0, ω, F; + + # enter the simple harmonic oscillator + julia> diff_eom = DifferentialEquation( d(x,t,2) + ω0^2 * x ~ F *cos(ω*t), x); + + # expand x in the harmonic ω + julia> add_harmonic!(diff_eom, x, ω); + + # get equations for the harmonics evolving in the slow time T to first order + julia> harmonic_eom = get_krylov_equations(diff_eom, order = 1) + + A set of 2 harmonic equations + Variables: u1(T), v1(T) + Parameters: ω, F, ω0 + + Harmonic ansatz: + xˍt(t) = + x(t) = u1(T)*cos(ωt) + v1(T)*sin(ωt) + + Harmonic equations: + + ((1//2)*(ω^2)*v1(T) - (1//2)*(ω0^2)*v1(T)) / ω ~ Differential(T)(u1(T)) + + ((1//2)*(ω0^2)*u1(T) - (1//2)*F - (1//2)*(ω^2)*u1(T)) / ω ~ Differential(T)(v1(T)) + ``` + + """ + function get_krylov_equations( + diff_eom::DifferentialEquation; order, fast_time=nothing, slow_time=nothing + ) + order < 1 && error("The order of the Krylov-Bogoliubov method must be at least 1!") + order > 2 && error("Krylov-Bogoliubov implementation only supports up to second order!") + + slow_time = isnothing(slow_time) ? (@variables T; T) : slow_time + fast_time = isnothing(fast_time) ? get_independent_variables(diff_eom)[1] : fast_time + + harmonics = values(diff_eom.harmonics) + all(isempty.(harmonics)) && error("No harmonics specified!") + any(isempty.(harmonics)) && + error("Krylov-Bogoliubov method needs all variables to have a single harmonic!") + any(length.(harmonics) .> 1) && + error("Krylov-Bogoliubov method only supports a single harmonic!") + + dEOM = deepcopy(diff_eom) + !is_rearranged_standard(dEOM) ? rearrange_standard!(dEOM) : nothing + first_order_transform!(dEOM, fast_time) + eom = van_der_Pol(dEOM, fast_time) + + eom = slow_flow(eom; fast_time=fast_time, slow_time=slow_time, degree=2) + + rearrange!(eom, d(get_variables(eom), slow_time)) + eom.equations = expand.(simplify.(eom.equations)) + eom.equations = expand.(simplify.(eom.equations)) + #^ need it two times to get it completely simplified due to some weird bug in Symbolics.jl + + if order == 1 + average!(eom, fast_time) + return eom + elseif order == 2 + vars_symb = get_variables(eom) + Fₜ = Num.(getfield.(eom.equations, :lhs)) + F₀ = Num.(getfield.(average(eom, fast_time), :lhs)) + Fₜ′ = substitute( + get_Jacobian(eom), Dict(zip(_remove_brackets.(vars_symb), vars_symb)) + ) + + Ḋ₁ = trig_reduce.(Fₜ - F₀) + D₁ = take_trig_integral.(Ḋ₁, get_harmonics(eom), fast_time) + D₁ = D₁ - average.(D₁, fast_time) + + Gₜ = trig_reduce.(Fₜ′ * D₁) + G₀ = average.(Gₜ, fast_time) + eom.equations = F₀ + G₀ .~ getfield.(eom.equations, :rhs) + end + + return eom + end + + function van_der_Pol(eom::DifferentialEquation, t::Num) + !is_harmonic(eom, t) && error("The differential equation is not harmonic in ", t, " !") + eqs = get_equations(eom) + rules, vars = Dict(), [] + + # keep count to label new variables + uv_idx = 1 + ω = first(flatten(unique(values(eom.harmonics)))) + nvars = get_variables(eom) + nvars = nvars[(length(nvars) ÷ 2 + 1):end] + + for nvar in nvars # sum over natural variables + rule_u, hvar_u = _create_harmonic_variable( + nvar, ω, t, "u"; new_symbol="u" * string(uv_idx) + ) + rule_v, hvar_v = _create_harmonic_variable( + nvar, ω, t, "v"; new_symbol="v" * string(uv_idx) + ) + rule = rule_u - rule_v + # ~ this is a choice, we use u*cos(ωt) + v*sin(ωt) as the ansatz + rules[nvar] = rule + + D = Differential(t) + nvar_t = diff2term(D(unwrap(nvar))) + vdP_rules = Dict(D(hvar_u.symbol) => 0, D(hvar_v.symbol) => 0) + rules[nvar_t] = Symbolics.substitute(expand_derivatives(D(rule)), vdP_rules) + + uv_idx += 1 + push!(vars, hvar_u, hvar_v) + end + eqs = expand_derivatives.(substitute_all(eqs, rules)) + return HarmonicEquation(eqs, Vector{HarmonicVariable}(vars), eom) + end + + function average!(eom::HarmonicEquation, t) + return eom.equations = average(eom, t) + end + function average(eom::HarmonicEquation, t) + eqs = similar(eom.equations) + for (i, eq) in pairs(eom.equations) + lhs = average(Num(eq.lhs), t) + rhs = average(Num(eq.rhs), t) + eqs[i] = lhs ~ rhs + end + return eqs + end + function average(x, t) + term = trig_reduce(x) + indep = get_independent(term, t) + ft = Num(simplify_complex(Symbolics.expand(indep))) + return Symbolics.expand(ft) + end + + function take_trig_integral(x::BasicSymbolic, ω, t) + if isdiv(x) + arg_num = arguments(x.num) + return simplify(expand(sum(take_trig_integral.(arg_num, ω, t)) * ω)) / (x.den * ω) + else + all_terms = get_all_terms(Num(x)) + trigs = filter(z -> is_trig(z), all_terms) + D = Differential(t) + + rules = [] + for trig in trigs + arg = first(arguments(trig.val)) + type = operation(trig.val) + + term = Num((type == cos ? sin(arg) : -cos(arg)) / expand_derivatives(D(arg))) + append!(rules, [trig => term]) + end + + return Symbolics.substitute(x, Dict(rules)) + end + end + take_trig_integral(x::Num, ω, t) = take_trig_integral(Symbolics.expand(unwrap(x)), ω, t) + + +export first_order_transform!, + is_rearranged_standard, rearrange_standard!, get_equations, get_krylov_equations + +end diff --git a/src/LimitCycles/LimitCycles.jl b/src/modules/LimitCycles/LimitCycles.jl similarity index 100% rename from src/LimitCycles/LimitCycles.jl rename to src/modules/LimitCycles/LimitCycles.jl diff --git a/src/LimitCycles/analysis.jl b/src/modules/LimitCycles/analysis.jl similarity index 100% rename from src/LimitCycles/analysis.jl rename to src/modules/LimitCycles/analysis.jl diff --git a/src/LimitCycles/gauge_fixing.jl b/src/modules/LimitCycles/gauge_fixing.jl similarity index 100% rename from src/LimitCycles/gauge_fixing.jl rename to src/modules/LimitCycles/gauge_fixing.jl diff --git a/src/LinearResponse/LinearResponse.jl b/src/modules/LinearResponse/LinearResponse.jl similarity index 100% rename from src/LinearResponse/LinearResponse.jl rename to src/modules/LinearResponse/LinearResponse.jl diff --git a/src/LinearResponse/Lorentzian_spectrum.jl b/src/modules/LinearResponse/Lorentzian_spectrum.jl similarity index 100% rename from src/LinearResponse/Lorentzian_spectrum.jl rename to src/modules/LinearResponse/Lorentzian_spectrum.jl diff --git a/src/LinearResponse/plotting.jl b/src/modules/LinearResponse/plotting.jl similarity index 100% rename from src/LinearResponse/plotting.jl rename to src/modules/LinearResponse/plotting.jl diff --git a/src/LinearResponse/response.jl b/src/modules/LinearResponse/response.jl similarity index 100% rename from src/LinearResponse/response.jl rename to src/modules/LinearResponse/response.jl diff --git a/src/LinearResponse/types.jl b/src/modules/LinearResponse/types.jl similarity index 100% rename from src/LinearResponse/types.jl rename to src/modules/LinearResponse/types.jl diff --git a/src/LinearResponse/utils.jl b/src/modules/LinearResponse/utils.jl similarity index 100% rename from src/LinearResponse/utils.jl rename to src/modules/LinearResponse/utils.jl diff --git a/test/code_quality.jl b/test/code_quality.jl index b536e083..5b680759 100644 --- a/test/code_quality.jl +++ b/test/code_quality.jl @@ -1,6 +1,4 @@ -using HarmonicBalance -using Test - +| @testset "Concretely typed" begin CI = get(ENV, "CI", nothing) == "true" || get(ENV, "GITHUB_TOKEN", nothing) !== nothing julia_version = VERSION >= v"1.11.0-DEV.0" # fails on 1.11 From 977473ecb167c90ade61f541147f3ea65bbaa897 Mon Sep 17 00:00:00 2001 From: Orjan Ameye Date: Thu, 21 Nov 2024 13:28:46 +0100 Subject: [PATCH 6/7] format --- src/DifferentialEquation.jl | 1 - src/modules/KrylovBogoliubov.jl | 287 ++++++++++++++++---------------- 2 files changed, 141 insertions(+), 147 deletions(-) diff --git a/src/DifferentialEquation.jl b/src/DifferentialEquation.jl index ae6ea218..b4646c85 100644 --- a/src/DifferentialEquation.jl +++ b/src/DifferentialEquation.jl @@ -137,7 +137,6 @@ function get_independent_variables(diff_eom::DifferentialEquation) return Num.(flatten(unique([x.val.arguments for x in keys(diff_eom.equations)]))) end - get_equations(eom::DifferentialEquation) = collect(values(eom.equations)) """ diff --git a/src/modules/KrylovBogoliubov.jl b/src/modules/KrylovBogoliubov.jl index 8d830f34..3c8a3d6a 100644 --- a/src/modules/KrylovBogoliubov.jl +++ b/src/modules/KrylovBogoliubov.jl @@ -8,11 +8,7 @@ using SymbolicUtils: BasicSymbolic, isdiv using HarmonicBalance using HarmonicBalance: - rearrange!, - flatten, - _create_harmonic_variable, - slow_flow, - _remove_brackets + rearrange!, flatten, _create_harmonic_variable, slow_flow, _remove_brackets using HarmonicBalance.ExprUtils: get_all_terms, @@ -23,176 +19,175 @@ using HarmonicBalance.ExprUtils: is_trig, is_harmonic - get_harmonic(var::HarmonicVariable) = var.ω - get_harmonics(eom::HarmonicEquation) = get_harmonic.(eom.variables) +get_harmonic(var::HarmonicVariable) = var.ω +get_harmonics(eom::HarmonicEquation) = get_harmonic.(eom.variables) - """ - $(TYPEDSIGNATURES) +""" +$(TYPEDSIGNATURES) - Apply the Krylov-Bogoliubov averaging method to a specific `order` to obtain a set of ODEs (the slow-flow equations) governing the harmonics of `diff_eom`. +Apply the Krylov-Bogoliubov averaging method to a specific `order` to obtain a set of ODEs (the slow-flow equations) governing the harmonics of `diff_eom`. - The harmonics evolve in `slow_time`, the oscillating terms themselves in `fast_time`. - If no input is used, a variable T is defined for `slow_time` and `fast_time` is taken as the independent variable - of `diff_eom`. +The harmonics evolve in `slow_time`, the oscillating terms themselves in `fast_time`. +If no input is used, a variable T is defined for `slow_time` and `fast_time` is taken as the independent variable +of `diff_eom`. - Krylov-Bogoliubov averaging method can be applied up to `order = 2`. +Krylov-Bogoliubov averaging method can be applied up to `order = 2`. - # Example - ```julia-repl - julia> @variables t, x(t), ω0, ω, F; +# Example +```julia-repl +julia> @variables t, x(t), ω0, ω, F; - # enter the simple harmonic oscillator - julia> diff_eom = DifferentialEquation( d(x,t,2) + ω0^2 * x ~ F *cos(ω*t), x); +# enter the simple harmonic oscillator +julia> diff_eom = DifferentialEquation( d(x,t,2) + ω0^2 * x ~ F *cos(ω*t), x); - # expand x in the harmonic ω - julia> add_harmonic!(diff_eom, x, ω); +# expand x in the harmonic ω +julia> add_harmonic!(diff_eom, x, ω); - # get equations for the harmonics evolving in the slow time T to first order - julia> harmonic_eom = get_krylov_equations(diff_eom, order = 1) +# get equations for the harmonics evolving in the slow time T to first order +julia> harmonic_eom = get_krylov_equations(diff_eom, order = 1) - A set of 2 harmonic equations - Variables: u1(T), v1(T) - Parameters: ω, F, ω0 +A set of 2 harmonic equations +Variables: u1(T), v1(T) +Parameters: ω, F, ω0 - Harmonic ansatz: - xˍt(t) = - x(t) = u1(T)*cos(ωt) + v1(T)*sin(ωt) +Harmonic ansatz: +xˍt(t) = +x(t) = u1(T)*cos(ωt) + v1(T)*sin(ωt) - Harmonic equations: +Harmonic equations: - ((1//2)*(ω^2)*v1(T) - (1//2)*(ω0^2)*v1(T)) / ω ~ Differential(T)(u1(T)) +((1//2)*(ω^2)*v1(T) - (1//2)*(ω0^2)*v1(T)) / ω ~ Differential(T)(u1(T)) - ((1//2)*(ω0^2)*u1(T) - (1//2)*F - (1//2)*(ω^2)*u1(T)) / ω ~ Differential(T)(v1(T)) - ``` +((1//2)*(ω0^2)*u1(T) - (1//2)*F - (1//2)*(ω^2)*u1(T)) / ω ~ Differential(T)(v1(T)) +``` - """ - function get_krylov_equations( - diff_eom::DifferentialEquation; order, fast_time=nothing, slow_time=nothing - ) - order < 1 && error("The order of the Krylov-Bogoliubov method must be at least 1!") - order > 2 && error("Krylov-Bogoliubov implementation only supports up to second order!") +""" +function get_krylov_equations( + diff_eom::DifferentialEquation; order, fast_time=nothing, slow_time=nothing +) + order < 1 && error("The order of the Krylov-Bogoliubov method must be at least 1!") + order > 2 && error("Krylov-Bogoliubov implementation only supports up to second order!") - slow_time = isnothing(slow_time) ? (@variables T; T) : slow_time - fast_time = isnothing(fast_time) ? get_independent_variables(diff_eom)[1] : fast_time + slow_time = isnothing(slow_time) ? (@variables T; T) : slow_time + fast_time = isnothing(fast_time) ? get_independent_variables(diff_eom)[1] : fast_time - harmonics = values(diff_eom.harmonics) - all(isempty.(harmonics)) && error("No harmonics specified!") - any(isempty.(harmonics)) && - error("Krylov-Bogoliubov method needs all variables to have a single harmonic!") - any(length.(harmonics) .> 1) && - error("Krylov-Bogoliubov method only supports a single harmonic!") + harmonics = values(diff_eom.harmonics) + all(isempty.(harmonics)) && error("No harmonics specified!") + any(isempty.(harmonics)) && + error("Krylov-Bogoliubov method needs all variables to have a single harmonic!") + any(length.(harmonics) .> 1) && + error("Krylov-Bogoliubov method only supports a single harmonic!") - dEOM = deepcopy(diff_eom) - !is_rearranged_standard(dEOM) ? rearrange_standard!(dEOM) : nothing - first_order_transform!(dEOM, fast_time) - eom = van_der_Pol(dEOM, fast_time) + dEOM = deepcopy(diff_eom) + !is_rearranged_standard(dEOM) ? rearrange_standard!(dEOM) : nothing + first_order_transform!(dEOM, fast_time) + eom = van_der_Pol(dEOM, fast_time) - eom = slow_flow(eom; fast_time=fast_time, slow_time=slow_time, degree=2) + eom = slow_flow(eom; fast_time=fast_time, slow_time=slow_time, degree=2) - rearrange!(eom, d(get_variables(eom), slow_time)) - eom.equations = expand.(simplify.(eom.equations)) - eom.equations = expand.(simplify.(eom.equations)) - #^ need it two times to get it completely simplified due to some weird bug in Symbolics.jl - - if order == 1 - average!(eom, fast_time) - return eom - elseif order == 2 - vars_symb = get_variables(eom) - Fₜ = Num.(getfield.(eom.equations, :lhs)) - F₀ = Num.(getfield.(average(eom, fast_time), :lhs)) - Fₜ′ = substitute( - get_Jacobian(eom), Dict(zip(_remove_brackets.(vars_symb), vars_symb)) - ) - - Ḋ₁ = trig_reduce.(Fₜ - F₀) - D₁ = take_trig_integral.(Ḋ₁, get_harmonics(eom), fast_time) - D₁ = D₁ - average.(D₁, fast_time) - - Gₜ = trig_reduce.(Fₜ′ * D₁) - G₀ = average.(Gₜ, fast_time) - eom.equations = F₀ + G₀ .~ getfield.(eom.equations, :rhs) - end + rearrange!(eom, d(get_variables(eom), slow_time)) + eom.equations = expand.(simplify.(eom.equations)) + eom.equations = expand.(simplify.(eom.equations)) + #^ need it two times to get it completely simplified due to some weird bug in Symbolics.jl + if order == 1 + average!(eom, fast_time) return eom + elseif order == 2 + vars_symb = get_variables(eom) + Fₜ = Num.(getfield.(eom.equations, :lhs)) + F₀ = Num.(getfield.(average(eom, fast_time), :lhs)) + Fₜ′ = substitute( + get_Jacobian(eom), Dict(zip(_remove_brackets.(vars_symb), vars_symb)) + ) + + Ḋ₁ = trig_reduce.(Fₜ - F₀) + D₁ = take_trig_integral.(Ḋ₁, get_harmonics(eom), fast_time) + D₁ = D₁ - average.(D₁, fast_time) + + Gₜ = trig_reduce.(Fₜ′ * D₁) + G₀ = average.(Gₜ, fast_time) + eom.equations = F₀ + G₀ .~ getfield.(eom.equations, :rhs) end - function van_der_Pol(eom::DifferentialEquation, t::Num) - !is_harmonic(eom, t) && error("The differential equation is not harmonic in ", t, " !") - eqs = get_equations(eom) - rules, vars = Dict(), [] - - # keep count to label new variables - uv_idx = 1 - ω = first(flatten(unique(values(eom.harmonics)))) - nvars = get_variables(eom) - nvars = nvars[(length(nvars) ÷ 2 + 1):end] - - for nvar in nvars # sum over natural variables - rule_u, hvar_u = _create_harmonic_variable( - nvar, ω, t, "u"; new_symbol="u" * string(uv_idx) - ) - rule_v, hvar_v = _create_harmonic_variable( - nvar, ω, t, "v"; new_symbol="v" * string(uv_idx) - ) - rule = rule_u - rule_v - # ~ this is a choice, we use u*cos(ωt) + v*sin(ωt) as the ansatz - rules[nvar] = rule - - D = Differential(t) - nvar_t = diff2term(D(unwrap(nvar))) - vdP_rules = Dict(D(hvar_u.symbol) => 0, D(hvar_v.symbol) => 0) - rules[nvar_t] = Symbolics.substitute(expand_derivatives(D(rule)), vdP_rules) - - uv_idx += 1 - push!(vars, hvar_u, hvar_v) - end - eqs = expand_derivatives.(substitute_all(eqs, rules)) - return HarmonicEquation(eqs, Vector{HarmonicVariable}(vars), eom) - end + return eom +end - function average!(eom::HarmonicEquation, t) - return eom.equations = average(eom, t) - end - function average(eom::HarmonicEquation, t) - eqs = similar(eom.equations) - for (i, eq) in pairs(eom.equations) - lhs = average(Num(eq.lhs), t) - rhs = average(Num(eq.rhs), t) - eqs[i] = lhs ~ rhs - end - return eqs +function van_der_Pol(eom::DifferentialEquation, t::Num) + !is_harmonic(eom, t) && error("The differential equation is not harmonic in ", t, " !") + eqs = get_equations(eom) + rules, vars = Dict(), [] + + # keep count to label new variables + uv_idx = 1 + ω = first(flatten(unique(values(eom.harmonics)))) + nvars = get_variables(eom) + nvars = nvars[(length(nvars) ÷ 2 + 1):end] + + for nvar in nvars # sum over natural variables + rule_u, hvar_u = _create_harmonic_variable( + nvar, ω, t, "u"; new_symbol="u" * string(uv_idx) + ) + rule_v, hvar_v = _create_harmonic_variable( + nvar, ω, t, "v"; new_symbol="v" * string(uv_idx) + ) + rule = rule_u - rule_v + # ~ this is a choice, we use u*cos(ωt) + v*sin(ωt) as the ansatz + rules[nvar] = rule + + D = Differential(t) + nvar_t = diff2term(D(unwrap(nvar))) + vdP_rules = Dict(D(hvar_u.symbol) => 0, D(hvar_v.symbol) => 0) + rules[nvar_t] = Symbolics.substitute(expand_derivatives(D(rule)), vdP_rules) + + uv_idx += 1 + push!(vars, hvar_u, hvar_v) end - function average(x, t) - term = trig_reduce(x) - indep = get_independent(term, t) - ft = Num(simplify_complex(Symbolics.expand(indep))) - return Symbolics.expand(ft) + eqs = expand_derivatives.(substitute_all(eqs, rules)) + return HarmonicEquation(eqs, Vector{HarmonicVariable}(vars), eom) +end + +function average!(eom::HarmonicEquation, t) + return eom.equations = average(eom, t) +end +function average(eom::HarmonicEquation, t) + eqs = similar(eom.equations) + for (i, eq) in pairs(eom.equations) + lhs = average(Num(eq.lhs), t) + rhs = average(Num(eq.rhs), t) + eqs[i] = lhs ~ rhs end + return eqs +end +function average(x, t) + term = trig_reduce(x) + indep = get_independent(term, t) + ft = Num(simplify_complex(Symbolics.expand(indep))) + return Symbolics.expand(ft) +end - function take_trig_integral(x::BasicSymbolic, ω, t) - if isdiv(x) - arg_num = arguments(x.num) - return simplify(expand(sum(take_trig_integral.(arg_num, ω, t)) * ω)) / (x.den * ω) - else - all_terms = get_all_terms(Num(x)) - trigs = filter(z -> is_trig(z), all_terms) - D = Differential(t) - - rules = [] - for trig in trigs - arg = first(arguments(trig.val)) - type = operation(trig.val) - - term = Num((type == cos ? sin(arg) : -cos(arg)) / expand_derivatives(D(arg))) - append!(rules, [trig => term]) - end - - return Symbolics.substitute(x, Dict(rules)) +function take_trig_integral(x::BasicSymbolic, ω, t) + if isdiv(x) + arg_num = arguments(x.num) + return simplify(expand(sum(take_trig_integral.(arg_num, ω, t)) * ω)) / (x.den * ω) + else + all_terms = get_all_terms(Num(x)) + trigs = filter(z -> is_trig(z), all_terms) + D = Differential(t) + + rules = [] + for trig in trigs + arg = first(arguments(trig.val)) + type = operation(trig.val) + + term = Num((type == cos ? sin(arg) : -cos(arg)) / expand_derivatives(D(arg))) + append!(rules, [trig => term]) end - end - take_trig_integral(x::Num, ω, t) = take_trig_integral(Symbolics.expand(unwrap(x)), ω, t) + return Symbolics.substitute(x, Dict(rules)) + end +end +take_trig_integral(x::Num, ω, t) = take_trig_integral(Symbolics.expand(unwrap(x)), ω, t) export first_order_transform!, is_rearranged_standard, rearrange_standard!, get_equations, get_krylov_equations From 6b468685a5881ca2d6ee5466f4621b3304e6a9dc Mon Sep 17 00:00:00 2001 From: Orjan Ameye Date: Thu, 21 Nov 2024 14:22:07 +0100 Subject: [PATCH 7/7] draft=false --- docs/make.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/make.jl b/docs/make.jl index 82d44e06..59e6b989 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -43,7 +43,7 @@ makedocs(; pages=pages, source="src", build="build", - draft=true, + draft=false, warnonly=true, doctest=false, # We test it in the CI, no need to run it here plugins=[bib],