From 9994b34a0bfefd168737d3e6f06031ce3216d9fb Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Sat, 18 May 2024 13:43:22 +0000 Subject: [PATCH] build based on 522635e --- previews/PR106/assets/documenter.js | 331 ++++++++++++++++++ previews/PR106/assets/search.js | 267 ++++++++++++++ .../PR106/assets/themes/documenter-dark.css | 7 + .../PR106/assets/themes/documenter-light.css | 9 + previews/PR106/assets/themeswap.js | 66 ++++ previews/PR106/assets/warner.js | 49 +++ previews/PR106/fig/2dPBu.png | Bin 0 -> 19897 bytes previews/PR106/fig/2dPBy.png | Bin 0 -> 41515 bytes previews/PR106/fig/torus.png | Bin 0 -> 23256 bytes previews/PR106/index.html | 9 + previews/PR106/poisson-boltzman/index.html | 57 +++ previews/PR106/reference/index.html | 73 ++++ previews/PR106/search/index.html | 2 + previews/PR106/search_index.js | 3 + previews/PR106/siteinfo.js | 1 + previews/PR106/tore/index.html | 99 ++++++ 16 files changed, 973 insertions(+) create mode 100644 previews/PR106/assets/documenter.js create mode 100644 previews/PR106/assets/search.js create mode 100644 previews/PR106/assets/themes/documenter-dark.css create mode 100644 previews/PR106/assets/themes/documenter-light.css create mode 100644 previews/PR106/assets/themeswap.js create mode 100644 previews/PR106/assets/warner.js create mode 100644 previews/PR106/fig/2dPBu.png create mode 100644 previews/PR106/fig/2dPBy.png create mode 100644 previews/PR106/fig/torus.png create mode 100644 previews/PR106/index.html create mode 100644 previews/PR106/poisson-boltzman/index.html create mode 100644 previews/PR106/reference/index.html create mode 100644 previews/PR106/search/index.html create mode 100644 previews/PR106/search_index.js create mode 100644 previews/PR106/siteinfo.js create mode 100644 previews/PR106/tore/index.html diff --git a/previews/PR106/assets/documenter.js b/previews/PR106/assets/documenter.js new file mode 100644 index 0000000..6adfbbb --- /dev/null +++ b/previews/PR106/assets/documenter.js @@ -0,0 +1,331 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fas", "fa-copy"); + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-times"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-times"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function() { + $('#documenter .docs-navbar').headroom({ + "tolerance": {"up": 10, "down": 10}, + }); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function() { + var settings = $('#documenter-settings'); + $('#documenter-settings-button').click(function(){ + settings.toggleClass('is-active'); + }); + // Close the dialog if X is clicked + $('#documenter-settings button.delete').click(function(){ + settings.removeClass('is-active'); + }); + // Close dialog if ESC is pressed + $(document).keyup(function(e) { + if (e.keyCode == 27) settings.removeClass('is-active'); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function() { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button") + sidebar_button.click(function(ev) { + ev.preventDefault(); + sidebar.toggleClass('visible'); + if (sidebar.hasClass('visible')) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind('click', function(ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + }); +}) + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function() { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css('max-width'), 10); + var L0 = e.width(); + if(L0 > L) { + var h0 = parseInt(e.css('font-size'), 10); + e.css('font-size', L * h0 / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on('orientationchange', resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function() { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if(typeof active !== 'undefined') { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +function set_theme(theme) { + var active = null; + var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/previews/PR106/assets/search.js b/previews/PR106/assets/search.js new file mode 100644 index 0000000..c133f74 --- /dev/null +++ b/previews/PR106/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
  • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR106/assets/themes/documenter-dark.css b/previews/PR106/assets/themes/documenter-dark.css new file mode 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content 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Gets put into the tag.. +function set_theme_from_local_storage() { + // Intialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if(window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the browser supports user color preference + var darkPreference = false; + // Check if the users preference is for dark color scheme + if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { + darkPreference = true; + } + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; var disabled = []; var darkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if(themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null); + // Check if the theme is primary dark theme + var isDarkTheme = (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null); + // If ss is for dark theme then set the value of darkTheme to the name of the theme + if(isDarkTheme) darkTheme = themename; + // If we find a matching theme (and it's not the default), we'll set active to non-null + if(themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if(themename !== theme) disabled.push(ss); + } + if(active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + theme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + else if(darkTheme !== null && darkPreference === true) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + darkTheme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + if (ss.ownerNode.getAttribute("data-theme-name") !== darkTheme) { + ss.disabled = true; + } + }); + } +} +set_theme_from_local_storage(); diff --git a/previews/PR106/assets/warner.js b/previews/PR106/assets/warner.js new file mode 100644 index 0000000..5531c88 --- /dev/null +++ b/previews/PR106/assets/warner.js @@ -0,0 +1,49 @@ +function maybeAddWarning () { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return + }; + + // Current version is not a version number, so we can't tell if it's the newest version. 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zpl8<@6ktCmK^le_=aQ%_7)bIO2k0&&I>;)^FP0jf(Ebpa-B5*_}cVx(28H4Ky? +Introduction · PDENLPModels.jl diff --git a/previews/PR106/poisson-boltzman/index.html b/previews/PR106/poisson-boltzman/index.html new file mode 100644 index 0000000..ae9037e --- /dev/null +++ b/previews/PR106/poisson-boltzman/index.html @@ -0,0 +1,57 @@ + +PDE-constrained optimization · PDENLPModels.jl
    Edit on GitHub

    PDE-contrained optimization

    Poisson-Boltzman problem

    In this tutorial, we solve a control problem where the constraint is a 2D Poisson-Boltzman equation:

    \[\left\lbrace +\begin{aligned} +\min\limits_{y \in H_0^1(\Omega), u \in L^2(\Omega) } \ & \frac{1}{2}\int_{\Omega} |y - y_d(x)|^2 + \frac{1}{2}\alpha \int_\Omega |u|^2dx, \\ +\text{ s.t. } & -\Delta y + \sinh{y} = h + u, \quad \text{in } \Omega:=(-1,1)^2,\\ + & y = 0, \quad \text{in } \partial\Omega, +\end{aligned} +\right.\]

    with the forcing term $h(x_1,x_2)=-\sin(\omega x_1) \sin(\omega x_2)$, $\omega = \pi - \frac{1}{8}$, and target state

    \[\begin{aligned} + y_d(x) = \begin{cases} + 10 \quad \text{if } x \in [0.25,0.75]^2, \\ + 5 \quad \text{otherwise}. + \end{cases} +\end{aligned}\]

    We refer to [1] for more details on Poisson-Boltzman equations.

    The implementation as a GridapPDENLPModel is given as follows.

        using Gridap, PDENLPModels
+    #Domain
+    n = 100
+    model = CartesianDiscreteModel((-1,1,-1,1), (n,n))
+
+    #Definition of the spaces:
+    order = 1
+    valuetype = Float64
+    reffe = ReferenceFE(lagrangian, valuetype, order)
+    Xpde = TestFESpace(
+      model,
+      reffe;
+      conformity = :H1,
+      dirichlet_tags="boundary",
+    )
+    Ypde = TrialFESpace(Xpde, 0.0)
+    Xcon = TestFESpace(model, reffe; conformity = :L2)
+    Ycon = TrialFESpace(Xcon)
+    Y = MultiFieldFESpace([Ypde, Ycon])
+
+    #Integration machinery
+    trian = Triangulation(model)
+    degree = 1
+    dΩ = Measure(trian,degree)
+
+    #Objective function:
+    yd(x) = min(x[1]-0.25, 0.75-x[1],x[2]-0.25, 0.75-x[2])>=0. ? 10. : 5.
+    function f(y, u)
+        ∫( 0.5 * (yd - y) * (yd - y) + 0.5 * 1e-4 * u * u )dΩ
+    end
+
+    #Definition of the constraint operator
+    ω = π - 1/8
+    h(x) = - sin(ω*x[1])*sin(ω*x[2])
+    function res(y, u, v)
+     ∫( ∇(v) ⊙ ∇(y) + (sinh ∘ y)*v - u*v - v * h )dΩ
+    end
+    op = FEOperator(res, Y, Xpde)
+    xin = zeros(Gridap.FESpaces.num_free_dofs(Y))
+    nlp = GridapPDENLPModel(xin, f, trian, Ypde, Ycon, Xpde, Xcon, op)

    Then, one can solve the problem with Ipopt via NLPModelsIpopt.jl and plot the solution as a VTK file.

    using NLPModelsIpopt
+stats = ipopt(nlp, print_level = 0)

    Switching again the discrete solution as a FEFunction the result can written as a VTK-file using Gridap's facilities.

    yfv = stats.solution[1:Gridap.FESpaces.num_free_dofs(nlp.pdemeta.Ypde)]
+yh  = FEFunction(nlp.pdemeta.Ypde, yfv)
+ufv = stats.solution[1+Gridap.FESpaces.num_free_dofs(nlp.pdemeta.Ypde):end]
+uh  = FEFunction(nlp.pdemeta.Ycon, ufv)
+writevtk(nlp.pdemeta.tnrj.trian,"results",cellfields=["uh"=>uh, "yh"=>yh])

    Finally, the solution is obtained using any software reading VTK, e.g. Paraview.

    Solution of P-B equationControl of P-B equation

    References

    [1] Michael J. Holst The Poisson-Boltzmann equation: Analysis and multilevel numerical solution. Applied Mathematics and CRPC, California Institute of Technology. (1994). Hols94d.pdf

    diff --git a/previews/PR106/reference/index.html b/previews/PR106/reference/index.html new file mode 100644 index 0000000..799b85b --- /dev/null +++ b/previews/PR106/reference/index.html @@ -0,0 +1,73 @@ + +Reference · PDENLPModels.jl
    Edit on GitHub

    Reference

    ​

    Contents

    ​

    ​

    Index

    ​

    ​

    PDENLPModels.EnergyFETerm — Type

    AbstractEnergyTerm modeling the objective function of the optimization problem

    \[\begin{aligned} +\int_{\Omega} f(y,u) d\Omega. +\end{aligned}\]

    Constructor:

    EnergyFETerm(:: Function, :: Triangulation, :: Measure)

    See also: MixedEnergyFETerm, NoFETerm, _obj_cell_integral, _obj_integral, _compute_gradient_k!

    source
    PDENLPModels.GridapPDENLPModel — Type

    GridapPDENLPModel returns an instance of an AbstractNLPModel using Gridap.jl for the discretization of the domain with finite-elements. Given a domain Ω ⊂ ℜᵈ Find a state function y: Ω -> Y, a control function u: Ω -> U and an algebraic vector κ ∈ ℜⁿ satisfying

    \[\begin{aligned} +\min_{κ,y,u} \ & ∫_Ω​ f(κ,y,u) dΩ​ \\ +\mbox{ s.t. } & y \mbox{ solution of } PDE(κ,u)=0, \\ +& lcon <= c(κ,y,u) <= ucon, \\ +& lvar <= (κ,y,u) <= uvar. +\end{aligned}\]

    The weak formulation of the PDE is then: res((y,u),(v,q)) = ∫ v PDE(κ,y,u) + ∫ q c(κ,y,u)

    where the unknown (y,u) is a MultiField see Tutorials 7 and 8 of Gridap.

    Constructors

    Main constructor:

    GridapPDENLPModel(::NLPModelMeta, ::Counters, ::PDENLPMeta, ::PDEWorkspace)

    This is the main constructors with the attributes of the GridapPDENLPModel:

    • meta::NLPModelMeta: usual meta for NLPModels, see doc here;
    • counters::Counters: usual counters for NLPModels, see doc here;
    • pdemeta::PDENLPMeta: metadata specific to GridapPDENLPModel;
    • workspace::PDEWorkspace: Pre-allocated memory for GridapPDENLPModel.

    More practical constructors are also available.

    • For unconstrained problems:

      GridapPDENLPModel(x0, ::Function, ::Union{Measure, Triangulation}, Ypde::FESpace, Xpde::FESpace; kwargs...)

      GridapPDENLPModel(x0, ::AbstractEnergyTerm, ::Union{Measure, Triangulation}, Ypde::FESpace, Xpde::FESpace; kwargs...)

    • For constrained problems without controls:

      GridapPDENLPModel(x0, ::Function, ::Union{Measure, Triangulation}, Ypde::FESpace, Xpde::FESpace, c::Union{Function, FEOperator}; kwargs...)

      GridapPDENLPModel(x0, ::AbstractEnergyTerm, Ypde::FESpace, Xpde::FESpace, c::Union{Function, FEOperator}; kwargs...)

    • For general constrained problems:

      GridapPDENLPModel(x0, ::Function, ::Union{Measure, Triangulation}, Ypde::FESpace, Ycon::FESpace, Xpde::FESpace, Xcon::FESpace, c::Union{Function, FEOperator}; kwargs...)

      GridapPDENLPModel(x0, ::AbstractEnergyTerm, Ypde::FESpace, Ycon::FESpace, Xpde::FESpace, Xcon::FESpace, c::Union{Function, FEOperator}; kwargs...)

    where the different arguments are:

    • x0: initial guess for the system of size ≥ num_free_dofs(Ypde) + num_free_dofs(Ycon);
    • f: objective function, the number of arguments depend on the application (y) or (y,u) or (y,u,θ);
    • Ypde: trial space for the state;
    • Ycon: trial space for the control (VoidFESpace if none);
    • Xpde: test space for the state;
    • Xcon: test space for the control (VoidFESpace if none);
    • c: operator/function for the PDE-constraint, were we assume by default that the right-hand side is zero (otw. use lcon and ucon keywords), the number of arguments depend on the application (y,v) or (y,u,v) or (y,u,θ,v).

    If length(x0) > num_free_dofs(Ypde) + num_free_dofs(Ycon), then the additional components are considered algebraic variables.

    The function f and c must return integrals complying with Gridap's functions with a Measure/Triangulation given in the arguments of GridapPDENLPModel. Internally, the objective function f and the Measure/Triangulation are combined to instantiate an AbstractEnergyTerm.

    The following keyword arguments are available to all constructors:

    • name: The name of the model (default: "Generic")

    The following keyword arguments are available to the constructors for constrained problems:

    • lin: An array of indexes of the linear constraints (default: Int[])

    The following keyword arguments are available to the constructors for constrained problems explictly giving lcon and ucon:

    • y0: An inital estimate to the Lagrangian multipliers (default: zeros)

    The bounds on the variables are given as AbstractVector via keywords arguments as well:

    • either with lvar and uvar, or,
    • lvary, lvaru, lvark, and uvary, uvaru, uvark.

    Notes:

    • We handle two types of FEOperator: AffineFEOperator, and FEOperatorFromWeakForm.
    • If lcon and ucon are not given, they are assumed zeros.
    • If the type can't be deduced from the argument, it is Float64.

    Example

    using Gridap, PDENLPModels
+
+  # Definition of the domain
+  n = 100
+  domain = (-1, 1, -1, 1)
+  partition = (n, n)
+  model = CartesianDiscreteModel(domain, partition)
+
+  # Definition of the spaces:
+  valuetype = Float64
+  reffe = ReferenceFE(lagrangian, valuetype, 2)
+  Xpde = TestFESpace(model, reffe; conformity = :H1, dirichlet_tags = "boundary")
+  y0(x) = 0.0
+  Ypde = TrialFESpace(Xpde, y0)
+
+  reffe_con = ReferenceFE(lagrangian, valuetype, 1)
+  Xcon = TestFESpace(model, reffe_con; conformity = :H1)
+  Ycon = TrialFESpace(Xcon)
+
+  # Integration machinery
+  trian = Triangulation(model)
+  degree = 1
+  dΩ = Measure(trian, degree)
+
+  # Objective function:
+  yd(x) = -x[1]^2
+  α = 1e-2
+  function f(y, u)
+    ∫(0.5 * (yd - y) * (yd - y) + 0.5 * α * u * u) * dΩ
+  end
+
+  # Definition of the constraint operator
+  ω = π - 1 / 8
+  h(x) = -sin(ω * x[1]) * sin(ω * x[2])
+  function res(y, u, v)
+    ∫(∇(v) ⊙ ∇(y) - v * u - v * h) * dΩ
+  end
+
+  # initial guess
+  npde = num_free_dofs(Ypde)
+  ncon = num_free_dofs(Ycon)
+  xin = zeros(npde + ncon)
+
+  nlp = GridapPDENLPModel(xin, f, trian, Ypde, Ycon, Xpde, Xcon, res, name = "Control elastic membrane")

    You can also check the tutorial Solve a PDE-constrained optimization problem on JSO's website, juliasmoothoptimizers.github.io.

    We refer to the folder test/problems for more examples of problems of different types:

    • calculus of variations,
    • optimal control problem,
    • PDE-constrained problems,
    • mixed PDE-contrained problems with both function and algebraic unknowns.

    An alternative is to visit the repository PDEOptimizationProblems that contains a collection of test problems.

    Without objective function, the problem reduces to a classical PDE and we refer to Gridap tutorials for examples.

    source
    PDENLPModels.MixedEnergyFETerm — Type

    AbstractEnergyTerm modeling the objective function of the optimization problem with functional and discrete unknowns

    \[\begin{aligned} +\int_{\Omega} f(y,u,\kappa) d\Omega. +\end{aligned}\]

    Constructor:

    MixedEnergyFETerm(:: Function, :: Triangulation, :: Int)

    See also: EnergyFETerm, NoFETerm, _obj_cell_integral, _obj_integral, _compute_gradient_k!

    source
    PDENLPModels.NoFETerm — Type

    AbstractEnergyTerm modeling the objective function when there are no integral objective

    \[\begin{aligned} + f(\kappa). +\end{aligned}\]

    Constructors: NoFETerm() NoFETerm(:: Function)

    See also: MixedEnergyFETerm, EnergyFETerm, _obj_cell_integral, _obj_integral, _compute_gradient_k!

    source
    PDENLPModels.PDENLPMeta — Type
    PDENLPMeta

    A composite type that represents the main features of the PDE-constrained optimization problem

    PDENLPMeta contains the following attributes:

    • tnrj : structure representing the objective term
    • Ypde : TrialFESpace for the solution of the PDE
    • Ycon : TrialFESpace for the parameter
    • Xpde : TestFESpace for the solution of the PDE
    • Xcon : TestFESpace for the parameter
    • Y : concatenated TrialFESpace
    • X : concatenated TestFESpace
    • op : operator representing the PDE-constraint (nothing if no constraints)
    • nvar_pde :number of dofs in the solution functions
    • nvar_con : number of dofs in the control functions
    • nparam : number of real unknowns
    • nnzh_obj : number of nonzeros elements in the objective hessian
    • Hrows : store the structure for the hessian of the lagrangian
    • Hcols : store the structure for the hessian of the lagrangian
    • Jrows : store the structure for the hessian of the jacobian
    • Jcols : store the structure for the hessian of the jacobian
    source
    PDENLPModels._compute_gradient! — Function

    Return the gradient of the objective function and set it in place.

    _compute_gradient!(:: AbstractVector, :: EnergyFETerm, :: AbstractVector, :: FEFunctionType, :: FESpace, :: FESpace)

    See also: MixedEnergyFETerm, EnergyFETerm, NoFETerm, _obj_integral, _obj_cell_integral, _compute_hess_k_coo

    source
    PDENLPModels._compute_gradient_k! — Function

    Return the derivative of the objective function w.r.t. κ.

    _compute_gradient_k!(::AbstractVector, :: AbstractEnergyTerm, :: FEFunctionType, :: AbstractVector)

    See also: MixedEnergyFETerm, EnergyFETerm, NoFETerm, _obj_integral, _obj_cell_integral, _compute_hess_k_coo

    source
    PDENLPModels._compute_hess_k_vals! — Function

    Return the values of the hessian w.r.t. κ of the objective function.

    _compute_hess_k_vals!(:: AbstractVector, :: AbstractNLPModel, :: AbstractEnergyTerm, :: AbstractVector, :: AbstractVector)

    See also: MixedEnergyFETerm, EnergyFETerm, NoFETerm, _obj_integral, _obj_cell_integral, _compute_gradient_k

    source
    PDENLPModels._compute_hess_structure — Method
    _compute_hess_structure(::AbstractEnergyTerm, Y, X, x0, nparam)
+_compute_hess_structure::AbstractEnergyTerm, op, Y, Ypde, Ycon, X, Xpde, x0, nparam)

    Return a triplet with the structure (rows, cols) and the number of non-zeros elements in the hessian w.r.t. y and u of the objective function.

    The rows and cols returned by _compute_hess_structure_obj are already shifter by nparam.

    source
    PDENLPModels._functions_to_vectors! — Method
    _functions_to_vectors!(nini :: Int, nfields :: Int, trian :: Triangulation, lfunc :: Function, ufunc :: Function, cell_xm :: Gridap.Arrays.AppliedArray, Y :: FESpace, lvar :: AbstractVector, uvar :: AbstractVector)

    Iterate for k = 1 to nfields and switch lfunc[k] and ufunc[k] to vectors, allocated in lvar and uvar in place starting from nini + 1. It returns nini + the number of allocations.

    source
    PDENLPModels._obj_integral — Function

    Return the integral of the objective function

    _obj_integral(:: AbstractEnergyTerm, :: FEFunctionType, :: AbstractVector)

    See also: MixedEnergyFETerm, EnergyFETerm, NoFETerm, _obj_cell_integral, _compute_gradient_k, _compute_hess_k_coo

    source
    PDENLPModels._split_FEFunction — Method
    _split_FEFunction(:: AbstractVector,  :: FESpace, :: Union{FESpace, Nothing})

    Split the vector x into two FEFunction corresponding to the solution y and the control u. Returns nothing for the control u if Ycon == nothing.

    Do not verify the compatible length.

    source
    PDENLPModels._split_vector — Method
    _split_vector(:: AbstractVector,  :: FESpace, :: Union{FESpace, Nothing})

    Split the vector x into three vectors: y, u, k. Returns nothing for the control u if Ycon == nothing.

    Do not verify the compatible length.

    source
    PDENLPModels.bounds_functions_to_vectors — Method
    bounds_functions_to_vectors(Y :: MultiFieldFESpace, Ycon :: Union{FESpace, Nothing},  Ypde :: FESpace, trian :: Triangulation, lyfunc :: Union{Function, AbstractVector}, uyfunc :: Union{Function, AbstractVector}, lufunc :: Union{Function, AbstractVector}, uufunc :: Union{Function, AbstractVector})

    Return the bounds lvar and uvar.

    source
    diff --git a/previews/PR106/search/index.html b/previews/PR106/search/index.html new file mode 100644 index 0000000..e745012 --- /dev/null +++ b/previews/PR106/search/index.html @@ -0,0 +1,2 @@ + +Search · PDENLPModels.jl

    Loading search...

      diff --git a/previews/PR106/search_index.js b/previews/PR106/search_index.js new file mode 100644 index 0000000..eb90b42 --- /dev/null +++ b/previews/PR106/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"poisson-boltzman/#PDE-contrained-optimization","page":"PDE-constrained optimization","title":"PDE-contrained optimization","text":"","category":"section"},{"location":"poisson-boltzman/#Poisson-Boltzman-problem","page":"PDE-constrained optimization","title":"Poisson-Boltzman problem","text":"","category":"section"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":"In this tutorial, we solve a control problem where the constraint is a 2D Poisson-Boltzman equation:","category":"page"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":"leftlbrace\nbeginaligned\nminlimits_y in H_0^1(Omega) u in L^2(Omega) frac12int_Omega y - y_d(x)^2 + frac12alpha int_Omega u^2dx \ntext st -Delta y + sinhy = h + u quad textin Omega=(-11)^2\n y = 0 quad textin partialOmega\nendaligned\nright","category":"page"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":"with the forcing term h(x_1x_2)=-sin(omega x_1) sin(omega x_2), omega = pi - frac18, and target state","category":"page"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":"beginaligned\n y_d(x) = begincases\n 10 quad textif x in 025075^2 \n 5 quad textotherwise\n endcases\nendaligned","category":"page"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":"We refer to [1] for more details on Poisson-Boltzman equations.","category":"page"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":"The implementation as a GridapPDENLPModel is given as follows.","category":"page"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":" using Gridap, PDENLPModels\n #Domain\n n = 100\n model = CartesianDiscreteModel((-1,1,-1,1), (n,n))\n\n #Definition of the spaces:\n order = 1\n valuetype = Float64\n reffe = ReferenceFE(lagrangian, valuetype, order)\n Xpde = TestFESpace(\n model,\n reffe;\n conformity = :H1,\n dirichlet_tags=\"boundary\",\n )\n Ypde = TrialFESpace(Xpde, 0.0)\n Xcon = TestFESpace(model, reffe; conformity = :L2)\n Ycon = TrialFESpace(Xcon)\n Y = MultiFieldFESpace([Ypde, Ycon])\n\n #Integration machinery\n trian = Triangulation(model)\n degree = 1\n dΩ = Measure(trian,degree)\n\n #Objective function:\n yd(x) = min(x[1]-0.25, 0.75-x[1],x[2]-0.25, 0.75-x[2])>=0. ? 10. : 5.\n function f(y, u)\n ∫( 0.5 * (yd - y) * (yd - y) + 0.5 * 1e-4 * u * u )dΩ\n end\n\n #Definition of the constraint operator\n ω = π - 1/8\n h(x) = - sin(ω*x[1])*sin(ω*x[2])\n function res(y, u, v)\n ∫( ∇(v) ⊙ ∇(y) + (sinh ∘ y)*v - u*v - v * h )dΩ\n end\n op = FEOperator(res, Y, Xpde)\n xin = zeros(Gridap.FESpaces.num_free_dofs(Y))\n nlp = GridapPDENLPModel(xin, f, trian, Ypde, Ycon, Xpde, Xcon, op)","category":"page"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":"Then, one can solve the problem with Ipopt via NLPModelsIpopt.jl and plot the solution as a VTK file.","category":"page"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":"using NLPModelsIpopt\nstats = ipopt(nlp, print_level = 0)","category":"page"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":"Switching again the discrete solution as a FEFunction the result can written as a VTK-file using Gridap's facilities.","category":"page"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":"yfv = stats.solution[1:Gridap.FESpaces.num_free_dofs(nlp.pdemeta.Ypde)]\nyh = FEFunction(nlp.pdemeta.Ypde, yfv)\nufv = stats.solution[1+Gridap.FESpaces.num_free_dofs(nlp.pdemeta.Ypde):end]\nuh = FEFunction(nlp.pdemeta.Ycon, ufv)\nwritevtk(nlp.pdemeta.tnrj.trian,\"results\",cellfields=[\"uh\"=>uh, \"yh\"=>yh])","category":"page"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":"Finally, the solution is obtained using any software reading VTK, e.g. Paraview.","category":"page"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":"(Image: Solution of P-B equation)(Image: Control of P-B equation)","category":"page"},{"location":"poisson-boltzman/#References","page":"PDE-constrained optimization","title":"References","text":"","category":"section"},{"location":"poisson-boltzman/","page":"PDE-constrained optimization","title":"PDE-constrained optimization","text":"[1] Michael J. Holst The Poisson-Boltzmann equation: Analysis and multilevel numerical solution. Applied Mathematics and CRPC, California Institute of Technology. (1994). Hols94d.pdf","category":"page"},{"location":"reference/#Reference","page":"Reference","title":"Reference","text":"","category":"section"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/#Contents","page":"Reference","title":"Contents","text":"","category":"section"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"Pages = [\"reference.md\"]","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/#Index","page":"Reference","title":"Index","text":"","category":"section"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"Pages = [\"reference.md\"]","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"Modules = [PDENLPModels]","category":"page"},{"location":"reference/#PDENLPModels.EnergyFETerm","page":"Reference","title":"PDENLPModels.EnergyFETerm","text":"AbstractEnergyTerm modeling the objective function of the optimization problem\n\nbeginaligned\nint_Omega f(yu) dOmega\nendaligned\n\nConstructor:\n\nEnergyFETerm(:: Function, :: Triangulation, :: Measure)\n\nSee also: MixedEnergyFETerm, NoFETerm, _obj_cell_integral, _obj_integral, _compute_gradient_k!\n\n\n\n\n\n","category":"type"},{"location":"reference/#PDENLPModels.GridapPDENLPModel","page":"Reference","title":"PDENLPModels.GridapPDENLPModel","text":"GridapPDENLPModel returns an instance of an AbstractNLPModel using Gridap.jl for the discretization of the domain with finite-elements. Given a domain Ω ⊂ ℜᵈ Find a state function y: Ω -> Y, a control function u: Ω -> U and an algebraic vector κ ∈ ℜⁿ satisfying\n\nbeginaligned\nmin_κyu _Ω f(κyu) dΩ \nmbox st y mbox solution of PDE(κu)=0 \n lcon = c(κyu) = ucon \n lvar = (κyu) = uvar\nendaligned\n\nThe weak formulation of the PDE is then: res((y,u),(v,q)) = ∫ v PDE(κ,y,u) + ∫ q c(κ,y,u)\n\nwhere the unknown (y,u) is a MultiField see Tutorials 7 and 8 of Gridap.\n\nConstructors\n\nMain constructor:\n\nGridapPDENLPModel(::NLPModelMeta, ::Counters, ::PDENLPMeta, ::PDEWorkspace)\n\nThis is the main constructors with the attributes of the GridapPDENLPModel:\n\nmeta::NLPModelMeta: usual meta for NLPModels, see doc here;\ncounters::Counters: usual counters for NLPModels, see doc here;\npdemeta::PDENLPMeta: metadata specific to GridapPDENLPModel;\nworkspace::PDEWorkspace: Pre-allocated memory for GridapPDENLPModel.\n\nMore practical constructors are also available.\n\nFor unconstrained problems:\nGridapPDENLPModel(x0, ::Function, ::Union{Measure, Triangulation}, Ypde::FESpace, Xpde::FESpace; kwargs...)\nGridapPDENLPModel(x0, ::AbstractEnergyTerm, ::Union{Measure, Triangulation}, Ypde::FESpace, Xpde::FESpace; kwargs...)\nFor constrained problems without controls:\nGridapPDENLPModel(x0, ::Function, ::Union{Measure, Triangulation}, Ypde::FESpace, Xpde::FESpace, c::Union{Function, FEOperator}; kwargs...)\nGridapPDENLPModel(x0, ::AbstractEnergyTerm, Ypde::FESpace, Xpde::FESpace, c::Union{Function, FEOperator}; kwargs...)\nFor general constrained problems:\nGridapPDENLPModel(x0, ::Function, ::Union{Measure, Triangulation}, Ypde::FESpace, Ycon::FESpace, Xpde::FESpace, Xcon::FESpace, c::Union{Function, FEOperator}; kwargs...)\nGridapPDENLPModel(x0, ::AbstractEnergyTerm, Ypde::FESpace, Ycon::FESpace, Xpde::FESpace, Xcon::FESpace, c::Union{Function, FEOperator}; kwargs...)\n\nwhere the different arguments are:\n\nx0: initial guess for the system of size ≥ num_free_dofs(Ypde) + num_free_dofs(Ycon);\nf: objective function, the number of arguments depend on the application (y) or (y,u) or (y,u,θ);\nYpde: trial space for the state;\nYcon: trial space for the control (VoidFESpace if none);\nXpde: test space for the state;\nXcon: test space for the control (VoidFESpace if none);\nc: operator/function for the PDE-constraint, were we assume by default that the right-hand side is zero (otw. use lcon and ucon keywords), the number of arguments depend on the application (y,v) or (y,u,v) or (y,u,θ,v).\n\nIf length(x0) > num_free_dofs(Ypde) + num_free_dofs(Ycon), then the additional components are considered algebraic variables.\n\nThe function f and c must return integrals complying with Gridap's functions with a Measure/Triangulation given in the arguments of GridapPDENLPModel. Internally, the objective function f and the Measure/Triangulation are combined to instantiate an AbstractEnergyTerm.\n\nThe following keyword arguments are available to all constructors:\n\nname: The name of the model (default: \"Generic\")\n\nThe following keyword arguments are available to the constructors for constrained problems:\n\nlin: An array of indexes of the linear constraints (default: Int[])\n\nThe following keyword arguments are available to the constructors for constrained problems explictly giving lcon and ucon:\n\ny0: An inital estimate to the Lagrangian multipliers (default: zeros)\n\nThe bounds on the variables are given as AbstractVector via keywords arguments as well:\n\neither with lvar and uvar, or,\nlvary, lvaru, lvark, and uvary, uvaru, uvark.\n\nNotes:\n\nWe handle two types of FEOperator: AffineFEOperator, and FEOperatorFromWeakForm.\nIf lcon and ucon are not given, they are assumed zeros.\nIf the type can't be deduced from the argument, it is Float64.\n\nExample\n\nusing Gridap, PDENLPModels\n\n # Definition of the domain\n n = 100\n domain = (-1, 1, -1, 1)\n partition = (n, n)\n model = CartesianDiscreteModel(domain, partition)\n\n # Definition of the spaces:\n valuetype = Float64\n reffe = ReferenceFE(lagrangian, valuetype, 2)\n Xpde = TestFESpace(model, reffe; conformity = :H1, dirichlet_tags = \"boundary\")\n y0(x) = 0.0\n Ypde = TrialFESpace(Xpde, y0)\n\n reffe_con = ReferenceFE(lagrangian, valuetype, 1)\n Xcon = TestFESpace(model, reffe_con; conformity = :H1)\n Ycon = TrialFESpace(Xcon)\n\n # Integration machinery\n trian = Triangulation(model)\n degree = 1\n dΩ = Measure(trian, degree)\n\n # Objective function:\n yd(x) = -x[1]^2\n α = 1e-2\n function f(y, u)\n ∫(0.5 * (yd - y) * (yd - y) + 0.5 * α * u * u) * dΩ\n end\n\n # Definition of the constraint operator\n ω = π - 1 / 8\n h(x) = -sin(ω * x[1]) * sin(ω * x[2])\n function res(y, u, v)\n ∫(∇(v) ⊙ ∇(y) - v * u - v * h) * dΩ\n end\n\n # initial guess\n npde = num_free_dofs(Ypde)\n ncon = num_free_dofs(Ycon)\n xin = zeros(npde + ncon)\n\n nlp = GridapPDENLPModel(xin, f, trian, Ypde, Ycon, Xpde, Xcon, res, name = \"Control elastic membrane\")\n\nYou can also check the tutorial Solve a PDE-constrained optimization problem on JSO's website, juliasmoothoptimizers.github.io.\n\nWe refer to the folder test/problems for more examples of problems of different types:\n\ncalculus of variations,\noptimal control problem,\nPDE-constrained problems,\nmixed PDE-contrained problems with both function and algebraic unknowns. \n\nAn alternative is to visit the repository PDEOptimizationProblems that contains a collection of test problems.\n\nWithout objective function, the problem reduces to a classical PDE and we refer to Gridap tutorials for examples.\n\n\n\n\n\n","category":"type"},{"location":"reference/#PDENLPModels.MixedEnergyFETerm","page":"Reference","title":"PDENLPModels.MixedEnergyFETerm","text":"AbstractEnergyTerm modeling the objective function of the optimization problem with functional and discrete unknowns\n\nbeginaligned\nint_Omega f(yukappa) dOmega\nendaligned\n\nConstructor:\n\nMixedEnergyFETerm(:: Function, :: Triangulation, :: Int)\n\nSee also: EnergyFETerm, NoFETerm, _obj_cell_integral, _obj_integral, _compute_gradient_k!\n\n\n\n\n\n","category":"type"},{"location":"reference/#PDENLPModels.NoFETerm","page":"Reference","title":"PDENLPModels.NoFETerm","text":"AbstractEnergyTerm modeling the objective function when there are no integral objective\n\nbeginaligned\n f(kappa)\nendaligned\n\nConstructors: NoFETerm() NoFETerm(:: Function)\n\nSee also: MixedEnergyFETerm, EnergyFETerm, _obj_cell_integral, _obj_integral, _compute_gradient_k!\n\n\n\n\n\n","category":"type"},{"location":"reference/#PDENLPModels.PDENLPMeta","page":"Reference","title":"PDENLPModels.PDENLPMeta","text":"PDENLPMeta\n\nA composite type that represents the main features of the PDE-constrained optimization problem\n\n\n\nPDENLPMeta contains the following attributes:\n\ntnrj : structure representing the objective term\nYpde : TrialFESpace for the solution of the PDE\nYcon : TrialFESpace for the parameter\nXpde : TestFESpace for the solution of the PDE\nXcon : TestFESpace for the parameter\nY : concatenated TrialFESpace\nX : concatenated TestFESpace\nop : operator representing the PDE-constraint (nothing if no constraints)\nnvar_pde :number of dofs in the solution functions\nnvar_con : number of dofs in the control functions\nnparam : number of real unknowns\nnnzh_obj : number of nonzeros elements in the objective hessian\nHrows : store the structure for the hessian of the lagrangian\nHcols : store the structure for the hessian of the lagrangian\nJrows : store the structure for the hessian of the jacobian\nJcols : store the structure for the hessian of the jacobian\n\n\n\n\n\n","category":"type"},{"location":"reference/#PDENLPModels.PDEWorkspace","page":"Reference","title":"PDENLPModels.PDEWorkspace","text":"PDEWorkspace\n\nPre-allocated memory for GridapPDENLPModel.\n\n\n\n\n\n","category":"type"},{"location":"reference/#PDENLPModels._compute_gradient!","page":"Reference","title":"PDENLPModels._compute_gradient!","text":"Return the gradient of the objective function and set it in place.\n\n_compute_gradient!(:: AbstractVector, :: EnergyFETerm, :: AbstractVector, :: FEFunctionType, :: FESpace, :: FESpace)\n\nSee also: MixedEnergyFETerm, EnergyFETerm, NoFETerm, _obj_integral, _obj_cell_integral, _compute_hess_k_coo\n\n\n\n\n\n","category":"function"},{"location":"reference/#PDENLPModels._compute_gradient_k!","page":"Reference","title":"PDENLPModels._compute_gradient_k!","text":"Return the derivative of the objective function w.r.t. κ.\n\n_compute_gradient_k!(::AbstractVector, :: AbstractEnergyTerm, :: FEFunctionType, :: AbstractVector)\n\nSee also: MixedEnergyFETerm, EnergyFETerm, NoFETerm, _obj_integral, _obj_cell_integral, _compute_hess_k_coo\n\n\n\n\n\n","category":"function"},{"location":"reference/#PDENLPModels._compute_hess_k_vals!","page":"Reference","title":"PDENLPModels._compute_hess_k_vals!","text":"Return the values of the hessian w.r.t. κ of the objective function.\n\n_compute_hess_k_vals!(:: AbstractVector, :: AbstractNLPModel, :: AbstractEnergyTerm, :: AbstractVector, :: AbstractVector)\n\nSee also: MixedEnergyFETerm, EnergyFETerm, NoFETerm, _obj_integral, _obj_cell_integral, _compute_gradient_k\n\n\n\n\n\n","category":"function"},{"location":"reference/#PDENLPModels._compute_hess_structure-Tuple{AbstractEnergyTerm, Vararg{Any, 4}}","page":"Reference","title":"PDENLPModels._compute_hess_structure","text":"_compute_hess_structure(::AbstractEnergyTerm, Y, X, x0, nparam)\n_compute_hess_structure::AbstractEnergyTerm, op, Y, Ypde, Ycon, X, Xpde, x0, nparam)\n\nReturn a triplet with the structure (rows, cols) and the number of non-zeros elements in the hessian w.r.t. y and u of the objective function.\n\nThe rows and cols returned by _compute_hess_structure_obj are already shifter by nparam.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels._functions_to_vectors!-Tuple{Integer, Integer, Gridap.Geometry.Triangulation, Function, Function, Any, Gridap.FESpaces.FESpace, AbstractVector, AbstractVector}","page":"Reference","title":"PDENLPModels._functions_to_vectors!","text":"_functions_to_vectors!(nini :: Int, nfields :: Int, trian :: Triangulation, lfunc :: Function, ufunc :: Function, cell_xm :: Gridap.Arrays.AppliedArray, Y :: FESpace, lvar :: AbstractVector, uvar :: AbstractVector)\n\nIterate for k = 1 to nfields and switch lfunc[k] and ufunc[k] to vectors, allocated in lvar and uvar in place starting from nini + 1. It returns nini + the number of allocations.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels._obj_integral","page":"Reference","title":"PDENLPModels._obj_integral","text":"Return the integral of the objective function\n\n_obj_integral(:: AbstractEnergyTerm, :: FEFunctionType, :: AbstractVector)\n\nSee also: MixedEnergyFETerm, EnergyFETerm, NoFETerm, _obj_cell_integral, _compute_gradient_k, _compute_hess_k_coo\n\n\n\n\n\n","category":"function"},{"location":"reference/#PDENLPModels._split_FEFunction-Tuple{AbstractVector, Gridap.FESpaces.FESpace, Gridap.FESpaces.FESpace}","page":"Reference","title":"PDENLPModels._split_FEFunction","text":"_split_FEFunction(:: AbstractVector, :: FESpace, :: Union{FESpace, Nothing})\n\nSplit the vector x into two FEFunction corresponding to the solution y and the control u. Returns nothing for the control u if Ycon == nothing.\n\nDo not verify the compatible length.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels._split_vector-Tuple{AbstractVector, Gridap.FESpaces.FESpace, Gridap.FESpaces.FESpace}","page":"Reference","title":"PDENLPModels._split_vector","text":"_split_vector(:: AbstractVector, :: FESpace, :: Union{FESpace, Nothing})\n\nSplit the vector x into three vectors: y, u, k. Returns nothing for the control u if Ycon == nothing.\n\nDo not verify the compatible length.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels._split_vectors-Tuple{AbstractVector, Gridap.FESpaces.FESpace, Gridap.FESpaces.FESpace}","page":"Reference","title":"PDENLPModels._split_vectors","text":"_split_vectors(x, Ypde, Ycon)\n\nTake a vector x and returns a splitting in terms of y, u and θ.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.bounds_functions_to_vectors-Tuple{Gridap.FESpaces.FESpace, Gridap.FESpaces.FESpace, Gridap.FESpaces.FESpace, Gridap.Geometry.Triangulation, Vararg{Function, 4}}","page":"Reference","title":"PDENLPModels.bounds_functions_to_vectors","text":"bounds_functions_to_vectors(Y :: MultiFieldFESpace, Ycon :: Union{FESpace, Nothing}, Ypde :: FESpace, trian :: Triangulation, lyfunc :: Union{Function, AbstractVector}, uyfunc :: Union{Function, AbstractVector}, lufunc :: Union{Function, AbstractVector}, uufunc :: Union{Function, AbstractVector})\n\nReturn the bounds lvar and uvar.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_Hcols-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_Hcols","text":"get_Hcols(nlp)\nget_Hcols(meta)\n\nReturn the value Hcols from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_Hrows-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_Hrows","text":"get_Hrows(nlp)\nget_Hrows(meta)\n\nReturn the value Hrows from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_Jcols-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_Jcols","text":"get_Jcols(nlp)\nget_Jcols(meta)\n\nReturn the value Jcols from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_Jrows-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_Jrows","text":"get_Jrows(nlp)\nget_Jrows(meta)\n\nReturn the value Jrows from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_X-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_X","text":"get_X(nlp)\nget_X(meta)\n\nReturn the value X from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_Xcon-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_Xcon","text":"get_Xcon(nlp)\nget_Xcon(meta)\n\nReturn the value Xcon from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_Xpde-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_Xpde","text":"get_Xpde(nlp)\nget_Xpde(meta)\n\nReturn the value Xpde from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_Y-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_Y","text":"get_Y(nlp)\nget_Y(meta)\n\nReturn the value Y from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_Ycon-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_Ycon","text":"get_Ycon(nlp)\nget_Ycon(meta)\n\nReturn the value Ycon from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_Ypde-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_Ypde","text":"get_Ypde(nlp)\nget_Ypde(meta)\n\nReturn the value Ypde from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_nnzh_obj-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_nnzh_obj","text":"get_nnzh_obj(nlp)\nget_nnzh_obj(meta)\n\nReturn the value nnzh_obj from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_nparam-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_nparam","text":"get_nparam(nlp)\nget_nparam(meta)\n\nReturn the value nparam from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_nvar_con-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_nvar_con","text":"get_nvar_con(nlp)\nget_nvar_con(meta)\n\nReturn the value nvar_con from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_nvar_pde-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_nvar_pde","text":"get_nvar_pde(nlp)\nget_nvar_pde(meta)\n\nReturn the value nvar_pde from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_op-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_op","text":"get_op(nlp)\nget_op(meta)\n\nReturn the value op from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.get_tnrj-Tuple{PDENLPModels.PDENLPMeta}","page":"Reference","title":"PDENLPModels.get_tnrj","text":"get_tnrj(nlp)\nget_tnrj(meta)\n\nReturn the value tnrj from meta or nlp.meta.\n\n\n\n\n\n","category":"method"},{"location":"reference/#PDENLPModels.split_vectors-Tuple{GridapPDENLPModel, AbstractVector}","page":"Reference","title":"PDENLPModels.split_vectors","text":"split_vectors(::GridapPDENLPModel, x)\n\nTake a vector x and returns a splitting in terms of y, u and θ.\n\n\n\n\n\n","category":"method"},{"location":"tore/#Calculus-of-Variations","page":"Calculus of Variations","title":"Calculus of Variations","text":"","category":"section"},{"location":"tore/#The-Brachistochrone-over-a-Tore","page":"Calculus of Variations","title":"The Brachistochrone over a Tore","text":"","category":"section"},{"location":"tore/","page":"Calculus of Variations","title":"Calculus of Variations","text":"In this example, we present how to model the classical brachistochrone problem [1] over the torus with PDENLPModels.jl in polar coordinates. We want to model the following problem:","category":"page"},{"location":"tore/","page":"Calculus of Variations","title":"Calculus of Variations","text":"leftlbrace\nbeginaligned\nmin_varphi theta int_0^1 a^2 dotvarphi^2 + (c + a cos(varphi))^2 dottheta^2dt\n 0 leq theta varphi leq 2pi\n varphi(0)= 0 varphi(1)= pi\n theta(0) = 0 theta(1) = pi\nendaligned\nright","category":"page"},{"location":"tore/","page":"Calculus of Variations","title":"Calculus of Variations","text":"with a=1 and c=3. We also refer to [2] for the analytical solutions of this problem.","category":"page"},{"location":"tore/","page":"Calculus of Variations","title":"Calculus of Variations","text":" using Gridap, PDENLPModels\n\n n = 100 #discretization size\n domain = (0,1) \n model = CartesianDiscreteModel(domain, n)\n \n labels = get_face_labeling(model)\n add_tag_from_tags!(labels,\"diri1\",[2])\n add_tag_from_tags!(labels,\"diri0\",[1])\n\n x0 = zeros(2) # initial values\n xf = π * ones(2) # final values\n \n order = 1\n valuetype = Float64\n reffe = ReferenceFE(lagrangian, valuetype, order)\n V0 = TestFESpace(\n model,\n reffe;\n conformity = :H1,\n dirichlet_tags=[\"diri0\",\"diri1\"],\n )\n V1 = TestFESpace(\n model,\n reffe;\n conformity = :H1,\n dirichlet_tags=[\"diri0\",\"diri1\"],\n )\n \n U0 = TrialFESpace(V0, [x0[1], xf[1]])\n U1 = TrialFESpace(V0, [x0[2], xf[2]])\n \n V = MultiFieldFESpace([V0, V1])\n U = MultiFieldFESpace([U0, U1])\n nU0 = Gridap.FESpaces.num_free_dofs(U0)\n nU1 = Gridap.FESpaces.num_free_dofs(U1)\n \n trian = Triangulation(model)\n degree = 1\n dΩ = Measure(trian, degree)\n\n # The function under the integral:\n # To use the function cos in Gridap: `operate(cos, x)` vaut cos(x)\n # The square function is not available, so: `x*x` holds for $x^2$, \n # and `∇(φ) ⊙ ∇(φ)` for `φ'^2`.\n a = 1\n c = 3\n function f(x)\n φ, θ = x\n ∫(a * a * ∇(φ) ⊙ ∇(φ) + (c + a * (cos ∘ φ)) * (c + a * (cos ∘ φ)) * ∇(θ) ⊙ ∇(θ))dΩ\n end\n\n # boundaries\n xmin = 0\n xmax = 2*π\n \n nlp = GridapPDENLPModel(\n zeros(nU0 + nU1),\n f,\n trian,\n U,\n V,\n lvar = xmin * ones(nU0+nU1),\n uvar = xmax * ones(nU0+nU1),\n )","category":"page"},{"location":"tore/","page":"Calculus of Variations","title":"Calculus of Variations","text":"Then, one can solve the problem with Ipopt via NLPModelsIpopt.jl and plot the solution.","category":"page"},{"location":"tore/","page":"Calculus of Variations","title":"Calculus of Variations","text":"using NLPModelsIpopt\n\nstats = ipopt(nlp, print_level = 0)\n\nnn = Int(nlp.pdemeta.nvar_pde/2)\nφs = stats.solution[1:nn]\nθs = stats.solution[nn+1:2*nn]\n\nxs = (c .+ a * cos.(φs)) .* cos.(θs)\nys = (c .+ a * cos.(φs)) .* sin.(θs)\nzs = a * sin.(φs)\n\nL = stats.objective\n\nplotlyjs()\n\nlinspace(from, to, npoints) = range(from, stop=to, length=npoints)\n\n#plot a torus\nM = 100\nαs = linspace(0, 2π, M)\nβs = linspace(0, 2π, M)\nXs = (c .+ a * cos.(αs)) * cos.(βs)'\nYs = (c .+ a * cos.(αs)) * sin.(βs)'\nZs = (a * sin.(αs)) * ones(M)'\nplot3d(Xs, Ys, Zs, st=:surface, grid=false, c=:grays, axis=false, colorbar=false)\nplot3d!(xs, ys, zs, linewidth=4, color=:red, title=@sprintf(\"Geodesic on a Torus (length=%4.f)\", L), legend=false)","category":"page"},{"location":"tore/","page":"Calculus of Variations","title":"Calculus of Variations","text":"(Image: Geodesic over the tore)","category":"page"},{"location":"tore/#References","page":"Calculus of Variations","title":"References","text":"","category":"section"},{"location":"tore/","page":"Calculus of Variations","title":"Calculus of Variations","text":"[1] Weisstein, Eric W. Brachistochrone Problem. From MathWorld–A Wolfram Web Resource. mathworld.wolfram.com/BrachistochroneProblem.html","category":"page"},{"location":"tore/","page":"Calculus of Variations","title":"Calculus of Variations","text":"[2] Mark L. Irons The Curvature and Geodesics of the Torus (2005). torus.geodesics.pdf","category":"page"},{"location":"#PDENLPModels.jl-Documentation","page":"Introduction","title":"PDENLPModels.jl Documentation","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"PDENLPModels is a Julia package that specializes the NLPModel API for modeling and discretizing optimization problems with mixed algebraic and PDE in the constraints.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"We consider optimization problems of the form: find functions (y,u) and κ ∈ ℜⁿ satisfying","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"leftlbrace\nbeginaligned\nminlimits_κyu int_Omega f(κyu)dx \ntext st texty solution of a PDE(κu)\n lcon leq c(κyu) leq ucon\n lvar leq (κyu) leq uvar\nendaligned\nright","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"The main challenges in modeling such a problem are to be able to discretize the domain and generate corresponding discretizations of the objective and constraints, and their evaluate derivatives with respect to all variables. We use Gridap.jl to define the domain, meshes, function spaces, and finite-element families to approximate unknowns, and to model functionals and sets of PDEs in a weak form. PDENLPModels extends Gridap.jl's differentiation facilities to also obtain derivatives useful for optimization, i.e., first and second derivatives of the objective and constraint functions with respect to controls and finite-dimensional variables.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"After discretization of the domain Omega, the integral, and the derivatives, the resulting problem is a nonlinear optimization problem. PDENLPModels exports the GridapPDENLPModel type, an instance of an AbstractNLPModel, as defined in NLPModels.jl, which provides access to objective and constraint function values, to their first and second derivatives, and to any information that a solver might request from a model. The role of NLPModels.jl is to define an API that users and solvers can rely on. It is the role of other packages to implement facilities that create models compliant with the NLPModels API. We refer to juliasmoothoptimizers.github.io for tutorials on the NLPModel API.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"As such, PDENLPModels offers an interface between generic PDE-constrained optimization problems and cutting-edge optimization solvers such as Artelys Knitro via NLPModelsKnitro.jl, Ipopt via NLPModelsIpopt.jl , DCISolver.jl, Percival.jl, and any solver accepting an AbstractNLPModel as input, see JuliaSmoothOptimizers.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"Migot, T., Orban D., & Siqueira A. S. PDENLPModels.jl: A NLPModel API for optimization problems with PDE-constraints Journal of Open Source Software 7(80), 4736 (2022). 10.21105/joss.04736","category":"page"},{"location":"#Installation","page":"Introduction","title":"Installation","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"] add PDENLPModels","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"The current version of PDENLPModels relies on Gridap v0.15.5.","category":"page"},{"location":"#Table-of-Contents","page":"Introduction","title":"Table of Contents","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"},{"location":"#Examples","page":"Introduction","title":"Examples","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"You can also check the tutorial Solve a PDE-constrained optimization problem on our site, juliasmoothoptimizers.github.io.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"We refer to the folder test/problems for more examples of problems of different types: calculus of variations, optimal control problem, PDE-constrained problems, and mixed PDE-contrained problems with both function and vector unknowns. An alternative is to visit the repository PDEOptimizationProblems that contains a collection of test problems. Without objective function, the problem reduces to a classical PDE and we refer to Gridap tutorials for examples.","category":"page"},{"location":"#References","page":"Introduction","title":"References","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Gridap.jl Badia, S., Verdugo, F. (2020). Gridap: An extensible Finite Element toolbox in Julia. Journal of Open Source Software, 5(52), 2520.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"NLPModels.jl D. Orban, A. S. Siqueira and contributors (2020). NLPModels.jl: Data Structures for Optimization Models","category":"page"},{"location":"#Bug-reports-and-discussions","page":"Introduction","title":"Bug reports and discussions","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"If you think you found a bug, feel free to open an issue. Focused suggestions and requests can also be opened as issues. Before opening a pull request, start an issue or a discussion on the topic, please.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"If you want to ask a question not suited for a bug report, feel free to start a discussion here. This forum is for general discussion about this repository and the JuliaSmoothOptimizers, so questions about any of our packages are welcome.","category":"page"}] +} diff --git a/previews/PR106/siteinfo.js b/previews/PR106/siteinfo.js new file mode 100644 index 0000000..deec958 --- /dev/null +++ b/previews/PR106/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR106"; diff --git a/previews/PR106/tore/index.html b/previews/PR106/tore/index.html new file mode 100644 index 0000000..95e750c --- /dev/null +++ b/previews/PR106/tore/index.html @@ -0,0 +1,99 @@ + +Calculus of Variations · PDENLPModels.jl
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      Calculus of Variations

      The Brachistochrone over a Tore

      In this example, we present how to model the classical brachistochrone problem [1] over the torus with PDENLPModels.jl in polar coordinates. We want to model the following problem:

      \[\left\lbrace +\begin{aligned} +\min_{\varphi, \theta} \ & \ \int_0^1 a^2 \dot{\varphi}^2 + (c + a \cos(\varphi))^2 \dot{\theta}^2dt,\\ +& \ 0 \leq \theta, \varphi \leq 2\pi,\\ +& \ \varphi(0)= 0, \varphi(1)= \pi,\\ +& \ \theta(0) = 0, \theta(1) = \pi,\\ +\end{aligned} +\right.\]

      with $a=1$ and $c=3$. We also refer to [2] for the analytical solutions of this problem.

        using Gridap, PDENLPModels
+
+  n = 100 #discretization size
+  domain = (0,1) 
+  model = CartesianDiscreteModel(domain, n)
+      
+  labels = get_face_labeling(model)
+  add_tag_from_tags!(labels,"diri1",[2])
+  add_tag_from_tags!(labels,"diri0",[1])
+
+  x0 = zeros(2) # initial values
+  xf = π * ones(2) # final values
+  
+  order = 1
+  valuetype = Float64
+  reffe = ReferenceFE(lagrangian, valuetype, order)
+  V0 = TestFESpace(
+    model,
+    reffe;
+    conformity = :H1,
+    dirichlet_tags=["diri0","diri1"],
+  )
+  V1 = TestFESpace(
+    model,
+    reffe;
+    conformity = :H1,
+    dirichlet_tags=["diri0","diri1"],
+  )
+  
+  U0  = TrialFESpace(V0, [x0[1], xf[1]])
+  U1  = TrialFESpace(V0, [x0[2], xf[2]])
+  
+  V = MultiFieldFESpace([V0, V1])
+  U = MultiFieldFESpace([U0, U1])
+  nU0 = Gridap.FESpaces.num_free_dofs(U0)
+  nU1 = Gridap.FESpaces.num_free_dofs(U1)
+  
+  trian = Triangulation(model)
+  degree = 1
+  dΩ = Measure(trian, degree)
+
+  # The function under the integral:
+  # To use the function cos in Gridap: `operate(cos, x)` vaut cos(x)
+  # The square function is not available, so: `x*x` holds for $x^2$, 
+  # and `∇(φ) ⊙ ∇(φ)` for `φ'^2`.
+  a = 1
+  c = 3
+  function f(x)
+    φ, θ = x
+    ∫(a * a * ∇(φ) ⊙ ∇(φ) + (c + a * (cos ∘ φ)) * (c + a * (cos ∘ φ)) * ∇(θ) ⊙ ∇(θ))dΩ
+  end
+
+  # boundaries
+  xmin = 0
+  xmax = 2*π
+  
+  nlp = GridapPDENLPModel(
+    zeros(nU0 + nU1),
+    f,
+    trian,
+    U,
+    V,
+    lvar = xmin * ones(nU0+nU1),
+    uvar = xmax * ones(nU0+nU1),
+  )

      Then, one can solve the problem with Ipopt via NLPModelsIpopt.jl and plot the solution.

      using NLPModelsIpopt
+
+stats = ipopt(nlp, print_level = 0)
+
+nn = Int(nlp.pdemeta.nvar_pde/2)
+φs = stats.solution[1:nn]
+θs = stats.solution[nn+1:2*nn]
+
+xs = (c .+ a * cos.(φs)) .* cos.(θs)
+ys = (c .+ a * cos.(φs)) .* sin.(θs)
+zs = a * sin.(φs)
+
+L = stats.objective
+
+plotlyjs()
+
+linspace(from, to, npoints) = range(from, stop=to, length=npoints)
+
+#plot a torus
+M = 100
+αs = linspace(0, 2π, M)
+βs = linspace(0, 2π, M)
+Xs = (c .+ a * cos.(αs)) * cos.(βs)'
+Ys = (c .+ a * cos.(αs)) * sin.(βs)'
+Zs = (a * sin.(αs)) * ones(M)'
+plot3d(Xs, Ys, Zs, st=:surface, grid=false, c=:grays, axis=false, colorbar=false)
+plot3d!(xs, ys, zs, linewidth=4, color=:red, title=@sprintf("Geodesic on a Torus (length=%4.f)", L), legend=false)

      Geodesic over the tore

      References

      [1] Weisstein, Eric W. Brachistochrone Problem. From MathWorld–A Wolfram Web Resource. mathworld.wolfram.com/BrachistochroneProblem.html

      [2] Mark L. Irons The Curvature and Geodesics of the Torus (2005). torus.geodesics.pdf

      Edit on GitHub

      PDENLPModels.jl Documentation

      PDENLPModels is a Julia package that specializes the NLPModel API for modeling and discretizing optimization problems with mixed algebraic and PDE in the constraints.

      We consider optimization problems of the form: find functions (y,u) and κ ∈ ℜⁿ satisfying

      \[\left\lbrace +\begin{aligned} +\min\limits_{κ,y,u} \ & \int_{\Omega} f(κ,y,u)dx, \\ +\text{ s.t. } & \text{y solution of a PDE(κ,u)},\\ + & lcon \leq c(κ,y,u) \leq ucon,\\ + & lvar \leq (κ,y,u) \leq uvar.\\ +\end{aligned} +\right.\]

      The main challenges in modeling such a problem are to be able to discretize the domain and generate corresponding discretizations of the objective and constraints, and their evaluate derivatives with respect to all variables. We use Gridap.jl to define the domain, meshes, function spaces, and finite-element families to approximate unknowns, and to model functionals and sets of PDEs in a weak form. PDENLPModels extends Gridap.jl's differentiation facilities to also obtain derivatives useful for optimization, i.e., first and second derivatives of the objective and constraint functions with respect to controls and finite-dimensional variables.

      After discretization of the domain $\Omega$, the integral, and the derivatives, the resulting problem is a nonlinear optimization problem. PDENLPModels exports the GridapPDENLPModel type, an instance of an AbstractNLPModel, as defined in NLPModels.jl, which provides access to objective and constraint function values, to their first and second derivatives, and to any information that a solver might request from a model. The role of NLPModels.jl is to define an API that users and solvers can rely on. It is the role of other packages to implement facilities that create models compliant with the NLPModels API. We refer to juliasmoothoptimizers.github.io for tutorials on the NLPModel API.

      As such, PDENLPModels offers an interface between generic PDE-constrained optimization problems and cutting-edge optimization solvers such as Artelys Knitro via NLPModelsKnitro.jl, Ipopt via NLPModelsIpopt.jl , DCISolver.jl, Percival.jl, and any solver accepting an AbstractNLPModel as input, see JuliaSmoothOptimizers.

      Migot, T., Orban D., & Siqueira A. S. PDENLPModels.jl: A NLPModel API for optimization problems with PDE-constraints Journal of Open Source Software 7(80), 4736 (2022). 10.21105/joss.04736

      Installation

      ] add PDENLPModels

      The current version of PDENLPModels relies on Gridap v0.15.5.

      Table of Contents

      Examples

      You can also check the tutorial Solve a PDE-constrained optimization problem on our site, juliasmoothoptimizers.github.io.

      We refer to the folder test/problems for more examples of problems of different types: calculus of variations, optimal control problem, PDE-constrained problems, and mixed PDE-contrained problems with both function and vector unknowns. An alternative is to visit the repository PDEOptimizationProblems that contains a collection of test problems. Without objective function, the problem reduces to a classical PDE and we refer to Gridap tutorials for examples.

      References

      Gridap.jl Badia, S., Verdugo, F. (2020). Gridap: An extensible Finite Element toolbox in Julia. Journal of Open Source Software, 5(52), 2520.

      NLPModels.jl D. Orban, A. S. Siqueira and contributors (2020). NLPModels.jl: Data Structures for Optimization Models

      Bug reports and discussions

      If you think you found a bug, feel free to open an issue. Focused suggestions and requests can also be opened as issues. Before opening a pull request, start an issue or a discussion on the topic, please.

      If you want to ask a question not suited for a bug report, feel free to start a discussion here. This forum is for general discussion about this repository and the JuliaSmoothOptimizers, so questions about any of our packages are welcome.