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'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(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "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-xmark"); + 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-xmark"); + }, 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 () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // 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 + const stopWords = new Set([ + "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", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`${querystring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(querystring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// 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 + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` + + `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// 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 = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // 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) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// 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/PR230/assets/favicon.ico b/previews/PR230/assets/favicon.ico new file mode 100644 index 0000000000000000000000000000000000000000..3c6bd470373d2cccea2154d70907b0e02ab202c8 GIT binary patch literal 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.button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark 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kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark 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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 #fff #fff !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-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fffaeb;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fff7de;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fff3d1;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--documenter-dark .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--documenter-dark .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--documenter-dark div.icon-text{display:flex}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--documenter-dark .image.is-4by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--documenter-dark .image.is-3by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--documenter-dark .image.is-3by2 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--documenter-dark .image.is-5by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--documenter-dark .image.is-5by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--documenter-dark .image.is-16by9 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 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+ Maintainer: @highlightjs/core-team + Website: https://highlightjs.org/ + License: see project LICENSE + Touched: 2021 +*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/previews/PR230/assets/themeswap.js b/previews/PR230/assets/themeswap.js new file mode 100644 index 00000000..9f5eebe6 --- /dev/null +++ b/previews/PR230/assets/themeswap.js @@ -0,0 +1,84 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize 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 users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === 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 primaryLightTheme = null; + var primaryDarkTheme = 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. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = 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); + } + var activeTheme = null; + 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; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + 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; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/previews/PR230/assets/warner.js b/previews/PR230/assets/warner.js new file mode 100644 index 00000000..3f6f5d00 --- /dev/null +++ b/previews/PR230/assets/warner.js @@ -0,0 +1,52 @@ +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. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; + + document.getElementsByTagName("head")[0].appendChild(meta); + } + + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/previews/PR230/index.html b/previews/PR230/index.html new file mode 100644 index 00000000..27274cfc --- /dev/null +++ b/previews/PR230/index.html @@ -0,0 +1,252 @@ + +DataInterpolations.jl · DataInterpolations.jl
GitHub

DataInterpolations.jl

DataInterpolations.jl is a library for performing interpolations of one-dimensional data. By "data interpolations" we mean techniques for interpolating possibly noisy data, and thus some methods are mixtures of regressions with interpolations (i.e. do not hit the data points exactly, smoothing out the lines). This library can be used to fill in intermediate data points in applications like timeseries data.

Installation

To install DataInterpolations.jl, use the Julia package manager:

using Pkg
+Pkg.add("DataInterpolations")

Available Interpolations

In all cases, u an AbstractVector of values and t is an AbstractVector of timepoints corresponding to (u,t) pairs.

  • ConstantInterpolation(u,t) - A piecewise constant interpolation.

  • LinearInterpolation(u,t) - A linear interpolation.

  • QuadraticInterpolation(u,t) - A quadratic interpolation.

  • LagrangeInterpolation(u,t,n) - A Lagrange interpolation of order n.

  • QuadraticSpline(u,t) - A quadratic spline interpolation.

  • CubicSpline(u,t) - A cubic spline interpolation.

  • AkimaInterpolation(u, t) - Akima spline interpolation provides a smoothing effect and is computationally efficient.

  • BSplineInterpolation(u,t,d,pVec,knotVec) - An interpolation B-spline. This is a B-spline that hits each of the data points. The argument choices are:

    • d - degree of B-spline
    • pVec - Symbol to Parameters Vector, pVec = :Uniform for uniformly spaced parameters, and pVec = :ArcLen for parameters generated by the chord length method.
    • knotVec - Symbol to Knot Vector, knotVec = :Uniform for uniform knot vector, knotVec = :Average for average spaced knot vector.

  • BSplineApprox(u,t,d,h,pVec,knotVec) - A regression B-spline which smooths the fitting curve. The argument choices are the same as the BSplineInterpolation, with the additional parameter h<length(t) which is the number of control points to use, with smaller h indicating more smoothing.

Extension Methods

The following methods require extra dependencies and will be loaded as package extensions.

  • Curvefit(u,t,m,p,alg) - An interpolation which is done by fitting a user-given functional form m(t,p) where p is the vector of parameters. The user's input p is an initial value for a least-squares fitting, alg is the algorithm choice to use to optimize the cost function (sum of squared deviations) via Optim.jl and optimal ps are used in the interpolation. Requires using Optim.
  • RegularizationSmooth(u,t,d;λ,alg) - A regularization algorithm (ridge regression) which is done by minimizing an objective function (l2 loss + derivatives of order d) integrated in the time span. It is a global method which creates a smooth curve. Requires using RegularizationTools.

Plotting

DataInterpolations.jl is tied into the Plots.jl ecosystem, by way of RecipesBase. Any interpolation can be plotted using the plot command (or any other), since they have type recipes associated with them.

For convenience, and to allow keyword arguments to propagate properly, DataInterpolations.jl also defines several series types, corresponding to different interpolations.

The series types defined are:

  • :linear_interp
  • :quadratic_interp
  • :lagrange_interp
  • :quadratic_spline
  • :cubic_spline

By and large, these accept the same keywords as their function counterparts.

Contributing

Reproducibility

The documentation of this SciML package was built using these direct dependencies,
Status `~/work/DataInterpolations.jl/DataInterpolations.jl/docs/Project.toml`
+  [82cc6244] DataInterpolations v4.6.0 `~/work/DataInterpolations.jl/DataInterpolations.jl`
+  [e30172f5] Documenter v1.3.0
+  [429524aa] Optim v1.9.2
+  [91a5bcdd] Plots v1.40.1
+  [29dad682] RegularizationTools v0.6.0
+  [860ef19b] StableRNGs v1.0.1
and using this machine and Julia version.
Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 4 × AMD EPYC 7763 64-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver3)
+Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
A more complete overview of all dependencies and their versions is also provided.
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diff --git a/previews/PR230/interface/index.html b/previews/PR230/interface/index.html new file mode 100644 index 00000000..ae8a7da7 --- /dev/null +++ b/previews/PR230/interface/index.html @@ -0,0 +1,29 @@ + +Interface · DataInterpolations.jl
GitHub

Interface for using the Interpolations object

We will again use the same data as the previous tutorial to demonstrate how to use the Interpolations object for computing interpolated values at any time point, as well as derivatives and integrals.

using DataInterpolations
+
+# Dependent variable
+u = [14.7, 11.51, 10.41, 14.95, 12.24, 11.22]
+
+# Independent variable
+t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
6-element Vector{Float64}:
+   0.0
+  62.25
+ 109.66
+ 162.66
+ 205.8
+ 252.3

Interpolated values

All interpolation methods return an object from which we can compute the value of the dependent variable at any time point.

We will use the CubicSpline method for demonstration, but the API is the same for all the methods. We can also pass the extrapolate=true keyword if we want to allow the interpolation to go beyond the range of the timepoints. The default value is extrapolate=false.

A1 = CubicSpline(u, t)
+
+# For interpolation do, A(t)
+A1(100.0)
+
+A2 = CubicSpline(u, t; extrapolate = true)
+
+# Extrapolation
+A2(300.0)
6.186306759108685
Note

The values computed beyond the range of the time points provided during interpolation will not be reliable, as these methods only perform well within the range and the first/last piece polynomial fit is extrapolated on either side which might not reflect the true nature of the data.

Derivatives

Derivatives of the interpolated curves can also be computed at any point for all the methods.

We will continue with the above example, but the API is the same for all the methods. If the interpolation is defined with extrapolate=true, derivatives can also be extrapolated.

# derivative(A, t)
+DataInterpolations.derivative(A1, 1.0)
+
+# Extrapolation
+DataInterpolations.derivative(A2, 300.0)
-0.23144961208831108

Integrals

Integrals of the interpolated curves can also be computed easily.

Note

Integrals for LagrangeInterpolation, BSplineInterpolation, BSplineApprox, Curvefit will error as there are no simple analytical solutions available. Please use numerical methods instead, such as Integrals.jl.

To compute the integrals from the start of time points provided during interpolation to any point, we can do:

# integral(A, t)
+DataInterpolations.integral(A1, 5.0)
129.64386171415265

If we want to compute integrals between two points, we can do:

# integral(A, t1, t2)
+DataInterpolations.integral(A1, 1.0, 5.0)
114.9694509973317

Again, if the interpolation is defined with extrapolate=true, the integral can be computed beyond the range of the timepoints.

# integral(A, t1, t2)
+DataInterpolations.integral(A2, 200.0, 300.0)
1065.2015077631368
Note

If the times provided in the integral go beyond the range of the time points provided during interpolation, it uses extrapolation methods to compute the values, and hence the integral can be misrepsentative and might not reflect the true nature of the data.

diff --git a/previews/PR230/manual/index.html b/previews/PR230/manual/index.html new file mode 100644 index 00000000..d57d3bfc --- /dev/null +++ b/previews/PR230/manual/index.html @@ -0,0 +1,2 @@ + +Manual · DataInterpolations.jl
GitHub

Methods

DataInterpolations.LinearInterpolation — Type
LinearInterpolation(u, t; extrapolate = false)

It is the method of interpolating between the data points using a linear polynomial. For any point, two data points one each side are chosen and connected with a line. Extrapolation extends the last linear polynomial on each side.

Arguments

  • u: data points.
  • t: time points.

Keyword Arguments

  • extrapolate: boolean value to allow extrapolation. Defaults to false.
source
DataInterpolations.QuadraticInterpolation — Type
QuadraticInterpolation(u, t, mode = :Forward; extrapolate = false)

It is the method of interpolating between the data points using quadratic polynomials. For any point, three data points nearby are taken to fit a quadratic polynomial. Extrapolation extends the last quadratic polynomial on each side.

Arguments

  • u: data points.
  • t: time points.
  • mode: :Forward or :Backward. If :Forward, two data points ahead of the point and one data point behind is taken for interpolation. If :Backward, two data points behind and one ahead is taken for interpolation.

Keyword Arguments

  • extrapolate: boolean value to allow extrapolation. Defaults to false.
source
DataInterpolations.LagrangeInterpolation — Type
LagrangeInterpolation(u, t, n = length(t) - 1; extrapolate = false)

It is the method of interpolation using Lagrange polynomials of (k-1)th order passing through all the data points where k is the number of data points.

Arguments

  • u: data points.
  • t: time points.
  • n: order of the polynomial. Currently only (k-1)th order where k is the number of data points.

Keyword Arguments

  • extrapolate: boolean value to allow extrapolation. Defaults to false.
source
DataInterpolations.AkimaInterpolation — Type
AkimaInterpolation(u, t; extrapolate = false)

It is a spline interpolation built from cubic polynomials. It forms a continuously differentiable function. For more details, refer: https://en.wikipedia.org/wiki/Akima_spline. Extrapolation extends the last cubic polynomial on each side.

Arguments

  • u: data points.
  • t: time points.

Keyword Arguments

  • extrapolate: boolean value to allow extrapolation. Defaults to false.
source
DataInterpolations.ConstantInterpolation — Type
ConstantInterpolation(u, t; dir = :left, extrapolate = false)

It is the method of interpolating using a constant polynomial. For any point, two adjacent data points are found on either side (left and right). The value at that point depends on dir. If it is :left, then the value at the left point is chosen and if it is :right, the value at the right point is chosen. Extrapolation extends the last constant polynomial at the end points on each side.

Arguments

  • u: data points.
  • t: time points.

Keyword Arguments

  • dir: indicates which value should be used for interpolation (:left or :right).
  • extrapolate: boolean value to allow extrapolation. Defaults to false.
source
DataInterpolations.QuadraticSpline — Type
QuadraticSpline(u, t; extrapolate = false)

It is a spline interpolation using piecewise quadratic polynomials between each pair of data points. Its first derivative is also continuous. Extrapolation extends the last quadratic polynomial on each side.

Arguments

  • u: data points.
  • t: time points.

Keyword Arguments

  • extrapolate: boolean value to allow extrapolation. Defaults to false.
source
DataInterpolations.CubicSpline — Type
QuadraticSpline(u, t; extrapolate = false)

It is a spline interpolation using piecewise cubic polynomials between each pair of data points. Its first and second derivative is also continuous. Extrapolation extends the last cubic polynomial on each side.

Arguments

  • u: data points.
  • t: time points.

Keyword Arguments

  • extrapolate: boolean value to allow extrapolation. Defaults to false.
source
DataInterpolations.BSplineInterpolation — Type
BSplineInterpolation(u, t, d, pVecType, knotVecType; extrapolate = false)

It is a curve defined by the linear combination of n basis functions of degree d where n is the number of data points. For more information, refer https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve.html. Extrapolation is a constant polynomial of the end points on each side.

Arguments

  • u: data points.
  • t: time points.
  • d: degree of the piecewise polynomial.
  • pVecType: symbol to parameters vector, :Uniform for uniform spaced parameters and :ArcLen for parameters generated by chord length method.
  • knotVecType: symbol to knot vector, :Uniform for uniform knot vector, :Average for average spaced knot vector.

Keyword Arguments

  • extrapolate: boolean value to allow extrapolation. Defaults to false.
source
DataInterpolations.BSplineApprox — Type
BSplineApprox(u, t, d, h, pVecType, knotVecType; extrapolate = false)

It is a regression based B-spline. The argument choices are the same as the BSplineInterpolation, with the additional parameter h < length(t) which is the number of control points to use, with smaller h indicating more smoothing. For more information, refer http://www.cad.zju.edu.cn/home/zhx/GM/009/00-bsia.pdf. Extrapolation is a constant polynomial of the end points on each side.

Arguments

  • u: data points.
  • t: time points.
  • d: degree of the piecewise polynomial.
  • h: number of control points to use.
  • pVecType: symbol to parameters vector, :Uniform for uniform spaced parameters and :ArcLen for parameters generated by chord length method.
  • knotVecType: symbol to knot vector, :Uniform for uniform knot vector, :Average for average spaced knot vector.

Keyword Arguments

  • extrapolate: boolean value to allow extrapolation. Defaults to false.
source

Utility Functions

DataInterpolations.bracketstrictlymontonic — Function
bracketstrictlymontonic(v, x, guess; lt=<comparison>, by=<transform>, rev=false)

Starting from an initial guess index, find indices (lo, hi) such that v[lo] ≤ x ≤ v[hi] according to the specified order, assuming that x is actually within the range of values found in v. If x is outside that range, either lo will be firstindex(v) or hi will be lastindex(v).

Note that the results will not typically satisfy lo ≤ guess ≤ hi. If x is precisely equal to a value that is not unique in the input v, there is no guarantee that (lo, hi) will encompass all indices corresponding to that value.

This algorithm is essentially an expanding binary search, which can be used as a precursor to searchsorted and related functions, which can take lo and hi as arguments. The purpose of using this function first would be to accelerate convergence in those functions by using correlated guesses for repeated calls. The best guess for the next call of this function would be the index returned by the previous call to searchsorted.

See sort! for an explanation of the keyword arguments by, lt and rev.

source
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b/previews/PR230/methods/index.html new file mode 100644 index 00000000..8011906a --- /dev/null +++ b/previews/PR230/methods/index.html @@ -0,0 +1,92 @@ + +Methods · DataInterpolations.jl
GitHub

Interpolation using different methods

We will use the following data to demonstrate interpolation methods.

using DataInterpolations, Plots
+
+# Dependent variable
+u = [14.7, 11.51, 10.41, 14.95, 12.24, 11.22]
+
+# Independent variable
+t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
6-element Vector{Float64}:
+   0.0
+  62.25
+ 109.66
+ 162.66
+ 205.8
+ 252.3

For each method, we will show how to perform the fit and use the plot recipe to show the fitting curve.

Linear Interpolation

This is a linear interpolation between the ends points of the interval of input data points.

A = LinearInterpolation(u, t)
+scatter(t, u, label = "input data")
+plot!(A)
Example block output

Quadratic Interpolation

This function fits a parabola passing through the two nearest points from the input data point as well as the next-closest point on the right or left, depending on whether the forward- or backward-looking mode is selected (default mode is forward-looking). It is continuous and piecewise differentiable.

A = QuadraticInterpolation(u, t) # same as QuadraticInterpolation(u,t,:Forward)
+# alternatively: A = QuadraticInterpolation(u,t,:Backward)
+scatter(t, u, label = "input data")
+plot!(A)
Example block output

Lagrange Interpolation

It fits a polynomial of degree d (=length(t)-1), and is thus a continuously differentiable function.

A = LagrangeInterpolation(u, t)
+scatter(t, u, label = "input data")
+plot!(A)
Example block output

Constant Interpolation

This function is constant between data points. By default, it takes the value at the left end of the interval. One can change that behavior by passing the keyword argument dir = :right.

A = ConstantInterpolation(u, t)
+scatter(t, u, label = "input data")
+plot!(A)
Example block output

Or using the right endpoints:

A = ConstantInterpolation(u, t, dir = :right)
+scatter(t, u, label = "input data")
+plot!(A)
Example block output

Quadratic Spline

This is the quadratic spline. It is a continuously differentiable interpolation which hits each of the data points exactly. Splines are a local interpolation method, meaning that the curve in a given spot is only affected by the points nearest to it.

A = QuadraticSpline(u, t)
+scatter(t, u, label = "input data")
+plot!(A)
Example block output

Cubic Spline

This is the cubic spline. It is a continuously twice differentiable interpolation which hits each of the data points exactly.

A = CubicSpline(u, t)
+scatter(t, u, label = "input data")
+plot!(A)
Example block output

B-Splines

This is an interpolating B-spline. B-splines are a global method, meaning that every data point is taken into account for each point of the curve. The interpolating B-spline is the version which hits each of the points. This method is described in more detail here. Let's plot a cubic B-spline (3rd order). Since the data points are not close to uniformly spaced, we will use the :ArcLen and :Average choices:

A = BSplineInterpolation(u, t, 3, :ArcLen, :Average)
+scatter(t, u, label = "input data")
+plot!(A)
Example block output

The approximating B-spline is a smoothed version of the B-spline. It again is a global method. In this case, we need to give a number of control points length(t)>h and this method fits a B-spline through the control points which is a least square approximation. This has a natural effect of smoothing the data. For example, if we use 4 control points, we get the result:

A = BSplineApprox(u, t, 3, 4, :ArcLen, :Average)
+scatter(t, u, label = "input data")
+plot!(A)
Example block output

Regularization Smoothing

Smoothing by regularization (a.k.a. ridge regression) finds a function $\hat{u}$ that minimizes the objective function:

$Q(\hat{u}) = \int_{t_1}^{t_N} |\hat{u}(t) - u(t)|^2 \mathrm{d}t + \lambda \int_{\hat{t}_1}^{\hat{t}_N} |\hat{u}^{(d)}(\hat{t})|^2 \mathrm{d} \hat{t}$

where $(d)$ denotes derivative order and $\lambda$ is the regularization (smoothing) parameter. The integrals are evaluated numerically at the set of $t$ values for the first term and $\hat{t}$ values for the second term (equal to $t$ if not provided). Regularization smoothing is a global method that creates a smooth curve directly. See Stickel (2010) Comput. Chem. Eng. 34:467 for details. The implementation in this package uses cubic splines to interpolate between the smoothed points after they are determined.

using RegularizationTools
+d = 2
+λ = 1e3
+A = RegularizationSmooth(u, t, d; λ = λ, alg = :fixed)
+û = A.û
+# interpolate using the smoothed values
+N = 200
+titp = collect(range(minimum(t), maximum(t), length = N))
+uitp = A.(titp)
+lw = 1.5
+scatter(t, u, label = "data")
+scatter!(t, û, marker = :square, label = "smoothed data")
+plot!(titp, uitp, lw = lw, label = "smoothed interpolation")
Example block output

Dense Data Demonstration

Some methods are better suited for dense data. Let's generate such data to demonstrate these methods.

import StableRNGs: StableRNG
+rng = StableRNG(318)
+t = sort(10 .* rand(rng, 100))
+u = sin.(t) .+ 0.5 * randn(rng, 100);
100-element Vector{Float64}:
+ -0.4891563556934994
+ -0.7411337336203204
+  0.303260759772529
+ -0.03721116720925663
+ -0.5073147206014983
+  0.1956851914978695
+  0.5717256362165741
+  0.29209309353794644
+  0.6444380583968424
+  0.5907863715716408
+  ⋮
+  1.4566016140618308
+  1.016810621114802
+  0.32542000692979595
+  1.1323247210598848
+ -0.0495435623347093
+  0.1762559989623056
+ -0.5319640155153034
+ -0.9932887141154423
+ -1.2766512199488596

Regularization Smoothing

Although smoothing by regularization can be used to interpolate sparse data as shown above, it is especially useful for dense as well as scattered data (unequally spaced, unordered, and/or repeat-valued). Generalized cross validation (GCV) or so-called L-curve methods can be used to determine an "optimal" value for the smoothing parameter. In this example, we perform smoothing in two ways. In the first, we find smooth values at the original $t$ values and then interpolate. In the second, we perform the smoothing for the interpolant $\hat{t}$ values directly. GCV is used to determine the regularization parameter for both cases.

d = 4
+A = RegularizationSmooth(u, t, d; alg = :gcv_svd)
+û = A.û
+N = 200
+titp = collect(range(minimum(t), maximum(t), length = N))
+uitp = A.(titp)
+Am = RegularizationSmooth(u, t, titp, d; alg = :gcv_svd)
+ûm = Am.û
+scatter(t, u, label = "simulated data", legend = :top)
+scatter!(t, û, marker = (:square, 4), label = "smoothed data")
+plot!(titp, uitp, lw = lw, label = "smoothed interpolation")
+plot!(titp, ûm, lw = lw, linestyle = :dash, label = "smoothed, more points")
Example block output

Curve Fits

A curve fit works with both dense and sparse data. We will demonstrate the curve fit on the dense data since we generated it based on sin(t), so this is the curve we want to fit through it. To do so, let's define a similar function with parameters. Let's choose the form:

m(t, p) = @. p[1] * sin(p[2] * t) + p[3] * cos(p[4] * t)
m (generic function with 1 method)

Notice that this is a function on the whole array of t and expects an array for the predicted u out. This choice of m is based on the assumption that our function is of the form p1*sin(p2*t)+p3*cos(p4*t). We want to find the p to match our data. Let's start with the guess of every p being zero, that is p=ones(4). Then we would fit this curve using:

using Optim
+A = Curvefit(u, t, m, ones(4), LBFGS())
+scatter(t, u, label = "points", legend = :bottomright)
+plot!(A)
Example block output

We can check what the fitted parameters are via:

A.pmin
4-element Vector{Float64}:
+  1.00251731850411
+  1.0396588440319725
+ -0.13178842465264956
+  1.0670107400675999

Notice that it essentially made p3=0 with p1=p2=1, meaning it approximately found sin(t)! But note that the ability to fit is dependent on the initial parameters. For example, with p=zeros(4) as the initial parameters, the fit is not good:

A = Curvefit(u, t, m, zeros(4), LBFGS())
+scatter(t, u, label = "points", legend = :bottomright)
+plot!(A)
Example block output

And the parameters show the issue:

A.pmin
4-element Vector{Float64}:
+ 0.0
+ 0.0
+ 0.042632088464589324
+ 0.0
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We can also pass the extrapolate=true keyword if we want to allow the interpolation to go beyond the range of the timepoints. The default value is extrapolate=false.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"A1 = CubicSpline(u, t)\n\n# For interpolation do, A(t)\nA1(100.0)\n\nA2 = CubicSpline(u, t; extrapolate = true)\n\n# Extrapolation\nA2(300.0)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"note: Note\nThe values computed beyond the range of the time points provided during interpolation will not be reliable, as these methods only perform well within the range and the first/last piece polynomial fit is extrapolated on either side which might not reflect the true nature of the data.","category":"page"},{"location":"interface/#Derivatives","page":"Interface","title":"Derivatives","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"Derivatives of the interpolated curves can also be computed at any point for all the methods.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"We will continue with the above example, but the API is the same for all the methods. If the interpolation is defined with extrapolate=true, derivatives can also be extrapolated.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"# derivative(A, t)\nDataInterpolations.derivative(A1, 1.0)\n\n# Extrapolation\nDataInterpolations.derivative(A2, 300.0)","category":"page"},{"location":"interface/#Integrals","page":"Interface","title":"Integrals","text":"","category":"section"},{"location":"interface/","page":"Interface","title":"Interface","text":"Integrals of the interpolated curves can also be computed easily.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"note: Note\nIntegrals for LagrangeInterpolation, BSplineInterpolation, BSplineApprox, Curvefit will error as there are no simple analytical solutions available. Please use numerical methods instead, such as Integrals.jl.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"To compute the integrals from the start of time points provided during interpolation to any point, we can do:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"# integral(A, t)\nDataInterpolations.integral(A1, 5.0)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"If we want to compute integrals between two points, we can do:","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"# integral(A, t1, t2)\nDataInterpolations.integral(A1, 1.0, 5.0)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"Again, if the interpolation is defined with extrapolate=true, the integral can be computed beyond the range of the timepoints.","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"# integral(A, t1, t2)\nDataInterpolations.integral(A2, 200.0, 300.0)","category":"page"},{"location":"interface/","page":"Interface","title":"Interface","text":"note: Note\nIf the times provided in the integral go beyond the range of the time points provided during interpolation, it uses extrapolation methods to compute the values, and hence the integral can be misrepsentative and might not reflect the true nature of the data.","category":"page"},{"location":"manual/#Methods","page":"Manual","title":"Methods","text":"","category":"section"},{"location":"manual/","page":"Manual","title":"Manual","text":"LinearInterpolation\nQuadraticInterpolation\nLagrangeInterpolation\nAkimaInterpolation\nConstantInterpolation\nQuadraticSpline\nCubicSpline\nBSplineInterpolation\nBSplineApprox","category":"page"},{"location":"manual/#DataInterpolations.LinearInterpolation","page":"Manual","title":"DataInterpolations.LinearInterpolation","text":"LinearInterpolation(u, t; extrapolate = false)\n\nIt is the method of interpolating between the data points using a linear polynomial. For any point, two data points one each side are chosen and connected with a line. Extrapolation extends the last linear polynomial on each side.\n\nArguments\n\nu: data points.\nt: time points.\n\nKeyword Arguments\n\nextrapolate: boolean value to allow extrapolation. Defaults to false.\n\n\n\n\n\n","category":"type"},{"location":"manual/#DataInterpolations.QuadraticInterpolation","page":"Manual","title":"DataInterpolations.QuadraticInterpolation","text":"QuadraticInterpolation(u, t, mode = :Forward; extrapolate = false)\n\nIt is the method of interpolating between the data points using quadratic polynomials. For any point, three data points nearby are taken to fit a quadratic polynomial. Extrapolation extends the last quadratic polynomial on each side.\n\nArguments\n\nu: data points.\nt: time points.\nmode: :Forward or :Backward. If :Forward, two data points ahead of the point and one data point behind is taken for interpolation. If :Backward, two data points behind and one ahead is taken for interpolation.\n\nKeyword Arguments\n\nextrapolate: boolean value to allow extrapolation. Defaults to false.\n\n\n\n\n\n","category":"type"},{"location":"manual/#DataInterpolations.LagrangeInterpolation","page":"Manual","title":"DataInterpolations.LagrangeInterpolation","text":"LagrangeInterpolation(u, t, n = length(t) - 1; extrapolate = false)\n\nIt is the method of interpolation using Lagrange polynomials of (k-1)th order passing through all the data points where k is the number of data points.\n\nArguments\n\nu: data points.\nt: time points.\nn: order of the polynomial. Currently only (k-1)th order where k is the number of data points.\n\nKeyword Arguments\n\nextrapolate: boolean value to allow extrapolation. Defaults to false.\n\n\n\n\n\n","category":"type"},{"location":"manual/#DataInterpolations.AkimaInterpolation","page":"Manual","title":"DataInterpolations.AkimaInterpolation","text":"AkimaInterpolation(u, t; extrapolate = false)\n\nIt is a spline interpolation built from cubic polynomials. It forms a continuously differentiable function. For more details, refer: https://en.wikipedia.org/wiki/Akima_spline. Extrapolation extends the last cubic polynomial on each side.\n\nArguments\n\nu: data points.\nt: time points.\n\nKeyword Arguments\n\nextrapolate: boolean value to allow extrapolation. Defaults to false.\n\n\n\n\n\n","category":"type"},{"location":"manual/#DataInterpolations.ConstantInterpolation","page":"Manual","title":"DataInterpolations.ConstantInterpolation","text":"ConstantInterpolation(u, t; dir = :left, extrapolate = false)\n\nIt is the method of interpolating using a constant polynomial. For any point, two adjacent data points are found on either side (left and right). The value at that point depends on dir. If it is :left, then the value at the left point is chosen and if it is :right, the value at the right point is chosen. Extrapolation extends the last constant polynomial at the end points on each side.\n\nArguments\n\nu: data points.\nt: time points.\n\nKeyword Arguments\n\ndir: indicates which value should be used for interpolation (:left or :right).\nextrapolate: boolean value to allow extrapolation. Defaults to false.\n\n\n\n\n\n","category":"type"},{"location":"manual/#DataInterpolations.QuadraticSpline","page":"Manual","title":"DataInterpolations.QuadraticSpline","text":"QuadraticSpline(u, t; extrapolate = false)\n\nIt is a spline interpolation using piecewise quadratic polynomials between each pair of data points. Its first derivative is also continuous. Extrapolation extends the last quadratic polynomial on each side.\n\nArguments\n\nu: data points.\nt: time points.\n\nKeyword Arguments\n\nextrapolate: boolean value to allow extrapolation. Defaults to false.\n\n\n\n\n\n","category":"type"},{"location":"manual/#DataInterpolations.CubicSpline","page":"Manual","title":"DataInterpolations.CubicSpline","text":"QuadraticSpline(u, t; extrapolate = false)\n\nIt is a spline interpolation using piecewise cubic polynomials between each pair of data points. Its first and second derivative is also continuous. Extrapolation extends the last cubic polynomial on each side.\n\nArguments\n\nu: data points.\nt: time points.\n\nKeyword Arguments\n\nextrapolate: boolean value to allow extrapolation. Defaults to false.\n\n\n\n\n\n","category":"type"},{"location":"manual/#DataInterpolations.BSplineInterpolation","page":"Manual","title":"DataInterpolations.BSplineInterpolation","text":"BSplineInterpolation(u, t, d, pVecType, knotVecType; extrapolate = false)\n\nIt is a curve defined by the linear combination of n basis functions of degree d where n is the number of data points. For more information, refer https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve.html. Extrapolation is a constant polynomial of the end points on each side.\n\nArguments\n\nu: data points.\nt: time points.\nd: degree of the piecewise polynomial.\npVecType: symbol to parameters vector, :Uniform for uniform spaced parameters and :ArcLen for parameters generated by chord length method.\nknotVecType: symbol to knot vector, :Uniform for uniform knot vector, :Average for average spaced knot vector.\n\nKeyword Arguments\n\nextrapolate: boolean value to allow extrapolation. Defaults to false.\n\n\n\n\n\n","category":"type"},{"location":"manual/#DataInterpolations.BSplineApprox","page":"Manual","title":"DataInterpolations.BSplineApprox","text":"BSplineApprox(u, t, d, h, pVecType, knotVecType; extrapolate = false)\n\nIt is a regression based B-spline. The argument choices are the same as the BSplineInterpolation, with the additional parameter h < length(t) which is the number of control points to use, with smaller h indicating more smoothing. For more information, refer http://www.cad.zju.edu.cn/home/zhx/GM/009/00-bsia.pdf. Extrapolation is a constant polynomial of the end points on each side.\n\nArguments\n\nu: data points.\nt: time points.\nd: degree of the piecewise polynomial.\nh: number of control points to use.\npVecType: symbol to parameters vector, :Uniform for uniform spaced parameters and :ArcLen for parameters generated by chord length method.\nknotVecType: symbol to knot vector, :Uniform for uniform knot vector, :Average for average spaced knot vector.\n\nKeyword Arguments\n\nextrapolate: boolean value to allow extrapolation. Defaults to false.\n\n\n\n\n\n","category":"type"},{"location":"manual/#Utility-Functions","page":"Manual","title":"Utility Functions","text":"","category":"section"},{"location":"manual/","page":"Manual","title":"Manual","text":"DataInterpolations.bracketstrictlymontonic","category":"page"},{"location":"manual/#DataInterpolations.bracketstrictlymontonic","page":"Manual","title":"DataInterpolations.bracketstrictlymontonic","text":"bracketstrictlymontonic(v, x, guess; lt=, by=, rev=false)\n\nStarting from an initial guess index, find indices (lo, hi) such that v[lo] ≤ x ≤ v[hi] according to the specified order, assuming that x is actually within the range of values found in v. If x is outside that range, either lo will be firstindex(v) or hi will be lastindex(v).\n\nNote that the results will not typically satisfy lo ≤ guess ≤ hi. If x is precisely equal to a value that is not unique in the input v, there is no guarantee that (lo, hi) will encompass all indices corresponding to that value.\n\nThis algorithm is essentially an expanding binary search, which can be used as a precursor to searchsorted and related functions, which can take lo and hi as arguments. The purpose of using this function first would be to accelerate convergence in those functions by using correlated guesses for repeated calls. The best guess for the next call of this function would be the index returned by the previous call to searchsorted.\n\nSee sort! for an explanation of the keyword arguments by, lt and rev.\n\n\n\n\n\n","category":"function"},{"location":"methods/#Interpolation-using-different-methods","page":"Methods","title":"Interpolation using different methods","text":"","category":"section"},{"location":"methods/","page":"Methods","title":"Methods","text":"We will use the following data to demonstrate interpolation methods.","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"using DataInterpolations, Plots\ngr() # hide\n\n# Dependent variable\nu = [14.7, 11.51, 10.41, 14.95, 12.24, 11.22]\n\n# Independent variable\nt = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"For each method, we will show how to perform the fit and use the plot recipe to show the fitting curve.","category":"page"},{"location":"methods/#Linear-Interpolation","page":"Methods","title":"Linear Interpolation","text":"","category":"section"},{"location":"methods/","page":"Methods","title":"Methods","text":"This is a linear interpolation between the ends points of the interval of input data points.","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"A = LinearInterpolation(u, t)\nscatter(t, u, label = \"input data\")\nplot!(A)","category":"page"},{"location":"methods/#Quadratic-Interpolation","page":"Methods","title":"Quadratic Interpolation","text":"","category":"section"},{"location":"methods/","page":"Methods","title":"Methods","text":"This function fits a parabola passing through the two nearest points from the input data point as well as the next-closest point on the right or left, depending on whether the forward- or backward-looking mode is selected (default mode is forward-looking). It is continuous and piecewise differentiable.","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"A = QuadraticInterpolation(u, t) # same as QuadraticInterpolation(u,t,:Forward)\n# alternatively: A = QuadraticInterpolation(u,t,:Backward)\nscatter(t, u, label = \"input data\")\nplot!(A)","category":"page"},{"location":"methods/#Lagrange-Interpolation","page":"Methods","title":"Lagrange Interpolation","text":"","category":"section"},{"location":"methods/","page":"Methods","title":"Methods","text":"It fits a polynomial of degree d (=length(t)-1), and is thus a continuously differentiable function.","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"A = LagrangeInterpolation(u, t)\nscatter(t, u, label = \"input data\")\nplot!(A)","category":"page"},{"location":"methods/#Constant-Interpolation","page":"Methods","title":"Constant Interpolation","text":"","category":"section"},{"location":"methods/","page":"Methods","title":"Methods","text":"This function is constant between data points. By default, it takes the value at the left end of the interval. One can change that behavior by passing the keyword argument dir = :right.","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"A = ConstantInterpolation(u, t)\nscatter(t, u, label = \"input data\")\nplot!(A)","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"Or using the right endpoints:","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"A = ConstantInterpolation(u, t, dir = :right)\nscatter(t, u, label = \"input data\")\nplot!(A)","category":"page"},{"location":"methods/#Quadratic-Spline","page":"Methods","title":"Quadratic Spline","text":"","category":"section"},{"location":"methods/","page":"Methods","title":"Methods","text":"This is the quadratic spline. It is a continuously differentiable interpolation which hits each of the data points exactly. Splines are a local interpolation method, meaning that the curve in a given spot is only affected by the points nearest to it.","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"A = QuadraticSpline(u, t)\nscatter(t, u, label = \"input data\")\nplot!(A)","category":"page"},{"location":"methods/#Cubic-Spline","page":"Methods","title":"Cubic Spline","text":"","category":"section"},{"location":"methods/","page":"Methods","title":"Methods","text":"This is the cubic spline. It is a continuously twice differentiable interpolation which hits each of the data points exactly.","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"A = CubicSpline(u, t)\nscatter(t, u, label = \"input data\")\nplot!(A)","category":"page"},{"location":"methods/#B-Splines","page":"Methods","title":"B-Splines","text":"","category":"section"},{"location":"methods/","page":"Methods","title":"Methods","text":"This is an interpolating B-spline. B-splines are a global method, meaning that every data point is taken into account for each point of the curve. The interpolating B-spline is the version which hits each of the points. This method is described in more detail here. Let's plot a cubic B-spline (3rd order). Since the data points are not close to uniformly spaced, we will use the :ArcLen and :Average choices:","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"A = BSplineInterpolation(u, t, 3, :ArcLen, :Average)\nscatter(t, u, label = \"input data\")\nplot!(A)","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"The approximating B-spline is a smoothed version of the B-spline. It again is a global method. In this case, we need to give a number of control points length(t)>h and this method fits a B-spline through the control points which is a least square approximation. This has a natural effect of smoothing the data. For example, if we use 4 control points, we get the result:","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"A = BSplineApprox(u, t, 3, 4, :ArcLen, :Average)\nscatter(t, u, label = \"input data\")\nplot!(A)","category":"page"},{"location":"methods/#Regularization-Smoothing","page":"Methods","title":"Regularization Smoothing","text":"","category":"section"},{"location":"methods/","page":"Methods","title":"Methods","text":"Smoothing by regularization (a.k.a. ridge regression) finds a function hatu that minimizes the objective function:","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"Q(hatu) = int_t_1^t_N hatu(t) - u(t)^2 mathrmdt + lambda int_hatt_1^hatt_N hatu^(d)(hatt)^2 mathrmd hatt","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"where (d) denotes derivative order and lambda is the regularization (smoothing) parameter. The integrals are evaluated numerically at the set of t values for the first term and hatt values for the second term (equal to t if not provided). Regularization smoothing is a global method that creates a smooth curve directly. See Stickel (2010) Comput. Chem. Eng. 34:467 for details. The implementation in this package uses cubic splines to interpolate between the smoothed points after they are determined.","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"using RegularizationTools\nd = 2\nλ = 1e3\nA = RegularizationSmooth(u, t, d; λ = λ, alg = :fixed)\nû = A.û\n# interpolate using the smoothed values\nN = 200\ntitp = collect(range(minimum(t), maximum(t), length = N))\nuitp = A.(titp)\nlw = 1.5\nscatter(t, u, label = \"data\")\nscatter!(t, û, marker = :square, label = \"smoothed data\")\nplot!(titp, uitp, lw = lw, label = \"smoothed interpolation\")","category":"page"},{"location":"methods/#Dense-Data-Demonstration","page":"Methods","title":"Dense Data Demonstration","text":"","category":"section"},{"location":"methods/","page":"Methods","title":"Methods","text":"Some methods are better suited for dense data. Let's generate such data to demonstrate these methods.","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"import StableRNGs: StableRNG\nrng = StableRNG(318)\nt = sort(10 .* rand(rng, 100))\nu = sin.(t) .+ 0.5 * randn(rng, 100);","category":"page"},{"location":"methods/#Regularization-Smoothing-2","page":"Methods","title":"Regularization Smoothing","text":"","category":"section"},{"location":"methods/","page":"Methods","title":"Methods","text":"Although smoothing by regularization can be used to interpolate sparse data as shown above, it is especially useful for dense as well as scattered data (unequally spaced, unordered, and/or repeat-valued). Generalized cross validation (GCV) or so-called L-curve methods can be used to determine an \"optimal\" value for the smoothing parameter. In this example, we perform smoothing in two ways. In the first, we find smooth values at the original t values and then interpolate. In the second, we perform the smoothing for the interpolant hatt values directly. GCV is used to determine the regularization parameter for both cases.","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"d = 4\nA = RegularizationSmooth(u, t, d; alg = :gcv_svd)\nû = A.û\nN = 200\ntitp = collect(range(minimum(t), maximum(t), length = N))\nuitp = A.(titp)\nAm = RegularizationSmooth(u, t, titp, d; alg = :gcv_svd)\nûm = Am.û\nscatter(t, u, label = \"simulated data\", legend = :top)\nscatter!(t, û, marker = (:square, 4), label = \"smoothed data\")\nplot!(titp, uitp, lw = lw, label = \"smoothed interpolation\")\nplot!(titp, ûm, lw = lw, linestyle = :dash, label = \"smoothed, more points\")","category":"page"},{"location":"methods/#Curve-Fits","page":"Methods","title":"Curve Fits","text":"","category":"section"},{"location":"methods/","page":"Methods","title":"Methods","text":"A curve fit works with both dense and sparse data. We will demonstrate the curve fit on the dense data since we generated it based on sin(t), so this is the curve we want to fit through it. To do so, let's define a similar function with parameters. Let's choose the form:","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"m(t, p) = @. p[1] * sin(p[2] * t) + p[3] * cos(p[4] * t)","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"Notice that this is a function on the whole array of t and expects an array for the predicted u out. This choice of m is based on the assumption that our function is of the form p1*sin(p2*t)+p3*cos(p4*t). We want to find the p to match our data. Let's start with the guess of every p being zero, that is p=ones(4). Then we would fit this curve using:","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"using Optim\nA = Curvefit(u, t, m, ones(4), LBFGS())\nscatter(t, u, label = \"points\", legend = :bottomright)\nplot!(A)","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"We can check what the fitted parameters are via:","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"A.pmin","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"Notice that it essentially made p3=0 with p1=p2=1, meaning it approximately found sin(t)! But note that the ability to fit is dependent on the initial parameters. For example, with p=zeros(4) as the initial parameters, the fit is not good:","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"A = Curvefit(u, t, m, zeros(4), LBFGS())\nscatter(t, u, label = \"points\", legend = :bottomright)\nplot!(A)","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"And the parameters show the issue:","category":"page"},{"location":"methods/","page":"Methods","title":"Methods","text":"A.pmin","category":"page"},{"location":"#DataInterpolations.jl","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"","category":"section"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"DataInterpolations.jl is a library for performing interpolations of one-dimensional data. By \"data interpolations\" we mean techniques for interpolating possibly noisy data, and thus some methods are mixtures of regressions with interpolations (i.e. do not hit the data points exactly, smoothing out the lines). This library can be used to fill in intermediate data points in applications like timeseries data.","category":"page"},{"location":"#Installation","page":"DataInterpolations.jl","title":"Installation","text":"","category":"section"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"To install DataInterpolations.jl, use the Julia package manager:","category":"page"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"using Pkg\nPkg.add(\"DataInterpolations\")","category":"page"},{"location":"#Available-Interpolations","page":"DataInterpolations.jl","title":"Available Interpolations","text":"","category":"section"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"In all cases, u an AbstractVector of values and t is an AbstractVector of timepoints corresponding to (u,t) pairs.","category":"page"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"ConstantInterpolation(u,t) - A piecewise constant interpolation.\nLinearInterpolation(u,t) - A linear interpolation.\nQuadraticInterpolation(u,t) - A quadratic interpolation.\nLagrangeInterpolation(u,t,n) - A Lagrange interpolation of order n.\nQuadraticSpline(u,t) - A quadratic spline interpolation.\nCubicSpline(u,t) - A cubic spline interpolation.\nAkimaInterpolation(u, t) - Akima spline interpolation provides a smoothing effect and is computationally efficient.\nBSplineInterpolation(u,t,d,pVec,knotVec) - An interpolation B-spline. This is a B-spline that hits each of the data points. The argument choices are:\nd - degree of B-spline\npVec - Symbol to Parameters Vector, pVec = :Uniform for uniformly spaced parameters, and pVec = :ArcLen for parameters generated by the chord length method.\nknotVec - Symbol to Knot Vector, knotVec = :Uniform for uniform knot vector, knotVec = :Average for average spaced knot vector.\nBSplineApprox(u,t,d,h,pVec,knotVec) - A regression B-spline which smooths the fitting curve. The argument choices are the same as the BSplineInterpolation, with the additional parameter hThe documentation of this SciML package was built using these direct dependencies,","category":"page"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"using Pkg # hide\nPkg.status() # hide","category":"page"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"","category":"page"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"
and using this machine and Julia version.","category":"page"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"using InteractiveUtils # hide\nversioninfo() # hide","category":"page"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"
","category":"page"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"
A more complete overview of all dependencies and their versions is also provided.","category":"page"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"using Pkg # hide\nPkg.status(; mode = PKGMODE_MANIFEST) # hide","category":"page"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"
","category":"page"},{"location":"","page":"DataInterpolations.jl","title":"DataInterpolations.jl","text":"using TOML\nusing Markdown\nversion = TOML.parse(read(\"../../Project.toml\", String))[\"version\"]\nname = TOML.parse(read(\"../../Project.toml\", String))[\"name\"]\nlink_manifest = \"https://github.com/SciML/\" * name * \".jl/tree/gh-pages/v\" * version *\n \"/assets/Manifest.toml\"\nlink_project = \"https://github.com/SciML/\" * name * \".jl/tree/gh-pages/v\" * version *\n \"/assets/Project.toml\"\nMarkdown.parse(\"\"\"You can also download the\n[manifest]($link_manifest)\nfile and the\n[project]($link_project)\nfile.\n\"\"\")","category":"page"}] +} diff --git a/previews/PR230/siteinfo.js b/previews/PR230/siteinfo.js new file mode 100644 index 00000000..cce8edae --- /dev/null +++ b/previews/PR230/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR230";