diff --git a/index.html b/index.html index 1a6cc116..6a5afc30 100644 --- a/index.html +++ b/index.html @@ -1,2 +1,2 @@ - + diff --git a/stable b/stable new file mode 120000 index 00000000..5469c48c --- /dev/null +++ b/stable @@ -0,0 +1 @@ +v4.1.0 \ No newline at end of file diff --git a/v4 b/v4 new file mode 120000 index 00000000..5469c48c --- /dev/null +++ b/v4 @@ -0,0 +1 @@ +v4.1.0 \ No newline at end of file diff --git a/v4.1 b/v4.1 new file mode 120000 index 00000000..5469c48c --- /dev/null +++ b/v4.1 @@ -0,0 +1 @@ +v4.1.0 \ No newline at end of file diff --git a/v4.1.0/.documenter-siteinfo.json b/v4.1.0/.documenter-siteinfo.json new file mode 100644 index 00000000..aee774d6 --- /dev/null +++ b/v4.1.0/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-09-23T14:09:22","documenter_version":"1.0.1"}} \ No newline at end of file diff --git a/v4.1.0/assets/documenter.js b/v4.1.0/assets/documenter.js new file mode 100644 index 00000000..7002e251 --- /dev/null +++ b/v4.1.0/assets/documenter.js @@ -0,0 +1,874 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + 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 () { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + + 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(); + } 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(); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, 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 () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'minisearch'], function($, minisearch) { + +// In general, most search related things will have "search" as a prefix. +// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +let results = []; +let timer = undefined; + +let data = documenterSearchIndex["docs"].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 search 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@!]+$/, ""); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + boost: { title: 100 }, + fuzzy: 2, + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + tokenize: (string) => string.split(/[\s\-\.]+/), + }, +}); + +index.addAll(data); + +let filters = [...new Set(data.map((x) => x.category))]; +var modal_filters = make_modal_body_filters(filters); +var filter_results = []; + +$(document).on("keyup", ".documenter-search-input", function (event) { + // Adding a debounce to prevent disruptions from super-speed typing! + debounce(() => update_search(filter_results), 300); +}); + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + $(this).removeClass("search-filter-selected"); + } else { + $(this).addClass("search-filter-selected"); + } + + // Adding a debounce to prevent disruptions from crazy clicking! + debounce(() => get_filters(), 300); +}); + +/** + * A debounce function, takes a function and an optional timeout in milliseconds + * + * @function callback + * @param {number} timeout + */ +function debounce(callback, timeout = 300) { + clearTimeout(timer); + timer = setTimeout(callback, timeout); +} + +/** + * Make/Update the search component + * + * @param {string[]} selected_filters + */ +function update_search(selected_filters = []) { + let initial_search_body = ` +
Type something to get started!
+ `; + + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + results = index.search(querystring, { + filter: (result) => { + // Filtering results + if (selected_filters.length === 0) { + return result.score >= 1; + } else { + return ( + result.score >= 1 && selected_filters.includes(result.category) + ); + } + }, + }); + + let search_result_container = ``; + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + results.forEach(function (result) { + if (result.location) { + // Checking for duplication of results for the same page + if (!links.includes(result.location)) { + search_results += make_search_result(result, querystring); + count++; + } + + links.push(result.location); + } + }); + + let result_count = `
${count} result(s)
`; + + 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"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + filter_results = []; + modal_filters = make_modal_body_filters(filters, filter_results); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(initial_search_body); + } +} + +/** + * Make the modal filter html + * + * @param {string[]} filters + * @param {string[]} selected_filters + * @returns string + */ +function make_modal_body_filters(filters, selected_filters = []) { + let str = ``; + + filters.forEach((val) => { + if (selected_filters.includes(val)) { + str += `${val}`; + } else { + str += `${val}`; + } + }); + + let filter_html = ` +
+ Filters: + ${str} +
+ `; + + return filter_html; +} + +/** + * Make the result component given a minisearch result data object and the value of the search input as queryString. + * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ +function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`\\b${querystring}\\b`, "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 = ` + +
+
${result.title}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; +} + +/** + * Get selected filters, remake the filter html and lastly update the search modal + */ +function get_filters() { + let ele = $(".search-filters .search-filter-selected").get(); + filter_results = ele.map((x) => $(x).text().toLowerCase()); + modal_filters = make_modal_body_filters(filters, filter_results); + update_search(filter_results); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// 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 + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +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/v4.1.0/assets/favicon.ico b/v4.1.0/assets/favicon.ico new file mode 100644 index 00000000..3c6bd470 Binary files /dev/null and b/v4.1.0/assets/favicon.ico differ diff --git a/v4.1.0/assets/logo.png b/v4.1.0/assets/logo.png new file mode 100644 index 00000000..6f4c3e26 Binary files /dev/null and b/v4.1.0/assets/logo.png differ diff --git a/v4.1.0/assets/themes/documenter-dark.css b/v4.1.0/assets/themes/documenter-dark.css new file mode 100644 index 00000000..691b83ab --- /dev/null +++ b/v4.1.0/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ +html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark 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html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark 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html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#e5eaec;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(236,240,241,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#dde4e6;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark 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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 .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content 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 kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus:not(:active),html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--documenter-dark .button.is-primary.is-focused:not(:active),html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(55,90,127,0.25)}html.theme--documenter-dark .button.is-primary:active,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:active,html.theme--documenter-dark .button.is-primary.is-active,html.theme--documenter-dark .docstring>section>a.button.is-active.docs-sourcelink{background-color:#2f4d6d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary[disabled],html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:#375a7f;box-shadow:none}html.theme--documenter-dark .button.is-primary.is-inverted,html.theme--documenter-dark .docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;color:#375a7f}html.theme--documenter-dark .button.is-primary.is-inverted:hover,html.theme--documenter-dark .docstring>section>a.button.is-inverted.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-inverted.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-hovered.docs-sourcelink{background-color:#f2f2f2}html.theme--documenter-dark .button.is-primary.is-inverted[disabled],html.theme--documenter-dark .docstring>section>a.button.is-inverted.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;border-color:transparent;box-shadow:none;color:#375a7f}html.theme--documenter-dark .button.is-primary.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-loading.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#375a7f;color:#375a7f}html.theme--documenter-dark .button.is-primary.is-outlined:hover,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-outlined.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#375a7f;border-color:#375a7f;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #375a7f #375a7f !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#375a7f;box-shadow:none;color:#375a7f}html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:hover,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.is-focused.docs-sourcelink{background-color:#fff;color:#375a7f}html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #375a7f #375a7f !important}html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary.is-light,html.theme--documenter-dark .docstring>section>a.button.is-light.docs-sourcelink{background-color:#f1f5f9;color:#4d7eb2}html.theme--documenter-dark .button.is-primary.is-light:hover,html.theme--documenter-dark .docstring>section>a.button.is-light.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-light.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#e8eef5;border-color:transparent;color:#4d7eb2}html.theme--documenter-dark .button.is-primary.is-light:active,html.theme--documenter-dark .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--documenter-dark .button.is-primary.is-light.is-active,html.theme--documenter-dark .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#dfe8f1;border-color:transparent;color:#4d7eb2}html.theme--documenter-dark .button.is-link{background-color:#1abc9c;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-link:hover,html.theme--documenter-dark .button.is-link.is-hovered{background-color:#18b193;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-link:focus,html.theme--documenter-dark .button.is-link.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-link:focus:not(:active),html.theme--documenter-dark .button.is-link.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(26,188,156,0.25)}html.theme--documenter-dark .button.is-link:active,html.theme--documenter-dark .button.is-link.is-active{background-color:#17a689;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-link[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link{background-color:#1abc9c;border-color:#1abc9c;box-shadow:none}html.theme--documenter-dark .button.is-link.is-inverted{background-color:#fff;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted:hover,html.theme--documenter-dark .button.is-link.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-link.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#1abc9c;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-outlined.is-focused{background-color:#1abc9c;border-color:#1abc9c;color:#fff}html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #1abc9c #1abc9c !important}html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#1abc9c;box-shadow:none;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #1abc9c #1abc9c !important}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-link.is-light{background-color:#edfdf9;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:hover,html.theme--documenter-dark .button.is-link.is-light.is-hovered{background-color:#e2fbf6;border-color:transparent;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:active,html.theme--documenter-dark .button.is-link.is-light.is-active{background-color:#d7f9f3;border-color:transparent;color:#15987e}html.theme--documenter-dark .button.is-info{background-color:#024c7d;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:hover,html.theme--documenter-dark .button.is-info.is-hovered{background-color:#024470;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:focus,html.theme--documenter-dark .button.is-info.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info:focus:not(:active),html.theme--documenter-dark .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(2,76,125,0.25)}html.theme--documenter-dark .button.is-info:active,html.theme--documenter-dark .button.is-info.is-active{background-color:#023d64;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-info[disabled],fieldset[disabled] html.theme--documenter-dark 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.button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-info.is-light{background-color:#ebf7ff;color:#0e9dfb}html.theme--documenter-dark .button.is-info.is-light:hover,html.theme--documenter-dark .button.is-info.is-light.is-hovered{background-color:#def2fe;border-color:transparent;color:#0e9dfb}html.theme--documenter-dark .button.is-info.is-light:active,html.theme--documenter-dark .button.is-info.is-light.is-active{background-color:#d2edfe;border-color:transparent;color:#0e9dfb}html.theme--documenter-dark .button.is-success{background-color:#008438;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:hover,html.theme--documenter-dark .button.is-success.is-hovered{background-color:#073;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-success:focus,html.theme--documenter-dark 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.button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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.button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .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 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html.theme--documenter-dark .navbar-dropdown,html.theme--documenter-dark .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--documenter-dark .navbar-dropdown.is-right{left:auto;right:0}html.theme--documenter-dark .navbar-divider{display:block}html.theme--documenter-dark .navbar>.container .navbar-brand,html.theme--documenter-dark .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--documenter-dark .navbar>.container .navbar-menu,html.theme--documenter-dark .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop,html.theme--documenter-dark .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark 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a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--documenter-dark .pagination{font-size:1rem;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--documenter-dark .pagination.is-medium{font-size:1.25rem}html.theme--documenter-dark .pagination.is-large{font-size:1.5rem}html.theme--documenter-dark .pagination.is-rounded .pagination-previous,html.theme--documenter-dark #documenter .docs-sidebar 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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} diff --git a/v4.1.0/assets/themeswap.js b/v4.1.0/assets/themeswap.js new file mode 100644 index 00000000..9f5eebe6 --- /dev/null +++ b/v4.1.0/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. 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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/v4.1.0/index.html b/v4.1.0/index.html new file mode 100644 index 00000000..4f520a88 --- /dev/null +++ b/v4.1.0/index.html @@ -0,0 +1,244 @@ + +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 which hits each of the data points. The argument choices are:

    • d - degree of B-spline
    • pVec - Symbol to Parameters Vector, pVec = :Uniform for uniform spaced parameters and pVec = :ArcLen for parameters generated by 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 follow 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 a an initial value for a least-square fitting, alg is the algorithm choice to use for optimize the cost function (sum of squared deviations) via Optim.jl and optimal ps are used in the interpolation. 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 v4.1.0 `~/work/DataInterpolations.jl/DataInterpolations.jl`
+  [e30172f5] Documenter v1.0.1
+  [429524aa] Optim v1.7.7
+  [91a5bcdd] Plots v1.39.0
+  [29dad682] RegularizationTools v0.6.0
+  [860ef19b] StableRNGs v1.0.0
and using this machine and Julia version.
Julia Version 1.9.3
+Commit bed2cd540a1 (2023-08-24 14:43 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 2 × Intel(R) Xeon(R) CPU E5-2673 v4 @ 2.30GHz
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-14.0.6 (ORCJIT, broadwell)
+  Threads: 1 on 2 virtual cores
A more complete overview of all dependencies and their versions is also provided.
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You can also download the manifest file and the project file.

diff --git a/v4.1.0/interface/index.html b/v4.1.0/interface/index.html new file mode 100644 index 00000000..a18f7241 --- /dev/null +++ b/v4.1.0/interface/index.html @@ -0,0 +1,20 @@ + +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, its 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 CubicSpline method for demonstration but the API is same for all the methods.

A = CubicSpline(u, t)
+
+# For interpolation do, A(t)
+A(100.0)
10.101397401671347
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 sides 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 same for all the methods.

# derivative(A, t)
+DataInterpolations.derivative(A, 1.0)
-0.051048168999699245

Integrals

Integrals of the interpolated curves can also be computed easily.

Currently, this is implemented only for a few methods - ConstantInterpolation, LinearInterpolation, QuadraticInterpolation, QuadraticSpline and CubicSpline.

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

# integral(A, t)
+DataInterpolations.integral(A, 5.0)
72.86338611822583

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

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

If the times provided in the integral goes 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.

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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 ends points of interval of input data point.

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 in the right or the 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 polynomial of degree d (=length(t)-1), and is thuse 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 value at 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 and 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.Aitp.(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 and also 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 interpolatant $\hat{t}$ 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.Aitp.(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. Do 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 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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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 and 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.Aitp.(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 and also 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 interpolatant 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.Aitp.(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. Do 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 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 which hits each of the data points. The argument choices are:\nd - degree of B-spline\npVec - Symbol to Parameters Vector, pVec = :Uniform for uniform spaced parameters and pVec = :ArcLen for parameters generated by 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/v4.1.0/siteinfo.js b/v4.1.0/siteinfo.js new file mode 100644 index 00000000..e9c06d2c --- /dev/null +++ b/v4.1.0/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v4.1.0"; diff --git a/versions.js b/versions.js index 4ec0f8f9..0ca3bfd3 100644 --- a/versions.js +++ b/versions.js @@ -1,5 +1,7 @@ var DOC_VERSIONS = [ + "stable", + "v4.1", "dev", ]; -var DOCUMENTER_NEWEST = "dev"; -var DOCUMENTER_STABLE = "dev"; +var DOCUMENTER_NEWEST = "v4.1.0"; +var DOCUMENTER_STABLE = "stable";