From 64660fcd538e2c730b74d7db91689801987e6ad5 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Fri, 17 Jan 2025 14:35:39 +0000 Subject: [PATCH] build based on 1e6801d --- dev/.documenter-siteinfo.json | 1 + dev/assets/documenter.js | 945 ++- dev/assets/search.js | 267 - dev/assets/themes/catppuccin-frappe.css | 1 + dev/assets/themes/catppuccin-latte.css | 1 + dev/assets/themes/catppuccin-macchiato.css | 1 + dev/assets/themes/catppuccin-mocha.css | 1 + dev/assets/themes/documenter-dark.css | 4 +- dev/assets/themes/documenter-light.css | 4 +- dev/assets/themeswap.js | 82 +- dev/assets/warner.js | 87 +- dev/censored/index.html | 4 +- dev/cholesky/index.html | 2 +- dev/convolution/index.html | 2 +- dev/density_interface/index.html | 2 +- dev/extends/index.html | 6 +- dev/fit/index.html | 6 +- dev/index.html | 2 +- dev/matrix/index.html | 18 +- dev/mixture/index.html | 6 +- dev/multivariate/index.html | 14 +- dev/objects.inv | Bin 0 -> 3795 bytes dev/order_statistics/index.html | 6 +- dev/product/index.html | 4 +- dev/reshape/index.html | 4 +- dev/search/index.html | 2 - dev/starting/index.html | 4 +- dev/truncate/index.html | 4 +- dev/types/index.html | 6 +- dev/univariate/0580360f.svg | 168 + dev/univariate/0b667b58.svg | 78 + dev/univariate/125e6624.svg | 157 + dev/univariate/142e6921.svg | 159 + dev/univariate/1acbd2e6.svg | 172 + dev/univariate/1c7e7aa0.svg | 155 + dev/univariate/25640e27.svg | 187 + dev/univariate/280b1b99.svg | 155 + dev/univariate/31488667.svg | 148 + dev/univariate/34252d0e.svg | 158 + dev/univariate/364bf45d.svg | 148 + dev/univariate/38a02592.svg | 142 + dev/univariate/3914aee9.svg | 187 + dev/univariate/3e229bfb.svg | 161 + dev/univariate/3ed5c8b9.svg | 188 + dev/univariate/400e5edd.svg | 161 + dev/univariate/427e36a5.svg | 124 + dev/univariate/491dc70e.svg | 148 + dev/univariate/555891ca.svg | 168 + dev/univariate/596be976.svg | 177 + dev/univariate/5975e5fa.svg | 181 + dev/univariate/62c704d2.svg | 172 + dev/univariate/65f664e1.svg | 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dev/univariate/fddd572a.svg | 168 + dev/univariate/index.html | 8460 +------------------- 81 files changed, 9402 insertions(+), 8894 deletions(-) create mode 100644 dev/.documenter-siteinfo.json delete mode 100644 dev/assets/search.js create mode 100644 dev/assets/themes/catppuccin-frappe.css create mode 100644 dev/assets/themes/catppuccin-latte.css create mode 100644 dev/assets/themes/catppuccin-macchiato.css create mode 100644 dev/assets/themes/catppuccin-mocha.css create mode 100644 dev/objects.inv delete mode 100644 dev/search/index.html create mode 100644 dev/univariate/0580360f.svg create mode 100644 dev/univariate/0b667b58.svg create mode 100644 dev/univariate/125e6624.svg create mode 100644 dev/univariate/142e6921.svg create mode 100644 dev/univariate/1acbd2e6.svg create mode 100644 dev/univariate/1c7e7aa0.svg create mode 100644 dev/univariate/25640e27.svg create mode 100644 dev/univariate/280b1b99.svg create mode 100644 dev/univariate/31488667.svg create mode 100644 dev/univariate/34252d0e.svg create mode 100644 dev/univariate/364bf45d.svg create mode 100644 dev/univariate/38a02592.svg create mode 100644 dev/univariate/3914aee9.svg create mode 100644 dev/univariate/3e229bfb.svg create mode 100644 dev/univariate/3ed5c8b9.svg create mode 100644 dev/univariate/400e5edd.svg create mode 100644 dev/univariate/427e36a5.svg create mode 100644 dev/univariate/491dc70e.svg create mode 100644 dev/univariate/555891ca.svg create mode 100644 dev/univariate/596be976.svg create mode 100644 dev/univariate/5975e5fa.svg create mode 100644 dev/univariate/62c704d2.svg create mode 100644 dev/univariate/65f664e1.svg create mode 100644 dev/univariate/6f82faad.svg create mode 100644 dev/univariate/722912b9.svg create mode 100644 dev/univariate/73367db0.svg create mode 100644 dev/univariate/76744ad4.svg create mode 100644 dev/univariate/7d93ebe0.svg create mode 100644 dev/univariate/8420d6ed.svg create mode 100644 dev/univariate/8e15b54a.svg create mode 100644 dev/univariate/8f742776.svg create mode 100644 dev/univariate/96d4c7ad.svg create mode 100644 dev/univariate/99cd6927.svg create mode 100644 dev/univariate/a1cf0420.svg create mode 100644 dev/univariate/a23c4c8c.svg create mode 100644 dev/univariate/a47387a1.svg create mode 100644 dev/univariate/ab0f0f73.svg create mode 100644 dev/univariate/b0d654a7.svg create mode 100644 dev/univariate/c5a27cde.svg create mode 100644 dev/univariate/cb4e1da6.svg create mode 100644 dev/univariate/cca28a2e.svg create mode 100644 dev/univariate/cdba44f9.svg create mode 100644 dev/univariate/d1f83474.svg create mode 100644 dev/univariate/d2c23af2.svg create mode 100644 dev/univariate/dab8273a.svg create mode 100644 dev/univariate/e1f36d43.svg create mode 100644 dev/univariate/e88d4750.svg create mode 100644 dev/univariate/f06485cb.svg create mode 100644 dev/univariate/f458d223.svg create mode 100644 dev/univariate/fa001fa3.svg create mode 100644 dev/univariate/fddd572a.svg diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json new file mode 100644 index 0000000000..fe623e6316 --- /dev/null +++ b/dev/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2025-01-17T14:35:30","documenter_version":"1.8.0"}} \ No newline at end of file diff --git a/dev/assets/documenter.js b/dev/assets/documenter.js index 6adfbbbf4b..7d68cd808b 100644 --- a/dev/assets/documenter.js +++ b/dev/assets/documenter.js @@ -1,15 +1,15 @@ // Generated by Documenter.jl requirejs.config({ paths: { - 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min', + '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/1.12.1/jquery-ui.min', - 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', - 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.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/0.13.24/katex.min', - 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', - 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + '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": { @@ -70,13 +70,96 @@ $(document).ready(function() { hljs.highlightAll(); }) +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on( + "click", + ".docstring .docstring-article-toggle-button", + function () { + let articleToggleTitle = "Expand docstring"; + const parent = $(this).parent(); + + debounce(() => { + if (parent.siblings("section").is(":visible")) { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + parent + .children(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + parent.siblings("section").slideToggle(); + }); + } +); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + }) //////////////////////////////////////////////////////////////////////////////// require([], function() { function addCopyButtonCallbacks() { for (const el of document.getElementsByTagName("pre")) { const button = document.createElement("button"); - button.classList.add("copy-button", "fas", "fa-copy"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + el.appendChild(button); const success = function () { @@ -85,7 +168,7 @@ function addCopyButtonCallbacks() { }; const failure = function () { - button.classList.add("error", "fa-times"); + button.classList.add("error", "fa-xmark"); button.classList.remove("fa-copy"); }; @@ -94,7 +177,7 @@ function addCopyButtonCallbacks() { setTimeout(function () { button.classList.add("fa-copy"); - button.classList.remove("success", "fa-check", "fa-times"); + button.classList.remove("success", "fa-check", "fa-xmark"); }, 5000); }); } @@ -138,29 +221,602 @@ require(['jquery', 'headroom', 'headroom-jquery'], function($, 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() { - $('#documenter .docs-navbar').headroom({ - "tolerance": {"up": 10, "down": 10}, +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + }) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * RegX escape function from MDN + * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + searchstring = escapeRegExp(querystring); + let textindex = new RegExp(`${searchstring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + combineWith: "AND", + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +/////// SEARCH MAIN /////// + +function runSearchMainCode() { + // `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! + const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), + ]; + const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; + const worker_blob = new Blob([worker_str], { type: "text/javascript" }); + const worker = new Worker(URL.createObjectURL(worker_blob)); + + // Whether the worker is currently handling a search. This is a boolean + // as the worker only ever handles 1 or 0 searches at a time. + var worker_is_running = false; + + // The last search text that was sent to the worker. This is used to determine + // if the worker should be launched again when it reports back results. + var last_search_text = ""; + + // The results of the last search. This, in combination with the state of the filters + // in the DOM, is used compute the results to display on calls to update_search. + var unfiltered_results = []; + + // Which filter is currently selected + var selected_filter = ""; + + $(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } + }); + + function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); + } + + worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); + }; + + $(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); + }); + + /** + * Make/Update the search component + */ + function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } + } + + /** + * Make the modal filter html + * + * @returns string + */ + function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; + } +} + +function waitUntilSearchIndexAvailable() { + // It is possible that the documenter.js script runs before the page + // has finished loading and documenterSearchIndex gets defined. + // So we need to wait until the search index actually loads before setting + // up all the search-related stuff. + if (typeof documenterSearchIndex !== "undefined") { + runSearchMainCode(); + } else { + console.warn("Search Index not available, waiting"); + setTimeout(waitUntilSearchIndexAvailable, 1000); + } +} + +// The actual entry point to the search code +waitUntilSearchIndexAvailable(); }) //////////////////////////////////////////////////////////////////////////////// require(['jquery'], function($) { // Modal settings dialog -$(document).ready(function() { - var settings = $('#documenter-settings'); - $('#documenter-settings-button').click(function(){ - settings.toggleClass('is-active'); +$(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'); + $("#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'); + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); }); }); @@ -168,151 +824,246 @@ $(document).ready(function() { //////////////////////////////////////////////////////////////////////////////// require(['jquery'], function($) { +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` + + `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + // Manages the showing and hiding of the sidebar. -$(document).ready(function() { +$(document).ready(function () { var sidebar = $("#documenter > .docs-sidebar"); - var sidebar_button = $("#documenter-sidebar-button") - sidebar_button.click(function(ev) { + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { ev.preventDefault(); - sidebar.toggleClass('visible'); - if (sidebar.hasClass('visible')) { + 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) { + $("#documenter > .docs-main").bind("click", function (ev) { if ($(ev.target).is(sidebar_button)) { return; } - if (sidebar.hasClass('visible')) { - sidebar.removeClass('visible'); + 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 -$(document).ready(function() { +$(document).ready(function () { e = $("#documenter .docs-autofit"); function resize() { - var L = parseInt(e.css('max-width'), 10); + 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); + 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); + $(window).on("orientationchange", resize); }); // Scroll the navigation bar to the currently selected menu item -$(document).ready(function() { +$(document).ready(function () { var sidebar = $("#documenter .docs-menu").get(0); var active = $("#documenter .docs-menu .is-active").get(0); - if(typeof active !== 'undefined') { + if (typeof active !== "undefined") { sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; } -}) +}); }) //////////////////////////////////////////////////////////////////////////////// require(['jquery'], function($) { -function set_theme(theme) { - var active = null; - var disabled = []; - for (var i = 0; i < document.styleSheets.length; i++) { - var ss = document.styleSheets[i]; - var themename = ss.ownerNode.getAttribute("data-theme-name"); - if(themename === null) continue; // ignore non-theme stylesheets - // Find the active theme - if(themename === theme) active = ss; - else disabled.push(ss); - } - if(active !== null) { - active.disabled = false; - if(active.ownerNode.getAttribute("data-theme-primary") === null) { - document.getElementsByTagName('html')[0].className = "theme--" + theme; - } else { - document.getElementsByTagName('html')[0].className = ""; - } - disabled.forEach(function(ss){ - ss.disabled = true; - }); - } - - // Store the theme in localStorage - if(typeof(window.localStorage) !== "undefined") { - window.localStorage.setItem("documenter-theme", theme); - } else { - console.error("Browser does not support window.localStorage"); - } -} - // Theme picker setup -$(document).ready(function() { +$(document).ready(function () { // onchange callback - $('#documenter-themepicker').change(function themepick_callback(ev){ - var themename = $('#documenter-themepicker option:selected').attr('value'); - set_theme(themename); + $("#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); - }) - } else { - $('#documenter-themepicker option').each(function(i,e) { - e.selected = $("html").hasClass(`theme--${e.value}`); - }) + 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 -$(document).ready(function() { +$(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) { + 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; + 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 = $(""); + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); version_selector_select.append(option); } - if (typeof DOC_VERSIONS !== 'undefined') { + 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_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 = $(""); + var option = $( + "" + ); version_selector_select.append(option); } else { var option = existing_versions[existing_id]; @@ -326,6 +1077,6 @@ $(document).ready(function() { if (version_selector_select.children("option").length > 0) { version_selector.toggleClass("visible"); } -}) +}); }) diff --git a/dev/assets/search.js b/dev/assets/search.js deleted file mode 100644 index c133f74101..0000000000 --- a/dev/assets/search.js +++ /dev/null @@ -1,267 +0,0 @@ -// Generated by Documenter.jl -requirejs.config({ - paths: { - 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', - 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', - 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', - } -}); -//////////////////////////////////////////////////////////////////////////////// -require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { - -$(document).ready(function() { - // parseUri 1.2.2 - // (c) Steven Levithan - // MIT License - function parseUri (str) { - var o = parseUri.options, - m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), - uri = {}, - i = 14; - - while (i--) uri[o.key[i]] = m[i] || ""; - - uri[o.q.name] = {}; - uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { - if ($1) uri[o.q.name][$1] = $2; - }); - - return uri; - }; - parseUri.options = { - strictMode: false, - key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], - q: { - name: "queryKey", - parser: /(?:^|&)([^&=]*)=?([^&]*)/g - }, - parser: { - strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, - loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ - } - }; - - $("#search-form").submit(function(e) { - e.preventDefault() - }) - - // list below is the lunr 2.1.3 list minus the intersect with names(Base) - // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) - // ideally we'd just filter the original list but it's not available as a variable - lunr.stopWordFilter = lunr.generateStopWordFilter([ - 'a', - 'able', - 'about', - 'across', - 'after', - 'almost', - 'also', - 'am', - 'among', - 'an', - 'and', - 'are', - 'as', - 'at', - 'be', - 'because', - 'been', - 'but', - 'by', - 'can', - 'cannot', - 'could', - 'dear', - 'did', - 'does', - 'either', - 'ever', - 'every', - 'from', - 'got', - 'had', - 'has', - 'have', - 'he', - 'her', - 'hers', - 'him', - 'his', - 'how', - 'however', - 'i', - 'if', - 'into', - 'it', - 'its', - 'just', - 'least', - 'like', - 'likely', - 'may', - 'me', - 'might', - 'most', - 'must', - 'my', - 'neither', - 'no', - 'nor', - 'not', - 'of', - 'off', - 'often', - 'on', - 'or', - 'other', - 'our', - 'own', - 'rather', - 'said', - 'say', - 'says', - 'she', - 'should', - 'since', - 'so', - 'some', - 'than', - 'that', - 'the', - 'their', - 'them', - 'then', - 'there', - 'these', - 'they', - 'this', - 'tis', - 'to', - 'too', - 'twas', - 'us', - 'wants', - 'was', - 'we', - 'were', - 'what', - 'when', - 'who', - 'whom', - 'why', - 'will', - 'would', - 'yet', - 'you', - 'your' - ]) - - // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" - // would not find anything if searching for "add!", only for the entire qualification - lunr.tokenizer.separator = /[\s\-\.]+/ - - // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names - lunr.trimmer = function (token) { - return token.update(function (s) { - return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') - }) - } - - lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') - lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') - - var index = lunr(function () { - this.ref('location') - this.field('title',{boost: 100}) - this.field('text') - documenterSearchIndex['docs'].forEach(function(e) { - this.add(e) - }, this) - }) - var store = {} - - documenterSearchIndex['docs'].forEach(function(e) { - store[e.location] = {title: e.title, category: e.category, page: e.page} - }) - - $(function(){ - searchresults = $('#documenter-search-results'); - searchinfo = $('#documenter-search-info'); - searchbox = $('#documenter-search-query'); - searchform = $('.docs-search'); - sidebar = $('.docs-sidebar'); - function update_search(querystring) { - tokens = lunr.tokenizer(querystring) - results = index.query(function (q) { - tokens.forEach(function (t) { - q.term(t.toString(), { - fields: ["title"], - boost: 100, - usePipeline: true, - editDistance: 0, - wildcard: lunr.Query.wildcard.NONE - }) - q.term(t.toString(), { - fields: ["title"], - boost: 10, - usePipeline: true, - editDistance: 2, - wildcard: lunr.Query.wildcard.NONE - }) - q.term(t.toString(), { - fields: ["text"], - boost: 1, - usePipeline: true, - editDistance: 0, - wildcard: lunr.Query.wildcard.NONE - }) - }) - }) - searchinfo.text("Number of results: " + results.length) - searchresults.empty() - results.forEach(function(result) { - data = store[result.ref] - link = $(''+data.title+'') - link.attr('href', documenterBaseURL+'/'+result.ref) - if (data.category != "page"){ - cat = $('('+data.category+', '+data.page+')') - } else { - cat = $('('+data.category+')') - } - li = $('
  • ').append(link).append(" ").append(cat) - searchresults.append(li) - }) - } - - function update_search_box() { - querystring = searchbox.val() - update_search(querystring) - } - - searchbox.keyup(_.debounce(update_search_box, 250)) - searchbox.change(update_search_box) - - // Disable enter-key form submission for the searchbox on the search page - // and just re-run search rather than refresh the whole page. - searchform.keypress( - function(event){ - if (event.which == '13') { - if (sidebar.hasClass('visible')) { - sidebar.removeClass('visible'); - } - update_search_box(); - event.preventDefault(); - } - } - ); - - search_query_uri = parseUri(window.location).queryKey["q"] - if(search_query_uri !== undefined) { - search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) - searchbox.val(search_query) - } - update_search_box(); - }) -}) - -}) diff --git a/dev/assets/themes/catppuccin-frappe.css b/dev/assets/themes/catppuccin-frappe.css new file mode 100644 index 0000000000..32e3f00823 --- /dev/null +++ b/dev/assets/themes/catppuccin-frappe.css @@ -0,0 +1 @@ +html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link,html.theme--catppuccin-frappe .pagination-ellipsis,html.theme--catppuccin-frappe .file-cta,html.theme--catppuccin-frappe .file-name,html.theme--catppuccin-frappe .select select,html.theme--catppuccin-frappe .textarea,html.theme--catppuccin-frappe .input,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-frappe .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 - 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.button.is-text[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-text{background-color:transparent;border-color:transparent;box-shadow:none}html.theme--catppuccin-frappe .button.is-ghost{background:none;border-color:rgba(0,0,0,0);color:#8caaee;text-decoration:none}html.theme--catppuccin-frappe .button.is-ghost:hover,html.theme--catppuccin-frappe .button.is-ghost.is-hovered{color:#8caaee;text-decoration:underline}html.theme--catppuccin-frappe .button.is-white{background-color:#fff;border-color:transparent;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white:hover,html.theme--catppuccin-frappe .button.is-white.is-hovered{background-color:#f9f9f9;border-color:transparent;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white:focus,html.theme--catppuccin-frappe .button.is-white.is-focused{border-color:transparent;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white:focus:not(:active),html.theme--catppuccin-frappe .button.is-white.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-frappe .button.is-white:active,html.theme--catppuccin-frappe .button.is-white.is-active{background-color:#f2f2f2;border-color:transparent;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-white{background-color:#fff;border-color:#fff;box-shadow:none}html.theme--catppuccin-frappe .button.is-white.is-inverted{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-frappe .button.is-white.is-inverted:hover,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-hovered{background-color:#000}html.theme--catppuccin-frappe .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-white.is-outlined:hover,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-white.is-outlined:focus,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-black:hover,html.theme--catppuccin-frappe .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-black:focus,html.theme--catppuccin-frappe .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-black:focus:not(:active),html.theme--catppuccin-frappe .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-frappe .button.is-black:active,html.theme--catppuccin-frappe .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-frappe .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-inverted:hover,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-outlined:hover,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-black.is-outlined:focus,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:hover,html.theme--catppuccin-frappe .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:focus,html.theme--catppuccin-frappe .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light:focus:not(:active),html.theme--catppuccin-frappe .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-frappe .button.is-light:active,html.theme--catppuccin-frappe .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-frappe .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-inverted:hover,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-outlined:hover,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-light.is-outlined:focus,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-dark,html.theme--catppuccin-frappe .content kbd.button{background-color:#414559;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-dark:hover,html.theme--catppuccin-frappe .content kbd.button:hover,html.theme--catppuccin-frappe .button.is-dark.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-hovered{background-color:#3c3f52;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-dark:focus,html.theme--catppuccin-frappe .content kbd.button:focus,html.theme--catppuccin-frappe .button.is-dark.is-focused,html.theme--catppuccin-frappe .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-dark:focus:not(:active),html.theme--catppuccin-frappe .content kbd.button:focus:not(:active),html.theme--catppuccin-frappe .button.is-dark.is-focused:not(:active),html.theme--catppuccin-frappe .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(65,69,89,0.25)}html.theme--catppuccin-frappe .button.is-dark:active,html.theme--catppuccin-frappe .content kbd.button:active,html.theme--catppuccin-frappe .button.is-dark.is-active,html.theme--catppuccin-frappe .content kbd.button.is-active{background-color:#363a4a;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-dark[disabled],html.theme--catppuccin-frappe .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button{background-color:#414559;border-color:#414559;box-shadow:none}html.theme--catppuccin-frappe .button.is-dark.is-inverted,html.theme--catppuccin-frappe .content kbd.button.is-inverted{background-color:#fff;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-dark.is-inverted[disabled],html.theme--catppuccin-frappe .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-loading::after,html.theme--catppuccin-frappe .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-dark.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-focused{background-color:#414559;border-color:#414559;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #414559 #414559 !important}html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-frappe .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-dark.is-outlined[disabled],html.theme--catppuccin-frappe .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-frappe .content 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!important}html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-focused{background-color:#81c8be;border-color:#81c8be;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-light{background-color:#f1f9f8;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:hover,html.theme--catppuccin-frappe .button.is-info.is-light.is-hovered{background-color:#e8f5f3;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:active,html.theme--catppuccin-frappe .button.is-info.is-light.is-active{background-color:#dff1ef;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:hover,html.theme--catppuccin-frappe .button.is-success.is-hovered{background-color:#9fcd80;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus,html.theme--catppuccin-frappe .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus:not(:active),html.theme--catppuccin-frappe .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,209,137,0.25)}html.theme--catppuccin-frappe .button.is-success:active,html.theme--catppuccin-frappe .button.is-success.is-active{background-color:#98ca77;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-focused{background-color:#a6d189;border-color:#a6d189;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:hover,html.theme--catppuccin-frappe .button.is-warning.is-hovered{background-color:#e3c386;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus,html.theme--catppuccin-frappe .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus:not(:active),html.theme--catppuccin-frappe .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(229,200,144,0.25)}html.theme--catppuccin-frappe .button.is-warning:active,html.theme--catppuccin-frappe .button.is-warning.is-active{background-color:#e0be7b;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:#e5c890;box-shadow:none}html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-focused{background-color:#e5c890;border-color:#e5c890;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:hover,html.theme--catppuccin-frappe .button.is-danger.is-hovered{background-color:#e57779;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus,html.theme--catppuccin-frappe .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus:not(:active),html.theme--catppuccin-frappe .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(231,130,132,0.25)}html.theme--catppuccin-frappe .button.is-danger:active,html.theme--catppuccin-frappe .button.is-danger.is-active{background-color:#e36d6f;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:#e78284;box-shadow:none}html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #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--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .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--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-frappe .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-frappe .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-frappe .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-frappe .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-frappe .content blockquote{background-color:#292c3c;border-left:5px solid #626880;padding:1.25em 1.5em}html.theme--catppuccin-frappe .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-frappe .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-frappe .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-frappe .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-frappe .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-frappe .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-frappe .content ul ul ul{list-style-type:square}html.theme--catppuccin-frappe .content dd{margin-left:2em}html.theme--catppuccin-frappe .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-frappe .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-frappe .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-frappe .content figure img{display:inline-block}html.theme--catppuccin-frappe .content figure figcaption{font-style:italic}html.theme--catppuccin-frappe .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-frappe .content sup,html.theme--catppuccin-frappe .content sub{font-size:75%}html.theme--catppuccin-frappe .content table{width:100%}html.theme--catppuccin-frappe .content table td,html.theme--catppuccin-frappe .content table th{border:1px solid #626880;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-frappe .content table th{color:#b0bef1}html.theme--catppuccin-frappe .content table th:not([align]){text-align:inherit}html.theme--catppuccin-frappe .content table thead td,html.theme--catppuccin-frappe .content table thead th{border-width:0 0 2px;color:#b0bef1}html.theme--catppuccin-frappe .content table tfoot td,html.theme--catppuccin-frappe .content table tfoot th{border-width:2px 0 0;color:#b0bef1}html.theme--catppuccin-frappe .content table tbody tr:last-child td,html.theme--catppuccin-frappe .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-frappe .content .tabs li+li{margin-top:0}html.theme--catppuccin-frappe .content.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-frappe .content.is-normal{font-size:1rem}html.theme--catppuccin-frappe .content.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .content.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-frappe .icon.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-frappe .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-frappe .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-frappe .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-frappe .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-frappe .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-frappe div.icon-text{display:flex}html.theme--catppuccin-frappe .image,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-frappe .image img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-frappe .image img.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-frappe .image.is-fullwidth,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-frappe .image.is-square img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-frappe .image.is-square .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-frappe .image.is-1by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-frappe .image.is-1by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-frappe .image.is-5by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-frappe .image.is-5by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-frappe .image.is-4by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-frappe .image.is-4by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-frappe .image.is-3by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-frappe .image.is-5by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-frappe .image.is-5by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-frappe .image.is-16by9 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-frappe .image.is-16by9 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-frappe .image.is-2by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-frappe .image.is-2by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-frappe .image.is-3by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-frappe .image.is-3by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--catppuccin-frappe .image.is-4by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--catppuccin-frappe .image.is-4by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--catppuccin-frappe .image.is-3by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--catppuccin-frappe .image.is-3by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--catppuccin-frappe .image.is-2by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--catppuccin-frappe .image.is-2by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-frappe .image.is-3by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-frappe .image.is-9by16 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-frappe .image.is-9by16 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-frappe .image.is-1by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-frappe .image.is-1by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-frappe .image.is-1by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-frappe .image.is-1by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-frappe .image.is-square,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-frappe .image.is-1by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-frappe .image.is-5by4,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-frappe .image.is-4by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-frappe .image.is-3by2,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--catppuccin-frappe .image.is-5by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--catppuccin-frappe .image.is-16by9,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--catppuccin-frappe .image.is-2by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--catppuccin-frappe .image.is-3by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--catppuccin-frappe .image.is-4by5,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--catppuccin-frappe .image.is-3by4,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--catppuccin-frappe .image.is-2by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--catppuccin-frappe .image.is-3by5,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--catppuccin-frappe .image.is-9by16,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--catppuccin-frappe .image.is-1by2,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--catppuccin-frappe .image.is-1by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3{padding-top:300%}html.theme--catppuccin-frappe .image.is-16x16,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16x16{height:16px;width:16px}html.theme--catppuccin-frappe .image.is-24x24,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-24x24{height:24px;width:24px}html.theme--catppuccin-frappe .image.is-32x32,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-32x32{height:32px;width:32px}html.theme--catppuccin-frappe .image.is-48x48,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-48x48{height:48px;width:48px}html.theme--catppuccin-frappe .image.is-64x64,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-64x64{height:64px;width:64px}html.theme--catppuccin-frappe .image.is-96x96,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-96x96{height:96px;width:96px}html.theme--catppuccin-frappe .image.is-128x128,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-128x128{height:128px;width:128px}html.theme--catppuccin-frappe .notification{background-color:#292c3c;border-radius:.4em;position:relative;padding:1.25rem 2.5rem 1.25rem 1.5rem}html.theme--catppuccin-frappe .notification 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.button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus,html.theme--catppuccin-latte .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus:not(:active),html.theme--catppuccin-latte .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-latte .button.is-black:active,html.theme--catppuccin-latte .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:hover,html.theme--catppuccin-latte .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus,html.theme--catppuccin-latte .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus:not(:active),html.theme--catppuccin-latte .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-latte .button.is-light:active,html.theme--catppuccin-latte .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte 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.button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark,html.theme--catppuccin-latte .content kbd.button{background-color:#ccd0da;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:hover,html.theme--catppuccin-latte .content kbd.button:hover,html.theme--catppuccin-latte .button.is-dark.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-hovered{background-color:#c5c9d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:focus,html.theme--catppuccin-latte .content kbd.button:focus,html.theme--catppuccin-latte .button.is-dark.is-focused,html.theme--catppuccin-latte .content kbd.button.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte 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kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-focused{background-color:#ccd0da;border-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-primary,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:hover,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:focus,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:focus,html.theme--catppuccin-latte .button.is-primary.is-focused,html.theme--catppuccin-latte .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:focus:not(:active),html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--catppuccin-latte .button.is-primary.is-focused:not(:active),html.theme--catppuccin-latte .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(30,102,245,0.25)}html.theme--catppuccin-latte .button.is-primary:active,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:active,html.theme--catppuccin-latte .button.is-primary.is-active,html.theme--catppuccin-latte 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.button.is-primary.is-outlined:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--catppuccin-latte .button.is-primary.is-outlined:focus,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-focused,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#1e66f5;border-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-latte .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-primary.is-outlined[disabled],html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#1e66f5;box-shadow:none;color:#1e66f5}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink,html.theme--catppuccin-latte 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.docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-light,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-light.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--catppuccin-latte .button.is-primary.is-light.is-active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte 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.button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-info.is-light{background-color:#edfcfc;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:hover,html.theme--catppuccin-latte .button.is-info.is-light.is-hovered{background-color:#e2f9fb;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:active,html.theme--catppuccin-latte .button.is-info.is-light.is-active{background-color:#d7f7f9;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:hover,html.theme--catppuccin-latte .button.is-success.is-hovered{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus,html.theme--catppuccin-latte .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus:not(:active),html.theme--catppuccin-latte .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(64,160,43,0.25)}html.theme--catppuccin-latte .button.is-success:active,html.theme--catppuccin-latte .button.is-success.is-active{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:#40a02b;box-shadow:none}html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-outlined.is-focused{background-color:#40a02b;border-color:#40a02b;color:#fff}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #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--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .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--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte 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.file.is-link.is-active .file-cta{background-color:#0b57ef;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info .file-cta{background-color:#179299;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info:hover .file-cta,html.theme--catppuccin-latte .file.is-info.is-hovered .file-cta{background-color:#15878e;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-info:focus .file-cta,html.theme--catppuccin-latte .file.is-info.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(23,146,153,0.25);color:#fff}html.theme--catppuccin-latte .file.is-info:active .file-cta,html.theme--catppuccin-latte .file.is-info.is-active .file-cta{background-color:#147d83;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success .file-cta{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success:hover .file-cta,html.theme--catppuccin-latte .file.is-success.is-hovered .file-cta{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-success:focus .file-cta,html.theme--catppuccin-latte .file.is-success.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(64,160,43,0.25);color:#fff}html.theme--catppuccin-latte .file.is-success:active .file-cta,html.theme--catppuccin-latte .file.is-success.is-active .file-cta{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning .file-cta{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning:hover .file-cta,html.theme--catppuccin-latte .file.is-warning.is-hovered .file-cta{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-warning:focus .file-cta,html.theme--catppuccin-latte .file.is-warning.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(223,142,29,0.25);color:#fff}html.theme--catppuccin-latte .file.is-warning:active .file-cta,html.theme--catppuccin-latte .file.is-warning.is-active .file-cta{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger .file-cta{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger:hover .file-cta,html.theme--catppuccin-latte .file.is-danger.is-hovered .file-cta{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-danger:focus .file-cta,html.theme--catppuccin-latte .file.is-danger.is-focused .file-cta{border-color:transparent;box-shadow:0 0 0.5em rgba(210,15,57,0.25);color:#fff}html.theme--catppuccin-latte .file.is-danger:active .file-cta,html.theme--catppuccin-latte .file.is-danger.is-active .file-cta{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .file.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.file{font-size:.75rem}html.theme--catppuccin-latte .file.is-normal{font-size:1rem}html.theme--catppuccin-latte .file.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .file.is-medium .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-large{font-size:1.5rem}html.theme--catppuccin-latte .file.is-large .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.has-name .file-cta{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .file.has-name .file-name{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .file.has-name.is-empty .file-cta{border-radius:.4em}html.theme--catppuccin-latte .file.has-name.is-empty .file-name{display:none}html.theme--catppuccin-latte .file.is-boxed .file-label{flex-direction:column}html.theme--catppuccin-latte .file.is-boxed .file-cta{flex-direction:column;height:auto;padding:1em 3em}html.theme--catppuccin-latte .file.is-boxed .file-name{border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-boxed .file-icon{height:1.5em;width:1.5em}html.theme--catppuccin-latte .file.is-boxed .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-boxed.is-small .file-icon .fa,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-boxed .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .file.is-boxed.is-medium .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.is-boxed.is-large .file-icon .fa{font-size:35px}html.theme--catppuccin-latte .file.is-boxed.has-name .file-cta{border-radius:.4em .4em 0 0}html.theme--catppuccin-latte .file.is-boxed.has-name .file-name{border-radius:0 0 .4em .4em;border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-centered{justify-content:center}html.theme--catppuccin-latte .file.is-fullwidth .file-label{width:100%}html.theme--catppuccin-latte .file.is-fullwidth .file-name{flex-grow:1;max-width:none}html.theme--catppuccin-latte .file.is-right{justify-content:flex-end}html.theme--catppuccin-latte .file.is-right .file-cta{border-radius:0 .4em .4em 0}html.theme--catppuccin-latte .file.is-right .file-name{border-radius:.4em 0 0 .4em;border-width:1px 0 1px 1px;order:-1}html.theme--catppuccin-latte .file-label{align-items:stretch;display:flex;cursor:pointer;justify-content:flex-start;overflow:hidden;position:relative}html.theme--catppuccin-latte .file-label:hover .file-cta{background-color:#c5c9d5;color:#41445a}html.theme--catppuccin-latte .file-label:hover .file-name{border-color:#a5a9b8}html.theme--catppuccin-latte .file-label:active .file-cta{background-color:#bdc2cf;color:#41445a}html.theme--catppuccin-latte .file-label:active .file-name{border-color:#9ea2b3}html.theme--catppuccin-latte .file-input{height:100%;left:0;opacity:0;outline:none;position:absolute;top:0;width:100%}html.theme--catppuccin-latte .file-cta,html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-radius:.4em;font-size:1em;padding-left:1em;padding-right:1em;white-space:nowrap}html.theme--catppuccin-latte .file-cta{background-color:#ccd0da;color:#4c4f69}html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-style:solid;border-width:1px 1px 1px 0;display:block;max-width:16em;overflow:hidden;text-align:inherit;text-overflow:ellipsis}html.theme--catppuccin-latte .file-icon{align-items:center;display:flex;height:1em;justify-content:center;margin-right:.5em;width:1em}html.theme--catppuccin-latte .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .label{color:#41445a;display:block;font-size:1rem;font-weight:700}html.theme--catppuccin-latte .label:not(:last-child){margin-bottom:0.5em}html.theme--catppuccin-latte .label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.label{font-size:.75rem}html.theme--catppuccin-latte .label.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .label.is-large{font-size:1.5rem}html.theme--catppuccin-latte .help{display:block;font-size:.75rem;margin-top:0.25rem}html.theme--catppuccin-latte .help.is-white{color:#fff}html.theme--catppuccin-latte .help.is-black{color:#0a0a0a}html.theme--catppuccin-latte .help.is-light{color:#f5f5f5}html.theme--catppuccin-latte .help.is-dark,html.theme--catppuccin-latte .content kbd.help{color:#ccd0da}html.theme--catppuccin-latte .help.is-primary,html.theme--catppuccin-latte .docstring>section>a.help.docs-sourcelink{color:#1e66f5}html.theme--catppuccin-latte .help.is-link{color:#1e66f5}html.theme--catppuccin-latte .help.is-info{color:#179299}html.theme--catppuccin-latte .help.is-success{color:#40a02b}html.theme--catppuccin-latte .help.is-warning{color:#df8e1d}html.theme--catppuccin-latte .help.is-danger{color:#d20f39}html.theme--catppuccin-latte .field:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.has-addons{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.has-addons .control:not(:last-child){margin-right:-1px}html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .button,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .select select{border-radius:0}html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .select select{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .select select{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-hovered:not([disabled]){z-index:2}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]){z-index:3}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]):hover{z-index:4}html.theme--catppuccin-latte .field.has-addons .control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.has-addons.has-addons-centered{justify-content:center}html.theme--catppuccin-latte .field.has-addons.has-addons-right{justify-content:flex-end}html.theme--catppuccin-latte .field.has-addons.has-addons-fullwidth .control{flex-grow:1;flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.is-grouped>.control{flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped>.control:not(:last-child){margin-bottom:0;margin-right:.75rem}html.theme--catppuccin-latte .field.is-grouped>.control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.is-grouped.is-grouped-centered{justify-content:center}html.theme--catppuccin-latte .field.is-grouped.is-grouped-right{justify-content:flex-end}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline{flex-wrap:wrap}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:last-child,html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline:last-child{margin-bottom:-0.75rem}html.theme--catppuccin-latte 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.icon:only-child,html.theme--catppuccin-latte .navbar-link .icon:only-child{margin-left:-0.25rem;margin-right:-0.25rem}html.theme--catppuccin-latte a.navbar-item,html.theme--catppuccin-latte .navbar-link{cursor:pointer}html.theme--catppuccin-latte a.navbar-item:focus,html.theme--catppuccin-latte a.navbar-item:focus-within,html.theme--catppuccin-latte a.navbar-item:hover,html.theme--catppuccin-latte a.navbar-item.is-active,html.theme--catppuccin-latte .navbar-link:focus,html.theme--catppuccin-latte .navbar-link:focus-within,html.theme--catppuccin-latte .navbar-link:hover,html.theme--catppuccin-latte .navbar-link.is-active{background-color:rgba(0,0,0,0);color:#1e66f5}html.theme--catppuccin-latte .navbar-item{flex-grow:0;flex-shrink:0}html.theme--catppuccin-latte .navbar-item img{max-height:1.75rem}html.theme--catppuccin-latte .navbar-item.has-dropdown{padding:0}html.theme--catppuccin-latte .navbar-item.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .navbar-item.is-tab{border-bottom:1px solid transparent;min-height:4rem;padding-bottom:calc(0.5rem - 1px)}html.theme--catppuccin-latte .navbar-item.is-tab:focus,html.theme--catppuccin-latte .navbar-item.is-tab:hover{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5}html.theme--catppuccin-latte .navbar-item.is-tab.is-active{background-color:rgba(0,0,0,0);border-bottom-color:#1e66f5;border-bottom-style:solid;border-bottom-width:3px;color:#1e66f5;padding-bottom:calc(0.5rem - 3px)}html.theme--catppuccin-latte .navbar-content{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless){padding-right:2.5em}html.theme--catppuccin-latte .navbar-link:not(.is-arrowless)::after{border-color:#fff;margin-top:-0.375em;right:1.125em}html.theme--catppuccin-latte .navbar-dropdown{font-size:0.875rem;padding-bottom:0.5rem;padding-top:0.5rem}html.theme--catppuccin-latte .navbar-dropdown .navbar-item{padding-left:1.5rem;padding-right:1.5rem}html.theme--catppuccin-latte .navbar-divider{background-color:rgba(0,0,0,0.2);border:none;display:none;height:2px;margin:0.5rem 0}@media screen and (max-width: 1055px){html.theme--catppuccin-latte .navbar>.container{display:block}html.theme--catppuccin-latte .navbar-brand .navbar-item,html.theme--catppuccin-latte .navbar-tabs .navbar-item{align-items:center;display:flex}html.theme--catppuccin-latte .navbar-link::after{display:none}html.theme--catppuccin-latte .navbar-menu{background-color:#1e66f5;box-shadow:0 8px 16px rgba(10,10,10,0.1);padding:0.5rem 0}html.theme--catppuccin-latte .navbar-menu.is-active{display:block}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch,html.theme--catppuccin-latte .navbar.is-fixed-top-touch{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-touch.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte .navbar.is-fixed-top-touch{top:0}html.theme--catppuccin-latte .navbar.is-fixed-top .navbar-menu,html.theme--catppuccin-latte .navbar.is-fixed-top-touch .navbar-menu{-webkit-overflow-scrolling:touch;max-height:calc(100vh - 4rem);overflow:auto}html.theme--catppuccin-latte html.has-navbar-fixed-top-touch,html.theme--catppuccin-latte body.has-navbar-fixed-top-touch{padding-top:4rem}html.theme--catppuccin-latte html.has-navbar-fixed-bottom-touch,html.theme--catppuccin-latte body.has-navbar-fixed-bottom-touch{padding-bottom:4rem}}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .navbar,html.theme--catppuccin-latte .navbar-menu,html.theme--catppuccin-latte .navbar-start,html.theme--catppuccin-latte .navbar-end{align-items:stretch;display:flex}html.theme--catppuccin-latte .navbar{min-height:4rem}html.theme--catppuccin-latte .navbar.is-spaced{padding:1rem 2rem}html.theme--catppuccin-latte .navbar.is-spaced .navbar-start,html.theme--catppuccin-latte .navbar.is-spaced .navbar-end{align-items:center}html.theme--catppuccin-latte .navbar.is-spaced a.navbar-item,html.theme--catppuccin-latte .navbar.is-spaced .navbar-link{border-radius:.4em}html.theme--catppuccin-latte .navbar.is-transparent a.navbar-item:focus,html.theme--catppuccin-latte .navbar.is-transparent a.navbar-item:hover,html.theme--catppuccin-latte .navbar.is-transparent a.navbar-item.is-active,html.theme--catppuccin-latte .navbar.is-transparent .navbar-link:focus,html.theme--catppuccin-latte .navbar.is-transparent .navbar-link:hover,html.theme--catppuccin-latte .navbar.is-transparent .navbar-link.is-active{background-color:transparent !important}html.theme--catppuccin-latte .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link,html.theme--catppuccin-latte .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link,html.theme--catppuccin-latte .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within 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.navbar-dropdown.is-boxed,.navbar.is-spaced html.theme--catppuccin-latte .navbar-item.is-hoverable:hover .navbar-dropdown,html.theme--catppuccin-latte .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed{opacity:1;pointer-events:auto;transform:translateY(0)}html.theme--catppuccin-latte .navbar-menu{flex-grow:1;flex-shrink:0}html.theme--catppuccin-latte .navbar-start{justify-content:flex-start;margin-right:auto}html.theme--catppuccin-latte .navbar-end{justify-content:flex-end;margin-left:auto}html.theme--catppuccin-latte .navbar-dropdown{background-color:#1e66f5;border-bottom-left-radius:8px;border-bottom-right-radius:8px;border-top:1px solid rgba(0,0,0,0.2);box-shadow:0 8px 8px rgba(10,10,10,0.1);display:none;font-size:0.875rem;left:0;min-width:100%;position:absolute;top:100%;z-index:20}html.theme--catppuccin-latte .navbar-dropdown .navbar-item{padding:0.375rem 1rem;white-space:nowrap}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item{padding-right:3rem}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:focus,html.theme--catppuccin-latte .navbar-dropdown a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#8c8fa1}html.theme--catppuccin-latte .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#1e66f5}.navbar.is-spaced html.theme--catppuccin-latte .navbar-dropdown,html.theme--catppuccin-latte .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--catppuccin-latte .navbar-dropdown.is-right{left:auto;right:0}html.theme--catppuccin-latte .navbar-divider{display:block}html.theme--catppuccin-latte .navbar>.container .navbar-brand,html.theme--catppuccin-latte .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--catppuccin-latte .navbar>.container .navbar-menu,html.theme--catppuccin-latte .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop,html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop{bottom:0}html.theme--catppuccin-latte .navbar.is-fixed-bottom-desktop.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--catppuccin-latte .navbar.is-fixed-top-desktop{top:0}html.theme--catppuccin-latte html.has-navbar-fixed-top-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-top-desktop{padding-top:4rem}html.theme--catppuccin-latte html.has-navbar-fixed-bottom-desktop,html.theme--catppuccin-latte body.has-navbar-fixed-bottom-desktop{padding-bottom:4rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-top,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-top{padding-top:6rem}html.theme--catppuccin-latte html.has-spaced-navbar-fixed-bottom,html.theme--catppuccin-latte body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-latte a.navbar-item.is-active,html.theme--catppuccin-latte .navbar-link.is-active{color:#1e66f5}html.theme--catppuccin-latte a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-latte .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-latte .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-latte .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-latte .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-latte .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-latte .pagination.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--catppuccin-latte .pagination.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .pagination.is-large{font-size:1.5rem}html.theme--catppuccin-latte .pagination.is-rounded .pagination-previous,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-previous,html.theme--catppuccin-latte .pagination.is-rounded .pagination-next,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-next{padding-left:1em;padding-right:1em;border-radius:9999px}html.theme--catppuccin-latte .pagination.is-rounded .pagination-link,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.pagination .pagination-link{border-radius:9999px}html.theme--catppuccin-latte .pagination,html.theme--catppuccin-latte .pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link{border-color:#acb0be;color:#1e66f5;min-width:2.5em}html.theme--catppuccin-latte .pagination-previous:hover,html.theme--catppuccin-latte .pagination-next:hover,html.theme--catppuccin-latte .pagination-link:hover{border-color:#9ca0b0;color:#04a5e5}html.theme--catppuccin-latte .pagination-previous:focus,html.theme--catppuccin-latte .pagination-next:focus,html.theme--catppuccin-latte .pagination-link:focus{border-color:#9ca0b0}html.theme--catppuccin-latte .pagination-previous:active,html.theme--catppuccin-latte .pagination-next:active,html.theme--catppuccin-latte .pagination-link:active{box-shadow:inset 0 1px 2px rgba(10,10,10,0.2)}html.theme--catppuccin-latte .pagination-previous[disabled],html.theme--catppuccin-latte .pagination-previous.is-disabled,html.theme--catppuccin-latte .pagination-next[disabled],html.theme--catppuccin-latte .pagination-next.is-disabled,html.theme--catppuccin-latte .pagination-link[disabled],html.theme--catppuccin-latte .pagination-link.is-disabled{background-color:#acb0be;border-color:#acb0be;box-shadow:none;color:#616587;opacity:0.5}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next{padding-left:.75em;padding-right:.75em;white-space:nowrap}html.theme--catppuccin-latte .pagination-link.is-current{background-color:#1e66f5;border-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .pagination-ellipsis{color:#9ca0b0;pointer-events:none}html.theme--catppuccin-latte .pagination-list{flex-wrap:wrap}html.theme--catppuccin-latte .pagination-list li{list-style:none}@media screen and (max-width: 768px){html.theme--catppuccin-latte .pagination{flex-wrap:wrap}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .pagination-list li{flex-grow:1;flex-shrink:1}}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .pagination-list{flex-grow:1;flex-shrink:1;justify-content:flex-start;order:1}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{margin-bottom:0;margin-top:0}html.theme--catppuccin-latte .pagination-previous{order:2}html.theme--catppuccin-latte .pagination-next{order:3}html.theme--catppuccin-latte .pagination{justify-content:space-between;margin-bottom:0;margin-top:0}html.theme--catppuccin-latte .pagination.is-centered .pagination-previous{order:1}html.theme--catppuccin-latte .pagination.is-centered .pagination-list{justify-content:center;order:2}html.theme--catppuccin-latte .pagination.is-centered .pagination-next{order:3}html.theme--catppuccin-latte .pagination.is-right .pagination-previous{order:1}html.theme--catppuccin-latte .pagination.is-right .pagination-next{order:2}html.theme--catppuccin-latte .pagination.is-right .pagination-list{justify-content:flex-end;order:3}}html.theme--catppuccin-latte .panel{border-radius:8px;box-shadow:#171717;font-size:1rem}html.theme--catppuccin-latte .panel:not(:last-child){margin-bottom:1.5rem}html.theme--catppuccin-latte .panel.is-white .panel-heading{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .panel.is-white .panel-tabs a.is-active{border-bottom-color:#fff}html.theme--catppuccin-latte .panel.is-white .panel-block.is-active .panel-icon{color:#fff}html.theme--catppuccin-latte .panel.is-black .panel-heading{background-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .panel.is-black .panel-tabs a.is-active{border-bottom-color:#0a0a0a}html.theme--catppuccin-latte .panel.is-black .panel-block.is-active .panel-icon{color:#0a0a0a}html.theme--catppuccin-latte .panel.is-light .panel-heading{background-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .panel.is-light .panel-tabs a.is-active{border-bottom-color:#f5f5f5}html.theme--catppuccin-latte .panel.is-light .panel-block.is-active .panel-icon{color:#f5f5f5}html.theme--catppuccin-latte .panel.is-dark .panel-heading,html.theme--catppuccin-latte .content kbd.panel .panel-heading{background-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .panel.is-dark .panel-tabs a.is-active,html.theme--catppuccin-latte .content kbd.panel .panel-tabs a.is-active{border-bottom-color:#ccd0da}html.theme--catppuccin-latte .panel.is-dark .panel-block.is-active .panel-icon,html.theme--catppuccin-latte .content kbd.panel .panel-block.is-active .panel-icon{color:#ccd0da}html.theme--catppuccin-latte .panel.is-primary .panel-heading,html.theme--catppuccin-latte .docstring>section>a.panel.docs-sourcelink .panel-heading{background-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .panel.is-primary .panel-tabs a.is-active,html.theme--catppuccin-latte .docstring>section>a.panel.docs-sourcelink .panel-tabs a.is-active{border-bottom-color:#1e66f5}html.theme--catppuccin-latte .panel.is-primary .panel-block.is-active .panel-icon,html.theme--catppuccin-latte .docstring>section>a.panel.docs-sourcelink .panel-block.is-active .panel-icon{color:#1e66f5}html.theme--catppuccin-latte .panel.is-link .panel-heading{background-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .panel.is-link .panel-tabs a.is-active{border-bottom-color:#1e66f5}html.theme--catppuccin-latte .panel.is-link .panel-block.is-active .panel-icon{color:#1e66f5}html.theme--catppuccin-latte .panel.is-info 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kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-dark.is-outlined[disabled],html.theme--catppuccin-macchiato .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363a4f #363a4f !important}html.theme--catppuccin-macchiato 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.button.is-link.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-link.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-focused{background-color:#8aadf4;border-color:#8aadf4;color:#fff}html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #8aadf4 #8aadf4 !important}html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-link.is-outlined{background-color:transparent;border-color:#8aadf4;box-shadow:none;color:#8aadf4}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#8aadf4}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8aadf4 #8aadf4 !important}html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-link.is-light{background-color:#ecf2fd;color:#0e3b95}html.theme--catppuccin-macchiato .button.is-link.is-light:hover,html.theme--catppuccin-macchiato .button.is-link.is-light.is-hovered{background-color:#e1eafc;border-color:transparent;color:#0e3b95}html.theme--catppuccin-macchiato .button.is-link.is-light:active,html.theme--catppuccin-macchiato .button.is-link.is-light.is-active{background-color:#d5e2fb;border-color:transparent;color:#0e3b95}html.theme--catppuccin-macchiato 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.button.is-info{background-color:#8bd5ca;border-color:#8bd5ca;box-shadow:none}html.theme--catppuccin-macchiato .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-focused{background-color:#8bd5ca;border-color:#8bd5ca;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-light{background-color:#f0faf8;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:hover,html.theme--catppuccin-macchiato .button.is-info.is-light.is-hovered{background-color:#e7f6f4;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:active,html.theme--catppuccin-macchiato .button.is-info.is-light.is-active{background-color:#ddf3f0;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:hover,html.theme--catppuccin-macchiato .button.is-success.is-hovered{background-color:#9ed78c;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus,html.theme--catppuccin-macchiato .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus:not(:active),html.theme--catppuccin-macchiato .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,218,149,0.25)}html.theme--catppuccin-macchiato .button.is-success:active,html.theme--catppuccin-macchiato .button.is-success.is-active{background-color:#96d382;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:#a6da95;box-shadow:none}html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-focused{background-color:#a6da95;border-color:#a6da95;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato 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.button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #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--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-macchiato .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-macchiato .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused,html.theme--catppuccin-macchiato .buttons.has-addons .button:active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button:active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-macchiato .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-macchiato .buttons.is-centered{justify-content:center}html.theme--catppuccin-macchiato .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-macchiato .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-macchiato .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--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-macchiato .button.is-responsive.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-macchiato .button.is-responsive,html.theme--catppuccin-macchiato .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-macchiato .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-macchiato .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-macchiato .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-macchiato .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-macchiato .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-macchiato .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-macchiato .content li+li{margin-top:0.25em}html.theme--catppuccin-macchiato .content p:not(:last-child),html.theme--catppuccin-macchiato .content dl:not(:last-child),html.theme--catppuccin-macchiato .content ol:not(:last-child),html.theme--catppuccin-macchiato .content ul:not(:last-child),html.theme--catppuccin-macchiato .content blockquote:not(:last-child),html.theme--catppuccin-macchiato .content pre:not(:last-child),html.theme--catppuccin-macchiato .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-macchiato .content h1,html.theme--catppuccin-macchiato .content h2,html.theme--catppuccin-macchiato .content h3,html.theme--catppuccin-macchiato .content h4,html.theme--catppuccin-macchiato .content h5,html.theme--catppuccin-macchiato .content h6{color:#cad3f5;font-weight:600;line-height:1.125}html.theme--catppuccin-macchiato .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-macchiato .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-macchiato .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-macchiato .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-macchiato .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-macchiato .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-macchiato .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-macchiato .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-macchiato .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-macchiato .content blockquote{background-color:#1e2030;border-left:5px solid #5b6078;padding:1.25em 1.5em}html.theme--catppuccin-macchiato .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-macchiato .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-macchiato .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-macchiato .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-macchiato .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-macchiato .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-macchiato .content ul ul ul{list-style-type:square}html.theme--catppuccin-macchiato .content dd{margin-left:2em}html.theme--catppuccin-macchiato .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-macchiato .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-macchiato .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-macchiato .content figure img{display:inline-block}html.theme--catppuccin-macchiato .content figure figcaption{font-style:italic}html.theme--catppuccin-macchiato .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-macchiato .content sup,html.theme--catppuccin-macchiato .content sub{font-size:75%}html.theme--catppuccin-macchiato .content table{width:100%}html.theme--catppuccin-macchiato .content table td,html.theme--catppuccin-macchiato .content table th{border:1px solid #5b6078;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-macchiato .content table th{color:#b5c1f1}html.theme--catppuccin-macchiato .content table th:not([align]){text-align:inherit}html.theme--catppuccin-macchiato .content table thead td,html.theme--catppuccin-macchiato .content table thead th{border-width:0 0 2px;color:#b5c1f1}html.theme--catppuccin-macchiato .content table tfoot td,html.theme--catppuccin-macchiato .content table tfoot th{border-width:2px 0 0;color:#b5c1f1}html.theme--catppuccin-macchiato .content table tbody tr:last-child td,html.theme--catppuccin-macchiato .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-macchiato .content .tabs li+li{margin-top:0}html.theme--catppuccin-macchiato .content.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-macchiato .content.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .content.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .content.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-macchiato .icon.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-macchiato .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-macchiato .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-macchiato .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-macchiato .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-macchiato .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-macchiato .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-macchiato div.icon-text{display:flex}html.theme--catppuccin-macchiato .image,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-macchiato .image img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-macchiato .image img.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-macchiato .image.is-fullwidth,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-macchiato .image.is-square img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-macchiato .image.is-square .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-macchiato .image.is-1by1 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-macchiato .image.is-1by1 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-macchiato .image.is-5by4 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-macchiato .image.is-5by4 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-macchiato .image.is-4by3 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-macchiato .image.is-4by3 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-macchiato .image.is-3by2 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-macchiato .image.is-3by2 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-macchiato .image.is-5by3 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-macchiato .image.is-5by3 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-macchiato .image.is-16by9 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-macchiato .image.is-16by9 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-macchiato .image.is-2by1 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-macchiato .image.is-2by1 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-macchiato .image.is-3by1 img,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-macchiato .image.is-3by1 .has-ratio,html.theme--catppuccin-macchiato #documenter .docs-sidebar .docs-logo>img.is-3by1 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select[disabled]:-moz-placeholder,html.theme--catppuccin-macchiato .textarea[disabled]:-moz-placeholder,html.theme--catppuccin-macchiato .input[disabled]:-moz-placeholder,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input[disabled]:-moz-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .select select:-moz-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .textarea:-moz-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .input:-moz-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input:-moz-placeholder{color:rgba(245,247,253,0.3)}html.theme--catppuccin-macchiato .select select[disabled]:-ms-input-placeholder,html.theme--catppuccin-macchiato .textarea[disabled]:-ms-input-placeholder,html.theme--catppuccin-macchiato .input[disabled]:-ms-input-placeholder,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input[disabled]:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .select select:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .textarea:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato .input:-ms-input-placeholder,fieldset[disabled] html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input:-ms-input-placeholder{color:rgba(245,247,253,0.3)}html.theme--catppuccin-macchiato .textarea,html.theme--catppuccin-macchiato .input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input{box-shadow:inset 0 0.0625em 0.125em rgba(10,10,10,0.05);max-width:100%;width:100%}html.theme--catppuccin-macchiato .textarea[readonly],html.theme--catppuccin-macchiato .input[readonly],html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input[readonly]{box-shadow:none}html.theme--catppuccin-macchiato 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form.docs-search>input.is-active{box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-macchiato .is-black.textarea,html.theme--catppuccin-macchiato .is-black.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black{border-color:#0a0a0a}html.theme--catppuccin-macchiato .is-black.textarea:focus,html.theme--catppuccin-macchiato .is-black.input:focus,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:focus,html.theme--catppuccin-macchiato .is-black.is-focused.textarea,html.theme--catppuccin-macchiato .is-black.is-focused.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--catppuccin-macchiato .is-black.textarea:active,html.theme--catppuccin-macchiato .is-black.input:active,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:active,html.theme--catppuccin-macchiato 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kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .content 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html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-light{background-color:#ebf3fe;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:hover,html.theme--catppuccin-mocha .button.is-link.is-light.is-hovered{background-color:#dfebfe;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:active,html.theme--catppuccin-mocha .button.is-link.is-light.is-active{background-color:#d3e3fd;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:hover,html.theme--catppuccin-mocha .button.is-info.is-hovered{background-color:#8adfd1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus,html.theme--catppuccin-mocha .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus:not(:active),html.theme--catppuccin-mocha .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(148,226,213,0.25)}html.theme--catppuccin-mocha .button.is-info:active,html.theme--catppuccin-mocha .button.is-info.is-active{background-color:#80ddcd;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:#94e2d5;box-shadow:none}html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-focused{background-color:#94e2d5;border-color:#94e2d5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-light{background-color:#effbf9;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:hover,html.theme--catppuccin-mocha .button.is-info.is-light.is-hovered{background-color:#e5f8f5;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:active,html.theme--catppuccin-mocha .button.is-info.is-light.is-active{background-color:#dbf5f1;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:hover,html.theme--catppuccin-mocha .button.is-success.is-hovered{background-color:#9de097;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus,html.theme--catppuccin-mocha .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus:not(:active),html.theme--catppuccin-mocha .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,227,161,0.25)}html.theme--catppuccin-mocha .button.is-success:active,html.theme--catppuccin-mocha .button.is-success.is-active{background-color:#93dd8d;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:#a6e3a1;box-shadow:none}html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-focused{background-color:#a6e3a1;border-color:#a6e3a1;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #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--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons .button:focus:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-mocha .buttons.has-addons .button:active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-mocha .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-mocha .buttons.is-centered{justify-content:center}html.theme--catppuccin-mocha .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-mocha .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-mocha .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--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-mocha .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-mocha .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-mocha .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-mocha .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-mocha .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-mocha .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-mocha .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-mocha .content li+li{margin-top:0.25em}html.theme--catppuccin-mocha .content p:not(:last-child),html.theme--catppuccin-mocha .content dl:not(:last-child),html.theme--catppuccin-mocha .content ol:not(:last-child),html.theme--catppuccin-mocha .content ul:not(:last-child),html.theme--catppuccin-mocha .content blockquote:not(:last-child),html.theme--catppuccin-mocha .content pre:not(:last-child),html.theme--catppuccin-mocha .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-mocha .content h1,html.theme--catppuccin-mocha .content h2,html.theme--catppuccin-mocha .content h3,html.theme--catppuccin-mocha .content h4,html.theme--catppuccin-mocha .content h5,html.theme--catppuccin-mocha .content h6{color:#cdd6f4;font-weight:600;line-height:1.125}html.theme--catppuccin-mocha .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-mocha .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-mocha .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-mocha .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-mocha .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-mocha .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-mocha .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-mocha .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-mocha .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-mocha .content blockquote{background-color:#181825;border-left:5px solid #585b70;padding:1.25em 1.5em}html.theme--catppuccin-mocha .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-mocha .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-mocha .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-mocha .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-mocha .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-mocha .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-mocha .content ul ul ul{list-style-type:square}html.theme--catppuccin-mocha .content dd{margin-left:2em}html.theme--catppuccin-mocha .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-mocha .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-mocha .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-mocha .content figure img{display:inline-block}html.theme--catppuccin-mocha .content figure figcaption{font-style:italic}html.theme--catppuccin-mocha .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-mocha .content sup,html.theme--catppuccin-mocha .content sub{font-size:75%}html.theme--catppuccin-mocha .content table{width:100%}html.theme--catppuccin-mocha .content table 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.content.is-normal{font-size:1rem}html.theme--catppuccin-mocha .content.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .content.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-mocha .icon.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-mocha .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-mocha .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-mocha .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-mocha .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-mocha .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-mocha .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-mocha div.icon-text{display:flex}html.theme--catppuccin-mocha .image,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-mocha .image img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-mocha .image img.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-mocha .image.is-fullwidth,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-mocha .image.is-square img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-mocha .image.is-square .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-mocha .image.is-1by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar 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.has-ratio,html.theme--catppuccin-mocha .image.is-5by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-mocha .image.is-5by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-mocha .image.is-16by9 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-mocha .image.is-16by9 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-mocha .image.is-2by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-mocha .image.is-2by1 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-mocha .image.is-3by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-mocha 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img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-mocha .image.is-3by5 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-mocha .image.is-9by16 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-mocha .image.is-9by16 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-mocha .image.is-1by2 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-mocha .image.is-1by2 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-mocha .image.is-1by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-mocha .image.is-1by3 .has-ratio,html.theme--catppuccin-mocha 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content 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.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-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:3px;font-size:.85em}html.theme--documenter-dark .button.is-normal{font-size:15px}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:#dbdee0;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 / 2));top:calc(50% - (1em / 2));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:290486px;padding-left:1em;padding-right:1em}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:0.5rem}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){border-radius:3px;font-size:.85em}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 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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:left}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.85em}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:290486px}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 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table th{vertical-align:top}html.theme--documenter-dark table td:not([align]),html.theme--documenter-dark table th:not([align]){text-align:inherit}html.theme--documenter-dark table th{color:#f2f2f2}html.theme--documenter-dark .box{background-color:#343c3d;border-radius:8px;box-shadow:none;color:#fff;display:block;padding:1.25rem}html.theme--documenter-dark a.box:hover,html.theme--documenter-dark a.box:focus{box-shadow:0 0.5em 1em -0.125em rgba(10,10,10,0.1),0 0 0 1px #1abc9c}html.theme--documenter-dark a.box:active{box-shadow:inset 0 1px 2px rgba(10,10,10,0.2),0 0 0 1px #1abc9c}html.theme--documenter-dark .button{background-color:#282f2f;border-color:#4c5759;border-width:1px;color:#375a7f;cursor:pointer;justify-content:center;padding-bottom:calc(0.5em - 1px);padding-left:1em;padding-right:1em;padding-top:calc(0.5em - 1px);text-align:center;white-space:nowrap}html.theme--documenter-dark .button strong{color:inherit}html.theme--documenter-dark .button .icon,html.theme--documenter-dark 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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 .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:#ecf0f1;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) 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rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark 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.content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#1d2122;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:#282f2f;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .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 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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 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.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:#cb3c33}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 #cb3c33 #cb3c33 !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:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}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 + 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.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 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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 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Theme: Default Description: Original highlight.js style Author: (c) Ivan Sagalaev @@ -6,4 +6,4 @@ Website: https://highlightjs.org/ License: see project LICENSE Touched: 2021 -*/pre code.hljs{display:block;overflow-x:auto}code.hljs{padding:3px 5px}.hljs{background:#F0F0F0;color:#444}.hljs-comment{color:#888888}.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:#BC6060}.hljs-literal{color:#78A960}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#4d99bf}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold} +*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/dev/assets/themeswap.js b/dev/assets/themeswap.js index c58e993e3e..9f5eebe6aa 100644 --- a/dev/assets/themeswap.js +++ b/dev/assets/themeswap.js @@ -1,20 +1,17 @@ // Small function to quickly swap out themes. Gets put into the tag.. function set_theme_from_local_storage() { - // Intialize the theme to null, which means default + // 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) { + 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"); + theme = window.localStorage.getItem("documenter-theme"); } - // Check if the browser supports user color preference - var darkPreference = false; // Check if the users preference is for dark color scheme - if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { - darkPreference = true; - } + 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 @@ -24,43 +21,64 @@ function set_theme_from_local_storage() { // // - disabled: style sheets that should be disabled (i.e. all the theme style sheets // that are not the currently active theme) - var active = null; var disabled = []; var darkTheme = null; + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; for (var i = 0; i < document.styleSheets.length; i++) { var ss = document.styleSheets[i]; // The tag of each style sheet is expected to have a data-theme-name attribute // which must contain the name of the theme. The names in localStorage much match this. var themename = ss.ownerNode.getAttribute("data-theme-name"); // attribute not set => non-theme stylesheet => ignore - if(themename === null) continue; + if (themename === null) continue; // To distinguish the default (primary) theme, it needs to have the data-theme-primary // attribute set. - var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null); - // Check if the theme is primary dark theme - var isDarkTheme = (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null); - // If ss is for dark theme then set the value of darkTheme to the name of the theme - if(isDarkTheme) darkTheme = themename; + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } // If we find a matching theme (and it's not the default), we'll set active to non-null - if(themename === theme) active = i; + if (themename === theme) active = i; // Store the style sheets of inactive themes so that we could disable them - if(themename !== theme) disabled.push(ss); + if (themename !== theme) disabled.push(ss); } - if(active !== null) { + var activeTheme = null; + if (active !== null) { // If we did find an active theme, we'll (1) add the theme--$(theme) class to - document.getElementsByTagName('html')[0].className = "theme--" + theme; - // and (2) disable all the other theme stylesheets - disabled.forEach(function(ss){ - ss.disabled = true; - }); + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } } - else if(darkTheme !== null && darkPreference === true) { - // If we did find an active theme, we'll (1) add the theme--$(theme) class to - document.getElementsByTagName('html')[0].className = "theme--" + darkTheme; - // and (2) disable all the other theme stylesheets - disabled.forEach(function(ss){ - if (ss.ownerNode.getAttribute("data-theme-name") !== darkTheme) { - ss.disabled = true; - } - }); + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); } } set_theme_from_local_storage(); diff --git a/dev/assets/warner.js b/dev/assets/warner.js index 5531c8851b..3f6f5d0083 100644 --- a/dev/assets/warner.js +++ b/dev/assets/warner.js @@ -1,49 +1,52 @@ -function maybeAddWarning () { - // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE - // in siteinfo.js. - // If either of these are undefined something went horribly wrong, so we abort. - if ( - window.DOCUMENTER_NEWEST === undefined || - window.DOCUMENTER_CURRENT_VERSION === undefined || - window.DOCUMENTER_STABLE === undefined - ) { - return - }; +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } - // Current version is not a version number, so we can't tell if it's the newest version. Abort. - if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { - return - }; + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } - // Current version is newest version, so no need to add a warning. - if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { - return - }; + // 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'; + // 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); - }; + 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); -}; + 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); +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); } else { - maybeAddWarning(); -}; + maybeAddWarning(); +} diff --git a/dev/censored/index.html b/dev/censored/index.html index fe199bda90..3dd94c9a47 100644 --- a/dev/censored/index.html +++ b/dev/censored/index.html @@ -1,5 +1,5 @@ -Censored Distributions · Distributions.jl
    Edit on GitHub

    Censored Distributions

    In censoring of data, values exceeding an upper limit (right censoring) or falling below a lower limit (left censoring), or both (interval censoring) are replaced by the corresponding limit itself. The package provides the censored function, which creates the most appropriate distribution to represent a censored version of a given distribution.

    A censored distribution can be constructed using the following signature:

    Distributions.censored — Function
    censored(d0::UnivariateDistribution; [lower::Real], [upper::Real])
+Censored Distributions · Distributions.jl
    GitHub
    Censored Distributions
    In censoring of data, values exceeding an upper limit (right censoring) or falling below a lower limit (left censoring), or both (interval censoring) are replaced by the corresponding limit itself. The package provides the censored function, which creates the most appropriate distribution to represent a censored version of a given distribution.
    A censored distribution can be constructed using the following signature:
    Distributions.censored — Function
    censored(d0::UnivariateDistribution; [lower::Real], [upper::Real])
 censored(d0::UnivariateDistribution, lower::Real, upper::Real)
    A censored distribution d of a distribution d0 to the interval $[l, u]=$[lower, upper] has the probability density (mass) function:
    \[f(x; d_0, l, u) = \begin{cases}
     P_{Z \sim d_0}(Z \le l), & x = l \\
     f_{d_0}(x),              & l < x < u \\
@@ -7,4 +7,4 @@
   \end{cases}, \quad x \in [l, u]\]
    where $f_{d_0}(x)$ is the probability density (mass) function of $d_0$.
    If $Z \sim d_0$, and X = clamp(Z, l, u), then $X \sim d$. Note that this implies that even if $d_0$ is continuous, its censored form assigns positive probability to the bounds $l$ and $u$. Therefore, a censored continuous distribution has atoms and is a mixture of discrete and continuous components.
    The function falls back to constructing a Distributions.Censored wrapper.
    Usage
    censored(d0; lower=l)           # d0 left-censored to the interval [l, Inf)
 censored(d0; upper=u)           # d0 right-censored to the interval (-Inf, u]
 censored(d0; lower=l, upper=u)  # d0 interval-censored to the interval [l, u]
-censored(d0, l, u)              # d0 interval-censored to the interval [l, u]
    Implementation
    To implement a specialized censored form for distributions of type D, instead of overloading a method with one of the above signatures, one or more of the following methods should be implemented:
    • censored(d0::D, l::T, u::T) where {T <: Real}
    • censored(d0::D, ::Nothing, u::Real)
    • censored(d0::D, l::Real, ::Nothing)
    source
    In the general case, this will create a Distributions.Censored{typeof(d0)} structure, defined as follows:
    In general, censored should be called instead of the constructor of Censored, which is not exported.
    Many functions, including those for the evaluation of pdf and sampling, are defined for all censored univariate distributions:
    Some functions to compute statistics are available for the censored distribution if they are also available for its truncation:
    For example, these functions are available for the following uncensored distributions:
    • DiscreteUniform
    • Exponential
    • LogUniform
    • Normal
    • Uniform
    mode is not implemented for censored distributions.
    
+censored(d0, l, u)              # d0 interval-censored to the interval [l, u]

    Implementation

    To implement a specialized censored form for distributions of type D, instead of overloading a method with one of the above signatures, one or more of the following methods should be implemented:

    • censored(d0::D, l::T, u::T) where {T <: Real}
    • censored(d0::D, ::Nothing, u::Real)
    • censored(d0::D, l::Real, ::Nothing)
    source

    In the general case, this will create a Distributions.Censored{typeof(d0)} structure, defined as follows:

    In general, censored should be called instead of the constructor of Censored, which is not exported.

    Many functions, including those for the evaluation of pdf and sampling, are defined for all censored univariate distributions:

    Some functions to compute statistics are available for the censored distribution if they are also available for its truncation:

    For example, these functions are available for the following uncensored distributions:

    • DiscreteUniform
    • Exponential
    • LogUniform
    • Normal
    • Uniform

    mode is not implemented for censored distributions.

    diff --git a/dev/cholesky/index.html b/dev/cholesky/index.html index 94047bb880..6671ae2098 100644 --- a/dev/cholesky/index.html +++ b/dev/cholesky/index.html @@ -1,2 +1,2 @@ -Cholesky-variate Distributions · Distributions.jl
    Edit on GitHub

    Cholesky-variate Distributions

    Cholesky-variate distributions are distributions whose variate forms are CholeskyVariate. This means each draw is a factorization of a positive-definite matrix of type LinearAlgebra.Cholesky (the object produced by the function LinearAlgebra.cholesky applied to a dense positive-definite matrix.)

    Distributions

    Distributions.LKJCholesky — Type
    LKJCholesky(d::Int, η::Real, uplo='L')

    The LKJCholesky distribution of size $d$ with shape parameter $\eta$ is a distribution over LinearAlgebra.Cholesky factorisations of $d\times d$ real correlation matrices (positive-definite matrices with ones on the diagonal).

    Variates or samples of the distribution are LinearAlgebra.Cholesky objects, as might be returned by F = LinearAlgebra.cholesky(R), so that Matrix(F) ≈ R is a variate or sample of LKJ.

    Sampling LKJCholesky is faster than sampling LKJ, and often having the correlation matrix in factorized form makes subsequent computations cheaper as well.

    Note

    LinearAlgebra.Cholesky stores either the upper or lower Cholesky factor, related by F.U == F.L'. Both can be accessed with F.U and F.L, but if the factor not stored is requested, then a copy is made. The uplo parameter specifies whether the upper ('U') or lower ('L') Cholesky factor is stored when randomly generating samples. Set uplo to 'U' if the upper factor is desired to avoid allocating a copy when calling F.U.

    See LKJ for more details.

    External links

    • Lewandowski D, Kurowicka D, Joe H. Generating random correlation matrices based on vines and extended onion method, Journal of Multivariate Analysis (2009), 100(9): 1989-2001 doi: 10.1016/j.jmva.2009.04.008
    source

    Index

    +Cholesky-variate Distributions · Distributions.jl
    GitHub

    Cholesky-variate Distributions

    Cholesky-variate distributions are distributions whose variate forms are CholeskyVariate. This means each draw is a factorization of a positive-definite matrix of type LinearAlgebra.Cholesky (the object produced by the function LinearAlgebra.cholesky applied to a dense positive-definite matrix.)

    Distributions

    Distributions.LKJCholesky — Type
    LKJCholesky(d::Int, η::Real, uplo='L')

    The LKJCholesky distribution of size $d$ with shape parameter $\eta$ is a distribution over LinearAlgebra.Cholesky factorisations of $d\times d$ real correlation matrices (positive-definite matrices with ones on the diagonal).

    Variates or samples of the distribution are LinearAlgebra.Cholesky objects, as might be returned by F = LinearAlgebra.cholesky(R), so that Matrix(F) ≈ R is a variate or sample of LKJ.

    Sampling LKJCholesky is faster than sampling LKJ, and often having the correlation matrix in factorized form makes subsequent computations cheaper as well.

    Note

    LinearAlgebra.Cholesky stores either the upper or lower Cholesky factor, related by F.U == F.L'. Both can be accessed with F.U and F.L, but if the factor not stored is requested, then a copy is made. The uplo parameter specifies whether the upper ('U') or lower ('L') Cholesky factor is stored when randomly generating samples. Set uplo to 'U' if the upper factor is desired to avoid allocating a copy when calling F.U.

    See LKJ for more details.

    External links

    • Lewandowski D, Kurowicka D, Joe H. Generating random correlation matrices based on vines and extended onion method, Journal of Multivariate Analysis (2009), 100(9): 1989-2001 doi: 10.1016/j.jmva.2009.04.008
    source

    Index

    diff --git a/dev/convolution/index.html b/dev/convolution/index.html index c6699272a2..4ddad6636c 100644 --- a/dev/convolution/index.html +++ b/dev/convolution/index.html @@ -1,2 +1,2 @@ -Convolutions · Distributions.jl
    Edit on GitHub

    Convolutions

    A convolution of two probability distributions is the probability distribution of the sum of two independent random variables that are distributed according to these distributions.

    The convolution of two distributions can be constructed with convolve.

    Distributions.convolve — Function
    convolve(d1::Distribution, d2::Distribution)

    Convolve two distributions and return the distribution corresponding to the sum of independent random variables drawn from the underlying distributions.

    Currently, the function is only defined in cases where the convolution has a closed form. More precisely, the function is defined if the distributions of d1 and d2 are the same and one of

    External links: List of convolutions of probability distributions on Wikipedia

    source
    +Convolutions · Distributions.jl
    GitHub

    Convolutions

    A convolution of two probability distributions is the probability distribution of the sum of two independent random variables that are distributed according to these distributions.

    The convolution of two distributions can be constructed with convolve.

    Distributions.convolve — Function
    convolve(d1::Distribution, d2::Distribution)

    Convolve two distributions and return the distribution corresponding to the sum of independent random variables drawn from the underlying distributions.

    Currently, the function is only defined in cases where the convolution has a closed form. More precisely, the function is defined if the distributions of d1 and d2 are the same and one of

    External links: List of convolutions of probability distributions on Wikipedia

    source
    diff --git a/dev/density_interface/index.html b/dev/density_interface/index.html index ce66703b1c..41c7d3eff9 100644 --- a/dev/density_interface/index.html +++ b/dev/density_interface/index.html @@ -1,2 +1,2 @@ -Support for DensityInterface · Distributions.jl
    Edit on GitHub

    Support for DensityInterface

    Distributions supports DensityInterface for distributions.

    A probability distribution has a probability density, so DensityInterface.DensityKind(::Distribution) === HasDensity().

    For single variate values x, DensityInterface.logdensityof(d::Distribution, x) is equivalent to logpdf(d, x) and DensityInterface.densityof(d::Distribution, x) is equivalent to pdf(d, x).

    +Support for DensityInterface · Distributions.jl
    GitHub

    Support for DensityInterface

    Distributions supports DensityInterface for distributions.

    A probability distribution has a probability density, so DensityInterface.DensityKind(::Distribution) === HasDensity().

    For single variate values x, DensityInterface.logdensityof(d::Distribution, x) is equivalent to logpdf(d, x) and DensityInterface.densityof(d::Distribution, x) is equivalent to pdf(d, x).

    diff --git a/dev/extends/index.html b/dev/extends/index.html index fbcfa66cd3..b1e8926edf 100644 --- a/dev/extends/index.html +++ b/dev/extends/index.html @@ -1,5 +1,5 @@ -Create New Samplers and Distributions · Distributions.jl
    Edit on GitHub

    Create New Samplers and Distributions

    Whereas this package already provides a large collection of common distributions out of the box, there are still occasions where you want to create new distributions (e.g. your application requires a special kind of distribution, or you want to contribute to this package).

    Generally, you don't have to implement every API method listed in the documentation. This package provides a series of generic functions that turn a small number of internal methods into user-end API methods. What you need to do is to implement this small set of internal methods for your distributions.

    By default, Discrete sampleables have the support of type Int while Continuous sampleables have the support of type Float64. If this assumption does not hold for your new distribution or sampler, or its ValueSupport is neither Discrete nor Continuous, you should implement the eltype method in addition to the other methods listed below.

    Note: The methods that need to be implemented are different for distributions of different variate forms.

    Create a Sampler

    Unlike full-fledged distributions, a sampler, in general, only provides limited functionalities, mainly to support sampling.

    Univariate Sampler

    To implement a univariate sampler, one can define a subtype (say Spl) of Sampleable{Univariate,S} (where S can be Discrete or Continuous), and provide a rand method, as

    function rand(rng::AbstractRNG, s::Spl)
+Create New Samplers and Distributions · Distributions.jl
    GitHub
    Create New Samplers and Distributions
    Whereas this package already provides a large collection of common distributions out of the box, there are still occasions where you want to create new distributions (e.g. your application requires a special kind of distribution, or you want to contribute to this package).
    Generally, you don't have to implement every API method listed in the documentation. This package provides a series of generic functions that turn a small number of internal methods into user-end API methods. What you need to do is to implement this small set of internal methods for your distributions.
    By default, Discrete sampleables have the support of type Int while Continuous sampleables have the support of type Float64. If this assumption does not hold for your new distribution or sampler, or its ValueSupport is neither Discrete nor Continuous, you should implement the eltype method in addition to the other methods listed below.
    Note: The methods that need to be implemented are different for distributions of different variate forms.
    Create a Sampler
    Unlike full-fledged distributions, a sampler, in general, only provides limited functionalities, mainly to support sampling.
    Univariate Sampler
    To implement a univariate sampler, one can define a subtype (say Spl) of Sampleable{Univariate,S} (where S can be Discrete or Continuous), and provide a rand method, as
    function rand(rng::AbstractRNG, s::Spl)
     # ... generate a single sample from s
 end
    The package already implements a vectorized version of rand! and rand that repeatedly calls the scalar version to generate multiple samples; as wells as a one arg version that uses the default random number generator.
    Multivariate Sampler
    To implement a multivariate sampler, one can define a subtype of Sampleable{Multivariate,S}, and provide both length and _rand! methods, as
    Base.length(s::Spl) = ... # return the length of each sample
 
@@ -34,5 +34,5 @@
 
 function _rand!(rng::AbstractRNG, s::Spl, x::DenseMatrix{T}) where T<:Real
     # ... generate a single matrix sample to x
-end
    Note that you can assume x has correct dimensions in _rand! and don't have to perform dimension checking, the generic rand and rand! will do dimension checking and array allocation for you.
    Create a Distribution
    Most distributions should implement a sampler method to improve batch sampling efficiency.
    Distributions.sampler — Method
    sampler(d::Distribution) -> Sampleable
-sampler(s::Sampleable) -> s
    Samplers can often rely on pre-computed quantities (that are not parameters themselves) to improve efficiency. If such a sampler exists, it can be provided with this sampler method, which would be used for batch sampling. The general fallback is sampler(d::Distribution) = d.
    source
    Univariate Distribution
    A univariate distribution type should be defined as a subtype of DiscreteUnivarateDistribution or ContinuousUnivariateDistribution.
    The following methods need to be implemented for each univariate distribution type:
    It is also recommended that one also implements the following statistics functions:
    You may refer to the source file src/univariates.jl to see details about how generic fallback functions for univariates are implemented.
    Create a Multivariate Distribution
    A multivariate distribution type should be defined as a subtype of DiscreteMultivarateDistribution or ContinuousMultivariateDistribution.
    The following methods need to be implemented for each multivariate distribution type:
    Note that if there exist faster methods for batch evaluation, one should override _logpdf! and _pdf!.
    Furthermore, the generic loglikelihood function repeatedly calls _logpdf. If there is a better way to compute the log-likelihood, one should override loglikelihood.
    It is also recommended that one also implements the following statistics functions:
    Create a Matrix-Variate Distribution
    A matrix-variate distribution type should be defined as a subtype of DiscreteMatrixDistribution or ContinuousMatrixDistribution.
    The following methods need to be implemented for each matrix-variate distribution type:
    
+end

    Note that you can assume x has correct dimensions in _rand! and don't have to perform dimension checking, the generic rand and rand! will do dimension checking and array allocation for you.

    Create a Distribution

    Most distributions should implement a sampler method to improve batch sampling efficiency.

    Distributions.sampler — Method
    sampler(d::Distribution) -> Sampleable
+sampler(s::Sampleable) -> s

    Samplers can often rely on pre-computed quantities (that are not parameters themselves) to improve efficiency. If such a sampler exists, it can be provided with this sampler method, which would be used for batch sampling. The general fallback is sampler(d::Distribution) = d.

    source

    Univariate Distribution

    A univariate distribution type should be defined as a subtype of DiscreteUnivarateDistribution or ContinuousUnivariateDistribution.

    The following methods need to be implemented for each univariate distribution type:

    It is also recommended that one also implements the following statistics functions:

    You may refer to the source file src/univariates.jl to see details about how generic fallback functions for univariates are implemented.

    Create a Multivariate Distribution

    A multivariate distribution type should be defined as a subtype of DiscreteMultivarateDistribution or ContinuousMultivariateDistribution.

    The following methods need to be implemented for each multivariate distribution type:

    Note that if there exist faster methods for batch evaluation, one should override _logpdf! and _pdf!.

    Furthermore, the generic loglikelihood function repeatedly calls _logpdf. If there is a better way to compute the log-likelihood, one should override loglikelihood.

    It is also recommended that one also implements the following statistics functions:

    Create a Matrix-Variate Distribution

    A matrix-variate distribution type should be defined as a subtype of DiscreteMatrixDistribution or ContinuousMatrixDistribution.

    The following methods need to be implemented for each matrix-variate distribution type:

    diff --git a/dev/fit/index.html b/dev/fit/index.html index 027c233ceb..68553feade 100644 --- a/dev/fit/index.html +++ b/dev/fit/index.html @@ -1,6 +1,6 @@ -Distribution Fitting · Distributions.jl
    Edit on GitHub

    Distribution Fitting

    This package provides methods to fit a distribution to a given set of samples. Generally, one may write

    d = fit(D, x)

    This statement fits a distribution of type D to a given dataset x, where x should be an array comprised of all samples. The fit function will choose a reasonable way to fit the distribution, which, in most cases, is maximum likelihood estimation.

    Note

    One can use as the first argument simply the distribution name, like Binomial, or a concrete distribution with a type parameter, like Normal{Float64} or Exponential{Float32}. However, in the latter case the type parameter of the distribution will be ignored:

    julia> fit(Cauchy{Float32}, collect(-4:4))
-Cauchy{Float64}(μ=0.0, σ=2.0)

    Maximum Likelihood Estimation

    The function fit_mle is for maximum likelihood estimation.

    Synopsis

    Missing docstring.

    Missing docstring for fit(D, x). Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for fit(D, x, w). Check Documenter's build log for details.

    Distributions.fit_mle — Method
    fit_mle(D, x)

    Fit a distribution of type D to a given data set x.

    • For univariate distribution, x can be an array of arbitrary size.
    • For multivariate distribution, x should be a matrix, where each column is a sample.
    source
    Distributions.fit_mle — Method
    fit_mle(D, x, w)

    Fit a distribution of type D to a weighted data set x, with weights given by w.

    Here, w should be an array with length n, where n is the number of samples contained in x.

    source

    Applicable distributions

    The fit_mle method has been implemented for the following distributions:

    Univariate:

    Multivariate:

    For most of these distributions, the usage is as described above. For a few special distributions that require additional information for estimation, we have to use a modified interface:

    fit_mle(Binomial, n, x)        # n is the number of trials in each experiment
+Distribution Fitting · Distributions.jl
    GitHub
    Distribution Fitting
    This package provides methods to fit a distribution to a given set of samples. Generally, one may write
    d = fit(D, x)
    This statement fits a distribution of type D to a given dataset x, where x should be an array comprised of all samples. The fit function will choose a reasonable way to fit the distribution, which, in most cases, is maximum likelihood estimation.
    Note
    One can use as the first argument simply the distribution name, like Binomial, or a concrete distribution with a type parameter, like Normal{Float64} or Exponential{Float32}.  However, in the latter case the type parameter of the distribution will be ignored:
    julia> fit(Cauchy{Float32}, collect(-4:4))
+Cauchy{Float64}(μ=0.0, σ=2.0)
    Maximum Likelihood Estimation
    The function fit_mle is for maximum likelihood estimation.
    Synopsis
    Missing docstring.
    Missing docstring for fit(D, x). Check Documenter's build log for details.
    Missing docstring.
    Missing docstring for fit(D, x, w). Check Documenter's build log for details.
    Distributions.fit_mle — Method
    fit_mle(D, x)
    Fit a distribution of type D to a given data set x.
    • For univariate distribution, x can be an array of arbitrary size.
    • For multivariate distribution, x should be a matrix, where each column is a sample.
    source
    Distributions.fit_mle — Method
    fit_mle(D, x, w)
    Fit a distribution of type D to a weighted data set x, with weights given by w.
    Here, w should be an array with length n, where n is the number of samples contained in x.
    source
    Applicable distributions
    The fit_mle method has been implemented for the following distributions:
    Univariate:
    Multivariate:
    For most of these distributions, the usage is as described above. For a few special distributions that require additional information for estimation, we have to use a modified interface:
    fit_mle(Binomial, n, x)        # n is the number of trials in each experiment
 fit_mle(Binomial, n, x, w)
 
 fit_mle(Categorical, k, x)     # k is the space size (i.e. the number of distinct values)
@@ -10,4 +10,4 @@
 fit_mle(Categorical, x, w)
    Sufficient Statistics
    For many distributions, the estimation can be based on (sum of) sufficient statistics computed from a dataset. To simplify implementation, for such distributions, we implement suffstats method instead of fit_mle directly:
    ss = suffstats(D, x)        # ss captures the sufficient statistics of x
 ss = suffstats(D, x, w)     # ss captures the sufficient statistics of a weighted dataset
 
-d = fit_mle(D, ss)          # maximum likelihood estimation based on sufficient stats
    When fit_mle on D is invoked, a fallback fit_mle method will first call suffstats to compute the sufficient statistics, and then a fit_mle method on sufficient statistics to get the result. For some distributions, this way is not the most efficient, and we specialize the fit_mle method to implement more efficient estimation algorithms.
    Maximum-a-Posteriori Estimation
    Maximum-a-Posteriori (MAP) estimation is also supported by this package, which is implemented as part of the conjugate exponential family framework (see :ref:Conjugate Prior and Posterior <ref-conj>).
    
+d = fit_mle(D, ss)          # maximum likelihood estimation based on sufficient stats

    When fit_mle on D is invoked, a fallback fit_mle method will first call suffstats to compute the sufficient statistics, and then a fit_mle method on sufficient statistics to get the result. For some distributions, this way is not the most efficient, and we specialize the fit_mle method to implement more efficient estimation algorithms.

    Maximum-a-Posteriori Estimation

    Maximum-a-Posteriori (MAP) estimation is also supported by this package, which is implemented as part of the conjugate exponential family framework (see :ref:Conjugate Prior and Posterior <ref-conj>).

    diff --git a/dev/index.html b/dev/index.html index f5219354ff..5902652a64 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,2 +1,2 @@ -Distributions Package · Distributions.jl
    Edit on GitHub

    Distributions Package

    The Distributions package provides a large collection of probabilistic distributions and related functions. Particularly, Distributions implements:

    • Sampling from distributions
    • Moments (e.g mean, variance, skewness, and kurtosis), entropy, and other properties
    • Probability density/mass functions (pdf) and their logarithm (logpdf)
    • Moment-generating functions and characteristic functions
    • Maximum likelihood estimation
    • Distribution composition and derived distributions (Cartesian product of distributions, truncated distributions, censored distributions)
    +Distributions Package · Distributions.jl
    GitHub

    Distributions Package

    The Distributions package provides a large collection of probabilistic distributions and related functions. Particularly, Distributions implements:

    • Sampling from distributions
    • Moments (e.g mean, variance, skewness, and kurtosis), entropy, and other properties
    • Probability density/mass functions (pdf) and their logarithm (logpdf)
    • Moment-generating functions and characteristic functions
    • Maximum likelihood estimation
    • Distribution composition and derived distributions (Cartesian product of distributions, truncated distributions, censored distributions)
    diff --git a/dev/matrix/index.html b/dev/matrix/index.html index c27b3e31d6..012a18043e 100644 --- a/dev/matrix/index.html +++ b/dev/matrix/index.html @@ -1,31 +1,31 @@ -Matrix-variate Distributions · Distributions.jl
    Edit on GitHub

    Matrix-variate Distributions

    Matrix-variate distributions are the distributions whose variate forms are Matrixvariate (i.e each sample is a matrix). Abstract types for matrix-variate distributions:

    const MatrixDistribution{S<:ValueSupport} = Distribution{Matrixvariate,S}
+Matrix-variate Distributions · Distributions.jl
    GitHub
    Matrix-variate Distributions
    Matrix-variate distributions are the distributions whose variate forms are Matrixvariate (i.e each sample is a matrix). Abstract types for matrix-variate distributions:
    const MatrixDistribution{S<:ValueSupport} = Distribution{Matrixvariate,S}
 
 const DiscreteMatrixDistribution   = Distribution{Matrixvariate, Discrete}
-const ContinuousMatrixDistribution = Distribution{Matrixvariate, Continuous}
    More advanced functionalities related to random matrices can be found in the RandomMatrices.jl package.
    Common Interface
    All distributions implement the same set of methods:
    Base.size — Method
    size(d::MatrixDistribution)
    Return the size of each sample from distribution d.
    source
    Base.length — Method
    length(d::MatrixDistribution)
    The length (i.e number of elements) of each sample from the distribution d.
    source
    Statistics.var — Method
    var(d::MatrixDistribution)
    Compute the matrix of element-wise variances for distribution d.
    source
    Statistics.cov — Method
    cov(d::MatrixDistribution)
    Compute the covariance matrix for vec(X), where X is a random matrix with distribution d.
    source
    Distributions.pdf — Method
    pdf(d::Distribution{ArrayLikeVariate{N}}, x::AbstractArray{<:Real,N}) where {N}
    Evaluate the probability density function of d at x.
    This function checks if the size of x is compatible with distribution d. This check can be disabled by using @inbounds.
    Implementation
    Instead of pdf one should implement _pdf(d, x) which does not have to check the size of x. However, since the default definition of pdf(d, x) falls back to logpdf(d, x) usually it is sufficient to implement logpdf.
    See also: logpdf.
    source
    Distributions.logpdf — Method
    logpdf(d::Distribution{ArrayLikeVariate{N}}, x::AbstractArray{<:Real,N}) where {N}
    Evaluate the logarithm of the probability density function of d at x.
    This function checks if the size of x is compatible with distribution d. This check can be disabled by using @inbounds.
    Implementation
    Instead of logpdf one should implement _logpdf(d, x) which does not have to check the size of x.
    See also: pdf.
    source
    Missing docstring.
    Missing docstring for Distributions._rand!(::AbstractRNG, ::MatrixDistribution, A::AbstractMatrix). Check Documenter's build log for details.
    Distributions
    Distributions.MatrixNormal — Type
    MatrixNormal(M, U, V)
    M::AbstractMatrix  n x p mean
+const ContinuousMatrixDistribution = Distribution{Matrixvariate, Continuous}
    More advanced functionalities related to random matrices can be found in the RandomMatrices.jl package.
    Common Interface
    All distributions implement the same set of methods:
    Base.size — Method
    size(d::MatrixDistribution)
    Return the size of each sample from distribution d.
    source
    Base.length — Method
    length(d::MatrixDistribution)
    The length (i.e number of elements) of each sample from the distribution d.
    source
    Statistics.var — Method
    var(d::MatrixDistribution)
    Compute the matrix of element-wise variances for distribution d.
    source
    Statistics.cov — Method
    cov(d::MatrixDistribution)
    Compute the covariance matrix for vec(X), where X is a random matrix with distribution d.
    source
    Distributions.pdf — Method
    pdf(d::Distribution{ArrayLikeVariate{N}}, x::AbstractArray{<:Real,N}) where {N}
    Evaluate the probability density function of d at x.
    This function checks if the size of x is compatible with distribution d. This check can be disabled by using @inbounds.
    Implementation
    Instead of pdf one should implement _pdf(d, x) which does not have to check the size of x. However, since the default definition of pdf(d, x) falls back to logpdf(d, x) usually it is sufficient to implement logpdf.
    See also: logpdf.
    source
    Distributions.logpdf — Method
    logpdf(d::Distribution{ArrayLikeVariate{N}}, x::AbstractArray{<:Real,N}) where {N}
    Evaluate the logarithm of the probability density function of d at x.
    This function checks if the size of x is compatible with distribution d. This check can be disabled by using @inbounds.
    Implementation
    Instead of logpdf one should implement _logpdf(d, x) which does not have to check the size of x.
    See also: pdf.
    source
    Missing docstring.
    Missing docstring for Distributions._rand!(::AbstractRNG, ::MatrixDistribution, A::AbstractMatrix). Check Documenter's build log for details.
    Distributions
    Distributions.MatrixNormal — Type
    MatrixNormal(M, U, V)
    M::AbstractMatrix  n x p mean
 U::AbstractPDMat   n x n row covariance
-V::AbstractPDMat   p x p column covariance
    The matrix normal distribution generalizes the multivariate normal distribution to $n\times p$ real matrices $\mathbf{X}$. If $\mathbf{X}\sim \textrm{MN}_{n,p}(\mathbf{M}, \mathbf{U}, \mathbf{V})$, then its probability density function is
    \[f(\mathbf{X};\mathbf{M}, \mathbf{U}, \mathbf{V}) = \frac{\exp\left( -\frac{1}{2} \, \mathrm{tr}\left[ \mathbf{V}^{-1} (\mathbf{X} - \mathbf{M})^{\rm{T}} \mathbf{U}^{-1} (\mathbf{X} - \mathbf{M}) \right] \right)}{(2\pi)^{np/2} |\mathbf{V}|^{n/2} |\mathbf{U}|^{p/2}}.\]
    $\mathbf{X}\sim \textrm{MN}_{n,p}(\mathbf{M},\mathbf{U},\mathbf{V})$ if and only if $\text{vec}(\mathbf{X})\sim \textrm{N}(\text{vec}(\mathbf{M}),\mathbf{V}\otimes\mathbf{U})$.
    source
    Distributions.Wishart — Type
    Wishart(ν, S)
    ν::Real           degrees of freedom (whole number or a real number greater than p - 1)
+V::AbstractPDMat   p x p column covariance
    The matrix normal distribution generalizes the multivariate normal distribution to $n\times p$ real matrices $\mathbf{X}$. If $\mathbf{X}\sim \textrm{MN}_{n,p}(\mathbf{M}, \mathbf{U}, \mathbf{V})$, then its probability density function is
    \[f(\mathbf{X};\mathbf{M}, \mathbf{U}, \mathbf{V}) = \frac{\exp\left( -\frac{1}{2} \, \mathrm{tr}\left[ \mathbf{V}^{-1} (\mathbf{X} - \mathbf{M})^{\rm{T}} \mathbf{U}^{-1} (\mathbf{X} - \mathbf{M}) \right] \right)}{(2\pi)^{np/2} |\mathbf{V}|^{n/2} |\mathbf{U}|^{p/2}}.\]
    $\mathbf{X}\sim \textrm{MN}_{n,p}(\mathbf{M},\mathbf{U},\mathbf{V})$ if and only if $\text{vec}(\mathbf{X})\sim \textrm{N}(\text{vec}(\mathbf{M}),\mathbf{V}\otimes\mathbf{U})$.
    source
    Distributions.Wishart — Type
    Wishart(ν, S)
    ν::Real           degrees of freedom (whole number or a real number greater than p - 1)
 S::AbstractPDMat  p x p scale matrix
    The Wishart distribution generalizes the gamma distribution to $p\times p$ real, positive semidefinite matrices $\mathbf{H}$.
    If $\nu>p-1$, then $\mathbf{H}\sim \textrm{W}_p(\nu, \mathbf{S})$ has rank $p$ and its probability density function is
    \[f(\mathbf{H};\nu,\mathbf{S}) = \frac{1}{2^{\nu p/2} \left|\mathbf{S}\right|^{\nu/2} \Gamma_p\left(\frac {\nu}{2}\right ) }{\left|\mathbf{H}\right|}^{(\nu-p-1)/2} e^{-(1/2)\operatorname{tr}(\mathbf{S}^{-1}\mathbf{H})}.\]
    If $\nu\leq p-1$, then $\mathbf{H}$ is rank $\nu$ and it has a density with respect to a suitably chosen volume element on the space of positive semidefinite matrices. See here.
    For integer $\nu$, a random matrix given by
    \[\mathbf{H} = \mathbf{X}\mathbf{X}^{\rm{T}},
-\quad\mathbf{X} \sim \textrm{MN}_{p,\nu}(\mathbf{0}, \mathbf{S}, \mathbf{I}_{\nu})\]
    has $\mathbf{H}\sim \textrm{W}_p(\nu, \mathbf{S})$. For non-integer $\nu$, Wishart matrices can be generated via the Bartlett decomposition.
    source
    Distributions.InverseWishart — Type
    InverseWishart(ν, Ψ)
    ν::Real           degrees of freedom (greater than p - 1)
+\quad\mathbf{X} \sim \textrm{MN}_{p,\nu}(\mathbf{0}, \mathbf{S}, \mathbf{I}_{\nu})\]
    has $\mathbf{H}\sim \textrm{W}_p(\nu, \mathbf{S})$. For non-integer $\nu$, Wishart matrices can be generated via the Bartlett decomposition.
    source
    Distributions.InverseWishart — Type
    InverseWishart(ν, Ψ)
    ν::Real           degrees of freedom (greater than p - 1)
 Ψ::AbstractPDMat  p x p scale matrix
    The inverse Wishart distribution generalizes the inverse gamma distribution to $p\times p$ real, positive definite matrices $\boldsymbol{\Sigma}$. If $\boldsymbol{\Sigma}\sim \textrm{IW}_p(\nu,\boldsymbol{\Psi})$, then its probability density function is
    \[f(\boldsymbol{\Sigma}; \nu,\boldsymbol{\Psi}) =
-\frac{\left|\boldsymbol{\Psi}\right|^{\nu/2}}{2^{\nu p/2}\Gamma_p(\frac{\nu}{2})} \left|\boldsymbol{\Sigma}\right|^{-(\nu+p+1)/2} e^{-\frac{1}{2}\operatorname{tr}(\boldsymbol{\Psi}\boldsymbol{\Sigma}^{-1})}.\]
    $\mathbf{H}\sim \textrm{W}_p(\nu, \mathbf{S})$ if and only if $\mathbf{H}^{-1}\sim \textrm{IW}_p(\nu, \mathbf{S}^{-1})$.
    source
    Distributions.MatrixTDist — Type
    MatrixTDist(ν, M, Σ, Ω)
    ν::Real            positive degrees of freedom
+\frac{\left|\boldsymbol{\Psi}\right|^{\nu/2}}{2^{\nu p/2}\Gamma_p(\frac{\nu}{2})} \left|\boldsymbol{\Sigma}\right|^{-(\nu+p+1)/2} e^{-\frac{1}{2}\operatorname{tr}(\boldsymbol{\Psi}\boldsymbol{\Sigma}^{-1})}.\]
    $\mathbf{H}\sim \textrm{W}_p(\nu, \mathbf{S})$ if and only if $\mathbf{H}^{-1}\sim \textrm{IW}_p(\nu, \mathbf{S}^{-1})$.
    source
    Distributions.MatrixTDist — Type
    MatrixTDist(ν, M, Σ, Ω)
    ν::Real            positive degrees of freedom
 M::AbstractMatrix  n x p location
 Σ::AbstractPDMat   n x n scale
 Ω::AbstractPDMat   p x p scale
    The matrix t-distribution generalizes the multivariate t-distribution to $n\times p$ real matrices $\mathbf{X}$. If $\mathbf{X}\sim \textrm{MT}_{n,p}(\nu,\mathbf{M},\boldsymbol{\Sigma}, \boldsymbol{\Omega})$, then its probability density function is
    \[f(\mathbf{X} ; \nu,\mathbf{M},\boldsymbol{\Sigma}, \boldsymbol{\Omega}) =
 c_0 \left|\mathbf{I}_n + \boldsymbol{\Sigma}^{-1}(\mathbf{X} - \mathbf{M})\boldsymbol{\Omega}^{-1}(\mathbf{X}-\mathbf{M})^{\rm{T}}\right|^{-\frac{\nu+n+p-1}{2}},\]
    where
    \[c_0=\frac{\Gamma_p\left(\frac{\nu+n+p-1}{2}\right)}{(\pi)^\frac{np}{2} \Gamma_p\left(\frac{\nu+p-1}{2}\right)} |\boldsymbol{\Omega}|^{-\frac{n}{2}} |\boldsymbol{\Sigma}|^{-\frac{p}{2}}.\]
    If the joint distribution $p(\mathbf{S},\mathbf{X})=p(\mathbf{S})p(\mathbf{X}|\mathbf{S})$ is given by
    \[\begin{aligned}
 \mathbf{S}&\sim \textrm{IW}_n(\nu + n - 1, \boldsymbol{\Sigma})\\
 \mathbf{X}|\mathbf{S}&\sim \textrm{MN}_{n,p}(\mathbf{M}, \mathbf{S}, \boldsymbol{\Omega}),
-\end{aligned}\]
    then the marginal distribution of $\mathbf{X}$ is $\textrm{MT}_{n,p}(\nu,\mathbf{M},\boldsymbol{\Sigma},\boldsymbol{\Omega})$.
    source
    Distributions.MatrixBeta — Type
    MatrixBeta(p, n1, n2)
    p::Int    dimension
+\end{aligned}\]
    then the marginal distribution of $\mathbf{X}$ is $\textrm{MT}_{n,p}(\nu,\mathbf{M},\boldsymbol{\Sigma},\boldsymbol{\Omega})$.
    source
    Distributions.MatrixBeta — Type
    MatrixBeta(p, n1, n2)
    p::Int    dimension
 n1::Real  degrees of freedom (greater than p - 1)
 n2::Real  degrees of freedom (greater than p - 1)
    The matrix beta distribution generalizes the beta distribution to $p\times p$ real matrices $\mathbf{U}$ for which $\mathbf{U}$ and $\mathbf{I}_p-\mathbf{U}$ are both positive definite. If $\mathbf{U}\sim \textrm{MB}_p(n_1/2, n_2/2)$, then its probability density function is
    \[f(\mathbf{U}; n_1,n_2) = \frac{\Gamma_p(\frac{n_1+n_2}{2})}{\Gamma_p(\frac{n_1}{2})\Gamma_p(\frac{n_2}{2})}
-|\mathbf{U}|^{(n_1-p-1)/2}\left|\mathbf{I}_p-\mathbf{U}\right|^{(n_2-p-1)/2}.\]
    If $\mathbf{S}_1\sim \textrm{W}_p(n_1,\mathbf{I}_p)$ and $\mathbf{S}_2\sim \textrm{W}_p(n_2,\mathbf{I}_p)$ are independent, and we use $\mathcal{L}(\cdot)$ to denote the lower Cholesky factor, then
    \[\mathbf{U}=\mathcal{L}(\mathbf{S}_1+\mathbf{S}_2)^{-1}\mathbf{S}_1\mathcal{L}(\mathbf{S}_1+\mathbf{S}_2)^{-\rm{T}}\]
    has $\mathbf{U}\sim \textrm{MB}_p(n_1/2, n_2/2)$.
    source
    Distributions.MatrixFDist — Type
    MatrixFDist(n1, n2, B)
    n1::Real          degrees of freedom (greater than p - 1)
+|\mathbf{U}|^{(n_1-p-1)/2}\left|\mathbf{I}_p-\mathbf{U}\right|^{(n_2-p-1)/2}.\]
    If $\mathbf{S}_1\sim \textrm{W}_p(n_1,\mathbf{I}_p)$ and $\mathbf{S}_2\sim \textrm{W}_p(n_2,\mathbf{I}_p)$ are independent, and we use $\mathcal{L}(\cdot)$ to denote the lower Cholesky factor, then
    \[\mathbf{U}=\mathcal{L}(\mathbf{S}_1+\mathbf{S}_2)^{-1}\mathbf{S}_1\mathcal{L}(\mathbf{S}_1+\mathbf{S}_2)^{-\rm{T}}\]
    has $\mathbf{U}\sim \textrm{MB}_p(n_1/2, n_2/2)$.
    source
    Distributions.MatrixFDist — Type
    MatrixFDist(n1, n2, B)
    n1::Real          degrees of freedom (greater than p - 1)
 n2::Real          degrees of freedom (greater than p - 1)
 B::AbstractPDMat  p x p scale
    The matrix F-distribution (sometimes called the matrix beta type II distribution) generalizes the F-Distribution to $p\times p$ real, positive definite matrices $\boldsymbol{\Sigma}$. If $\boldsymbol{\Sigma}\sim \textrm{MF}_{p}(n_1/2,n_2/2,\mathbf{B})$, then its probability density function is
    \[f(\boldsymbol{\Sigma} ; n_1,n_2,\mathbf{B}) =
 \frac{\Gamma_p(\frac{n_1+n_2}{2})}{\Gamma_p(\frac{n_1}{2})\Gamma_p(\frac{n_2}{2})}
 |\mathbf{B}|^{n_2/2}|\boldsymbol{\Sigma}|^{(n_1-p-1)/2}|\mathbf{B}+\boldsymbol{\Sigma}|^{-(n_1+n_2)/2}.\]
    If the joint distribution $p(\boldsymbol{\Psi},\boldsymbol{\Sigma})=p(\boldsymbol{\Psi})p(\boldsymbol{\Sigma}|\boldsymbol{\Psi})$ is given by
    \[\begin{aligned}
 \boldsymbol{\Psi}&\sim \textrm{W}_p(n_1, \mathbf{B})\\
 \boldsymbol{\Sigma}|\boldsymbol{\Psi}&\sim \textrm{IW}_p(n_2, \boldsymbol{\Psi}),
-\end{aligned}\]
    then the marginal distribution of $\boldsymbol{\Sigma}$ is $\textrm{MF}_{p}(n_1/2,n_2/2,\mathbf{B})$.
    source
    Distributions.LKJ — Type
    LKJ(d, η)
    d::Int   dimension
+\end{aligned}\]
    then the marginal distribution of $\boldsymbol{\Sigma}$ is $\textrm{MF}_{p}(n_1/2,n_2/2,\mathbf{B})$.
    source
    Distributions.LKJ — Type
    LKJ(d, η)
    d::Int   dimension
 η::Real  positive shape
    The LKJ distribution is a distribution over $d\times d$ real correlation matrices (positive-definite matrices with ones on the diagonal). If $\mathbf{R}\sim \textrm{LKJ}_{d}(\eta)$, then its probability density function is
    \[f(\mathbf{R};\eta) = \left[\prod_{k=1}^{d-1}\pi^{\frac{k}{2}}
 \frac{\Gamma\left(\eta+\frac{d-1-k}{2}\right)}{\Gamma\left(\eta+\frac{d-1}{2}\right)}\right]^{-1}
-|\mathbf{R}|^{\eta-1}.\]
    If $\eta = 1$, then the LKJ distribution is uniform over the space of correlation matrices.
    Note
    if a Cholesky factor of the correlation matrix is desired, it is more efficient to use LKJCholesky, which avoids factorizing the matrix.
    source
    Internal Methods (for creating your own matrix-variate distributions)
    Missing docstring.
    Missing docstring for Distributions._logpdf(d::MatrixDistribution, x::AbstractMatrix{<:Real}). Check Documenter's build log for details.
    Index
    
+|\mathbf{R}|^{\eta-1}.\]
    If $\eta = 1$, then the LKJ distribution is uniform over the space of correlation matrices.
    Note
    if a Cholesky factor of the correlation matrix is desired, it is more efficient to use LKJCholesky, which avoids factorizing the matrix.
    source

    Internal Methods (for creating your own matrix-variate distributions)

    Missing docstring.

    Missing docstring for Distributions._logpdf(d::MatrixDistribution, x::AbstractMatrix{<:Real}). Check Documenter's build log for details.

    Index

    diff --git a/dev/mixture/index.html b/dev/mixture/index.html index d7936afa7a..1db864c058 100644 --- a/dev/mixture/index.html +++ b/dev/mixture/index.html @@ -1,5 +1,5 @@ -Mixture Models · Distributions.jl
    Edit on GitHub

    Mixture Models

    A mixture model is a probabilistic distribution that combines a set of components to represent the overall distribution. Generally, the probability density/mass function is given by a convex combination of the pdf/pmf of individual components, as

    \[f_{mix}(x; \Theta, \pi) = \sum_{k=1}^K \pi_k f(x; \theta_k)\]

    A mixture model is characterized by a set of component parameters $\Theta=\{\theta_1, \ldots, \theta_K\}$ and a prior distribution $\pi$ over these components.

    Type Hierarchy

    This package introduces a type MixtureModel, defined as follows, to represent a mixture model:

    abstract type AbstractMixtureModel{VF<:VariateForm,VS<:ValueSupport} <: Distribution{VF, VS} end
+Mixture Models · Distributions.jl
    GitHub
    Mixture Models
    A mixture model is a probabilistic distribution that combines a set of components to represent the overall distribution. Generally, the probability density/mass function is given by a convex combination of the pdf/pmf of individual components, as
    \[f_{mix}(x; \Theta, \pi) = \sum_{k=1}^K \pi_k f(x; \theta_k)\]
    A mixture model is characterized by a set of component parameters $\Theta=\{\theta_1, \ldots, \theta_K\}$ and a prior distribution $\pi$ over these components.
    Type Hierarchy
    This package introduces a type MixtureModel, defined as follows, to represent a mixture model:
    abstract type AbstractMixtureModel{VF<:VariateForm,VS<:ValueSupport} <: Distribution{VF, VS} end
 
 struct MixtureModel{VF<:VariateForm,VS<:ValueSupport,Component<:Distribution} <: AbstractMixtureModel{VF,VS}
     components::Vector{Component}
@@ -7,7 +7,7 @@
 end
 
 const UnivariateMixture    = AbstractMixtureModel{Univariate}
-const MultivariateMixture  = AbstractMixtureModel{Multivariate}
    Remarks:
    • We introduce AbstractMixtureModel as a base type, which allows one to define a mixture model with different internal implementations, while still being able to leverage the common methods defined for AbstractMixtureModel.
    Distributions.AbstractMixtureModel — Type
    All subtypes of AbstractMixtureModel should implement the following methods:
    • ncomponents(d): the number of components
    • component(d, k):  return the k-th component
    • probs(d):       return a vector of prior probabilities over components.
    source
    • The MixtureModel is a parametric type, with three type parameters:
      • VF: the variate form, which can be Univariate, Multivariate, or Matrixvariate.
      • VS: the value support, which can be Continuous or Discrete.
      • Component: the type of component distributions, e.g. Normal.
    • We define two aliases: UnivariateMixture and MultivariateMixture.
    With such a type system, the type for a mixture of univariate normal distributions can be written as
    MixtureModel{Univariate,Continuous,Normal}
    Constructors
    Distributions.MixtureModel — Type
    MixtureModel{VF<:VariateForm,VS<:ValueSupport,C<:Distribution,CT<:Real} A mixture of distributions, parametrized on:
    • VF,VS variate and support
    • C distribution family of the mixture
    • CT the type for probabilities of the prior
    source
    Examples
    # constructs a mixture of three normal distributions,
+const MultivariateMixture  = AbstractMixtureModel{Multivariate}
    Remarks:
    • We introduce AbstractMixtureModel as a base type, which allows one to define a mixture model with different internal implementations, while still being able to leverage the common methods defined for AbstractMixtureModel.
    Distributions.AbstractMixtureModel — Type
    All subtypes of AbstractMixtureModel should implement the following methods:
    • ncomponents(d): the number of components
    • component(d, k):  return the k-th component
    • probs(d):       return a vector of prior probabilities over components.
    source
    • The MixtureModel is a parametric type, with three type parameters:
      • VF: the variate form, which can be Univariate, Multivariate, or Matrixvariate.
      • VS: the value support, which can be Continuous or Discrete.
      • Component: the type of component distributions, e.g. Normal.
    • We define two aliases: UnivariateMixture and MultivariateMixture.
    With such a type system, the type for a mixture of univariate normal distributions can be written as
    MixtureModel{Univariate,Continuous,Normal}
    Constructors
    Distributions.MixtureModel — Type
    MixtureModel{VF<:VariateForm,VS<:ValueSupport,C<:Distribution,CT<:Real} A mixture of distributions, parametrized on:
    • VF,VS variate and support
    • C distribution family of the mixture
    • CT the type for probabilities of the prior
    source
    Examples
    # constructs a mixture of three normal distributions,
 # with prior probabilities [0.2, 0.5, 0.3]
 MixtureModel(Normal[
    Normal(-2.0, 1.2),
@@ -28,4 +28,4 @@
 
 # The following example shows how one can make a Gaussian mixture
 # where all components share the same unit variance
-MixtureModel(map(u -> Normal(u, 1.0), [-2.0, 0.0, 3.0]))
    Common Interface
    All subtypes of AbstractMixtureModel (obviously including MixtureModel) provide the following two methods:
    Distributions.probs — Method
    probs(d::AbstractMixtureModel)
    Get the vector of prior probabilities of all components of d.
    source
    In addition, for all subtypes of UnivariateMixture and MultivariateMixture, the following generic methods are provided:
    Statistics.mean — Method
    mean(d::Union{UnivariateMixture, MultivariateMixture})
    Compute the overall mean (expectation).
    source
    Statistics.var — Method
    var(d::UnivariateMixture)
    Compute the overall variance (only for UnivariateMixture).
    source
    Base.length — Method
    length(d::MultivariateMixture)
    The length of each sample (only for Multivariate).
    source
    Distributions.pdf — Method
    pdf(d::Union{UnivariateMixture, MultivariateMixture}, x)
    Evaluate the (mixed) probability density function over x. Here, x can be a single sample or an array of multiple samples.
    source
    Distributions.logpdf — Method
    logpdf(d::Union{UnivariateMixture, MultivariateMixture}, x)
    Evaluate the logarithm of the (mixed) probability density function over x. Here, x can be a single sample or an array of multiple samples.
    source
    Base.rand — Method
    rand(d::Union{UnivariateMixture, MultivariateMixture})
    Draw a sample from the mixture model d.
    rand(d::Union{UnivariateMixture, MultivariateMixture}, n)
    Draw n samples from d.
    source
    Random.rand! — Method
    rand!(d::Union{UnivariateMixture, MultivariateMixture}, r::AbstractArray)
    Draw multiple samples from d and write them to r.
    source
    Estimation
    There are several methods for the estimation of mixture models from data, and this problem remains an open research topic. This package does not provide facilities for estimating mixture models. One can resort to other packages, e.g. GaussianMixtures.jl, for this purpose.
    
+MixtureModel(map(u -> Normal(u, 1.0), [-2.0, 0.0, 3.0]))

    Common Interface

    All subtypes of AbstractMixtureModel (obviously including MixtureModel) provide the following two methods:

    Distributions.probs — Method
    probs(d::AbstractMixtureModel)

    Get the vector of prior probabilities of all components of d.

    source

    In addition, for all subtypes of UnivariateMixture and MultivariateMixture, the following generic methods are provided:

    Statistics.mean — Method
    mean(d::Union{UnivariateMixture, MultivariateMixture})

    Compute the overall mean (expectation).

    source
    Statistics.var — Method
    var(d::UnivariateMixture)

    Compute the overall variance (only for UnivariateMixture).

    source
    Base.length — Method
    length(d::MultivariateMixture)

    The length of each sample (only for Multivariate).

    source
    Distributions.pdf — Method
    pdf(d::Union{UnivariateMixture, MultivariateMixture}, x)

    Evaluate the (mixed) probability density function over x. Here, x can be a single sample or an array of multiple samples.

    source
    Distributions.logpdf — Method
    logpdf(d::Union{UnivariateMixture, MultivariateMixture}, x)

    Evaluate the logarithm of the (mixed) probability density function over x. Here, x can be a single sample or an array of multiple samples.

    source
    Base.rand — Method
    rand(d::Union{UnivariateMixture, MultivariateMixture})

    Draw a sample from the mixture model d.

    rand(d::Union{UnivariateMixture, MultivariateMixture}, n)

    Draw n samples from d.

    source
    Random.rand! — Method
    rand!(d::Union{UnivariateMixture, MultivariateMixture}, r::AbstractArray)

    Draw multiple samples from d and write them to r.

    source

    Estimation

    There are several methods for the estimation of mixture models from data, and this problem remains an open research topic. This package does not provide facilities for estimating mixture models. One can resort to other packages, e.g. GaussianMixtures.jl, for this purpose.

    diff --git a/dev/multivariate/index.html b/dev/multivariate/index.html index 18c304bb61..97a68559a2 100644 --- a/dev/multivariate/index.html +++ b/dev/multivariate/index.html @@ -1,11 +1,11 @@ -Multivariate Distributions · Distributions.jl
    Edit on GitHub

    Multivariate Distributions

    Multivariate distributions are the distributions whose variate forms are Multivariate (i.e each sample is a vector). Abstract types for multivariate distributions:

    const MultivariateDistribution{S<:ValueSupport} = Distribution{Multivariate,S}
+Multivariate Distributions · Distributions.jl
    GitHub
    Multivariate Distributions
    Multivariate distributions are the distributions whose variate forms are Multivariate (i.e each sample is a vector). Abstract types for multivariate distributions:
    const MultivariateDistribution{S<:ValueSupport} = Distribution{Multivariate,S}
 
 const DiscreteMultivariateDistribution   = Distribution{Multivariate, Discrete}
-const ContinuousMultivariateDistribution = Distribution{Multivariate, Continuous}
    Common Interface
    The methods listed below are implemented for each multivariate distribution, which provides a consistent interface to work with multivariate distributions.
    Computation of statistics
    Base.length — Method
    length(d::MultivariateDistribution) -> Int
    Return the sample dimension of distribution d.
    source
    Base.size — Method
    size(d::MultivariateDistribution)
    Return the sample size of distribution d, i.e (length(d),).
    source
    Base.eltype — Method
    eltype(::Type{Sampleable})
    The default element type of a sample. This is the type of elements of the samples generated by the rand method. However, one can provide an array of different element types to store the samples using rand!.
    source
    Statistics.mean — Method
    mean(d::MultivariateDistribution)
    Compute the mean vector of distribution d.
    source
    Statistics.var — Method
    var(d::MultivariateDistribution)
    Compute the vector of element-wise variances for distribution d.
    source
    Statistics.cov — Method
    cov(d::MultivariateDistribution)
    Compute the covariance matrix for distribution d. (cor is provided based on cov).
    source
    Statistics.cor — Method
    cor(d::MultivariateDistribution)
    Computes the correlation matrix for distribution d.
    source
    StatsBase.entropy — Method
    entropy(d::MultivariateDistribution, b::Real)
    Compute the entropy value of distribution $d$, w.r.t. a given base.
    source
    Probability evaluation
    Distributions.insupport — Method
    insupport(d::MultivariateDistribution, x::AbstractArray)
    If $x$ is a vector, it returns whether x is within the support of $d$. If $x$ is a matrix, it returns whether every column in $x$ is within the support of $d$.
    source
    Missing docstring.
    Missing docstring for pdf(::MultivariateDistribution, ::AbstractArray). Check Documenter's build log for details.
    Missing docstring.
    Missing docstring for logpdf(::MultivariateDistribution, ::AbstractArray). Check Documenter's build log for details.
    StatsAPI.loglikelihood — Method
    loglikelihood(d::Distribution{ArrayLikeVariate{N}}, x) where {N}
    The log-likelihood of distribution d with respect to all variate(s) contained in x.
    Here, x can be any output of rand(d, dims...) and rand!(d, x). For instance, x can be
    • an array of dimension N with size(x) == size(d),
    • an array of dimension N + 1 with size(x)[1:N] == size(d), or
    • an array of arrays xi of dimension N with size(xi) == size(d).
    source
    Note: For multivariate distributions, the pdf value is usually very small or large, and therefore direct evaluation of the pdf may cause numerical problems. It is generally advisable to perform probability computation in log scale.
    Sampling
    Base.rand — Method
    rand(::AbstractRNG, ::Sampleable)
    Samples from the sampler and returns the result.
    source
    Random.rand! — Method
    rand!(::AbstractRNG, ::Sampleable, ::AbstractArray)
    Samples in-place from the sampler and stores the result in the provided array.
    source
    Note: In addition to these common methods, each multivariate distribution has its special methods, as introduced below.
    Distributions
    Distributions.Multinomial — Type
    The Multinomial distribution generalizes the binomial distribution. Consider n independent draws from a Categorical distribution over a finite set of size k, and let $X = (X_1, ..., X_k)$ where $X_i$ represents the number of times the element $i$ occurs, then the distribution of $X$ is a multinomial distribution. Each sample of a multinomial distribution is a k-dimensional integer vector that sums to n.
    The probability mass function is given by
    \[f(x; n, p) = \frac{n!}{x_1! \cdots x_k!} \prod_{i=1}^k p_i^{x_i},
+const ContinuousMultivariateDistribution = Distribution{Multivariate, Continuous}

    Common Interface

    The methods listed below are implemented for each multivariate distribution, which provides a consistent interface to work with multivariate distributions.

    Computation of statistics

    Base.length — Method
    length(d::MultivariateDistribution) -> Int

    Return the sample dimension of distribution d.

    source
    Base.size — Method
    size(d::MultivariateDistribution)

    Return the sample size of distribution d, i.e (length(d),).

    source
    Base.eltype — Method
    eltype(::Type{Sampleable})

    The default element type of a sample. This is the type of elements of the samples generated by the rand method. However, one can provide an array of different element types to store the samples using rand!.

    source
    Statistics.mean — Method
    mean(d::MultivariateDistribution)

    Compute the mean vector of distribution d.

    source
    Statistics.var — Method
    var(d::MultivariateDistribution)

    Compute the vector of element-wise variances for distribution d.

    source
    Statistics.cov — Method
    cov(d::MultivariateDistribution)

    Compute the covariance matrix for distribution d. (cor is provided based on cov).

    source
    Statistics.cor — Method
    cor(d::MultivariateDistribution)

    Computes the correlation matrix for distribution d.

    source
    StatsBase.entropy — Method
    entropy(d::MultivariateDistribution, b::Real)

    Compute the entropy value of distribution $d$, w.r.t. a given base.

    source

    Probability evaluation

    Distributions.insupport — Method
    insupport(d::MultivariateDistribution, x::AbstractArray)

    If $x$ is a vector, it returns whether x is within the support of $d$. If $x$ is a matrix, it returns whether every column in $x$ is within the support of $d$.

    source
    Missing docstring.

    Missing docstring for pdf(::MultivariateDistribution, ::AbstractArray). Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for logpdf(::MultivariateDistribution, ::AbstractArray). Check Documenter's build log for details.

    StatsAPI.loglikelihood — Method
    loglikelihood(d::Distribution{ArrayLikeVariate{N}}, x) where {N}

    The log-likelihood of distribution d with respect to all variate(s) contained in x.

    Here, x can be any output of rand(d, dims...) and rand!(d, x). For instance, x can be

    • an array of dimension N with size(x) == size(d),
    • an array of dimension N + 1 with size(x)[1:N] == size(d), or
    • an array of arrays xi of dimension N with size(xi) == size(d).
    source

    Note: For multivariate distributions, the pdf value is usually very small or large, and therefore direct evaluation of the pdf may cause numerical problems. It is generally advisable to perform probability computation in log scale.

    Sampling

    Base.rand — Method
    rand(::AbstractRNG, ::Sampleable)

    Samples from the sampler and returns the result.

    source
    Random.rand! — Method
    rand!(::AbstractRNG, ::Sampleable, ::AbstractArray)

    Samples in-place from the sampler and stores the result in the provided array.

    source

    Note: In addition to these common methods, each multivariate distribution has its special methods, as introduced below.

    Distributions

    Distributions.Multinomial — Type

    The Multinomial distribution generalizes the binomial distribution. Consider n independent draws from a Categorical distribution over a finite set of size k, and let $X = (X_1, ..., X_k)$ where $X_i$ represents the number of times the element $i$ occurs, then the distribution of $X$ is a multinomial distribution. Each sample of a multinomial distribution is a k-dimensional integer vector that sums to n.

    The probability mass function is given by

    \[f(x; n, p) = \frac{n!}{x_1! \cdots x_k!} \prod_{i=1}^k p_i^{x_i}, \quad x_1 + \cdots + x_k = n\]

    Multinomial(n, p)   # Multinomial distribution for n trials with probability vector p
 Multinomial(n, k)   # Multinomial distribution for n trials with equal probabilities
-                    # over 1:k
    source
    Distributions.AbstractMvNormal — Type

    The Multivariate normal distribution is a multidimensional generalization of the normal distribution. The probability density function of a d-dimensional multivariate normal distribution with mean vector $\boldsymbol{\mu}$ and covariance matrix $\boldsymbol{\Sigma}$ is:

    \[f(\mathbf{x}; \boldsymbol{\mu}, \boldsymbol{\Sigma}) = \frac{1}{(2 \pi)^{d/2} |\boldsymbol{\Sigma}|^{1/2}} + # over 1:k

    source
    Distributions.AbstractMvNormal — Type

    The Multivariate normal distribution is a multidimensional generalization of the normal distribution. The probability density function of a d-dimensional multivariate normal distribution with mean vector $\boldsymbol{\mu}$ and covariance matrix $\boldsymbol{\Sigma}$ is:

    \[f(\mathbf{x}; \boldsymbol{\mu}, \boldsymbol{\Sigma}) = \frac{1}{(2 \pi)^{d/2} |\boldsymbol{\Sigma}|^{1/2}} \exp \left( - \frac{1}{2} (\mathbf{x} - \boldsymbol{\mu})^T \Sigma^{-1} (\mathbf{x} - \boldsymbol{\mu}) \right)\]

    We realize that the mean vector and the covariance often have special forms in practice, which can be exploited to simplify the computation. For example, the mean vector is sometimes just a zero vector, while the covariance matrix can be a diagonal matrix or even in the form of $\sigma^2 \mathbf{I}$. To take advantage of such special cases, we introduce a parametric type MvNormal, defined as below, which allows users to specify the special structure of the mean and covariance.

    struct MvNormal{T<:Real,Cov<:AbstractPDMat,Mean<:AbstractVector} <: AbstractMvNormal
     μ::Mean
     Σ::Cov
@@ -17,7 +17,7 @@
 const ZeroMeanDiagNormal{Axes} = MvNormal{Float64, PDiagMat{Float64,Vector{Float64}}, Zeros{Float64,1,Axes}}
 const ZeroMeanFullNormal{Axes} = MvNormal{Float64, PDMat{Float64,Matrix{Float64}},    Zeros{Float64,1,Axes}}

    Multivariate normal distributions support affine transformations:

    d = MvNormal(μ, Σ)
 c + B * d    # == MvNormal(B * μ + c, B * Σ * B')
-dot(b, d)    # == Normal(dot(b, μ), b' * Σ * b)
    source
    Distributions.MvNormal — Type
    MvNormal

    Generally, users don't have to worry about these internal details.

    We provide a common constructor MvNormal, which will construct a distribution of appropriate type depending on the input arguments.

    source
    Distributions.MvNormalCanon — Type
    MvNormalCanon

    The multivariate normal distribution is an exponential family distribution, with two canonical parameters: the potential vector $\mathbf{h}$ and the precision matrix $\mathbf{J}$. The relation between these parameters and the conventional representation (i.e. the one using mean $\boldsymbol{\mu}$ and covariance $\boldsymbol{\Sigma}$) is:

    \[\mathbf{h} = \boldsymbol{\Sigma}^{-1} \boldsymbol{\mu}, \quad \text{ and } \quad \mathbf{J} = \boldsymbol{\Sigma}^{-1}\]

    The canonical parameterization is widely used in Bayesian analysis. We provide a type MvNormalCanon, which is also a subtype of AbstractMvNormal to represent a multivariate normal distribution using canonical parameters. Particularly, MvNormalCanon is defined as:

    struct MvNormalCanon{T<:Real,P<:AbstractPDMat,V<:AbstractVector} <: AbstractMvNormal
+dot(b, d)    # == Normal(dot(b, μ), b' * Σ * b)
    source
    Distributions.MvNormal — Type
    MvNormal

    Generally, users don't have to worry about these internal details.

    We provide a common constructor MvNormal, which will construct a distribution of appropriate type depending on the input arguments.

    source
    Distributions.MvNormalCanon — Type
    MvNormalCanon

    The multivariate normal distribution is an exponential family distribution, with two canonical parameters: the potential vector $\mathbf{h}$ and the precision matrix $\mathbf{J}$. The relation between these parameters and the conventional representation (i.e. the one using mean $\boldsymbol{\mu}$ and covariance $\boldsymbol{\Sigma}$) is:

    \[\mathbf{h} = \boldsymbol{\Sigma}^{-1} \boldsymbol{\mu}, \quad \text{ and } \quad \mathbf{J} = \boldsymbol{\Sigma}^{-1}\]

    The canonical parameterization is widely used in Bayesian analysis. We provide a type MvNormalCanon, which is also a subtype of AbstractMvNormal to represent a multivariate normal distribution using canonical parameters. Particularly, MvNormalCanon is defined as:

    struct MvNormalCanon{T<:Real,P<:AbstractPDMat,V<:AbstractVector} <: AbstractMvNormal
     μ::V    # the mean vector
     h::V    # potential vector, i.e. inv(Σ) * μ
     J::P    # precision matrix, i.e. inv(Σ)
@@ -27,12 +27,12 @@
 
 const ZeroMeanFullNormalCanon{Axes} = MvNormalCanon{Float64, PDMat{Float64,Matrix{Float64}},    Zeros{Float64,1,Axes}}
 const ZeroMeanDiagNormalCanon{Axes} = MvNormalCanon{Float64, PDiagMat{Float64,Vector{Float64}}, Zeros{Float64,1,Axes}}
-const ZeroMeanIsoNormalCanon{Axes}  = MvNormalCanon{Float64, ScalMat{Float64},                  Zeros{Float64,1,Axes}}

    Note: MvNormalCanon share the same set of methods as MvNormal.

    source
    Distributions.MvLogitNormal — Type
    MvLogitNormal{<:AbstractMvNormal}

    The multivariate logit-normal distribution is a multivariate generalization of LogitNormal capable of handling correlations between variables.

    If $\mathbf{y} \sim \mathrm{MvNormal}(\boldsymbol{\mu}, \boldsymbol{\Sigma})$ is a length $d-1$ vector, then

    \[\mathbf{x} = \operatorname{softmax}\left(\begin{bmatrix}\mathbf{y} \\ 0 \end{bmatrix}\right) \sim \mathrm{MvLogitNormal}(\boldsymbol{\mu}, \boldsymbol{\Sigma})\]

    is a length $d$ probability vector.

    MvLogitNormal(μ, Σ)                 # MvLogitNormal with y ~ MvNormal(μ, Σ)
+const ZeroMeanIsoNormalCanon{Axes}  = MvNormalCanon{Float64, ScalMat{Float64},                  Zeros{Float64,1,Axes}}

    Note: MvNormalCanon share the same set of methods as MvNormal.

    source
    Distributions.MvLogitNormal — Type
    MvLogitNormal{<:AbstractMvNormal}

    The multivariate logit-normal distribution is a multivariate generalization of LogitNormal capable of handling correlations between variables.

    If $\mathbf{y} \sim \mathrm{MvNormal}(\boldsymbol{\mu}, \boldsymbol{\Sigma})$ is a length $d-1$ vector, then

    \[\mathbf{x} = \operatorname{softmax}\left(\begin{bmatrix}\mathbf{y} \\ 0 \end{bmatrix}\right) \sim \mathrm{MvLogitNormal}(\boldsymbol{\mu}, \boldsymbol{\Sigma})\]

    is a length $d$ probability vector.

    MvLogitNormal(μ, Σ)                 # MvLogitNormal with y ~ MvNormal(μ, Σ)
 MvLogitNormal(MvNormal(μ, Σ))       # same as above
-MvLogitNormal(MvNormalCanon(μ, J))  # MvLogitNormal with y ~ MvNormalCanon(μ, J)

    Fields

    • normal::AbstractMvNormal: contains the $d-1$-dimensional distribution of $y$
    source
    Distributions.MvLogNormal — Type
    MvLogNormal(d::MvNormal)

    The Multivariate lognormal distribution is a multidimensional generalization of the lognormal distribution.

    If $\boldsymbol X \sim \mathcal{N}(\boldsymbol\mu,\,\boldsymbol\Sigma)$ has a multivariate normal distribution then $\boldsymbol Y=\exp(\boldsymbol X)$ has a multivariate lognormal distribution.

    Mean vector $\boldsymbol{\mu}$ and covariance matrix $\boldsymbol{\Sigma}$ of the underlying normal distribution are known as the location and scale parameters of the corresponding lognormal distribution.

    source
    Distributions.Dirichlet — Type
    Dirichlet

    The Dirichlet distribution is often used as the conjugate prior for Categorical or Multinomial distributions. The probability density function of a Dirichlet distribution with parameter $\alpha = (\alpha_1, \ldots, \alpha_k)$ is:

    \[f(x; \alpha) = \frac{1}{B(\alpha)} \prod_{i=1}^k x_i^{\alpha_i - 1}, \quad \text{ with } +MvLogitNormal(MvNormalCanon(μ, J)) # MvLogitNormal with y ~ MvNormalCanon(μ, J)

    Fields

    • normal::AbstractMvNormal: contains the $d-1$-dimensional distribution of $y$
    source
    Distributions.MvLogNormal — Type
    MvLogNormal(d::MvNormal)

    The Multivariate lognormal distribution is a multidimensional generalization of the lognormal distribution.

    If $\boldsymbol X \sim \mathcal{N}(\boldsymbol\mu,\,\boldsymbol\Sigma)$ has a multivariate normal distribution then $\boldsymbol Y=\exp(\boldsymbol X)$ has a multivariate lognormal distribution.

    Mean vector $\boldsymbol{\mu}$ and covariance matrix $\boldsymbol{\Sigma}$ of the underlying normal distribution are known as the location and scale parameters of the corresponding lognormal distribution.

    source
    Distributions.Dirichlet — Type
    Dirichlet

    The Dirichlet distribution is often used as the conjugate prior for Categorical or Multinomial distributions. The probability density function of a Dirichlet distribution with parameter $\alpha = (\alpha_1, \ldots, \alpha_k)$ is:

    \[f(x; \alpha) = \frac{1}{B(\alpha)} \prod_{i=1}^k x_i^{\alpha_i - 1}, \quad \text{ with } B(\alpha) = \frac{\prod_{i=1}^k \Gamma(\alpha_i)}{\Gamma \left( \sum_{i=1}^k \alpha_i \right)}, \quad x_1 + \cdots + x_k = 1\]

    # Let alpha be a vector
 Dirichlet(alpha)         # Dirichlet distribution with parameter vector alpha
 
 # Let a be a positive scalar
-Dirichlet(k, a)          # Dirichlet distribution with parameter a * ones(k)
    source

    Addition Methods

    AbstractMvNormal

    In addition to the methods listed in the common interface above, we also provide the following methods for all multivariate distributions under the base type AbstractMvNormal:

    Distributions.sqmahal — Method
    sqmahal(d, x)

    Return the squared Mahalanobis distance from x to the center of d, w.r.t. the covariance. When x is a vector, it returns a scalar value. When x is a matrix, it returns a vector of length size(x,2).

    sqmahal!(r, d, x) with write the results to a pre-allocated array r.

    source
    Base.rand — Method
    rand(::AbstractRNG, ::Distributions.AbstractMvNormal)

    Sample a random vector from the provided multi-variate normal distribution.

    source
    Base.minimum — Method
    minimum(d::Distribution)

    Return the minimum of the support of d.

    source
    Base.maximum — Method
    maximum(d::Distribution)

    Return the maximum of the support of d.

    source
    Base.extrema — Method
    extrema(d::Distribution)

    Return the minimum and maximum of the support of d as a 2-tuple.

    source

    MvLogNormal

    In addition to the methods listed in the common interface above, we also provide the following methods:

    Distributions.location — Method
    location(d::MvLogNormal)

    Return the location vector of the distribution (the mean of the underlying normal distribution).

    source
    Distributions.scale — Method
    scale(d::MvLogNormal)

    Return the scale matrix of the distribution (the covariance matrix of the underlying normal distribution).

    source
    Statistics.median — Method
    median(d::MvLogNormal)

    Return the median vector of the lognormal distribution. which is strictly smaller than the mean.

    source
    StatsBase.mode — Method
    mode(d::MvLogNormal)

    Return the mode vector of the lognormal distribution, which is strictly smaller than the mean and median.

    source

    It can be necessary to calculate the parameters of the lognormal (location vector and scale matrix) from a given covariance and mean, median or mode. To that end, the following functions are provided.

    Distributions.location — Method
    location{D<:AbstractMvLogNormal}(::Type{D},s::Symbol,m::AbstractVector,S::AbstractMatrix)

    Calculate the location vector (the mean of the underlying normal distribution).

    • If s == :meancov, then m is taken as the mean, and S the covariance matrix of a lognormal distribution.
    • If s == :mean | :median | :mode, then m is taken as the mean, median or mode of the lognormal respectively, and S is interpreted as the scale matrix (the covariance of the underlying normal distribution).

    It is not possible to analytically calculate the location vector from e.g., median + covariance, or from mode + covariance.

    source
    Distributions.location! — Method
    location!{D<:AbstractMvLogNormal}(::Type{D},s::Symbol,m::AbstractVector,S::AbstractMatrix,μ::AbstractVector)

    Calculate the location vector (as above) and store the result in $μ$

    source
    Distributions.scale — Method
    scale{D<:AbstractMvLogNormal}(::Type{D},s::Symbol,m::AbstractVector,S::AbstractMatrix)

    Calculate the scale parameter, as defined for the location parameter above.

    source
    Distributions.scale! — Method
    scale!{D<:AbstractMvLogNormal}(::Type{D},s::Symbol,m::AbstractVector,S::AbstractMatrix,Σ::AbstractMatrix)

    Calculate the scale parameter, as defined for the location parameter above and store the result in Σ.

    source
    StatsAPI.params — Method
    params{D<:AbstractMvLogNormal}(::Type{D},m::AbstractVector,S::AbstractMatrix)

    Return (scale,location) for a given mean and covariance

    source

    Internal Methods (for creating your own multivariate distribution)

    Missing docstring.

    Missing docstring for Distributions._logpdf(d::MultivariateDistribution, x::AbstractArray). Check Documenter's build log for details.

    Index

    +Dirichlet(k, a) # Dirichlet distribution with parameter a * ones(k)    source

    Addition Methods

    AbstractMvNormal

    In addition to the methods listed in the common interface above, we also provide the following methods for all multivariate distributions under the base type AbstractMvNormal:

    Distributions.sqmahal — Method
    sqmahal(d, x)

    Return the squared Mahalanobis distance from x to the center of d, w.r.t. the covariance. When x is a vector, it returns a scalar value. When x is a matrix, it returns a vector of length size(x,2).

    sqmahal!(r, d, x) with write the results to a pre-allocated array r.

    source
    Base.rand — Method
    rand(::AbstractRNG, ::Distributions.AbstractMvNormal)

    Sample a random vector from the provided multi-variate normal distribution.

    source
    Base.minimum — Method
    minimum(d::Distribution)

    Return the minimum of the support of d.

    source
    Base.maximum — Method
    maximum(d::Distribution)

    Return the maximum of the support of d.

    source
    Base.extrema — Method
    extrema(d::Distribution)

    Return the minimum and maximum of the support of d as a 2-tuple.

    source

    MvLogNormal

    In addition to the methods listed in the common interface above, we also provide the following methods:

    Distributions.location — Method
    location(d::MvLogNormal)

    Return the location vector of the distribution (the mean of the underlying normal distribution).

    source
    Distributions.scale — Method
    scale(d::MvLogNormal)

    Return the scale matrix of the distribution (the covariance matrix of the underlying normal distribution).

    source
    Statistics.median — Method
    median(d::MvLogNormal)

    Return the median vector of the lognormal distribution. which is strictly smaller than the mean.

    source
    StatsBase.mode — Method
    mode(d::MvLogNormal)

    Return the mode vector of the lognormal distribution, which is strictly smaller than the mean and median.

    source

    It can be necessary to calculate the parameters of the lognormal (location vector and scale matrix) from a given covariance and mean, median or mode. To that end, the following functions are provided.

    Distributions.location — Method
    location{D<:AbstractMvLogNormal}(::Type{D},s::Symbol,m::AbstractVector,S::AbstractMatrix)

    Calculate the location vector (the mean of the underlying normal distribution).

    • If s == :meancov, then m is taken as the mean, and S the covariance matrix of a lognormal distribution.
    • If s == :mean | :median | :mode, then m is taken as the mean, median or mode of the lognormal respectively, and S is interpreted as the scale matrix (the covariance of the underlying normal distribution).

    It is not possible to analytically calculate the location vector from e.g., median + covariance, or from mode + covariance.

    source
    Distributions.location! — Method
    location!{D<:AbstractMvLogNormal}(::Type{D},s::Symbol,m::AbstractVector,S::AbstractMatrix,μ::AbstractVector)

    Calculate the location vector (as above) and store the result in $μ$

    source
    Distributions.scale — Method
    scale{D<:AbstractMvLogNormal}(::Type{D},s::Symbol,m::AbstractVector,S::AbstractMatrix)

    Calculate the scale parameter, as defined for the location parameter above.

    source
    Distributions.scale! — Method
    scale!{D<:AbstractMvLogNormal}(::Type{D},s::Symbol,m::AbstractVector,S::AbstractMatrix,Σ::AbstractMatrix)

    Calculate the scale parameter, as defined for the location parameter above and store the result in Σ.

    source
    StatsAPI.params — Method
    params{D<:AbstractMvLogNormal}(::Type{D},m::AbstractVector,S::AbstractMatrix)

    Return (scale,location) for a given mean and covariance

    source

    Internal Methods (for creating your own multivariate distribution)

    Missing docstring.

    Missing docstring for Distributions._logpdf(d::MultivariateDistribution, x::AbstractArray). Check Documenter's build log for details.

    Index

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    Edit on GitHub

    Order Statistics

    The $i$th Order Statistic of a random sample of size $n$ from a univariate distribution is the $i$th element after sorting in increasing order. As a special case, the first and $n$th order statistics are the minimum and maximum of the sample, while for odd $n$, the $\lceil \frac{n}{2} \rceil$th entry is the sample median.

    Given any univariate distribution and the sample size $n$, we can construct the distribution of its $i$th order statistic:

    Distributions.OrderStatistic — Type
    OrderStatistic{D<:UnivariateDistribution,S<:ValueSupport} <: UnivariateDistribution{S}

    The distribution of an order statistic from IID samples from a univariate distribution.

    OrderStatistic(dist::UnivariateDistribution, n::Int, rank::Int; check_args::Bool=true)

    Construct the distribution of the rank $=i$th order statistic from n independent samples from dist.

    The $i$th order statistic of a sample is the $i$th element of the sorted sample. For example, the 1st order statistic is the sample minimum, while the $n$th order statistic is the sample maximum.

    If $f$ is the probability density (mass) function of dist with distribution function $F$, then the probability density function $g$ of the order statistic for continuous dist is

    \[g(x; n, i) = {n \choose i} [F(x)]^{i-1} [1 - F(x)]^{n-i} f(x),\]

    and the probability mass function $g$ of the order statistic for discrete dist is

    \[g(x; n, i) = \sum_{k=i}^n {n \choose k} \left( [F(x)]^k [1 - F(x)]^{n-k} - [F(x_-)]^k [1 - F(x_-)]^{n-k} \right),\]

    where $x_-$ is the largest element in the support of dist less than $x$.

    For the joint distribution of a subset of order statistics, use JointOrderStatistics instead.

    Examples

    OrderStatistic(Cauchy(), 10, 1)              # distribution of the sample minimum
+Order Statistics · Distributions.jl
    GitHub
    Order Statistics
    The $i$th Order Statistic of a random sample of size $n$ from a univariate distribution is the $i$th element after sorting in increasing order. As a special case, the first and $n$th order statistics are the minimum and maximum of the sample, while for odd $n$, the $\lceil \frac{n}{2} \rceil$th entry is the sample median.
    Given any univariate distribution and the sample size $n$, we can construct the distribution of its $i$th order statistic:
    Distributions.OrderStatistic — Type
    OrderStatistic{D<:UnivariateDistribution,S<:ValueSupport} <: UnivariateDistribution{S}
    The distribution of an order statistic from IID samples from a univariate distribution.
    OrderStatistic(dist::UnivariateDistribution, n::Int, rank::Int; check_args::Bool=true)
    Construct the distribution of the rank $=i$th order statistic from n independent samples from dist.
    The $i$th order statistic of a sample is the $i$th element of the sorted sample. For example, the 1st order statistic is the sample minimum, while the $n$th order statistic is the sample maximum.
    If $f$ is the probability density (mass) function of dist with distribution function $F$, then the probability density function $g$ of the order statistic for continuous dist is
    \[g(x; n, i) = {n \choose i} [F(x)]^{i-1} [1 - F(x)]^{n-i} f(x),\]
    and the probability mass function $g$ of the order statistic for discrete dist is
    \[g(x; n, i) = \sum_{k=i}^n {n \choose k} \left( [F(x)]^k [1 - F(x)]^{n-k} - [F(x_-)]^k [1 - F(x_-)]^{n-k} \right),\]
    where $x_-$ is the largest element in the support of dist less than $x$.
    For the joint distribution of a subset of order statistics, use JointOrderStatistics instead.
    Examples
    OrderStatistic(Cauchy(), 10, 1)              # distribution of the sample minimum
 OrderStatistic(DiscreteUniform(10), 10, 10)  # distribution of the sample maximum
-OrderStatistic(Gamma(1, 1), 11, 5)           # distribution of the sample median
    source
    If we are interested in more than one order statistic, for continuous univariate distributions we can also construct the joint distribution of order statistics:
    Distributions.JointOrderStatistics — Type
    JointOrderStatistics <: ContinuousMultivariateDistribution
    The joint distribution of a subset of order statistics from a sample from a continuous univariate distribution.
    JointOrderStatistics(
+OrderStatistic(Gamma(1, 1), 11, 5)           # distribution of the sample median
    source
    If we are interested in more than one order statistic, for continuous univariate distributions we can also construct the joint distribution of order statistics:
    Distributions.JointOrderStatistics — Type
    JointOrderStatistics <: ContinuousMultivariateDistribution
    The joint distribution of a subset of order statistics from a sample from a continuous univariate distribution.
    JointOrderStatistics(
     dist::ContinuousUnivariateDistribution,
     n::Int,
     ranks=Base.OneTo(n);
     check_args::Bool=true,
 )
    Construct the joint distribution of order statistics for the specified ranks from an IID sample of size n from dist.
    The $i$th order statistic of a sample is the $i$th element of the sorted sample. For example, the 1st order statistic is the sample minimum, while the $n$th order statistic is the sample maximum.
    ranks must be a sorted vector or tuple of unique Ints between 1 and n.
    For a single order statistic, use OrderStatistic instead.
    Examples
    JointOrderStatistics(Normal(), 10)           # Product(fill(Normal(), 10)) restricted to ordered vectors
 JointOrderStatistics(Cauchy(), 10, 2:9)      # joint distribution of all but the extrema
-JointOrderStatistics(Cauchy(), 10, (1, 10))  # joint distribution of only the extrema
    source
    
+JointOrderStatistics(Cauchy(), 10, (1, 10))  # joint distribution of only the extrema
    source
    diff --git a/dev/product/index.html b/dev/product/index.html index 4ed573128f..72f62d1cf6 100644 --- a/dev/product/index.html +++ b/dev/product/index.html @@ -1,5 +1,5 @@ -Product Distributions · Distributions.jl
    Edit on GitHub

    Product Distributions

    Product distributions are joint distributions of multiple independent distributions. It is recommended to use product_distribution to construct product distributions. Depending on the type of the argument, it may construct a different distribution type.

    Multivariate products

    Distributions.product_distribution — Method
    product_distribution(dists::AbstractArray{<:Distribution{<:ArrayLikeVariate{M}},N})

    Create a distribution of M + N-dimensional arrays as a product distribution of independent M-dimensional distributions by stacking them.

    The function falls back to constructing a ProductDistribution distribution but specialized methods can be defined.

    source
    Distributions.product_distribution — Method
    product_distribution(dists::AbstractVector{<:Normal})

    Create a multivariate normal distribution by stacking the univariate normal distributions.

    The resulting distribution of type MvNormal has a diagonal covariance matrix.

    source
    Distributions.ProductDistribution — Type
    ProductDistribution <: Distribution{<:ValueSupport,<:ArrayLikeVariate}

    A distribution of M + N-dimensional arrays, constructed from an N-dimensional array of independent M-dimensional distributions by stacking them.

    Users should use product_distribution to construct a product distribution of independent distributions instead of constructing a ProductDistribution directly.

    source
    Distributions.Product — Type
    Product <: MultivariateDistribution

    An N dimensional MultivariateDistribution constructed from a vector of N independent UnivariateDistributions.

    Product(Uniform.(rand(10), 1)) # A 10-dimensional Product from 10 independent `Uniform` distributions.
    Note

    Product is deprecated and will be removed in the next breaking release. Use product_distribution instead.

    source

    NamedTuple-variate products

    Distributions.product_distribution — Method
    product_distribution(dists::NamedTuple{K,Tuple{Vararg{Distribution}}}) where {K}

    Create a distribution of NamedTuples as a product distribution of independent named distributions.

    The function falls back to constructing a ProductNamedTupleDistribution distribution but specialized methods can be defined.

    source
    Distributions.ProductNamedTupleDistribution — Type
    ProductNamedTupleDistribution{Tnames,Tdists,S<:ValueSupport,eltypes} <:
+Product Distributions · Distributions.jl
    GitHub
    Product Distributions
    Product distributions are joint distributions of multiple independent distributions. It is recommended to use product_distribution to construct product distributions. Depending on the type of the argument, it may construct a different distribution type.
    Multivariate products
    Distributions.product_distribution — Method
    product_distribution(dists::AbstractArray{<:Distribution{<:ArrayLikeVariate{M}},N})
    Create a distribution of M + N-dimensional arrays as a product distribution of independent M-dimensional distributions by stacking them.
    The function falls back to constructing a ProductDistribution distribution but specialized methods can be defined.
    source
    Distributions.product_distribution — Method
    product_distribution(dists::AbstractVector{<:Normal})
    Create a multivariate normal distribution by stacking the univariate normal distributions.
    The resulting distribution of type MvNormal has a diagonal covariance matrix.
    source
    Distributions.ProductDistribution — Type
    ProductDistribution <: Distribution{<:ValueSupport,<:ArrayLikeVariate}
    A distribution of M + N-dimensional arrays, constructed from an N-dimensional array of independent M-dimensional distributions by stacking them.
    Users should use product_distribution to construct a product distribution of independent distributions instead of constructing a ProductDistribution directly.
    source
    Distributions.Product — Type
    Product <: MultivariateDistribution
    An N dimensional MultivariateDistribution constructed from a vector of N independent UnivariateDistributions.
    Product(Uniform.(rand(10), 1)) # A 10-dimensional Product from 10 independent `Uniform` distributions.
    Note
    Product is deprecated and will be removed in the next breaking release. Use product_distribution instead.
    source
    NamedTuple-variate products
    Distributions.product_distribution — Method
    product_distribution(dists::NamedTuple{K,Tuple{Vararg{Distribution}}}) where {K}
    Create a distribution of NamedTuples as a product distribution of independent named distributions.
    The function falls back to constructing a ProductNamedTupleDistribution distribution but specialized methods can be defined.
    source
    Distributions.ProductNamedTupleDistribution — Type
    ProductNamedTupleDistribution{Tnames,Tdists,S<:ValueSupport,eltypes} <:
     Distribution{NamedTupleVariate{Tnames},S}
    A distribution of NamedTuples, constructed from a NamedTuple of independent named distributions.
    Users should use product_distribution to construct a product distribution of independent distributions instead of constructing a ProductNamedTupleDistribution directly.
    Examples
    julia> d = product_distribution((x=Normal(), y=Dirichlet([2, 4])))
 ProductNamedTupleDistribution{(:x, :y)}(
 x: Normal{Float64}(μ=0.0, σ=1.0)
@@ -23,4 +23,4 @@
 (x = 0.0, y = [0.3333333333333333, 0.6666666666666666])
 
 julia> var(d)  # var of marginals
-(x = 1.0, y = [0.031746031746031744, 0.031746031746031744])
    source
    Index
    
+(x = 1.0, y = [0.031746031746031744, 0.031746031746031744])
    source

    Index

    diff --git a/dev/reshape/index.html b/dev/reshape/index.html index fc57b4d73d..bf9c8bed28 100644 --- a/dev/reshape/index.html +++ b/dev/reshape/index.html @@ -1,3 +1,3 @@ -Reshaping distributions · Distributions.jl
    Edit on GitHub

    Reshaping distributions

    Distributions of array variates such as MultivariateDistributions and MatrixDistributions can be reshaped.

    Base.reshape — Function
    reshape(d::Distribution{<:ArrayLikeVariate}, dims::Int...)
-reshape(d::Distribution{<:ArrayLikeVariate}, dims::Dims)

    Return a Distribution of reshape(X, dims) where X is a random variable with distribution d.

    The default implementation returns a ReshapedDistribution. However, it can return more optimized distributions for specific types of distributions and numbers of dimensions. Therefore it is recommended to use reshape instead of the constructor of ReshapedDistribution.

    Implementation

    Since reshape(d, dims::Int...) calls reshape(d, dims::Dims), one should implement reshape(d, ::Dims) for desired distributions d.

    See also: vec

    source
    Base.vec — Function
    vec(d::Distribution{<:ArrayLikeVariate})

    Return a MultivariateDistribution of vec(X) where X is a random variable with distribution d.

    The default implementation returns a ReshapedDistribution. However, it can return more optimized distributions for specific types of distributions and numbers of dimensions. Therefore it is recommended to use vec instead of the constructor of ReshapedDistribution.

    Implementation

    Since vec(d) is defined as reshape(d, length(d)) one should implement reshape(d, ::Tuple{Int}) rather than vec.

    See also: reshape

    source
    +Reshaping distributions · Distributions.jl
    GitHub

    Reshaping distributions

    Distributions of array variates such as MultivariateDistributions and MatrixDistributions can be reshaped.

    Base.reshape — Function
    reshape(d::Distribution{<:ArrayLikeVariate}, dims::Int...)
+reshape(d::Distribution{<:ArrayLikeVariate}, dims::Dims)

    Return a Distribution of reshape(X, dims) where X is a random variable with distribution d.

    The default implementation returns a ReshapedDistribution. However, it can return more optimized distributions for specific types of distributions and numbers of dimensions. Therefore it is recommended to use reshape instead of the constructor of ReshapedDistribution.

    Implementation

    Since reshape(d, dims::Int...) calls reshape(d, dims::Dims), one should implement reshape(d, ::Dims) for desired distributions d.

    See also: vec

    source
    Base.vec — Function
    vec(d::Distribution{<:ArrayLikeVariate})

    Return a MultivariateDistribution of vec(X) where X is a random variable with distribution d.

    The default implementation returns a ReshapedDistribution. However, it can return more optimized distributions for specific types of distributions and numbers of dimensions. Therefore it is recommended to use vec instead of the constructor of ReshapedDistribution.

    Implementation

    Since vec(d) is defined as reshape(d, length(d)) one should implement reshape(d, ::Tuple{Int}) rather than vec.

    See also: reshape

    source
    diff --git a/dev/search/index.html b/dev/search/index.html deleted file mode 100644 index 3e6e24e7bd..0000000000 --- a/dev/search/index.html +++ /dev/null @@ -1,2 +0,0 @@ - -Search · Distributions.jl diff --git a/dev/starting/index.html b/dev/starting/index.html index 8afc70126f..f25ef7a88f 100644 --- a/dev/starting/index.html +++ b/dev/starting/index.html @@ -1,5 +1,5 @@ -Getting Started · Distributions.jl
    Edit on GitHub

    Getting Started

    Installation

    The Distributions package is available through the Julia package system by running Pkg.add("Distributions"). Throughout, we assume that you have installed the package.

    Starting With a Normal Distribution

    We start by drawing 100 observations from a standard-normal random variable.

    The first step is to set up the environment:

    julia> using Random, Distributions
+Getting Started · Distributions.jl
    GitHub
    Getting Started
    Installation
    The Distributions package is available through the Julia package system by running Pkg.add("Distributions"). Throughout, we assume that you have installed the package.
    Starting With a Normal Distribution
    We start by drawing 100 observations from a standard-normal random variable.
    The first step is to set up the environment:
    julia> using Random, Distributions
 
 julia> Random.seed!(123) # Setting the seed
    Then, we create a standard-normal distribution d and obtain samples using rand:
    julia> d = Normal()
 Normal(μ=0.0, σ=1.0)
    The object d represents a probability distribution, in our case the standard-normal distribution. One can query its properties such as the mean:
    julia> mean(d)
@@ -17,4 +17,4 @@
 2-element Array{Symbol,1}:
  :μ
  :β
    This tells you that a Cauchy distribution is initialized with location μ and scale β.
    Estimate the Parameters
    It is often useful to approximate an empirical distribution with a theoretical distribution. As an example, we can use the array x we created above and ask which normal distribution best describes it:
    julia> fit(Normal, x)
-Normal(μ=0.036692077201688635, σ=1.1228280164716382)
    Since x is a random draw from Normal, it's easy to check that the fitted values are sensible. Indeed, the estimates [0.04, 1.12] are close to the true values of [0.0, 1.0] that we used to generate x.
    
+Normal(μ=0.036692077201688635, σ=1.1228280164716382)

    Since x is a random draw from Normal, it's easy to check that the fitted values are sensible. Indeed, the estimates [0.04, 1.12] are close to the true values of [0.0, 1.0] that we used to generate x.

    diff --git a/dev/truncate/index.html b/dev/truncate/index.html index 54804bea47..d7a9448ab3 100644 --- a/dev/truncate/index.html +++ b/dev/truncate/index.html @@ -1,6 +1,6 @@ -Truncated Distributions · Distributions.jl
    Edit on GitHub

    Truncated Distributions

    The package provides the truncated function which creates the most appropriate distribution to represent a truncated version of a given distribution.

    A truncated distribution can be constructed using the following signature:

    Distributions.truncated — Function
    truncated(d0::UnivariateDistribution; [lower::Real], [upper::Real])
+Truncated Distributions · Distributions.jl
    GitHub
    Truncated Distributions
    The package provides the truncated function which creates the most appropriate distribution to represent a truncated version of a given distribution.
    A truncated distribution can be constructed using the following signature:
    Distributions.truncated — Function
    truncated(d0::UnivariateDistribution; [lower::Real], [upper::Real])
 truncated(d0::UnivariateDistribution, lower::Real, upper::Real)
    A truncated distribution d of a distribution d0 to the interval $[l, u]=$[lower, upper] has the probability density (mass) function:
    \[f(x; d_0, l, u) = \frac{f_{d_0}(x)}{P_{Z \sim d_0}(l \le Z \le u)}, \quad x \in [l, u],\]
    where $f_{d_0}(x)$ is the probability density (mass) function of $d_0$.
    The function throws an error if $l > u$.
    truncated(d0; lower=l)           # d0 left-truncated to the interval [l, Inf)
 truncated(d0; upper=u)           # d0 right-truncated to the interval (-Inf, u]
 truncated(d0; lower=l, upper=u)  # d0 truncated to the interval [l, u]
-truncated(d0, l, u)              # d0 truncated to the interval [l, u]
    The function falls back to constructing a Truncated wrapper.
    Implementation
    To implement a specialized truncated form for distributions of type D, one or more of the following methods should be implemented:
    • truncated(d0::D, l::T, u::T) where {T <: Real}: interval-truncated
    • truncated(d0::D, ::Nothing, u::Real): right-truncated
    • truncated(d0::D, l::Real, u::Nothing): left-truncated
    source
    In the general case, this will create a Truncated{typeof(d)} structure, defined as follows:
    Distributions.Truncated — Type
    Truncated
    Generic wrapper for a truncated distribution.
    The truncated normal distribution is a particularly important one in the family of truncated distributions. Unlike the general case, truncated normal distributions support mean, mode, modes, var, std, and entropy.
    source
    Many functions, including those for the evaluation of pdf and sampling, are defined for all truncated univariate distributions:
    Functions to compute statistics, such as mean, mode, var, std, and entropy, are not available for generic truncated distributions. Generally, there are no easy ways to compute such quantities due to the complications incurred by truncation. However, these methods are supported for truncated normal distributions Truncated{<:Normal} which can be constructed with truncated(::Normal, ...).
    
+truncated(d0, l, u)              # d0 truncated to the interval [l, u]

    The function falls back to constructing a Truncated wrapper.

    Implementation

    To implement a specialized truncated form for distributions of type D, one or more of the following methods should be implemented:

    • truncated(d0::D, l::T, u::T) where {T <: Real}: interval-truncated
    • truncated(d0::D, ::Nothing, u::Real): right-truncated
    • truncated(d0::D, l::Real, u::Nothing): left-truncated
    source

    In the general case, this will create a Truncated{typeof(d)} structure, defined as follows:

    Distributions.Truncated — Type
    Truncated

    Generic wrapper for a truncated distribution.

    The truncated normal distribution is a particularly important one in the family of truncated distributions. Unlike the general case, truncated normal distributions support mean, mode, modes, var, std, and entropy.

    source

    Many functions, including those for the evaluation of pdf and sampling, are defined for all truncated univariate distributions:

    Functions to compute statistics, such as mean, mode, var, std, and entropy, are not available for generic truncated distributions. Generally, there are no easy ways to compute such quantities due to the complications incurred by truncation. However, these methods are supported for truncated normal distributions Truncated{<:Normal} which can be constructed with truncated(::Normal, ...).

    diff --git a/dev/types/index.html b/dev/types/index.html index afc4cc12ee..53e9cec4ea 100644 --- a/dev/types/index.html +++ b/dev/types/index.html @@ -1,6 +1,6 @@ -Type Hierarchy · Distributions.jl
    Edit on GitHub

    Type Hierarchy

    All samplers and distributions provided in this package are organized into a type hierarchy described as follows.

    Sampleable

    The root of this type hierarchy is Sampleable. The abstract type Sampleable subsumes any types of objects from which one can draw samples, which particularly includes samplers and distributions. Formally, Sampleable is defined as

    abstract type Sampleable{F<:VariateForm,S<:ValueSupport} end

    It has two type parameters that define the kind of samples that can be drawn therefrom.

    Distributions.Sampleable
-Base.rand(::Distributions.Sampleable)

    VariateForm

    Distributions.VariateForm

    The VariateForm subtypes defined in Distributions.jl are:

    TypeA single sampleMultiple samples
    Univariate == ArrayLikeVariate{0}a scalar numberA numeric array of arbitrary shape, each element being a sample
    Multivariate == ArrayLikeVariate{1}a numeric vectorA matrix, each column being a sample
    Matrixvariate == ArrayLikeVariate{2}a numeric matrixAn array of matrices, each element being a sample matrix

    ValueSupport

    The ValueSupport sub-types defined in Distributions.jl are:

    Distributions.Discrete — Type
    Discrete <: ValueSupport

    This type represents the support of a discrete random variable.

    It is countable. For instance, it can be a finite set or a countably infinite set such as the natural numbers.

    See also: Continuous, ValueSupport

    source
    TypeDefault element typeDescriptionExamples
    DiscreteIntSamples take countably many values$\{0,1,2,3\}$, $\mathbb{N}$
    ContinuousFloat64Samples take uncountably many values$[0, 1]$, $\mathbb{R}$

    Multiple samples are often organized into an array, depending on the variate form.

    The basic functionalities that a sampleable object provides are to retrieve information about the samples it generates and to draw samples. Particularly, the following functions are provided for sampleable objects:

    Base.length — Method
    length(s::Sampleable)

    The length of each sample. Always returns 1 when s is univariate.

    source
    Base.size — Method
    size(s::Sampleable)

    The size (i.e. shape) of each sample. Always returns () when s is univariate, and (length(s),) when s is multivariate.

    source
    Distributions.nsamples — Method
    nsamples(s::Sampleable)

    The number of values contained in one sample of s. Multiple samples are often organized into an array, depending on the variate form.

    source
    Base.eltype — Method
    eltype(::Type{Sampleable})

    The default element type of a sample. This is the type of elements of the samples generated by the rand method. However, one can provide an array of different element types to store the samples using rand!.

    source
    Base.rand — Method
    rand(::AbstractRNG, ::Sampleable)

    Samples from the sampler and returns the result.

    source
    Random.rand! — Method
    rand!(::AbstractRNG, ::Sampleable, ::AbstractArray)

    Samples in-place from the sampler and stores the result in the provided array.

    source

    Distributions

    We use Distribution, a subtype of Sampleable as defined below, to capture probabilistic distributions. In addition to being sampleable, a distribution typically comes with an explicit way to combine its domain, probability density function, and many other quantities.

    abstract type Distribution{F<:VariateForm,S<:ValueSupport} <: Sampleable{F,S} end
    Distributions.Distribution

    To simplify the use in practice, we introduce a series of type alias as follows:

    const UnivariateDistribution{S<:ValueSupport}   = Distribution{Univariate,S}
+Type Hierarchy · Distributions.jl
    GitHub
    Type Hierarchy
    All samplers and distributions provided in this package are organized into a type hierarchy described as follows.
    Sampleable
    The root of this type hierarchy is Sampleable. The abstract type Sampleable subsumes any types of objects from which one can draw samples, which particularly includes samplers and distributions. Formally, Sampleable is defined as
    abstract type Sampleable{F<:VariateForm,S<:ValueSupport} end
    It has two type parameters that define the kind of samples that can be drawn therefrom.
    Distributions.Sampleable
+Base.rand(::Distributions.Sampleable)
    VariateForm
    Distributions.VariateForm
    The VariateForm subtypes defined in Distributions.jl are:
    TypeA single sampleMultiple samples
    Univariate == ArrayLikeVariate{0}a scalar numberA numeric array of arbitrary shape, each element being a sample
    Multivariate == ArrayLikeVariate{1}a numeric vectorA matrix, each column being a sample
    Matrixvariate == ArrayLikeVariate{2}a numeric matrixAn array of matrices, each element being a sample matrix
    ValueSupport
    The ValueSupport sub-types defined in Distributions.jl are:
    Distributions.Discrete — Type
    Discrete <: ValueSupport
    This type represents the support of a discrete random variable.
    It is countable. For instance, it can be a finite set or a countably infinite set such as the natural numbers.
    See also: Continuous, ValueSupport
    source
    TypeDefault element typeDescriptionExamples
    DiscreteIntSamples take countably many values$\{0,1,2,3\}$, $\mathbb{N}$
    ContinuousFloat64Samples take uncountably many values$[0, 1]$, $\mathbb{R}$
    Multiple samples are often organized into an array, depending on the variate form.
    The basic functionalities that a sampleable object provides are to retrieve information about the samples it generates and to draw samples. Particularly, the following functions are provided for sampleable objects:
    Base.length — Method
    length(s::Sampleable)
    The length of each sample. Always returns 1 when s is univariate.
    source
    Base.size — Method
    size(s::Sampleable)
    The size (i.e. shape) of each sample. Always returns () when s is univariate, and (length(s),) when s is multivariate.
    source
    Distributions.nsamples — Method
    nsamples(s::Sampleable)
    The number of values contained in one sample of s. Multiple samples are often organized into an array, depending on the variate form.
    source
    Base.eltype — Method
    eltype(::Type{Sampleable})
    The default element type of a sample. This is the type of elements of the samples generated by the rand method. However, one can provide an array of different element types to store the samples using rand!.
    source
    Base.rand — Method
    rand(::AbstractRNG, ::Sampleable)
    Samples from the sampler and returns the result.
    source
    Random.rand! — Method
    rand!(::AbstractRNG, ::Sampleable, ::AbstractArray)
    Samples in-place from the sampler and stores the result in the provided array.
    source
    Distributions
    We use Distribution, a subtype of Sampleable as defined below, to capture probabilistic distributions. In addition to being sampleable, a distribution typically comes with an explicit way to combine its domain, probability density function, and many other quantities.
    abstract type Distribution{F<:VariateForm,S<:ValueSupport} <: Sampleable{F,S} end
    Distributions.Distribution
    To simplify the use in practice, we introduce a series of type alias as follows:
    const UnivariateDistribution{S<:ValueSupport}   = Distribution{Univariate,S}
 const MultivariateDistribution{S<:ValueSupport} = Distribution{Multivariate,S}
 const MatrixDistribution{S<:ValueSupport}       = Distribution{Matrixvariate,S}
 const NonMatrixDistribution = Union{UnivariateDistribution, MultivariateDistribution}
@@ -13,4 +13,4 @@
 const DiscreteMultivariateDistribution   = Distribution{Multivariate,  Discrete}
 const ContinuousMultivariateDistribution = Distribution{Multivariate,  Continuous}
 const DiscreteMatrixDistribution         = Distribution{Matrixvariate, Discrete}
-const ContinuousMatrixDistribution       = Distribution{Matrixvariate, Continuous}
    All methods applicable to Sampleable also apply to Distribution. The API for distributions of different variate forms are different (refer to univariates, multivariates, and matrix for details).
    
+const ContinuousMatrixDistribution       = Distribution{Matrixvariate, Continuous}

    All methods applicable to Sampleable also apply to Distribution. The API for distributions of different variate forms are different (refer to univariates, multivariates, and matrix for details).

    diff --git a/dev/univariate/0580360f.svg b/dev/univariate/0580360f.svg new file mode 100644 index 0000000000..ee7ef2c9a6 --- /dev/null +++ b/dev/univariate/0580360f.svg @@ -0,0 +1,168 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +0 + + +0.1 + + +0.2 + + +0.3 + + +0.4 + + +0.5 + + +0 + + +2 + + +4 + + +6 + + +8 + + +10 + + +FDist(10, 1) + + +x + + +density + + + diff --git a/dev/univariate/0b667b58.svg b/dev/univariate/0b667b58.svg new file mode 100644 index 0000000000..0147b8b53d --- /dev/null +++ b/dev/univariate/0b667b58.svg @@ -0,0 +1,78 @@ + + + + + + + + + + + + + + + +0.1 + + + + + + + +0.15 + + + + + + + +0.2 + + + + + + + +0.25 + + + + +- + + +π + + + + + + + +0 + + + + + + + +π + + + + +VonMises(0.5) + + +x + + +density + + + diff --git a/dev/univariate/125e6624.svg 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100644 --- a/dev/univariate/index.html +++ b/dev/univariate/index.html @@ -1,8 +1,8 @@ -Univariate Distributions · Distributions.jl
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    Univariate Distributions

    Univariate distributions are the distributions whose variate forms are Univariate (i.e each sample is a scalar). Abstract types for univariate distributions:

    const UnivariateDistribution{S<:ValueSupport} = Distribution{Univariate,S}
+Univariate Distributions · Distributions.jl
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    Univariate Distributions
    Univariate distributions are the distributions whose variate forms are Univariate (i.e each sample is a scalar). Abstract types for univariate distributions:
    const UnivariateDistribution{S<:ValueSupport} = Distribution{Univariate,S}
 
 const DiscreteUnivariateDistribution   = Distribution{Univariate, Discrete}
-const ContinuousUnivariateDistribution = Distribution{Univariate, Continuous}
    Common Interface
    A series of methods is implemented for each univariate distribution, which provides useful functionalities such as moment computation, pdf evaluation, and sampling (i.e. random number generation).
    Parameter Retrieval
    Note: params are defined for all univariate distributions, while other parameter retrieval methods are only defined for those distributions for which these parameters make sense. See below for details.
    StatsAPI.params — Method
    params(d::UnivariateDistribution)
    Return a tuple of parameters. Let d be a distribution of type D, then D(params(d)...) will construct exactly the same distribution as $d$.
    source
    For distributions for which success and failure have a meaning, the following methods are defined:
    Computation of statistics
    Base.maximum — Method
    maximum(d::Distribution)
    Return the maximum of the support of d.
    source
    Base.minimum — Method
    minimum(d::Distribution)
    Return the minimum of the support of d.
    source
    Base.extrema — Method
    extrema(d::Distribution)
    Return the minimum and maximum of the support of d as a 2-tuple.
    source
    Statistics.var — Method
    var(d::UnivariateDistribution)
    Compute the variance. (A generic std is provided as std(d) = sqrt(var(d)))
    source
    Statistics.std — Method
    std(d::UnivariateDistribution)
    Return the standard deviation of distribution d, i.e. sqrt(var(d)).
    source
    Statistics.median — Method
    median(d::UnivariateDistribution)
    Return the median value of distribution d. The median is the smallest x in the support of d for which cdf(d, x) ≥ 1/2. Corresponding to this definition as 1/2-quantile, a fallback is provided calling the quantile function.
    source
    StatsBase.kurtosis — Method
    kurtosis(d::Distribution, correction::Bool)
    Computes excess kurtosis by default. Proper kurtosis can be returned with correction=false
    source
    StatsBase.entropy — Method
    entropy(d::UnivariateDistribution, b::Real)
    Compute the entropy value of distribution d, w.r.t. a given base.
    source
    StatsBase.entropy — Method
    entropy(d::UnivariateDistribution, b::Real)
    Compute the entropy value of distribution d, w.r.t. a given base.
    source
    Distributions.cf — Method
    cf(d::UnivariateDistribution, t)
    Evaluate the characteristic function of distribution d.
    source
    Distributions.pdfsquaredL2norm — Function
    pdfsquaredL2norm(d::Distribution)
    Return the square of the L2 norm of the probability density function $f(x)$ of the distribution d:
    \[\int_{S} f(x)^{2} \mathrm{d} x\]
    where $S$ is the support of $f(x)$.
    source
    Probability Evaluation
    Distributions.insupport — Method
    insupport(d::UnivariateDistribution, x::Any)
    When x is a scalar, it returns whether x is within the support of d (e.g., insupport(d, x) = minimum(d) <= x <= maximum(d)). When x is an array, it returns whether every element in x is within the support of d.
    Generic fallback methods are provided, but it is often the case that insupport can be done more efficiently, and a specialized insupport is thus desirable. You should also override this function if the support is composed of multiple disjoint intervals.
    source
    Distributions.logpdf — Method
    logpdf(d::UnivariateDistribution, x::Real)
    Evaluate the logarithm of probability density (mass) at x.
    See also: pdf.
    source
    Missing docstring.
    Missing docstring for loglikelihood(::UnivariateDistribution, ::AbstractArray). Check Documenter's build log for details.
    Distributions.logcdf — Method
    logcdf(d::UnivariateDistribution, x::Real)
    The logarithm of the cumulative function value(s) evaluated at x, i.e. log(cdf(x)).
    source
    Distributions.logdiffcdf — Method
    logdiffcdf(d::UnivariateDistribution, x::Real, y::Real)
    The natural logarithm of the difference between the cumulative density function at x and y, i.e. log(cdf(x) - cdf(y)).
    source
    Distributions.ccdf — Method
    ccdf(d::UnivariateDistribution, x::Real)
    The complementary cumulative function evaluated at x, i.e. 1 - cdf(d, x).
    source
    Distributions.logccdf — Method
    logccdf(d::UnivariateDistribution, x::Real)
    The logarithm of the complementary cumulative function values evaluated at x, i.e. log(ccdf(x)).
    source
    Statistics.quantile — Method
    quantile(d::UnivariateDistribution, q::Real)
    Evaluate the (generalized) inverse cumulative distribution function at q.
    For a given 0 ≤ q ≤ 1, quantile(d, q) is the smallest value x in the support of d for which cdf(d, x) ≥ q.
    See also: cquantile, invlogcdf, and invlogccdf.
    source
    Distributions.invlogcdf — Method
    invlogcdf(d::UnivariateDistribution, lp::Real)
    The (generalized) inverse function of logcdf.
    For a given lp ≤ 0, invlogcdf(d, lp) is the smallest value x in the support of d for which logcdf(d, x) ≥ lp.
    source
    Distributions.invlogccdf — Method
    invlogccdf(d::UnivariateDistribution, lp::Real)
    The (generalized) inverse function of logccdf.
    For a given lp ≤ 0, invlogccdf(d, lp) is the smallest value x in the support of d for which logccdf(d, x) ≤ lp.
    source
    Sampling (Random number generation)
    Base.rand — Method
    rand(rng::AbstractRNG, d::UnivariateDistribution)
    Generate a scalar sample from d. The general fallback is quantile(d, rand()).
    source
    Random.rand! — Method
    rand!(::AbstractRNG, ::Sampleable, ::AbstractArray)
    Samples in-place from the sampler and stores the result in the provided array.
    source
    Continuous Distributions
    Distributions.Arcsine — Type
    Arcsine(a,b)
    The Arcsine distribution has probability density function
    \[f(x) = \frac{1}{\pi \sqrt{(x - a) (b - x)}}, \quad x \in [a, b]\]
    Arcsine()        # Arcsine distribution with support [0, 1]
+const ContinuousUnivariateDistribution = Distribution{Univariate, Continuous}
    Common Interface
    A series of methods is implemented for each univariate distribution, which provides useful functionalities such as moment computation, pdf evaluation, and sampling (i.e. random number generation).
    Parameter Retrieval
    Note: params are defined for all univariate distributions, while other parameter retrieval methods are only defined for those distributions for which these parameters make sense. See below for details.
    StatsAPI.params — Method
    params(d::UnivariateDistribution)
    Return a tuple of parameters. Let d be a distribution of type D, then D(params(d)...) will construct exactly the same distribution as $d$.
    source
    For distributions for which success and failure have a meaning, the following methods are defined:
    Computation of statistics
    Base.maximum — Method
    maximum(d::Distribution)
    Return the maximum of the support of d.
    source
    Base.minimum — Method
    minimum(d::Distribution)
    Return the minimum of the support of d.
    source
    Base.extrema — Method
    extrema(d::Distribution)
    Return the minimum and maximum of the support of d as a 2-tuple.
    source
    Statistics.var — Method
    var(d::UnivariateDistribution)
    Compute the variance. (A generic std is provided as std(d) = sqrt(var(d)))
    source
    Statistics.std — Method
    std(d::UnivariateDistribution)
    Return the standard deviation of distribution d, i.e. sqrt(var(d)).
    source
    Statistics.median — Method
    median(d::UnivariateDistribution)
    Return the median value of distribution d. The median is the smallest x in the support of d for which cdf(d, x) ≥ 1/2. Corresponding to this definition as 1/2-quantile, a fallback is provided calling the quantile function.
    source
    StatsBase.kurtosis — Method
    kurtosis(d::Distribution, correction::Bool)
    Computes excess kurtosis by default. Proper kurtosis can be returned with correction=false
    source
    StatsBase.entropy — Method
    entropy(d::UnivariateDistribution, b::Real)
    Compute the entropy value of distribution d, w.r.t. a given base.
    source
    StatsBase.entropy — Method
    entropy(d::UnivariateDistribution, b::Real)
    Compute the entropy value of distribution d, w.r.t. a given base.
    source
    Distributions.cf — Method
    cf(d::UnivariateDistribution, t)
    Evaluate the characteristic function of distribution d.
    source
    Distributions.pdfsquaredL2norm — Function
    pdfsquaredL2norm(d::Distribution)
    Return the square of the L2 norm of the probability density function $f(x)$ of the distribution d:
    \[\int_{S} f(x)^{2} \mathrm{d} x\]
    where $S$ is the support of $f(x)$.
    source
    Probability Evaluation
    Distributions.insupport — Method
    insupport(d::UnivariateDistribution, x::Any)
    When x is a scalar, it returns whether x is within the support of d (e.g., insupport(d, x) = minimum(d) <= x <= maximum(d)). When x is an array, it returns whether every element in x is within the support of d.
    Generic fallback methods are provided, but it is often the case that insupport can be done more efficiently, and a specialized insupport is thus desirable. You should also override this function if the support is composed of multiple disjoint intervals.
    source
    Distributions.logpdf — Method
    logpdf(d::UnivariateDistribution, x::Real)
    Evaluate the logarithm of probability density (mass) at x.
    See also: pdf.
    source
    Missing docstring.
    Missing docstring for loglikelihood(::UnivariateDistribution, ::AbstractArray). Check Documenter's build log for details.
    Distributions.logcdf — Method
    logcdf(d::UnivariateDistribution, x::Real)
    The logarithm of the cumulative function value(s) evaluated at x, i.e. log(cdf(x)).
    source
    Distributions.logdiffcdf — Method
    logdiffcdf(d::UnivariateDistribution, x::Real, y::Real)
    The natural logarithm of the difference between the cumulative density function at x and y, i.e. log(cdf(x) - cdf(y)).
    source
    Distributions.ccdf — Method
    ccdf(d::UnivariateDistribution, x::Real)
    The complementary cumulative function evaluated at x, i.e. 1 - cdf(d, x).
    source
    Distributions.logccdf — Method
    logccdf(d::UnivariateDistribution, x::Real)
    The logarithm of the complementary cumulative function values evaluated at x, i.e. log(ccdf(x)).
    source
    Statistics.quantile — Method
    quantile(d::UnivariateDistribution, q::Real)
    Evaluate the (generalized) inverse cumulative distribution function at q.
    For a given 0 ≤ q ≤ 1, quantile(d, q) is the smallest value x in the support of d for which cdf(d, x) ≥ q.
    See also: cquantile, invlogcdf, and invlogccdf.
    source
    Distributions.invlogcdf — Method
    invlogcdf(d::UnivariateDistribution, lp::Real)
    The (generalized) inverse function of logcdf.
    For a given lp ≤ 0, invlogcdf(d, lp) is the smallest value x in the support of d for which logcdf(d, x) ≥ lp.
    source
    Distributions.invlogccdf — Method
    invlogccdf(d::UnivariateDistribution, lp::Real)
    The (generalized) inverse function of logccdf.
    For a given lp ≤ 0, invlogccdf(d, lp) is the smallest value x in the support of d for which logccdf(d, x) ≤ lp.
    source
    Sampling (Random number generation)
    Base.rand — Method
    rand(rng::AbstractRNG, d::UnivariateDistribution)
    Generate a scalar sample from d. The general fallback is quantile(d, rand()).
    source
    Random.rand! — Method
    rand!(::AbstractRNG, ::Sampleable, ::AbstractArray)
    Samples in-place from the sampler and stores the result in the provided array.
    source
    Continuous Distributions
    Distributions.Arcsine — Type
    Arcsine(a,b)
    The Arcsine distribution has probability density function
    \[f(x) = \frac{1}{\pi \sqrt{(x - a) (b - x)}}, \quad x \in [a, b]\]
    Arcsine()        # Arcsine distribution with support [0, 1]
 Arcsine(b)       # Arcsine distribution with support [0, b]
 Arcsine(a, b)    # Arcsine distribution with support [a, b]
 
@@ -10,2455 +10,53 @@
 minimum(d)       # Get the lower bound, i.e. a
 maximum(d)       # Get the upper bound, i.e. b
 location(d)      # Get the left bound, i.e. a
-scale(d)         # Get the span of the support, i.e. b - a
    External links
    Use Arcsine(a, b, check_args=false) to bypass argument checks.
    source
    Distributions.Beta — Type
    Beta(α, β)
    The Beta distribution has probability density function
    \[f(x; \alpha, \beta) = \frac{1}{B(\alpha, \beta)}
+scale(d)         # Get the span of the support, i.e. b - a

    External links

    Use Arcsine(a, b, check_args=false) to bypass argument checks.

    sourceExample block output
    Distributions.Beta — Type
    Beta(α, β)

    The Beta distribution has probability density function

    \[f(x; \alpha, \beta) = \frac{1}{B(\alpha, \beta)} x^{\alpha - 1} (1 - x)^{\beta - 1}, \quad x \in [0, 1]\]

    The Beta distribution is related to the Gamma distribution via the property that if $X \sim \operatorname{Gamma}(\alpha)$ and $Y \sim \operatorname{Gamma}(\beta)$ independently, then $X / (X + Y) \sim \operatorname{Beta}(\alpha, \beta)$.

    Beta()        # equivalent to Beta(1, 1)
 Beta(α)       # equivalent to Beta(α, α)
 Beta(α, β)    # Beta distribution with shape parameters α and β
 
-params(d)     # Get the parameters, i.e. (α, β)

    External links

    source
    Example block output
    Distributions.BetaPrime — Type
    BetaPrime(α, β)

    The Beta prime distribution has probability density function

    \[f(x; \alpha, \beta) = \frac{1}{B(\alpha, \beta)} x^{\alpha - 1} (1 + x)^{- (\alpha + \beta)}, \quad x > 0\]

    The Beta prime distribution is related to the Beta distribution via the relationship that if $X \sim \operatorname{Beta}(\alpha, \beta)$ then $\frac{X}{1 - X} \sim \operatorname{BetaPrime}(\alpha, \beta)$

    BetaPrime()        # equivalent to BetaPrime(1, 1)
 BetaPrime(α)       # equivalent to BetaPrime(α, α)
 BetaPrime(α, β)    # Beta prime distribution with shape parameters α and β
 
-params(d)          # Get the parameters, i.e. (α, β)

    External links

    source
    Distributions.Cauchy — Type
    Cauchy(μ, σ)

    The Cauchy distribution with location μ and scale σ has probability density function

    \[f(x; \mu, \sigma) = \frac{1}{\pi \sigma \left(1 + \left(\frac{x - \mu}{\sigma} \right)^2 \right)}\]

    Cauchy()         # Standard Cauchy distribution, i.e. Cauchy(0, 1)
+params(d)          # Get the parameters, i.e. (α, β)

    External links

    source
    Example block outputExample block output
    Distributions.Cauchy — Type
    Cauchy(μ, σ)

    The Cauchy distribution with location μ and scale σ has probability density function

    \[f(x; \mu, \sigma) = \frac{1}{\pi \sigma \left(1 + \left(\frac{x - \mu}{\sigma} \right)^2 \right)}\]

    Cauchy()         # Standard Cauchy distribution, i.e. Cauchy(0, 1)
 Cauchy(μ)        # Cauchy distribution with location μ and unit scale, i.e. Cauchy(μ, 1)
 Cauchy(μ, σ)     # Cauchy distribution with location μ and scale σ
 
 params(d)        # Get the parameters, i.e. (μ, σ)
 location(d)      # Get the location parameter, i.e. μ
-scale(d)         # Get the scale parameter, i.e. σ

    External links

    source
    Distributions.Chernoff — Type
    Chernoff()

    The Chernoff distribution is the distribution of the random variable

    \[\underset{t \in (-\infty,\infty)}{\arg\max} ( G(t) - t^2 ),\]

    where $G$ is standard two-sided Brownian motion.

    The distribution arises as the limit distribution of various cube-root-n consistent estimators, including the isotonic regression estimator of Brunk, the isotonic density estimator of Grenander, the least median of squares estimator of Rousseeuw, and the maximum score estimator of Manski.

    For theoretical results, see e.g. Kim and Pollard, Annals of Statistics, 1990. The code for the computation of pdf and cdf is based on the algorithm described in Groeneboom and Wellner, Journal of Computational and Graphical Statistics, 2001.

    cdf(Chernoff(),-x)              # For tail probabilities, use this instead of 1-cdf(Chernoff(),x)
    source
    Distributions.Chi — Type
    Chi(ν)

    The Chi distribution ν degrees of freedom has probability density function

    \[f(x; \nu) = \frac{1}{\Gamma(\nu/2)} 2^{1 - \nu/2} x^{\nu-1} e^{-x^2/2}, \quad x > 0\]

    It is the distribution of the square-root of a Chisq variate.

    Chi(ν)       # Chi distribution with ν degrees of freedom
+scale(d)         # Get the scale parameter, i.e. σ

    External links

    source
    Example block output
    Distributions.Chernoff — Type
    Chernoff()

    The Chernoff distribution is the distribution of the random variable

    \[\underset{t \in (-\infty,\infty)}{\arg\max} ( G(t) - t^2 ),\]

    where $G$ is standard two-sided Brownian motion.

    The distribution arises as the limit distribution of various cube-root-n consistent estimators, including the isotonic regression estimator of Brunk, the isotonic density estimator of Grenander, the least median of squares estimator of Rousseeuw, and the maximum score estimator of Manski.

    For theoretical results, see e.g. Kim and Pollard, Annals of Statistics, 1990. The code for the computation of pdf and cdf is based on the algorithm described in Groeneboom and Wellner, Journal of Computational and Graphical Statistics, 2001.

    cdf(Chernoff(),-x)              # For tail probabilities, use this instead of 1-cdf(Chernoff(),x)
    source
    Example block output
    Distributions.Chi — Type
    Chi(ν)

    The Chi distribution ν degrees of freedom has probability density function

    \[f(x; \nu) = \frac{1}{\Gamma(\nu/2)} 2^{1 - \nu/2} x^{\nu-1} e^{-x^2/2}, \quad x > 0\]

    It is the distribution of the square-root of a Chisq variate.

    Chi(ν)       # Chi distribution with ν degrees of freedom
 
 params(d)    # Get the parameters, i.e. (ν,)
-dof(d)       # Get the degrees of freedom, i.e. ν

    External links

    source
    Distributions.Chisq — Type
    Chisq(ν)

    The Chi squared distribution (typically written χ²) with ν degrees of freedom has the probability density function

    \[f(x; \nu) = \frac{x^{\nu/2 - 1} e^{-x/2}}{2^{\nu/2} \Gamma(\nu/2)}, \quad x > 0.\]

    If ν is an integer, then it is the distribution of the sum of squares of ν independent standard Normal variates.

    Chisq(ν)     # Chi-squared distribution with ν degrees of freedom
+dof(d)       # Get the degrees of freedom, i.e. ν

    External links

    source
    Example block output
    Distributions.Chisq — Type
    Chisq(ν)

    The Chi squared distribution (typically written χ²) with ν degrees of freedom has the probability density function

    \[f(x; \nu) = \frac{x^{\nu/2 - 1} e^{-x/2}}{2^{\nu/2} \Gamma(\nu/2)}, \quad x > 0.\]

    If ν is an integer, then it is the distribution of the sum of squares of ν independent standard Normal variates.

    Chisq(ν)     # Chi-squared distribution with ν degrees of freedom
 
 params(d)    # Get the parameters, i.e. (ν,)
-dof(d)       # Get the degrees of freedom, i.e. ν

    External links

    source
    Example block outputExample block outputExample block output
    Distributions.Erlang — Type
    Erlang(α,θ)

    The Erlang distribution is a special case of a Gamma distribution with integer shape parameter.

    Erlang()       # Erlang distribution with unit shape and unit scale, i.e. Erlang(1, 1)
 Erlang(a)      # Erlang distribution with shape parameter a and unit scale, i.e. Erlang(a, 1)
-Erlang(a, s)   # Erlang distribution with shape parameter a and scale s

    External links

    source
    Distributions.Exponential — Type
    Exponential(θ)

    The Exponential distribution with scale parameter θ has probability density function

    \[f(x; \theta) = \frac{1}{\theta} e^{-\frac{x}{\theta}}, \quad x > 0\]

    Exponential()      # Exponential distribution with unit scale, i.e. Exponential(1)
+Erlang(a, s)   # Erlang distribution with shape parameter a and scale s

    External links

    source
    Example block output
    Distributions.Exponential — Type
    Exponential(θ)

    The Exponential distribution with scale parameter θ has probability density function

    \[f(x; \theta) = \frac{1}{\theta} e^{-\frac{x}{\theta}}, \quad x > 0\]

    Exponential()      # Exponential distribution with unit scale, i.e. Exponential(1)
 Exponential(θ)     # Exponential distribution with scale θ
 
 params(d)          # Get the parameters, i.e. (θ,)
 scale(d)           # Get the scale parameter, i.e. θ
-rate(d)            # Get the rate parameter, i.e. 1 / θ

    External links

    source
    Example block output
    Distributions.FDist — Type
    FDist(ν1, ν2)

    The F distribution has probability density function

    \[f(x; \nu_1, \nu_2) = \frac{1}{x B(\nu_1/2, \nu_2/2)} \sqrt{\frac{(\nu_1 x)^{\nu_1} \cdot \nu_2^{\nu_2}}{(\nu_1 x + \nu_2)^{\nu_1 + \nu_2}}}, \quad x>0\]

    It is related to the Chisq distribution via the property that if $X_1 \sim \operatorname{Chisq}(\nu_1)$ and $X_2 \sim \operatorname{Chisq}(\nu_2)$, then $(X_1/\nu_1) / (X_2 / \nu_2) \sim \operatorname{FDist}(\nu_1, \nu_2)$.

    FDist(ν1, ν2)     # F-Distribution with parameters ν1 and ν2
 
-params(d)         # Get the parameters, i.e. (ν1, ν2)

    External links

    source
    Distributions.Frechet — Type
    Frechet(α,θ)

    The Fréchet distribution with shape α and scale θ has probability density function

    \[f(x; \alpha, \theta) = \frac{\alpha}{\theta} \left( \frac{x}{\theta} \right)^{-\alpha-1} +params(d) # Get the parameters, i.e. (ν1, ν2)

    External links

    source
    Example block output
    Distributions.Frechet — Type
    Frechet(α,θ)

    The Fréchet distribution with shape α and scale θ has probability density function

    \[f(x; \alpha, \theta) = \frac{\alpha}{\theta} \left( \frac{x}{\theta} \right)^{-\alpha-1} e^{-(x/\theta)^{-\alpha}}, \quad x > 0\]

    Frechet()        # Fréchet distribution with unit shape and unit scale, i.e. Frechet(1, 1)
 Frechet(α)       # Fréchet distribution with shape α and unit scale, i.e. Frechet(α, 1)
 Frechet(α, θ)    # Fréchet distribution with shape α and scale θ
 
 params(d)        # Get the parameters, i.e. (α, θ)
 shape(d)         # Get the shape parameter, i.e. α
-scale(d)         # Get the scale parameter, i.e. θ

    External links

    source
    Distributions.Gamma — Type
    Gamma(α,θ)

    The Gamma distribution with shape parameter α and scale θ has probability density function

    \[f(x; \alpha, \theta) = \frac{x^{\alpha-1} e^{-x/\theta}}{\Gamma(\alpha) \theta^\alpha}, +scale(d) # Get the scale parameter, i.e. θ

    External links

    source
    Example block output
    Distributions.Gamma — Type
    Gamma(α,θ)

    The Gamma distribution with shape parameter α and scale θ has probability density function

    \[f(x; \alpha, \theta) = \frac{x^{\alpha-1} e^{-x/\theta}}{\Gamma(\alpha) \theta^\alpha}, \quad x > 0\]

    Gamma()          # Gamma distribution with unit shape and unit scale, i.e. Gamma(1, 1)
 Gamma(α)         # Gamma distribution with shape α and unit scale, i.e. Gamma(α, 1)
 Gamma(α, θ)      # Gamma distribution with shape α and scale θ
 
 params(d)        # Get the parameters, i.e. (α, θ)
 shape(d)         # Get the shape parameter, i.e. α
-scale(d)         # Get the scale parameter, i.e. θ

    External links

    source
    Example block output
    Distributions.GeneralizedExtremeValue — Type
    GeneralizedExtremeValue(μ, σ, ξ)

    The Generalized extreme value distribution with shape parameter ξ, scale σ and location μ has probability density function

    \[f(x; \xi, \sigma, \mu) = \begin{cases} \frac{1}{\sigma} \left[ 1+\left(\frac{x-\mu}{\sigma}\right)\xi\right]^{-1/\xi-1} \exp\left\{-\left[ 1+ \left(\frac{x-\mu}{\sigma}\right)\xi\right]^{-1/\xi} \right\} & \text{for } \xi \neq 0 \\ \frac{1}{\sigma} \exp\left\{-\frac{x-\mu}{\sigma}\right\} \exp\left\{-\exp\left[-\frac{x-\mu}{\sigma}\right]\right\} & \text{for } \xi = 0 \\ \end{cases}\]

    for

    \[x \in \begin{cases} @@ -2470,175 +68,7 @@ params(d) # Get the parameters, i.e. (μ, σ, ξ) location(d) # Get the location parameter, i.e. μ scale(d) # Get the scale parameter, i.e. σ -shape(d) # Get the shape parameter, i.e. ξ (sometimes called c)

    External links

    source
    Example block output
    Distributions.GeneralizedPareto — Type
    GeneralizedPareto(μ, σ, ξ)

    The Generalized Pareto distribution (GPD) with shape parameter ξ, scale σ and location μ has probability density function

    \[f(x; \mu, \sigma, \xi) = \begin{cases} \frac{1}{\sigma}(1 + \xi \frac{x - \mu}{\sigma} )^{-\frac{1}{\xi} - 1} & \text{for } \xi \neq 0 \\ \frac{1}{\sigma} e^{-\frac{\left( x - \mu \right) }{\sigma}} & \text{for } \xi = 0 \end{cases}~, @@ -2653,1838 +83,52 @@ params(d) # Get the parameters, i.e. (μ, σ, ξ) location(d) # Get the location parameter, i.e. μ scale(d) # Get the scale parameter, i.e. σ -shape(d) # Get the shape parameter, i.e. ξ

    External links

    source
    Example block output
    Distributions.Gumbel — Type
    Gumbel(μ, θ)

    The Gumbel (maxima) distribution with location μ and scale θ has probability density function

    \[f(x; \mu, \theta) = \frac{1}{\theta} e^{-(z + e^{-z})}, \quad \text{ with } z = \frac{x - \mu}{\theta}\]

    Gumbel()            # Gumbel distribution with zero location and unit scale, i.e. Gumbel(0, 1)
 Gumbel(μ)           # Gumbel distribution with location μ and unit scale, i.e. Gumbel(μ, 1)
 Gumbel(μ, θ)        # Gumbel distribution with location μ and scale θ
 
 params(d)        # Get the parameters, i.e. (μ, θ)
 location(d)      # Get the location parameter, i.e. μ
-scale(d)         # Get the scale parameter, i.e. θ

    External links

    source
    Distributions.InverseGamma — Type
    InverseGamma(α, θ)

    The inverse Gamma distribution with shape parameter α and scale θ has probability density function

    \[f(x; \alpha, \theta) = \frac{\theta^\alpha x^{-(\alpha + 1)}}{\Gamma(\alpha)} +scale(d) # Get the scale parameter, i.e. θ

    External links

    source
    Example block output
    Distributions.InverseGamma — Type
    InverseGamma(α, θ)

    The inverse Gamma distribution with shape parameter α and scale θ has probability density function

    \[f(x; \alpha, \theta) = \frac{\theta^\alpha x^{-(\alpha + 1)}}{\Gamma(\alpha)} e^{-\frac{\theta}{x}}, \quad x > 0\]

    It is related to the Gamma distribution: if $X \sim \operatorname{Gamma}(\alpha, \beta)$, then $1 / X \sim \operatorname{InverseGamma}(\alpha, \beta^{-1})$.

    InverseGamma()        # Inverse Gamma distribution with unit shape and unit scale, i.e. InverseGamma(1, 1)
 InverseGamma(α)       # Inverse Gamma distribution with shape α and unit scale, i.e. InverseGamma(α, 1)
 InverseGamma(α, θ)    # Inverse Gamma distribution with shape α and scale θ
 
 params(d)        # Get the parameters, i.e. (α, θ)
 shape(d)         # Get the shape parameter, i.e. α
-scale(d)         # Get the scale parameter, i.e. θ

    External links

    source
    Example block output
    Distributions.InverseGaussian — Type
    InverseGaussian(μ,λ)

    The inverse Gaussian distribution with mean μ and shape λ has probability density function

    \[f(x; \mu, \lambda) = \sqrt{\frac{\lambda}{2\pi x^3}} \exp\!\left(\frac{-\lambda(x-\mu)^2}{2\mu^2x}\right), \quad x > 0\]

    InverseGaussian()              # Inverse Gaussian distribution with unit mean and unit shape, i.e. InverseGaussian(1, 1)
 InverseGaussian(μ),            # Inverse Gaussian distribution with mean μ and unit shape, i.e. InverseGaussian(μ, 1)
 InverseGaussian(μ, λ)          # Inverse Gaussian distribution with mean μ and shape λ
 
 params(d)           # Get the parameters, i.e. (μ, λ)
 mean(d)             # Get the mean parameter, i.e. μ
-shape(d)            # Get the shape parameter, i.e. λ

    External links

    source
    Distributions.JohnsonSU — Type
    JohnsonSU(ξ, λ, γ, δ)

    The Johnson's $S_U$-distribution with parameters ξ, λ, γ and δ is a transformation of the normal distribution:

    If

    \[X = \lambda\sinh\Bigg( \frac{Z - \gamma}{\delta} \Bigg) + \xi\]

    where $Z \sim \mathcal{N}(0,1)$, then $X \sim \operatorname{Johnson}(\xi, \lambda, \gamma, \delta)$.

    JohnsonSU()           # Equivalent to JohnsonSU(0, 1, 0, 1)
+shape(d)            # Get the shape parameter, i.e. λ

    External links

    source
    Example block output
    Distributions.JohnsonSU — Type
    JohnsonSU(ξ, λ, γ, δ)

    The Johnson's $S_U$-distribution with parameters ξ, λ, γ and δ is a transformation of the normal distribution:

    If

    \[X = \lambda\sinh\Bigg( \frac{Z - \gamma}{\delta} \Bigg) + \xi\]

    where $Z \sim \mathcal{N}(0,1)$, then $X \sim \operatorname{Johnson}(\xi, \lambda, \gamma, \delta)$.

    JohnsonSU()           # Equivalent to JohnsonSU(0, 1, 0, 1)
 JohnsonSU(ξ, λ, γ, δ) # JohnsonSU's S_U-distribution with parameters ξ, λ, γ and δ
 
 params(d)           # Get the parameters, i.e. (ξ, λ, γ, δ)
 shape(d)            # Get the shape parameter, i.e. ξ
-scale(d)            # Get the scale parameter, i.e. λ

    External links

    source
    Distributions.Kolmogorov — Type
    Kolmogorov()

    Kolmogorov distribution defined as

    \[\sup_{t \in [0,1]} |B(t)|\]

    where $B(t)$ is a Brownian bridge used in the Kolmogorov–Smirnov test for large n.

    source
    Distributions.KSDist — Type
    KSDist(n)

    Distribution of the (two-sided) Kolmogorov-Smirnoff statistic

    \[D_n = \sup_x | \hat{F}_n(x) -F(x)|\]

    $D_n$ converges a.s. to the Kolmogorov distribution.

    source
    Distributions.KSOneSided — Type
    KSOneSided(n)

    Distribution of the one-sided Kolmogorov-Smirnov test statistic:

    \[D^+_n = \sup_x (\hat{F}_n(x) -F(x))\]

    source
    Distributions.Kumaraswamy — Type
    Kumaraswamy(a, b)

    The Kumaraswamy distribution with shape parameters a > 0 and b > 0 has probability density function

    \[f(x; a, b) = a b x^{a - 1} (1 - x^a)^{b - 1}, \quad 0 < x < 1\]

    It is related to the Beta distribution by the following identity: if $X \sim \operatorname{Kumaraswamy}(a, b)$ then $X^a \sim \operatorname{Beta}(1, b)$. In particular, if $X \sim \operatorname{Kumaraswamy}(1, 1)$ then $X \sim \operatorname{Uniform}(0, 1)$.

    External links

    References

    • Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology. 46(1-2), 79-88.
    source
    Distributions.Laplace — Type
    Laplace(μ,θ)

    The Laplace distribution with location μ and scale θ has probability density function

    \[f(x; \mu, \theta) = \frac{1}{2 \theta} \exp \left(- \frac{|x - \mu|}{\theta} \right)\]

    Laplace()       # Laplace distribution with zero location and unit scale, i.e. Laplace(0, 1)
+scale(d)            # Get the scale parameter, i.e. λ

    External links

    source
    Example block output
    Distributions.Kolmogorov — Type
    Kolmogorov()

    Kolmogorov distribution defined as

    \[\sup_{t \in [0,1]} |B(t)|\]

    where $B(t)$ is a Brownian bridge used in the Kolmogorov–Smirnov test for large n.

    source
    Example block output
    Distributions.KSDist — Type
    KSDist(n)

    Distribution of the (two-sided) Kolmogorov-Smirnoff statistic

    \[D_n = \sup_x | \hat{F}_n(x) -F(x)|\]

    $D_n$ converges a.s. to the Kolmogorov distribution.

    source
    Distributions.KSOneSided — Type
    KSOneSided(n)

    Distribution of the one-sided Kolmogorov-Smirnov test statistic:

    \[D^+_n = \sup_x (\hat{F}_n(x) -F(x))\]

    source
    Distributions.Kumaraswamy — Type
    Kumaraswamy(a, b)

    The Kumaraswamy distribution with shape parameters a > 0 and b > 0 has probability density function

    \[f(x; a, b) = a b x^{a - 1} (1 - x^a)^{b - 1}, \quad 0 < x < 1\]

    It is related to the Beta distribution by the following identity: if $X \sim \operatorname{Kumaraswamy}(a, b)$ then $X^a \sim \operatorname{Beta}(1, b)$. In particular, if $X \sim \operatorname{Kumaraswamy}(1, 1)$ then $X \sim \operatorname{Uniform}(0, 1)$.

    External links

    References

    • Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology. 46(1-2), 79-88.
    source
    Example block output
    Distributions.Laplace — Type
    Laplace(μ,θ)

    The Laplace distribution with location μ and scale θ has probability density function

    \[f(x; \mu, \theta) = \frac{1}{2 \theta} \exp \left(- \frac{|x - \mu|}{\theta} \right)\]

    Laplace()       # Laplace distribution with zero location and unit scale, i.e. Laplace(0, 1)
 Laplace(μ)      # Laplace distribution with location μ and unit scale, i.e. Laplace(μ, 1)
 Laplace(μ, θ)   # Laplace distribution with location μ and scale θ
 
 params(d)       # Get the parameters, i.e., (μ, θ)
 location(d)     # Get the location parameter, i.e. μ
-scale(d)        # Get the scale parameter, i.e. θ

    External links

    source
    Example block output
    Distributions.Levy — Type
    Levy(μ, σ)

    The Lévy distribution with location μ and scale σ has probability density function

    \[f(x; \mu, \sigma) = \sqrt{\frac{\sigma}{2 \pi (x - \mu)^3}} \exp \left( - \frac{\sigma}{2 (x - \mu)} \right), \quad x > \mu\]

    Levy()         # Levy distribution with zero location and unit scale, i.e. Levy(0, 1)
 Levy(μ)        # Levy distribution with location μ and unit scale, i.e. Levy(μ, 1)
 Levy(μ, σ)     # Levy distribution with location μ and scale σ
 
 params(d)      # Get the parameters, i.e. (μ, σ)
-location(d)    # Get the location parameter, i.e. μ

    External links

    source
    Distributions.Lindley — Type
    Lindley(θ)

    The one-parameter Lindley distribution with shape θ > 0 has probability density function

    \[f(x; \theta) = \frac{\theta^2}{1 + \theta} (1 + x) e^{-\theta x}, \quad x > 0\]

    It was first described by Lindley[1] and was studied in greater detail by Ghitany et al.[2] Note that Lindley(θ) is a mixture of an Exponential(θ) and a Gamma(2, θ) with respective mixing weights p = θ/(1 + θ) and 1 - p.

    source
    Example block output
    Distributions.Lindley — Type
    Lindley(θ)

    The one-parameter Lindley distribution with shape θ > 0 has probability density function

    \[f(x; \theta) = \frac{\theta^2}{1 + \theta} (1 + x) e^{-\theta x}, \quad x > 0\]

    It was first described by Lindley[1] and was studied in greater detail by Ghitany et al.[2] Note that Lindley(θ) is a mixture of an Exponential(θ) and a Gamma(2, θ) with respective mixing weights p = θ/(1 + θ) and 1 - p.

    source
    Example block output
    Distributions.Logistic — Type
    Logistic(μ,θ)

    The Logistic distribution with location μ and scale θ has probability density function

    \[f(x; \mu, \theta) = \frac{1}{4 \theta} \mathrm{sech}^2 \left( \frac{x - \mu}{2 \theta} \right)\]

    Logistic()       # Logistic distribution with zero location and unit scale, i.e. Logistic(0, 1)
 Logistic(μ)      # Logistic distribution with location μ and unit scale, i.e. Logistic(μ, 1)
 Logistic(μ, θ)   # Logistic distribution with location μ and scale θ
 
 params(d)       # Get the parameters, i.e. (μ, θ)
 location(d)     # Get the location parameter, i.e. μ
-scale(d)        # Get the scale parameter, i.e. θ

    External links

    source
    Distributions.LogitNormal — Type
    LogitNormal(μ,σ)

    The logit normal distribution is the distribution of of a random variable whose logit has a Normal distribution. Or inversely, when applying the logistic function to a Normal random variable then the resulting random variable follows a logit normal distribution.

    If $X \sim \operatorname{Normal}(\mu, \sigma)$ then $\operatorname{logistic}(X) \sim \operatorname{LogitNormal}(\mu,\sigma)$.

    The probability density function is

    \[f(x; \mu, \sigma) = \frac{1}{x \sqrt{2 \pi \sigma^2}} +scale(d) # Get the scale parameter, i.e. θ

    External links

    source
    Example block output
    Distributions.LogitNormal — Type
    LogitNormal(μ,σ)

    The logit normal distribution is the distribution of of a random variable whose logit has a Normal distribution. Or inversely, when applying the logistic function to a Normal random variable then the resulting random variable follows a logit normal distribution.

    If $X \sim \operatorname{Normal}(\mu, \sigma)$ then $\operatorname{logistic}(X) \sim \operatorname{LogitNormal}(\mu,\sigma)$.

    The probability density function is

    \[f(x; \mu, \sigma) = \frac{1}{x \sqrt{2 \pi \sigma^2}} \exp \left( - \frac{(\text{logit}(x) - \mu)^2}{2 \sigma^2} \right), \quad x > 0\]

    where the logit-Function is

    \[\text{logit}(x) = \ln\left(\frac{x}{1-x}\right) \quad 0 < x < 1\]

    LogitNormal()        # Logit-normal distribution with zero logit-mean and unit scale
@@ -4495,151 +139,7 @@
 median(d)            # Get the median, i.e. logistic(μ)

    The following properties have no analytical solution but numerical approximations. In order to avoid package dependencies for numerical optimization, they are currently not implemented.

    mean(d)
 var(d)
 std(d)
-mode(d)

    Similarly, skewness, kurtosis, and entropy are not implemented.

    External links

    source
    Distributions.LogNormal — Type
    LogNormal(μ,σ)

    The log normal distribution is the distribution of the exponential of a Normal variate: if $X \sim \operatorname{Normal}(\mu, \sigma)$ then $\exp(X) \sim \operatorname{LogNormal}(\mu,\sigma)$. The probability density function is

    \[f(x; \mu, \sigma) = \frac{1}{x \sqrt{2 \pi \sigma^2}} +mode(d)

    Similarly, skewness, kurtosis, and entropy are not implemented.

    External links

    source
    Example block output
    Distributions.LogNormal — Type
    LogNormal(μ,σ)

    The log normal distribution is the distribution of the exponential of a Normal variate: if $X \sim \operatorname{Normal}(\mu, \sigma)$ then $\exp(X) \sim \operatorname{LogNormal}(\mu,\sigma)$. The probability density function is

    \[f(x; \mu, \sigma) = \frac{1}{x \sqrt{2 \pi \sigma^2}} \exp \left( - \frac{(\log(x) - \mu)^2}{2 \sigma^2} \right), \quad x > 0\]

    LogNormal()          # Log-normal distribution with zero log-mean and unit scale
 LogNormal(μ)         # Log-normal distribution with log-mean mu and unit scale
@@ -4648,2409 +148,39 @@
 params(d)            # Get the parameters, i.e. (μ, σ)
 meanlogx(d)          # Get the mean of log(X), i.e. μ
 varlogx(d)           # Get the variance of log(X), i.e. σ^2
-stdlogx(d)           # Get the standard deviation of log(X), i.e. σ

    External links

    source
    Distributions.NoncentralBeta — Type
    NoncentralBeta(α, β, λ)

    Noncentral Beta distribution with shape parameters α > 0 and β > 0 and noncentrality parameter λ >= 0.

    source
    Distributions.NoncentralChisq — Type
    NoncentralChisq(ν, λ)

    The noncentral chi-squared distribution with ν degrees of freedom and noncentrality parameter λ has the probability density function

    \[f(x; \nu, \lambda) = \frac{1}{2} e^{-(x + \lambda)/2} \left( \frac{x}{\lambda} \right)^{\nu/4-1/2} I_{\nu/2-1}(\sqrt{\lambda x}), \quad x > 0\]

    It is the distribution of the sum of squares of ν independent Normal variates with individual means $\mu_i$ and

    \[\lambda = \sum_{i=1}^\nu \mu_i^2\]

    NoncentralChisq(ν, λ)     # Noncentral chi-squared distribution with ν degrees of freedom and noncentrality parameter λ
+stdlogx(d)           # Get the standard deviation of log(X), i.e. σ

    External links

    source
    Example block outputExample block output
    Distributions.NoncentralBeta — Type
    NoncentralBeta(α, β, λ)

    Noncentral Beta distribution with shape parameters α > 0 and β > 0 and noncentrality parameter λ >= 0.

    source
    Example block output
    Distributions.NoncentralChisq — Type
    NoncentralChisq(ν, λ)

    The noncentral chi-squared distribution with ν degrees of freedom and noncentrality parameter λ has the probability density function

    \[f(x; \nu, \lambda) = \frac{1}{2} e^{-(x + \lambda)/2} \left( \frac{x}{\lambda} \right)^{\nu/4-1/2} I_{\nu/2-1}(\sqrt{\lambda x}), \quad x > 0\]

    It is the distribution of the sum of squares of ν independent Normal variates with individual means $\mu_i$ and

    \[\lambda = \sum_{i=1}^\nu \mu_i^2\]

    NoncentralChisq(ν, λ)     # Noncentral chi-squared distribution with ν degrees of freedom and noncentrality parameter λ
 
-params(d)    # Get the parameters, i.e. (ν, λ)

    External links

    source
    Distributions.NoncentralF — Type
    NoncentralF(ν1, ν2, λ)

    Noncentral F-distribution with ν1 > 0 and ν2 > 0 degrees of freedom and noncentrality parameter λ >= 0.

    source
    Distributions.NoncentralT — Type
    NoncentralT(ν, λ)

    Noncentral Student's t-distribution with v > 0 degrees of freedom and noncentrality parameter λ.

    source
    Example block output
    Distributions.NoncentralF — Type
    NoncentralF(ν1, ν2, λ)

    Noncentral F-distribution with ν1 > 0 and ν2 > 0 degrees of freedom and noncentrality parameter λ >= 0.

    source
    Example block output
    Distributions.NoncentralT — Type
    NoncentralT(ν, λ)

    Noncentral Student's t-distribution with v > 0 degrees of freedom and noncentrality parameter λ.

    source
    Example block output
    Distributions.Normal — Type
    Normal(μ,σ)

    The Normal distribution with mean μ and standard deviation σ≥0 has probability density function

    \[f(x; \mu, \sigma) = \frac{1}{\sqrt{2 \pi \sigma^2}} \exp \left( - \frac{(x - \mu)^2}{2 \sigma^2} \right)\]

    Note that if σ == 0, then the distribution is a point mass concentrated at μ. Though not technically a continuous distribution, it is allowed so as to account for cases where σ may have underflowed, and the functions are defined by taking the pointwise limit as $σ → 0$.

    Normal()          # standard Normal distribution with zero mean and unit variance
 Normal(μ)         # Normal distribution with mean μ and unit variance
 Normal(μ, σ)      # Normal distribution with mean μ and variance σ^2
 
 params(d)         # Get the parameters, i.e. (μ, σ)
 mean(d)           # Get the mean, i.e. μ
-std(d)            # Get the standard deviation, i.e. σ

    External links

    source
    Distributions.NormalCanon — Type
    NormalCanon(η, λ)

    Canonical parametrisation of the Normal distribution with canonical parameters η and λ.

    The two canonical parameters of a normal distribution $\mathcal{N}(\mu, \sigma^2)$ with mean $\mu$ and standard deviation $\sigma$ are $\eta = \sigma^{-2} \mu$ and $\lambda = \sigma^{-2}$.

    source
    Distributions.NormalInverseGaussian — Type
    NormalInverseGaussian(μ,α,β,δ)

    The Normal-inverse Gaussian distribution with location μ, tail heaviness α, asymmetry parameter β and scale δ has probability density function

    \[f(x; \mu, \alpha, \beta, \delta) = \frac{\alpha\delta K_1 \left(\alpha\sqrt{\delta^2 + (x - \mu)^2}\right)}{\pi \sqrt{\delta^2 + (x - \mu)^2}} \; e^{\delta \gamma + \beta (x - \mu)}\]

    where $K_j$ denotes a modified Bessel function of the third kind.

    External links

    source
    Distributions.Pareto — Type
    Pareto(α,θ)

    The Pareto distribution with shape α and scale θ has probability density function

    \[f(x; \alpha, \theta) = \frac{\alpha \theta^\alpha}{x^{\alpha + 1}}, \quad x \ge \theta\]

    Pareto()            # Pareto distribution with unit shape and unit scale, i.e. Pareto(1, 1)
+std(d)            # Get the standard deviation, i.e. σ

    External links

    source
    Example block output
    Distributions.NormalCanon — Type
    NormalCanon(η, λ)

    Canonical parametrisation of the Normal distribution with canonical parameters η and λ.

    The two canonical parameters of a normal distribution $\mathcal{N}(\mu, \sigma^2)$ with mean $\mu$ and standard deviation $\sigma$ are $\eta = \sigma^{-2} \mu$ and $\lambda = \sigma^{-2}$.

    source
    Example block output
    Distributions.NormalInverseGaussian — Type
    NormalInverseGaussian(μ,α,β,δ)

    The Normal-inverse Gaussian distribution with location μ, tail heaviness α, asymmetry parameter β and scale δ has probability density function

    \[f(x; \mu, \alpha, \beta, \delta) = \frac{\alpha\delta K_1 \left(\alpha\sqrt{\delta^2 + (x - \mu)^2}\right)}{\pi \sqrt{\delta^2 + (x - \mu)^2}} \; e^{\delta \gamma + \beta (x - \mu)}\]

    where $K_j$ denotes a modified Bessel function of the third kind.

    External links

    source
    Example block output
    Distributions.Pareto — Type
    Pareto(α,θ)

    The Pareto distribution with shape α and scale θ has probability density function

    \[f(x; \alpha, \theta) = \frac{\alpha \theta^\alpha}{x^{\alpha + 1}}, \quad x \ge \theta\]

    Pareto()            # Pareto distribution with unit shape and unit scale, i.e. Pareto(1, 1)
 Pareto(α)           # Pareto distribution with shape α and unit scale, i.e. Pareto(α, 1)
 Pareto(α, θ)        # Pareto distribution with shape α and scale θ
 
 params(d)        # Get the parameters, i.e. (α, θ)
 shape(d)         # Get the shape parameter, i.e. α
-scale(d)         # Get the scale parameter, i.e. θ

    External links

    source
    Distributions.PGeneralizedGaussian — Type
    PGeneralizedGaussian(μ, α, p)

    The p-Generalized Gaussian distribution, more commonly known as the exponential power or the generalized normal distribution, with scale α, location μ, and shape p has the probability density function

    \[f(x, \mu, \alpha, p) = \frac{p}{2\alpha\Gamma(1/p)} e^{-(\frac{|x-\mu|}{\alpha})^p} \quad x \in (-\infty, +\infty) , \alpha > 0, p > 0\]

    The p-Generalized Gaussian (GGD) is a parametric distribution that incorporates the normal (p = 2) and Laplacian (p = 1) distributions as special cases. As p → ∞, the distribution approaches the Uniform distribution on [μ - α, μ + α].

    PGeneralizedGaussian()           # GGD with location 0, scale √2, and shape 2 (the normal distribution)
+scale(d)         # Get the scale parameter, i.e. θ

    External links

    source
    Example block output
    Distributions.PGeneralizedGaussian — Type
    PGeneralizedGaussian(μ, α, p)

    The p-Generalized Gaussian distribution, more commonly known as the exponential power or the generalized normal distribution, with scale α, location μ, and shape p has the probability density function

    \[f(x, \mu, \alpha, p) = \frac{p}{2\alpha\Gamma(1/p)} e^{-(\frac{|x-\mu|}{\alpha})^p} \quad x \in (-\infty, +\infty) , \alpha > 0, p > 0\]

    The p-Generalized Gaussian (GGD) is a parametric distribution that incorporates the normal (p = 2) and Laplacian (p = 1) distributions as special cases. As p → ∞, the distribution approaches the Uniform distribution on [μ - α, μ + α].

    PGeneralizedGaussian()           # GGD with location 0, scale √2, and shape 2 (the normal distribution)
 PGeneralizedGaussian(μ, α, p)    # GGD with location μ, scale α, and shape p
 
 params(d)                        # Get the parameters, i.e. (μ, α, p)
 location(d)                      # Get the location parameter, μ
 scale(d)                         # Get the scale parameter, α
-shape(d)                         # Get the shape parameter, p

    External Links

    source
    Distributions.Rayleigh — Type
    Rayleigh(σ)

    The Rayleigh distribution with scale σ has probability density function

    \[f(x; \sigma) = \frac{x}{\sigma^2} e^{-\frac{x^2}{2 \sigma^2}}, \quad x > 0\]

    It is related to the Normal distribution via the property that if $X, Y \sim \operatorname{Normal}(0,\sigma)$, independently, then $\sqrt{X^2 + Y^2} \sim \operatorname{Rayleigh}(\sigma)$.

    Rayleigh()       # Rayleigh distribution with unit scale, i.e. Rayleigh(1)
+shape(d)                         # Get the shape parameter, p

    External Links

    source
    Example block output
    Distributions.Rayleigh — Type
    Rayleigh(σ)

    The Rayleigh distribution with scale σ has probability density function

    \[f(x; \sigma) = \frac{x}{\sigma^2} e^{-\frac{x^2}{2 \sigma^2}}, \quad x > 0\]

    It is related to the Normal distribution via the property that if $X, Y \sim \operatorname{Normal}(0,\sigma)$, independently, then $\sqrt{X^2 + Y^2} \sim \operatorname{Rayleigh}(\sigma)$.

    Rayleigh()       # Rayleigh distribution with unit scale, i.e. Rayleigh(1)
 Rayleigh(σ)      # Rayleigh distribution with scale σ
 
 params(d)        # Get the parameters, i.e. (σ,)
-scale(d)         # Get the scale parameter, i.e. σ

    External links

    source
    Distributions.Rician — Type
    Rician(ν, σ)

    The Rician distribution with parameters ν and σ has probability density function:

    \[f(x; \nu, \sigma) = \frac{x}{\sigma^2} \exp\left( \frac{-(x^2 + \nu^2)}{2\sigma^2} \right) I_0\left( \frac{x\nu}{\sigma^2} \right).\]

    If shape and scale parameters K and Ω are given instead, ν and σ may be computed from them:

    \[\sigma = \sqrt{\frac{\Omega}{2(K + 1)}}, \quad \nu = \sigma\sqrt{2K}\]

    Rician()         # Rician distribution with parameters ν=0 and σ=1
+scale(d)         # Get the scale parameter, i.e. σ

    External links

    source
    Example block output
    Distributions.Rician — Type
    Rician(ν, σ)

    The Rician distribution with parameters ν and σ has probability density function:

    \[f(x; \nu, \sigma) = \frac{x}{\sigma^2} \exp\left( \frac{-(x^2 + \nu^2)}{2\sigma^2} \right) I_0\left( \frac{x\nu}{\sigma^2} \right).\]

    If shape and scale parameters K and Ω are given instead, ν and σ may be computed from them:

    \[\sigma = \sqrt{\frac{\Omega}{2(K + 1)}}, \quad \nu = \sigma\sqrt{2K}\]

    Rician()         # Rician distribution with parameters ν=0 and σ=1
 Rician(ν, σ)     # Rician distribution with parameters ν and σ
 
 params(d)        # Get the parameters, i.e. (ν, σ)
 shape(d)         # Get the shape parameter K = ν²/2σ²
-scale(d)         # Get the scale parameter Ω = ν² + 2σ²

    External links:

    source
    Distributions.Semicircle — Type
    Semicircle(r)

    The Wigner semicircle distribution with radius parameter r has probability density function

    \[f(x; r) = \frac{2}{\pi r^2} \sqrt{r^2 - x^2}, \quad x \in [-r, r].\]

    Semicircle(r)   # Wigner semicircle distribution with radius r
+scale(d)         # Get the scale parameter Ω = ν² + 2σ²

    External links:

    source
    Example block output
    Distributions.Semicircle — Type
    Semicircle(r)

    The Wigner semicircle distribution with radius parameter r has probability density function

    \[f(x; r) = \frac{2}{\pi r^2} \sqrt{r^2 - x^2}, \quad x \in [-r, r].\]

    Semicircle(r)   # Wigner semicircle distribution with radius r
 
-params(d)       # Get the radius parameter, i.e. (r,)

    External links

    source
    Example block output
    Distributions.SkewedExponentialPower — Type
    SkewedExponentialPower(μ, σ, p, α)

    The Skewed exponential power distribution, with location μ, scale σ, shape p, and skewness α, has the probability density function [1]

    \[f(x; \mu, \sigma, p, \alpha) = \begin{cases} \frac{1}{\sigma 2p^{1/p}\Gamma(1+1/p)} \exp \left\{ - \frac{1}{2p}\Big| \frac{x-\mu}{\alpha \sigma} \Big|^p \right\}, & \text{if } x \leq \mu \\ \frac{1}{\sigma 2p^{1/p}\Gamma(1+1/p)} \exp \left\{ - \frac{1}{2p}\Big| \frac{x-\mu}{(1-\alpha) \sigma} \Big|^p \right\}, & \text{if } x > \mu @@ -7063,726 +193,25 @@ params(d) # Get the parameters, i.e. (μ, σ, p, α) shape(d) # Get the shape parameter, i.e. p location(d) # Get the location parameter, i.e. μ -scale(d) # Get the scale parameter, i.e. σ

    source
    Distributions.SkewNormal — Type
    SkewNormal(ξ, ω, α)

    The skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness. Given a location ξ, scale ω, and shape α, it has the probability density function

    \[f(x; \xi, \omega, \alpha) = +scale(d) # Get the scale parameter, i.e. σ

    source
    Example block output
    Distributions.SkewNormal — Type
    SkewNormal(ξ, ω, α)

    The skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness. Given a location ξ, scale ω, and shape α, it has the probability density function

    \[f(x; \xi, \omega, \alpha) = \frac{2}{\omega \sqrt{2 \pi}} \exp{\bigg(-\frac{(x-\xi)^2}{2\omega^2}\bigg)} \int_{-\infty}^{\alpha\left(\frac{x-\xi}{\omega}\right)} -\frac{1}{\sqrt{2 \pi}} \exp{\bigg(-\frac{t^2}{2}\bigg)} \, \mathrm{d}t\]

    External links

    source
    Distributions.StudentizedRange — Type
    StudentizedRange(ν, k)

    The studentized range distribution has probability density function:

    \[f(q; k, \nu) = \frac{\sqrt{2\pi}k(k - 1)\nu^{\nu/2}}{\Gamma{\left(\frac{\nu}{2}\right)}2^{\nu/2 - 1}} \int_{0}^{\infty} {x^{\nu}\phi(\sqrt{\nu}x)} \left[\int_{-\infty}^{\infty} {\phi(u)\phi(u - qx)[\Phi(u) - \Phi(u - qx)]^{k - 2}}du\right]dx\]

    where

    \[\begin{aligned} +\frac{1}{\sqrt{2 \pi}} \exp{\bigg(-\frac{t^2}{2}\bigg)} \, \mathrm{d}t\]

    External links

    source
    Example block output
    Distributions.StudentizedRange — Type
    StudentizedRange(ν, k)

    The studentized range distribution has probability density function:

    \[f(q; k, \nu) = \frac{\sqrt{2\pi}k(k - 1)\nu^{\nu/2}}{\Gamma{\left(\frac{\nu}{2}\right)}2^{\nu/2 - 1}} \int_{0}^{\infty} {x^{\nu}\phi(\sqrt{\nu}x)} \left[\int_{-\infty}^{\infty} {\phi(u)\phi(u - qx)[\Phi(u) - \Phi(u - qx)]^{k - 2}}du\right]dx\]

    where

    \[\begin{aligned} \Phi(x) &= \frac{1 + erf(\frac{x}{\sqrt{2}})}{2} &&(\text{Normal Distribution CDF})\\ \phi(x) &= \Phi'(x) &&(\text{Normal Distribution PDF}) \end{aligned}\]

    StudentizedRange(ν, k)     # Studentized Range Distribution with parameters ν and k
 
-params(d)        # Get the parameters, i.e. (ν, k)

    External links

    source
    Distributions.SymTriangularDist — Type
    SymTriangularDist(μ, σ)

    The Symmetric triangular distribution with location μ and scale σ has probability density function

    \[f(x; \mu, \sigma) = \frac{1}{\sigma} \left( 1 - \left| \frac{x - \mu}{\sigma} \right| \right), \quad \mu - \sigma \le x \le \mu + \sigma\]

    SymTriangularDist()         # Symmetric triangular distribution with zero location and unit scale
+params(d)        # Get the parameters, i.e. (ν, k)

    External links

    source
    Distributions.SymTriangularDist — Type
    SymTriangularDist(μ, σ)

    The Symmetric triangular distribution with location μ and scale σ has probability density function

    \[f(x; \mu, \sigma) = \frac{1}{\sigma} \left( 1 - \left| \frac{x - \mu}{\sigma} \right| \right), \quad \mu - \sigma \le x \le \mu + \sigma\]

    SymTriangularDist()         # Symmetric triangular distribution with zero location and unit scale
 SymTriangularDist(μ)        # Symmetric triangular distribution with location μ and unit scale
 SymTriangularDist(μ, s)     # Symmetric triangular distribution with location μ and scale σ
 
 params(d)       # Get the parameters, i.e. (μ, σ)
 location(d)     # Get the location parameter, i.e. μ
-scale(d)        # Get the scale parameter, i.e. σ
    source
    Distributions.TDist — Type
    TDist(ν)

    The Students T distribution with ν degrees of freedom has probability density function

    \[f(x; \nu) = \frac{1}{\sqrt{\nu} B(1/2, \nu/2)} +scale(d) # Get the scale parameter, i.e. σ

    source
    Example block output
    Distributions.TDist — Type
    TDist(ν)

    The Students T distribution with ν degrees of freedom has probability density function

    \[f(x; \nu) = \frac{1}{\sqrt{\nu} B(1/2, \nu/2)} \left( 1 + \frac{x^2}{\nu} \right)^{-\frac{\nu + 1}{2}}\]

    TDist(d)      # t-distribution with ν degrees of freedom
 
 params(d)     # Get the parameters, i.e. (ν,)
-dof(d)        # Get the degrees of freedom, i.e. ν

    External links

    Student's T distribution on Wikipedia

    source
    Example block output
    Distributions.TriangularDist — Type
    TriangularDist(a,b,c)

    The triangular distribution with lower limit a, upper limit b and mode c has probability density function

    \[f(x; a, b, c)= \begin{cases} 0 & \mathrm{for\ } x < a, \\ \frac{2(x-a)}{(b-a)(c-a)} & \mathrm{for\ } a \le x \leq c, \\[4pt] \frac{2(b-x)}{(b-a)(b-c)} & \mathrm{for\ } c < x \le b, \\[4pt] @@ -7793,802 +222,23 @@ params(d) # Get the parameters, i.e. (a, b, c) minimum(d) # Get the lower bound, i.e. a maximum(d) # Get the upper bound, i.e. b -mode(d) # Get the mode, i.e. c

    External links

    source
    Distributions.Uniform — Type
    Uniform(a,b)

    The continuous uniform distribution over an interval $[a, b]$ has probability density function

    \[f(x; a, b) = \frac{1}{b - a}, \quad a \le x \le b\]

    Uniform()        # Uniform distribution over [0, 1]
+mode(d)         # Get the mode, i.e. c

    External links

    source
    Example block outputExample block output
    Distributions.Uniform — Type
    Uniform(a,b)

    The continuous uniform distribution over an interval $[a, b]$ has probability density function

    \[f(x; a, b) = \frac{1}{b - a}, \quad a \le x \le b\]

    Uniform()        # Uniform distribution over [0, 1]
 Uniform(a, b)    # Uniform distribution over [a, b]
 
 params(d)        # Get the parameters, i.e. (a, b)
 minimum(d)       # Get the lower bound, i.e. a
 maximum(d)       # Get the upper bound, i.e. b
 location(d)      # Get the location parameter, i.e. a
-scale(d)         # Get the scale parameter, i.e. b - a

    External links

    source
    Distributions.VonMises — Type
    VonMises(μ, κ)

    The von Mises distribution with mean μ and concentration κ has probability density function

    \[f(x; \mu, \kappa) = \frac{1}{2 \pi I_0(\kappa)} \exp \left( \kappa \cos (x - \mu) \right)\]

    VonMises()       # von Mises distribution with zero mean and unit concentration
+scale(d)         # Get the scale parameter, i.e. b - a

    External links

    source
    Example block output
    Distributions.VonMises — Type
    VonMises(μ, κ)

    The von Mises distribution with mean μ and concentration κ has probability density function

    \[f(x; \mu, \kappa) = \frac{1}{2 \pi I_0(\kappa)} \exp \left( \kappa \cos (x - \mu) \right)\]

    VonMises()       # von Mises distribution with zero mean and unit concentration
 VonMises(κ)      # von Mises distribution with zero mean and concentration κ
-VonMises(μ, κ)   # von Mises distribution with mean μ and concentration κ

    External links

    source
    Distributions.Weibull — Type
    Weibull(α,θ)

    The Weibull distribution with shape α and scale θ has probability density function

    \[f(x; \alpha, \theta) = \frac{\alpha}{\theta} \left( \frac{x}{\theta} \right)^{\alpha-1} e^{-(x/\theta)^\alpha}, +VonMises(μ, κ) # von Mises distribution with mean μ and concentration κ

    External links

    source
    Example block output
    Distributions.Weibull — Type
    Weibull(α,θ)

    The Weibull distribution with shape α and scale θ has probability density function

    \[f(x; \alpha, \theta) = \frac{\alpha}{\theta} \left( \frac{x}{\theta} \right)^{\alpha-1} e^{-(x/\theta)^\alpha}, \quad x \ge 0\]

    Weibull()        # Weibull distribution with unit shape and unit scale, i.e. Weibull(1, 1)
 Weibull(α)       # Weibull distribution with shape α and unit scale, i.e. Weibull(α, 1)
 Weibull(α, θ)    # Weibull distribution with shape α and scale θ
 
 params(d)        # Get the parameters, i.e. (α, θ)
 shape(d)         # Get the shape parameter, i.e. α
-scale(d)         # Get the scale parameter, i.e. θ

    External links

    source

    Discrete Distributions

    Example block output

    Discrete Distributions

    Distributions.Bernoulli — Type
    Bernoulli(p)

    A Bernoulli distribution is parameterized by a success rate p, which takes value 1 with probability p and 0 with probability 1-p.

    \[P(X = k) = \begin{cases} 1 - p & \quad \text{for } k = 0, \\ p & \quad \text{for } k = 1. \end{cases}\]

    Bernoulli()    # Bernoulli distribution with p = 0.5
@@ -8596,60 +246,60 @@
 
 params(d)      # Get the parameters, i.e. (p,)
 succprob(d)    # Get the success rate, i.e. p
-failprob(d)    # Get the failure rate, i.e. 1 - p

    External links:

    source
    Distributions.BernoulliLogit — Type
    BernoulliLogit(logitp=0.0)

    A Bernoulli distribution that is parameterized by the logit logitp = logit(p) = log(p/(1-p)) of its success rate p.

    \[P(X = k) = \begin{cases} \operatorname{logistic}(-logitp) = \frac{1}{1 + \exp{(logitp)}} & \quad \text{for } k = 0, \\ \operatorname{logistic}(logitp) = \frac{1}{1 + \exp{(-logitp)}} & \quad \text{for } k = 1. -\end{cases}\]

    External links:

    See also Bernoulli

    source
    Distributions.BetaBinomial — Type
    BetaBinomial(n,α,β)

    A Beta-binomial distribution is the compound distribution of the Binomial distribution where the probability of success p is distributed according to the Beta. It has three parameters: n, the number of trials and two shape parameters α, β

    \[P(X = k) = {n \choose k} B(k + \alpha, n - k + \beta) / B(\alpha, \beta), \quad \text{ for } k = 0,1,2, \ldots, n.\]

    BetaBinomial(n, α, β)      # BetaBinomial distribution with n trials and shape parameters α, β
+\end{cases}\]
    External links:
    See also Bernoulli
    source
    Distributions.BetaBinomial — Type
    BetaBinomial(n,α,β)

    A Beta-binomial distribution is the compound distribution of the Binomial distribution where the probability of success p is distributed according to the Beta. It has three parameters: n, the number of trials and two shape parameters α, β

    \[P(X = k) = {n \choose k} B(k + \alpha, n - k + \beta) / B(\alpha, \beta), \quad \text{ for } k = 0,1,2, \ldots, n.\]

    BetaBinomial(n, α, β)      # BetaBinomial distribution with n trials and shape parameters α, β
 
 params(d)       # Get the parameters, i.e. (n, α, β)
-ntrials(d)      # Get the number of trials, i.e. n

    External links:

    source
    Distributions.Binomial — Type
    Binomial(n,p)

    A Binomial distribution characterizes the number of successes in a sequence of independent trials. It has two parameters: n, the number of trials, and p, the probability of success in an individual trial, with the distribution:

    \[P(X = k) = {n \choose k}p^k(1-p)^{n-k}, \quad \text{ for } k = 0,1,2, \ldots, n.\]

    Binomial()      # Binomial distribution with n = 1 and p = 0.5
+ntrials(d)      # Get the number of trials, i.e. n

    External links:

    source
    Distributions.Binomial — Type
    Binomial(n,p)

    A Binomial distribution characterizes the number of successes in a sequence of independent trials. It has two parameters: n, the number of trials, and p, the probability of success in an individual trial, with the distribution:

    \[P(X = k) = {n \choose k}p^k(1-p)^{n-k}, \quad \text{ for } k = 0,1,2, \ldots, n.\]

    Binomial()      # Binomial distribution with n = 1 and p = 0.5
 Binomial(n)     # Binomial distribution for n trials with success rate p = 0.5
 Binomial(n, p)  # Binomial distribution for n trials with success rate p
 
 params(d)       # Get the parameters, i.e. (n, p)
 ntrials(d)      # Get the number of trials, i.e. n
 succprob(d)     # Get the success rate, i.e. p
-failprob(d)     # Get the failure rate, i.e. 1 - p

    External links:

    source
    Distributions.Categorical — Type
    Categorical(p)

    A Categorical distribution is parameterized by a probability vector p (of length K).

    \[P(X = k) = p[k] \quad \text{for } k = 1, 2, \ldots, K.\]

    Categorical(p)   # Categorical distribution with probability vector p
+failprob(d)     # Get the failure rate, i.e. 1 - p

    External links:

    source
    Distributions.Categorical — Type
    Categorical(p)

    A Categorical distribution is parameterized by a probability vector p (of length K).

    \[P(X = k) = p[k] \quad \text{for } k = 1, 2, \ldots, K.\]

    Categorical(p)   # Categorical distribution with probability vector p
 params(d)        # Get the parameters, i.e. (p,)
 probs(d)         # Get the probability vector, i.e. p
-ncategories(d)   # Get the number of categories, i.e. K

    Here, p must be a real vector, of which all components are nonnegative and sum to one.

    Note: The input vector p is directly used as a field of the constructed distribution, without being copied.

    Categorical is simply a type alias describing a special case of a DiscreteNonParametric distribution, so non-specialized methods defined for DiscreteNonParametric apply to Categorical as well.

    External links:

    source
    Distributions.Dirac — Type
    Dirac(x)

    A Dirac distribution is parameterized by its only value x, and takes its value with probability 1.

    \[P(X = \hat{x}) = \begin{cases} +ncategories(d) # Get the number of categories, i.e. K

    Here, p must be a real vector, of which all components are nonnegative and sum to one.

    Note: The input vector p is directly used as a field of the constructed distribution, without being copied.

    Categorical is simply a type alias describing a special case of a DiscreteNonParametric distribution, so non-specialized methods defined for DiscreteNonParametric apply to Categorical as well.

    External links:

    source
    Distributions.Dirac — Type
    Dirac(x)

    A Dirac distribution is parameterized by its only value x, and takes its value with probability 1.

    \[P(X = \hat{x}) = \begin{cases} 1 & \quad \text{for } \hat{x} = x, \\ 0 & \quad \text{for } \hat{x} \neq x. -\end{cases}\]

    Dirac(2.5)   # Dirac distribution with value x = 2.5

    External links:

    source
    Distributions.DiscreteUniform — Type
    DiscreteUniform(a,b)

    A Discrete uniform distribution is a uniform distribution over a consecutive sequence of integers between a and b, inclusive.

    \[P(X = k) = 1 / (b - a + 1) \quad \text{for } k = a, a+1, \ldots, b.\]

    DiscreteUniform(a, b)   # a uniform distribution over {a, a+1, ..., b}
+\end{cases}\]
    Dirac(2.5)   # Dirac distribution with value x = 2.5
    External links:
    source
    Distributions.DiscreteUniform — Type
    DiscreteUniform(a,b)

    A Discrete uniform distribution is a uniform distribution over a consecutive sequence of integers between a and b, inclusive.

    \[P(X = k) = 1 / (b - a + 1) \quad \text{for } k = a, a+1, \ldots, b.\]

    DiscreteUniform(a, b)   # a uniform distribution over {a, a+1, ..., b}
 
 params(d)       # Get the parameters, i.e. (a, b)
 span(d)         # Get the span of the support, i.e. (b - a + 1)
 probval(d)      # Get the probability value, i.e. 1 / (b - a + 1)
 minimum(d)      # Return a
-maximum(d)      # Return b

    External links

    source
    Distributions.DiscreteNonParametric — Type
    DiscreteNonParametric(xs, ps)

    A Discrete nonparametric distribution explicitly defines an arbitrary probability mass function in terms of a list of real support values and their corresponding probabilities

    d = DiscreteNonParametric(xs, ps)
 
 params(d)  # Get the parameters, i.e. (xs, ps)
 support(d) # Get a sorted AbstractVector describing the support (xs) of the distribution
-probs(d)   # Get a Vector of the probabilities (ps) associated with the support

    External links

    source
    Distributions.Geometric — Type
    Geometric(p)

    A Geometric distribution characterizes the number of failures before the first success in a sequence of independent Bernoulli trials with success rate p.

    \[P(X = k) = p (1 - p)^k, \quad \text{for } k = 0, 1, 2, \ldots.\]

    Geometric()    # Geometric distribution with success rate 0.5
+probs(d)   # Get a Vector of the probabilities (ps) associated with the support

    External links

    source
    Distributions.Geometric — Type
    Geometric(p)

    A Geometric distribution characterizes the number of failures before the first success in a sequence of independent Bernoulli trials with success rate p.

    \[P(X = k) = p (1 - p)^k, \quad \text{for } k = 0, 1, 2, \ldots.\]

    Geometric()    # Geometric distribution with success rate 0.5
 Geometric(p)   # Geometric distribution with success rate p
 
 params(d)      # Get the parameters, i.e. (p,)
 succprob(d)    # Get the success rate, i.e. p
-failprob(d)    # Get the failure rate, i.e. 1 - p

    External links

    source
    Distributions.Hypergeometric — Type
    Hypergeometric(s, f, n)

    A Hypergeometric distribution describes the number of successes in n draws without replacement from a finite population containing s successes and f failures.

    \[P(X = k) = {{{s \choose k} {f \choose {n-k}}}\over {s+f \choose n}}, \quad \text{for } k = \max(0, n - f), \ldots, \min(n, s).\]

    Hypergeometric(s, f, n)  # Hypergeometric distribution for a population with
+failprob(d)    # Get the failure rate, i.e. 1 - p

    External links

    source
    Distributions.Hypergeometric — Type
    Hypergeometric(s, f, n)

    A Hypergeometric distribution describes the number of successes in n draws without replacement from a finite population containing s successes and f failures.

    \[P(X = k) = {{{s \choose k} {f \choose {n-k}}}\over {s+f \choose n}}, \quad \text{for } k = \max(0, n - f), \ldots, \min(n, s).\]

    Hypergeometric(s, f, n)  # Hypergeometric distribution for a population with
                          # s successes and f failures, and a sequence of n trials.
 
-params(d)       # Get the parameters, i.e. (s, f, n)

    External links

    source
    Distributions.NegativeBinomial — Type
    NegativeBinomial(r,p)

    A Negative binomial distribution describes the number of failures before the rth success in a sequence of independent Bernoulli trials. It is parameterized by r, the number of successes, and p, the probability of success in an individual trial.

    \[P(X = k) = {k + r - 1 \choose k} p^r (1 - p)^k, \quad \text{for } k = 0,1,2,\ldots.\]

    The distribution remains well-defined for any positive r, in which case

    \[P(X = k) = \frac{\Gamma(k+r)}{k! \Gamma(r)} p^r (1 - p)^k, \quad \text{for } k = 0,1,2,\ldots.\]

    NegativeBinomial()        # Negative binomial distribution with r = 1 and p = 0.5
+params(d)       # Get the parameters, i.e. (s, f, n)

    External links

    source
    Distributions.NegativeBinomial — Type
    NegativeBinomial(r,p)

    A Negative binomial distribution describes the number of failures before the rth success in a sequence of independent Bernoulli trials. It is parameterized by r, the number of successes, and p, the probability of success in an individual trial.

    \[P(X = k) = {k + r - 1 \choose k} p^r (1 - p)^k, \quad \text{for } k = 0,1,2,\ldots.\]

    The distribution remains well-defined for any positive r, in which case

    \[P(X = k) = \frac{\Gamma(k+r)}{k! \Gamma(r)} p^r (1 - p)^k, \quad \text{for } k = 0,1,2,\ldots.\]

    NegativeBinomial()        # Negative binomial distribution with r = 1 and p = 0.5
 NegativeBinomial(r, p)    # Negative binomial distribution with r successes and success rate p
 
 params(d)       # Get the parameters, i.e. (r, p)
 succprob(d)     # Get the success rate, i.e. p
-failprob(d)     # Get the failure rate, i.e. 1 - p

    External links:

    source
    Distributions.Poisson — Type
    Poisson(λ)

    A Poisson distribution describes the number of independent events occurring within a unit time interval, given the average rate of occurrence λ.

    \[P(X = k) = \frac{\lambda^k}{k!} e^{-\lambda}, \quad \text{ for } k = 0,1,2,\ldots.\]

    Poisson()        # Poisson distribution with rate parameter 1
+failprob(d)     # Get the failure rate, i.e. 1 - p

    External links:

    source
    Distributions.Poisson — Type
    Poisson(λ)

    A Poisson distribution describes the number of independent events occurring within a unit time interval, given the average rate of occurrence λ.

    \[P(X = k) = \frac{\lambda^k}{k!} e^{-\lambda}, \quad \text{ for } k = 0,1,2,\ldots.\]

    Poisson()        # Poisson distribution with rate parameter 1
 Poisson(lambda)       # Poisson distribution with rate parameter lambda
 
 params(d)        # Get the parameters, i.e. (λ,)
-mean(d)          # Get the mean arrival rate, i.e. λ

    External links:

    source
    Distributions.PoissonBinomial — Type
    PoissonBinomial(p)

    A Poisson-binomial distribution describes the number of successes in a sequence of independent trials, wherein each trial has a different success rate. It is parameterized by a vector p (of length $K$), where $K$ is the total number of trials and p[i] corresponds to the probability of success of the ith trial.

    \[P(X = k) = \sum\limits_{A\in F_k} \prod\limits_{i\in A} p[i] \prod\limits_{j\in A^c} (1-p[j]), \quad \text{ for } k = 0,1,2,\ldots,K,\]

    where $F_k$ is the set of all subsets of $k$ integers that can be selected from $\{1,2,3,...,K\}$.

    PoissonBinomial(p)   # Poisson Binomial distribution with success rate vector p
+mean(d)          # Get the mean arrival rate, i.e. λ

    External links:

    source
    Distributions.PoissonBinomial — Type
    PoissonBinomial(p)

    A Poisson-binomial distribution describes the number of successes in a sequence of independent trials, wherein each trial has a different success rate. It is parameterized by a vector p (of length $K$), where $K$ is the total number of trials and p[i] corresponds to the probability of success of the ith trial.

    \[P(X = k) = \sum\limits_{A\in F_k} \prod\limits_{i\in A} p[i] \prod\limits_{j\in A^c} (1-p[j]), \quad \text{ for } k = 0,1,2,\ldots,K,\]

    where $F_k$ is the set of all subsets of $k$ integers that can be selected from $\{1,2,3,...,K\}$.

    PoissonBinomial(p)   # Poisson Binomial distribution with success rate vector p
 
 params(d)            # Get the parameters, i.e. (p,)
 succprob(d)          # Get the vector of success rates, i.e. p
-failprob(d)          # Get the vector of failure rates, i.e. 1-p

    External links:

    source
    Distributions.Skellam — Type
    Skellam(μ1, μ2)

    A Skellam distribution describes the difference between two independent Poisson variables, respectively with rate μ1 and μ2.

    \[P(X = k) = e^{-(\mu_1 + \mu_2)} \left( \frac{\mu_1}{\mu_2} \right)^{k/2} I_k(2 \sqrt{\mu_1 \mu_2}) \quad \text{for integer } k\]

    where $I_k$ is the modified Bessel function of the first kind.

    Skellam(μ1, μ2)     # Skellam distribution for the difference between two Poisson variables,
+failprob(d)          # Get the vector of failure rates, i.e. 1-p

    External links:

    source
    Distributions.Skellam — Type
    Skellam(μ1, μ2)

    A Skellam distribution describes the difference between two independent Poisson variables, respectively with rate μ1 and μ2.

    \[P(X = k) = e^{-(\mu_1 + \mu_2)} \left( \frac{\mu_1}{\mu_2} \right)^{k/2} I_k(2 \sqrt{\mu_1 \mu_2}) \quad \text{for integer } k\]

    where $I_k$ is the modified Bessel function of the first kind.

    Skellam(μ1, μ2)     # Skellam distribution for the difference between two Poisson variables,
                     # respectively with expected values μ1 and μ2.
 
-params(d)           # Get the parameters, i.e. (μ1, μ2)

    External links:

    source
    Distributions.Soliton — Type
    Soliton(K::Integer, M::Integer, δ::Real, atol::Real=0) <: Distribution{Univariate, Discrete}

    The Robust Soliton distribution of length K, mode M (i.e., the location of the robust component spike), peeling process failure probability δ, and minimum non-zero probability mass atol. More specifically, degrees i for which pdf(Ω, i)<atol are set to 0. Letting atol=0 yields the regular robust Soliton distribution.

    Soliton(K, M, δ)        # Robust Soliton distribution (with atol=0)
+params(d)           # Get the parameters, i.e. (μ1, μ2)

    External links:

    source
    Distributions.Soliton — Type
    Soliton(K::Integer, M::Integer, δ::Real, atol::Real=0) <: Distribution{Univariate, Discrete}

    The Robust Soliton distribution of length K, mode M (i.e., the location of the robust component spike), peeling process failure probability δ, and minimum non-zero probability mass atol. More specifically, degrees i for which pdf(Ω, i)<atol are set to 0. Letting atol=0 yields the regular robust Soliton distribution.

    Soliton(K, M, δ)        # Robust Soliton distribution (with atol=0)
 Soliton(K, M, δ, atol)  # Robust Soliton distribution with minimum non-zero probability mass atol
 
 params(Ω)               # Get the parameters ,i.e., (K, M, δ, atol)
@@ -8657,4 +307,4 @@
 pdf(Ω, i)               # Evaluate the pdf at i
 cdf(Ω, i)               # Evaluate the pdf at i
 rand(Ω)                 # Sample from Ω
-rand(Ω, n)              # Draw n samples from Ω

    External links:

    source

    Vectorized evaluation

    Vectorized computation and in-place vectorized computation have been deprecated.

    Index

    • 1Lindley, D. V. (1958). Fiducial Distributions and Bayes' Theorem. Journal of the Royal Statistical Society: Series B (Methodological), 20(1), 102–107.
    • 2Ghitany, M. E., Atieh, B., & Nadarajah, S. (2008). Lindley distribution and its application. Mathematics and Computers in Simulation, 78(4), 493–506.
    +rand(Ω, n) # Draw n samples from Ω

    External links:

    source

    Vectorized evaluation

    Vectorized computation and in-place vectorized computation have been deprecated.

    Index

    • 1Lindley, D. V. (1958). Fiducial Distributions and Bayes' Theorem. Journal of the Royal Statistical Society: Series B (Methodological), 20(1), 102–107.
    • 2Ghitany, M. E., Atieh, B., & Nadarajah, S. (2008). Lindley distribution and its application. Mathematics and Computers in Simulation, 78(4), 493–506.