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'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fas", "fa-copy"); + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-times"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-times"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function() { + $('#documenter .docs-navbar').headroom({ + "tolerance": {"up": 10, "down": 10}, + }); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function() { + var settings = $('#documenter-settings'); + $('#documenter-settings-button').click(function(){ + settings.toggleClass('is-active'); + }); + // Close the dialog if X is clicked + $('#documenter-settings button.delete').click(function(){ + settings.removeClass('is-active'); + }); + // Close dialog if ESC is pressed + $(document).keyup(function(e) { + if (e.keyCode == 27) settings.removeClass('is-active'); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function() { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button") + sidebar_button.click(function(ev) { + ev.preventDefault(); + sidebar.toggleClass('visible'); + if (sidebar.hasClass('visible')) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind('click', function(ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + }); +}) + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function() { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css('max-width'), 10); + var L0 = e.width(); + if(L0 > L) { + var h0 = parseInt(e.css('font-size'), 10); + e.css('font-size', L * h0 / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on('orientationchange', resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function() { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if(typeof active !== 'undefined') { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +function set_theme(theme) { + var active = null; + var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { + var option = $(""); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== 'undefined') { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); + DOC_VERSIONS.forEach(function(each) { + var version_url = documenterBaseURL + "/../" + each; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/v1.3.0/assets/logo-dark.svg b/v1.3.0/assets/logo-dark.svg new file mode 100644 index 0000000..acbf460 --- /dev/null +++ b/v1.3.0/assets/logo-dark.svg @@ -0,0 +1,87 @@ + + + + diff --git a/v1.3.0/assets/logo.svg b/v1.3.0/assets/logo.svg new file mode 100644 index 0000000..50b2cc1 --- /dev/null +++ b/v1.3.0/assets/logo.svg @@ -0,0 +1,87 @@ + + + + diff --git a/v1.3.0/assets/search.js b/v1.3.0/assets/search.js new file mode 100644 index 0000000..c133f74 --- /dev/null +++ b/v1.3.0/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
  • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/v1.3.0/assets/themes/documenter-dark.css b/v1.3.0/assets/themes/documenter-dark.css new file mode 100644 index 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html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:#fff;border-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus,html.theme--documenter-dark 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.button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:transparent;color:#282f2f}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#e5eaec;border-color:transparent;color:#282f2f}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:#282f2f}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(236,240,241,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#dde4e6;border-color:transparent;color:#282f2f}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:#ecf0f1;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:#282f2f;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:#1d2122}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:#282f2f;border-color:transparent;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:#ecf0f1;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:#ecf0f1;border-color:#ecf0f1;color:#282f2f}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !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:#282f2f;color:#282f2f}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:#282f2f;color:#ecf0f1}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#ecf0f1}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#ecf0f1}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .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:#ecf0f1}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:#ecf0f1}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:transparent;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#ecf0f1;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:#dde4e6}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:#ecf0f1;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 #ecf0f1 #ecf0f1 !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:#ecf0f1}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #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 kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#ecf0f1;color:#ecf0f1}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#ecf0f1;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#ecf0f1;box-shadow:none;color:#ecf0f1}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-outlined.is-focused{background-color:#9e1b0d;border-color:#9e1b0d;color:#fff}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-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 .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}html.theme--documenter-dark .container.is-fluid{margin-left:32px;margin-right:32px;max-width:none}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen{max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd{max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container{max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container{max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:left}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 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.image.is-square,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--documenter-dark .image.is-1by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--documenter-dark .image.is-5by4,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--documenter-dark .image.is-4by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--documenter-dark .image.is-3by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--documenter-dark .image.is-5by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--documenter-dark .image.is-16by9,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--documenter-dark .image.is-2by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--documenter-dark .image.is-3by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--documenter-dark .image.is-4by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--documenter-dark .image.is-3by4,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--documenter-dark .image.is-2by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--documenter-dark .image.is-3by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--documenter-dark .image.is-9by16,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--documenter-dark .image.is-1by2,html.theme--documenter-dark #documenter 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Gets put into the tag.. +function set_theme_from_local_storage() { + // Intialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if(window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the browser supports user color preference + var darkPreference = false; + // Check if the users preference is for dark color scheme + if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { + darkPreference = true; + } + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; var disabled = []; var darkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if(themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null); + // Check if the theme is primary dark theme + var isDarkTheme = (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null); + // If ss is for dark theme then set the value of darkTheme to the name of the theme + if(isDarkTheme) darkTheme = themename; + // If we find a matching theme (and it's not the default), we'll set active to non-null + if(themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if(themename !== theme) disabled.push(ss); + } + if(active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + theme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + else if(darkTheme !== null && darkPreference === true) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName('html')[0].className = "theme--" + darkTheme; + // and (2) disable all the other theme stylesheets + disabled.forEach(function(ss){ + if (ss.ownerNode.getAttribute("data-theme-name") !== darkTheme) { + ss.disabled = true; + } + }); + } +} +set_theme_from_local_storage(); diff --git a/v1.3.0/assets/warner.js b/v1.3.0/assets/warner.js new file mode 100644 index 0000000..5531c88 --- /dev/null +++ b/v1.3.0/assets/warner.js @@ -0,0 +1,49 @@ +function maybeAddWarning () { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return + }; + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return + }; + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return + }; + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement('meta'); + meta.name = 'robots'; + meta.content = 'noindex'; + + document.getElementsByTagName('head')[0].appendChild(meta); + }; + + const div = document.createElement('div'); + div.classList.add('outdated-warning-overlay'); + const closer = document.createElement('button'); + closer.classList.add('outdated-warning-closer', 'delete'); + closer.addEventListener('click', function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + '/../' + window.DOCUMENTER_STABLE; + div.innerHTML = 'This documentation is not for the latest stable release, but for either the development version or an older release.
    Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +}; + +if (document.readyState === 'loading') { + document.addEventListener('DOMContentLoaded', maybeAddWarning); +} else { + maybeAddWarning(); +}; diff --git a/v1.3.0/couplingfunctions/index.html b/v1.3.0/couplingfunctions/index.html new file mode 100644 index 0000000..5f63846 --- /dev/null +++ b/v1.3.0/couplingfunctions/index.html @@ -0,0 +1,36 @@ + +Spin-spin interactions · SpiDy.jl
    Edit on GitHub

    Spin-spin interactions

    SpiDy.Nchain — Function
    Nchain(N, J0; boundary=nothing)

    Create the spin-spin coupling matrix of a 1D chain of N sites with nearest-neighbour interactions of strength set by J0.

    Arguments

    • N: The number of sites in the chain.
    • J0: The nearest-neighbour coupling strength.
    • boundary=nothing: (Optional) Specifies the boundary condition of the chain. Default is nothing which corresponds to a chain open at the edges. Use :periodic for periodic boundary conditions.

    Returns

    An N×N array representing the coupling matrix.

    Examples

    julia> J = Nchain(4, 2.0)
+4×4 Matrix{Float64}:
+ 0.0  2.0  0.0  0.0
+ 2.0  0.0  2.0  0.0
+ 0.0  2.0  0.0  2.0
+ 0.0  0.0  2.0  0.0
+
+julia> J_periodic = Nchain(4, 2.0; boundary=:periodic)
+4×4 Matrix{Float64}:
+ 0.0  2.0  0.0  2.0
+ 2.0  0.0  2.0  0.0
+ 0.0  2.0  0.0  2.0
+ 2.0  0.0  2.0  0.0
    source
    SpiDy.NNlattice — Function
    NNlattice(N, Jh, Jv; boundary=nothing)

    Create the spin-spin coupling matrix of a NxN 2D lattice with nearest-neighbour interactions and specified horizontal and vertical coupling strengths, Jh and Jv respectively.

    Arguments

    • N: The size of the lattice (N x N).
    • Jh: The horizontal nearest-neighbour coupling strength.
    • Jv: The vertical nearest-neighbour coupling strength.
    • boundary=nothing: (Optional) Specifies the boundary condition of the lattice. Default is nothing which corresponds to open edges. Use :periodic for periodic boundary condition.

    Returns

    An N^2×N^2 array representing the coupling matrix of the lattice.

    Examples

    julia> J = NNlattice(3, 2.0, 1.0)
+9×9 LinearAlgebra.Symmetric{Float64, Matrix{Float64}}:
+ 0.0  2.0  0.0  1.0  0.0  0.0  0.0  0.0  0.0
+ 2.0  0.0  2.0  0.0  1.0  0.0  0.0  0.0  0.0
+ 0.0  2.0  0.0  0.0  0.0  1.0  0.0  0.0  0.0
+ 1.0  0.0  0.0  0.0  2.0  0.0  1.0  0.0  0.0
+ 0.0  1.0  0.0  2.0  0.0  2.0  0.0  1.0  0.0
+ 0.0  0.0  1.0  0.0  2.0  0.0  0.0  0.0  1.0
+ 0.0  0.0  0.0  1.0  0.0  0.0  0.0  2.0  0.0
+ 0.0  0.0  0.0  0.0  1.0  0.0  2.0  0.0  2.0
+ 0.0  0.0  0.0  0.0  0.0  1.0  0.0  2.0  0.0
+
+julia> J_periodic = NNlattice(2, 2.0, 1.0; boundary=:periodic)
+9×9 LinearAlgebra.Symmetric{Float64, Matrix{Float64}}:
+ 0.0  2.0  2.0  1.0  0.0  0.0  1.0  0.0  0.0
+ 2.0  0.0  2.0  0.0  1.0  0.0  0.0  1.0  0.0
+ 2.0  2.0  0.0  0.0  0.0  1.0  0.0  0.0  1.0
+ 1.0  0.0  0.0  0.0  2.0  2.0  1.0  0.0  0.0
+ 0.0  1.0  0.0  2.0  0.0  2.0  0.0  1.0  0.0
+ 0.0  0.0  1.0  2.0  2.0  0.0  0.0  0.0  1.0
+ 1.0  0.0  0.0  1.0  0.0  0.0  0.0  2.0  2.0
+ 0.0  1.0  0.0  0.0  1.0  0.0  2.0  0.0  2.0
+ 0.0  0.0  1.0  0.0  0.0  1.0  2.0  2.0  0.0
    source
    diff --git a/v1.3.0/couplingtensor/index.html b/v1.3.0/couplingtensor/index.html new file mode 100644 index 0000000..cbcb6e2 --- /dev/null +++ b/v1.3.0/couplingtensor/index.html @@ -0,0 +1,17 @@ + +Spin-environment coupling tensor · SpiDy.jl
    Edit on GitHub

    Environment coupling tensor

    SpiDy.Coupling — Type
    abstract type Coupling

    Abstract type used to represent different forms of the environment coupling tensor.

    source
    SpiDy.AnisoCoupling — Type
    struct AnisoCoupling{TT<:AbstractMatrix{T} where {T<:Real}} <: Coupling

    A subtype of Coupling used to represent generic anisotropic coupling between the spin and environment.

    Fields

    • C::TT: The coupling matrix, which must be a 3x3 matrix (of type Matrix{<:Real}).

    Examples

    For a system with environment coupling where the y coupling is twice as large as the x, and the z three times as large, one can do:

    julia> C = [1.0 0.0 0.0; 0.0 2.0 0.0; 0.0 0.0 3.0]
+3×3 Matrix{Float64}:
+ 1.0  0.0  0.0
+ 0.0  2.0  0.0
+ 0.0  0.0  3.0
+
+julia> coupling = AnisoCoupling(C)
+AnisoCoupling{Matrix{Float64}}([1.0 0.0 0.0; 0.0 2.0 0.0; 0.0 0.0 3.0])

    One can define effective 2D couplings by setting all coefficients in one of the dimensions to zero:

    julia> C = [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 0.0]
+3x3 Matrix{Float64}
+ 1.0 0.0 0.0
+ 0.0 1.0 0.0
+ 0.0 0.0 0.0
+
+julia> coupling_2d = AnisoCoupling(C)
+AnisoCoupling{Matrix{Float64}}([1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 0.0])

    Similarly, one can define effective 1D couplings by setting two of the components to zero.

    source
    SpiDy.IsoCoupling — Type
    struct IsoCoupling{TT<:Real} <: Coupling

    A subtype of Coupling used to represent isotropic coupling between spin and environment.

    Fields

    • C::Real: The coupling strength.

    Examples

    julia> coupling = IsoCoupling(2.5)
+IsoCoupling{Float64}(2.5)
    source
    diff --git a/v1.3.0/dynamics/index.html b/v1.3.0/dynamics/index.html new file mode 100644 index 0000000..2f126fd --- /dev/null +++ b/v1.3.0/dynamics/index.html @@ -0,0 +1,2 @@ + +Dynamics · SpiDy.jl
    Edit on GitHub

    Dynamics

    SpiDy.diffeqsolver — Function
    function diffeqsolver(s0, tspan, J::LorentzianSD, Jshared::LorentzianSD, bfields, bfieldshared, matrix::Coupling; JH=zero(I), S0=1/2, Bext=[0, 0, 1], saveat=[], save_fields=false, projection=true, alg=Tsit5(), atol=1e-3, rtol=1e-3)

    Solves the dynamics of a system of ineracting spins under the influence of both local (unique to each spin) and global (shared by all spins) stochastic noise from the environment.

    Arguments

    • s0: Array of length 3N specifying the initial conditions of the N spins. The order the initial consitions is first the Sx,Sy,Sz for the first spin, then for the second, and so on.
    • tspan: The time span to solve the equations over, specified as a tuple (tstart, tend).
    • Jlist::Vector{LorentzianSD}: The list of spectral densities of the environment(s).
    • bfield: An array of tuples of functions Array{Tuple{Function, Function, Function}} representing the time series of the noise for each environment.
    • bcoupling::Vector{Vector{T}} T <: Real: A vector (of length the number of baths) of vectors (of length the number of spins), specifying if each bath couples to each spin.
    • matrix::Vector{TT} TT <: Coupling: A vector of Coupling structs specifying the spin-environment coupling matrix for each environment.
    • JH=zero(I): (Optional) The spin-spin coupling matrix. Default is zero matrix (i.e. non-interacting spins).
    • S0=1/2: (Optional) The spin quantum number. Default is 1/2.
    • Bext=[0, 0, 1]: (Optional) The external magnetic field vector. Default is [0, 0, 1] (normalised length pointing in the z direction).
    • saveat=[]: (Optional) An array of time points where the solution should be saved. Default is empty, which saves the solution at the time steps chosen by the integration algorithm.
    • save_fields=false: (Optional) If true, also return the auxiliary fields encoding the environment memory.
    • projection=false: (Optional) Specifies whether to project the spin vectors onto the unit sphere at each time step, hence forcing the numerical conservation of the spin length. Default is false.
    • alg=Vern6(): (Optional) The differential equation solver algorithm. Default is Vern6(). See the DifferentialEquations.jl docs for choices.
    • atol=1e-6: (Optional) The absolute tolerance for the solver. Default is 1e-6.
    • rtol=1e-6: (Optional) The relative tolerance for the solver. Default is 1e-6.

    Note: The LorentzianSD type is provided by the SpectralDensities.jl package.

    Note: Additional keyword arguments will be passed on to the ODE solver (see the DifferentialEquations.jl docs)

    Returns

    An ODESolution struct from DifferentialEquations.jl containing the solution of the equations of motion.

    source
    function diffeqsolver(s0, tspan, J::LorentzianSD, Jshared::LorentzianSD, bfields, bfieldshared, matrix::Coupling; JH=zero(I), S0=1/2, Bext=[0, 0, 1], saveat=[], save_fields=false, projection=true, alg=Tsit5(), atol=1e-3, rtol=1e-3)

    Solves the dynamics of a system of ineracting spins under the influence of either local (unique to each spin) or global (shared by all spins) stochastic noise from the environment.

    Arguments

    • s0: Array of length 3N specifying the initial conditions of the N spins. The order the initial consitions is first the Sx,Sy,Sz for the first spin, then for the second, and so on.
    • tspan: The time span to solve the equations over, specified as a tuple (tstart, tend).
    • J::LorentzianSD: The spectral density of the noise acting on the spins (either local or shared depending on the value of bfields).
    • bfields: For local baths, an array of tuples of functions Array{Tuple{Function, Function, Function}} representing the time series of the local stochastic field for each spin. For a global bath, a tuple of functions Tuple{Function, Function, Function} representing the time series of the global stochastic field shared by all the spins.
    • matrix::Coupling: The spin-environment coupling matrix.
    • JH=zero(I): (Optional) The spin-spin coupling matrix. Default is zero matrix (i.e. non-interacting spins).
    • S0=1/2: (Optional) The spin quantum number. Default is 1/2.
    • Bext=[0, 0, 1]: (Optional) The external magnetic field vector. Default is [0, 0, 1] (normalised length pointing in the z direction).
    • saveat=[]: (Optional) An array of time points where the solution should be saved. Default is empty, which saves the solution at the time steps chosen by the integration algorithm.
    • save_fields=false: (Optional) If true, also return the auxiliary fields encoding the environment memory.
    • projection=false: (Optional) Specifies whether to project the spin vectors onto the unit sphere at each time step, hence forcing the numerical conservation of the spin length. Default is false.
    • alg=Vern6(): (Optional) The differential equation solver algorithm. Default is Vern6(). See the DifferentialEquations.jl docs for choices.
    • atol=1e-6: (Optional) The absolute tolerance for the solver. Default is 1e-6.
    • rtol=1e-6: (Optional) The relative tolerance for the solver. Default is 1e-6.

    Note: The LorentzianSD type is provided by the SpectralDensities.jl package.

    Note: Additional keyword arguments will be passed on to the ODE solver (see the DifferentialEquations.jl docs)

    Returns

    An ODESolution struct from DifferentialEquations.jl containing the solution of the equations of motion.

    source
    function diffeqsolver(x0, p0, tspan, J::LorentzianSD, bfield, matrix::Coupling; JH=zero(I), Ω=1.0, counter_term=true, saveat=[], save_fields=false, alg=Tsit5(), atol=1e-3, rtol=1e-3)

    Solves the dynamics of a system of ineracting oscillators under the influence of either local (unique to each oscillator) or global (shared by all oscillators) stochastic noise from the environment.

    Arguments

    • x0: Array of length N specifying the initial position of the N oscillators.
    • p0: Array of length N specifying the initial momentum of the N oscillators.
    • tspan: The time span to solve the equations over, specified as a tuple (tstart, tend).
    • J::LorentzianSD: The spectral density of the noise acting globally on the harmonic oscillators.
    • bfield: A tuple of functions Tuple{Function, Function, Function} representing the time series of the global stochastic field shared by all the harmonic oscillators.
    • matrix::Coupling: The harmonic oscillators-environment coupling matrix.
    • JH=zero(I): (Optional) The oscillator-oscillator coupling matrix. Default is zero matrix (i.e. non-interacting oscillators).
    • Ω=1.0: (Optional) The natural angular frequency of the harmonic oscillators (currently the same for all). Default is 1.
    • counter_term=true: (Optional) Whether to include the counter-term or not. Default is true.
    • saveat=[]: (Optional) An array of time points where the solution should be saved. Default is empty, which saves the solution at the time steps chosen by the integration algorithm.
    • save_fields=false: (Optional) If true, also return the auxiliary fields encoding the environment memory.
    • alg=Vern6(): (Optional) The differential equation solver algorithm. Default is Vern6(). See the DifferentialEquations.jl docs for choices.
    • atol=1e-6: (Optional) The absolute tolerance for the solver. Default is 1e-6.
    • rtol=1e-6: (Optional) The relative tolerance for the solver. Default is 1e-6.

    Note: The LorentzianSD type is provided by the SpectralDensities.jl package.

    Note: Additional keyword arguments will be passed on to the ODE solver (see the DifferentialEquations.jl docs)

    Returns

    An ODESolution struct from DifferentialEquations.jl containing the solution of the equations of motion.

    source
    diff --git a/v1.3.0/index.html b/v1.3.0/index.html new file mode 100644 index 0000000..195a93b --- /dev/null +++ b/v1.3.0/index.html @@ -0,0 +1,3 @@ + +Start with SpiDy.jl · SpiDy.jl
    Edit on GitHub

    SpiDy.jl documentation

    Start with SpiDy.jl

    SpiDy.jl is a Spin-Dynamics Julia package. The code is a generalization of the results obtained in the paper "Quantum Brownian motion for magnets" to account for arbitrary dimensional system-bath coupling. The system considered is a quantized three-dimensional spin + environment Hamiltonian. The code solves a set of differential equations for the spin vector where the damping accounts for memory, arbitrary noise and arbitrary statistics.

    The classical simulations in anisotropic coupling found in the pre-print "Quantum-classical correspondence in spin-boson equilibrium states at arbitrary coupling" have been generated using a very-early-version of this code.

    Install Julia

    If you are new to Julia, here is how to install it.

    If you are a Windows/Mac user, download Julia here and run the installer. On Mac, drag-and-drop the app to the Applications.

    If you are a Linux user, just open a terminal and use your package manager, e.g. on Debian-based distros run "sudo apt-get install julia", on RedHat-based distros run "sudo dnf install julia".

    Install SpiDy.jl

    Following the Julia General Registry guidelines, the package can be installed as follows. (NB: the entire installation of SpiDy and its dependencies takes about 5 minutes on a bare-bones Julia environment.)

    Start Julia and enter in Pkg REPL mode by pressing ] then run the following,

    add https://github.com/quantum-exeter/SpiDy.jl

    or alternatively run the following lines in your code,

    using Pkg;
+Pkg.add(url="https://github.com/quantum-exeter/SpiDy.jl")

    Run SpiDy.jl

    To run the code,

    • save run_dynamics.jl and run_steadystate.jl in your preferred location (right click -> save as... should work to save the file)
    • open the terminal or command line
    • run the following command,
    julia "path-to-your-file"/run_dynamics.jl

    where "path-to-your-file" is the one where you saved your file. Replace run_dynamics.jl with run_steadystate.jl to run the one of your choice.

    NB: the code can exploit parallel computation. To do this, run your files as

    julia -t 6 "path-to-your-file"/run_dynamics.jl

    where you want to replace "6" with the number of threads that you wish to use. As a general idea, you do not want to use more than 80% of the number of threads you have available in your machine, e.g. if you have a 4-core CPU, you are likely to have 8 threads and you may want to run the parallelization as indicated above.

    Units and choosing parameters

    See the section "Units and choosing parameters" for a discussion on the choice of units implemented in SpiDy.jl and how to choose these parameters given a concrete real problem.

    Index

    diff --git a/v1.3.0/noise/index.html b/v1.3.0/noise/index.html new file mode 100644 index 0000000..dc53619 --- /dev/null +++ b/v1.3.0/noise/index.html @@ -0,0 +1,2 @@ + +Noise · SpiDy.jl
    Edit on GitHub

    Noise

    SpiDy.Noise — Type
    abstract type Noise

    An abstract type used to represent different kinds of environment noise.

    Any user-defined subtype of Noise should implement a method spectrum(::NoiseSubType, ω) which returns the spectrum of the noise at the given frequency ω.

    source
    SpiDy.ClassicalNoise — Type
    struct ClassicalNoise{TT<:Real} <: Noise

    A subtype of Noise used to represent classical noise, with spectrum

    \[\mathcal{S}(\omega) = \frac{2k_\mathrm{B}T}{\hbar\omega}\]

    Fields

    • T::TT: The temperature of the environment associated with the noise.
    source
    SpiDy.QuantumNoise — Type
    struct QuantumNoise{TT<:Real} <: Noise

    A subtype of Noise used to represent quantum noise, with spectrum

    \[\mathcal{S}(\omega) = \coth\left(\frac{\hbar\omega}{2k_\mathrm{B}T}\right)\]

    Fields

    • T::TT: The temperature of the environment associated with the noise.
    source
    SpiDy.NoZeroQuantumNoise — Type
    struct NoZeroQuantumNoise{TT<:Real} <: Noise

    A subtype of Noise used to represent quantum noise with zero-point-fluctuations removed, that is with spectrum

    \[\mathcal{S}(\omega) = \coth\left(\frac{\hbar\omega}{2k_\mathrm{B}T}\right) - 1\]

    Fields

    • T::TT: The temperature of the environment associated with the noise.
    source
    SpiDy.spectrum — Function
    spectrum(::Noise)

    Return the spectrum of the given noise as a function of frequency.

    Arguments

    • n::Noise: The noise type.

    Returns

    A function that takes a frequency ω and returns the corresponding spectrum value.

    source
    SpiDy.psd — Function
    function psd(J::AbstractSD, noise::Noise)

    Calculate the Power Spectral Density (PSD) for a given environment spectral density J and noise model noise.

    Arguments

    • J::AbstractSD: The environment spectral density.
    • noise::Noise: The noise model for the environment.

    Note: The LorentzianSD type is provided by the SpectralDensities.jl package.

    Returns

    A function psd(ω) that calculates the PSD at a given frequency ω.

    source
    diff --git a/v1.3.0/search/index.html b/v1.3.0/search/index.html new file mode 100644 index 0000000..aeb062a --- /dev/null +++ b/v1.3.0/search/index.html @@ -0,0 +1,2 @@ + +Search · SpiDy.jl

    Loading search...

      diff --git a/v1.3.0/search_index.js b/v1.3.0/search_index.js new file mode 100644 index 0000000..2f9caba --- /dev/null +++ b/v1.3.0/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"couplingfunctions/#Spin-spin-interactions","page":"Spin-spin interactions","title":"Spin-spin interactions","text":"","category":"section"},{"location":"couplingfunctions/","page":"Spin-spin interactions","title":"Spin-spin interactions","text":"Nchain\nNNlattice","category":"page"},{"location":"couplingfunctions/#SpiDy.Nchain","page":"Spin-spin interactions","title":"SpiDy.Nchain","text":"Nchain(N, J0; boundary=nothing)\n\nCreate the spin-spin coupling matrix of a 1D chain of N sites with nearest-neighbour interactions of strength set by J0.\n\nArguments\n\nN: The number of sites in the chain.\nJ0: The nearest-neighbour coupling strength.\nboundary=nothing: (Optional) Specifies the boundary condition of the chain. Default is nothing which corresponds to a chain open at the edges. Use :periodic for periodic boundary conditions.\n\nReturns\n\nAn N×N array representing the coupling matrix.\n\nExamples\n\njulia> J = Nchain(4, 2.0)\n4×4 Matrix{Float64}:\n 0.0 2.0 0.0 0.0\n 2.0 0.0 2.0 0.0\n 0.0 2.0 0.0 2.0\n 0.0 0.0 2.0 0.0\n\njulia> J_periodic = Nchain(4, 2.0; boundary=:periodic)\n4×4 Matrix{Float64}:\n 0.0 2.0 0.0 2.0\n 2.0 0.0 2.0 0.0\n 0.0 2.0 0.0 2.0\n 2.0 0.0 2.0 0.0\n\n\n\n\n\n","category":"function"},{"location":"couplingfunctions/#SpiDy.NNlattice","page":"Spin-spin interactions","title":"SpiDy.NNlattice","text":"NNlattice(N, Jh, Jv; boundary=nothing)\n\nCreate the spin-spin coupling matrix of a NxN 2D lattice with nearest-neighbour interactions and specified horizontal and vertical coupling strengths, Jh and Jv respectively.\n\nArguments\n\nN: The size of the lattice (N x N).\nJh: The horizontal nearest-neighbour coupling strength.\nJv: The vertical nearest-neighbour coupling strength.\nboundary=nothing: (Optional) Specifies the boundary condition of the lattice. Default is nothing which corresponds to open edges. Use :periodic for periodic boundary condition.\n\nReturns\n\nAn N^2×N^2 array representing the coupling matrix of the lattice.\n\nExamples\n\njulia> J = NNlattice(3, 2.0, 1.0)\n9×9 LinearAlgebra.Symmetric{Float64, Matrix{Float64}}:\n 0.0 2.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0\n 2.0 0.0 2.0 0.0 1.0 0.0 0.0 0.0 0.0\n 0.0 2.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0\n 1.0 0.0 0.0 0.0 2.0 0.0 1.0 0.0 0.0\n 0.0 1.0 0.0 2.0 0.0 2.0 0.0 1.0 0.0\n 0.0 0.0 1.0 0.0 2.0 0.0 0.0 0.0 1.0\n 0.0 0.0 0.0 1.0 0.0 0.0 0.0 2.0 0.0\n 0.0 0.0 0.0 0.0 1.0 0.0 2.0 0.0 2.0\n 0.0 0.0 0.0 0.0 0.0 1.0 0.0 2.0 0.0\n\njulia> J_periodic = NNlattice(2, 2.0, 1.0; boundary=:periodic)\n9×9 LinearAlgebra.Symmetric{Float64, Matrix{Float64}}:\n 0.0 2.0 2.0 1.0 0.0 0.0 1.0 0.0 0.0\n 2.0 0.0 2.0 0.0 1.0 0.0 0.0 1.0 0.0\n 2.0 2.0 0.0 0.0 0.0 1.0 0.0 0.0 1.0\n 1.0 0.0 0.0 0.0 2.0 2.0 1.0 0.0 0.0\n 0.0 1.0 0.0 2.0 0.0 2.0 0.0 1.0 0.0\n 0.0 0.0 1.0 2.0 2.0 0.0 0.0 0.0 1.0\n 1.0 0.0 0.0 1.0 0.0 0.0 0.0 2.0 2.0\n 0.0 1.0 0.0 0.0 1.0 0.0 2.0 0.0 2.0\n 0.0 0.0 1.0 0.0 0.0 1.0 2.0 2.0 0.0\n\n\n\n\n\n","category":"function"},{"location":"noise/#Noise","page":"Noise","title":"Noise","text":"","category":"section"},{"location":"noise/","page":"Noise","title":"Noise","text":"Noise\nClassicalNoise\nQuantumNoise\nNoZeroQuantumNoise\nspectrum\npsd","category":"page"},{"location":"noise/#SpiDy.Noise","page":"Noise","title":"SpiDy.Noise","text":"abstract type Noise\n\nAn abstract type used to represent different kinds of environment noise.\n\nAny user-defined subtype of Noise should implement a method spectrum(::NoiseSubType, ω) which returns the spectrum of the noise at the given frequency ω.\n\n\n\n\n\n","category":"type"},{"location":"noise/#SpiDy.ClassicalNoise","page":"Noise","title":"SpiDy.ClassicalNoise","text":"struct ClassicalNoise{TT<:Real} <: Noise\n\nA subtype of Noise used to represent classical noise, with spectrum\n\nmathcalS(omega) = frac2k_mathrmBThbaromega\n\nFields\n\nT::TT: The temperature of the environment associated with the noise.\n\n\n\n\n\n","category":"type"},{"location":"noise/#SpiDy.QuantumNoise","page":"Noise","title":"SpiDy.QuantumNoise","text":"struct QuantumNoise{TT<:Real} <: Noise\n\nA subtype of Noise used to represent quantum noise, with spectrum\n\nmathcalS(omega) = cothleft(frachbaromega2k_mathrmBTright)\n\nFields\n\nT::TT: The temperature of the environment associated with the noise.\n\n\n\n\n\n","category":"type"},{"location":"noise/#SpiDy.NoZeroQuantumNoise","page":"Noise","title":"SpiDy.NoZeroQuantumNoise","text":"struct NoZeroQuantumNoise{TT<:Real} <: Noise\n\nA subtype of Noise used to represent quantum noise with zero-point-fluctuations removed, that is with spectrum\n\nmathcalS(omega) = cothleft(frachbaromega2k_mathrmBTright) - 1\n\nFields\n\nT::TT: The temperature of the environment associated with the noise.\n\n\n\n\n\n","category":"type"},{"location":"noise/#SpiDy.spectrum","page":"Noise","title":"SpiDy.spectrum","text":"spectrum(::Noise)\n\nReturn the spectrum of the given noise as a function of frequency.\n\nArguments\n\nn::Noise: The noise type.\n\nReturns\n\nA function that takes a frequency ω and returns the corresponding spectrum value.\n\n\n\n\n\n","category":"function"},{"location":"noise/#SpiDy.psd","page":"Noise","title":"SpiDy.psd","text":"function psd(J::AbstractSD, noise::Noise)\n\nCalculate the Power Spectral Density (PSD) for a given environment spectral density J and noise model noise.\n\nArguments\n\nJ::AbstractSD: The environment spectral density.\nnoise::Noise: The noise model for the environment.\n\nNote: The LorentzianSD type is provided by the SpectralDensities.jl package.\n\nReturns\n\nA function psd(ω) that calculates the PSD at a given frequency ω.\n\n\n\n\n\n","category":"function"},{"location":"units/#Units-and-choice-of-input-parameters","page":"Units and parameter choice","title":"Units and choice of input parameters","text":"","category":"section"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"In this document we describe the choice of units implemented in SpiDy.jl (which follows the conventions utilised in NJP 24 033020 (2022)) and how to appropriately choose the parameters that the library takes as input.","category":"page"},{"location":"units/#Equations-of-motion","page":"Units and parameter choice","title":"Equations of motion","text":"","category":"section"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"SpiDy.jl is designed to implement the equations of spins in presence of a bath of harmonic oscillators as derived in NJP 24 033020 (2022), which for a single spin mathbfS in presence of an external field mathbfB_mathrmext read","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"fracmathrmdmathbfSmathrmdt =\n gamma_emathbfStimesleft(mathbfB_mathrmext + mathbfb(t) + mathbfV(t)right)","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"where gamma_e is the electron gyromagnetic ratio, b(t) is the environment induced thermal stochastic field, and","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"mathbfV(t) = gamma_eint_-infty^tmathrmdt mathbfK(t-t)mathbfS(t)","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"where mathbfK(tau) is a memory kernel accounting for the non-Markovian evolution of the spin (see NJP 24 033020 (2022) for more details). SpiDy focuses on the case of an environment with a Lorentzian spectral density, in which case these equations of motion can be rewritten as","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"beginalign\nfracmathrmdmathbfSmathrmdt =\n gamma_emathbfStimesleft(mathbfB_mathrmext + mathbfb + mathbfVright) \nfracmathrmdmathbfVmathrmdt = mathbfW \nfracmathrmdmathbfWmathrmdt = gamma_e A mathbfS - omega_0^2mathbfV - GammamathbfW\nendalign","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"where A, omega_0, and Gamma parametrise the Lorentzian spectral density as","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"J(omega) = fracAGammapi fracomega(omega_0^2 - omega^2)^2 + omega^2Gamma^2","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"and the thermal stochastic mathbfb field is given by","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"mathbfb(t) = int_-infty^+inftymathrmdt F(t-t) xi(t)","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"with xi being white noise and","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"F(tau) = frac12piint_-infty^+inftymathrmdomega\n e^-iomegatau sqrtP(omega)","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"Here, P(omega) is the power spectral density of the environment, and it is given in terms of the Lorentzian spectral density J(omega) and the environment thermal noise N(omega) by P(omega) = hbarpi J(omega) N(omega). The noise N(omega) can be classical, \"quantum\", or \"quantum\" with no zero point fluctuations. For example, for the \"quantum\" case we have","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"N_mathrmqu(omega) = cothleft(frachbaromega2k_mathrmBTright)","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"Note that in these equations above, all quantities have standard units.","category":"page"},{"location":"units/#Units-rescaling","page":"Units and parameter choice","title":"Units rescaling","text":"","category":"section"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"SpiDy.jl implements these equations in a unit-free way, following the conventions of NJP 24 033020 (2022). In summary, consider a spin of length hbar S_0 is in presence of a reference magnetic field of magnitude B_0. We then define the Larmor frequency","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"omega_mathrmL = gamma_e B_0","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"with gamma_e the electron gyromagnetic ratio.","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"SpiDy.jl then takes as input parameters for the simulation the following unit free parameters:","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"S_0: the spin length (in units of hbar).\nbarB_mathrmext: external magnetic field.\nbart_mathrmend: final time of the evolution.\nmathrmdbart: time differential.\nbaromega_0: peak frequency of the Lorentzian spectral density.\nbarGamma: width of the Lorentzian spectral density.\nbaralpha: amplitude of the Lorentzian spectral density.\nbarT: the environment temperature.","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"These unit-free quantities (denoted hereon by a bar on top) are related to the unitful quantities in the previous section by the following conversions:","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"beginalign\nmathbfB_mathrmext = B_0 barB_mathrmext \nt_mathrmend = omega_mathrmL^-1 bart_mathrmend \nmathrmdt = omega_mathrmL^-1 mathrmdbart \nomega_0 = omega_mathrmL baromega_0 \nGamma = omega_mathrmL barGamma \nomega_0 = omega_mathrmL baromega_0 \nA = fracB_0^2omega_mathrmLhbar S_0 baralpha \nT = frachbaromega_mathrmLk_mathrmB barT\nendalign","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"Given these choices of rescaling and adimensionalisation and plugging them in the equations of motion of the previous section, one finally gets the equations being solved by SpiDy, that is","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"beginalign\nfracmathrmdbarmathbfSmathrmdbart =\n barmathbfStimesleft(barmathbfB_mathrmext + frac1sqrtS_0barmathbfb + barmathbfVright) \nfracmathrmdbarmathbfVmathrmdbart = barmathbfW \nfracmathrmdbarmathbfWmathrmdbart = baralphabarmathbfS - baromega_0^2barmathbfV - barGammabarmathbfW\nendalign","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"with environment Lorentzian spectral density","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"barJ(baromega) = fracbaralphabarGammapi fracbaromega(baromega_0^2 - baromega^2)^2 + baromega^2barGamma^2","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"and thermal stochastic noise barmathbfb with power spectral density ","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"barP(baromega) = pi barJ(baromega)barN(baromega)","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"For the \"quantum\" noise, the noise term is given by","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"barN_mathrmqu(baromega) = cothleft(fracbaromega2barTright)","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"while for \"classical\" noise we have","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"barN_mathrmcl(baromega) = frac2barTbaromega","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"Finally, note that with these definitions above, the unit-free Gilbert damping is given by (see NJP 24 033020 (2022))","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"eta = fracbaralphabarGammabaromega_0^4","category":"page"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"warning: Units convention in old versions of SpiDy.jl\nNote that the unit conversion just explained, in line with NJP 24 033020 (2022), is correct for SpiDy.jl versions 1.2.0 and later.Older version of SpiDy.jl used a different convention, which unfortunately meant that a change of spin length S_0 implied a change in temperature and time-scale, therefore requiring redefining the temperature, the paramerts of the Loretnzian, evolution time, etc.The change in units convetion means that versions of SpiDy.jl before and after 1.2.0 will produce different results. This breaking change was made to bring the code into consistency with the article NJP 24 033020 (2022) and to make the mapping of parameters used in SpiDy.jl to real units much easier and more straightforward (see also next section).Finally, it is worth noting that the behaviour of SpiDy.jl in older versions can be exactly recovered by passing the option S_0 = 1 to the integrator, since in that case both units conventions agree.","category":"page"},{"location":"units/#Extracting-Lorentzian-units-from-experimental-data","page":"Units and parameter choice","title":"Extracting Lorentzian units from experimental data","text":"","category":"section"},{"location":"units/","page":"Units and parameter choice","title":"Units and parameter choice","text":"To be written. See also EPL 139 36002 (2022).","category":"page"},{"location":"stochasticfield/#Stochastic-field","page":"Stochastic field","title":"Stochastic field","text":"","category":"section"},{"location":"stochasticfield/","page":"Stochastic field","title":"Stochastic field","text":"bfield\nestimate_bfield_parameters","category":"page"},{"location":"stochasticfield/#SpiDy.bfield","page":"Stochastic field","title":"SpiDy.bfield","text":"bfield(N, Δt, J::AbstractSD, noise::Noise; distro=Normal(0., 1/sqrt(Δt)), interpolation=true)\n\nGenerate a stochastic field realisation time series (of length N and spacing Δt) based on the given noise model noise and spectral density J.\n\nArguments\n\nN: The number of time steps.\nΔt: The time step size.\nJ::AbstractSD: The environment spectral density.\nnoise::Noise: The noise model for the environment.\ndistro=Normal(0., 1/sqrt(Δt)): (Optional) The distribution of noise samples. Default is a normal distribution with mean 0 and standard deviation 1/sqrt(Δt).\ninterpolation=true: (Optional) Specifies whether to use linear interpolation for the stochastic field time series. Default is true.\n\nNote: The AbstractSD type is provided by the SpectralDensities.jl package.\n\nReturns\n\nA time series of the stochastic field values.\n\n\n\n\n\nbfield(tend, J::AbstractSD, noise::Noise; distro=Normal(0., 1/sqrt(Δt)), interpolation=true, atol=0, rtol=sqrt(eps()), maxiters=Int(1e6))\n\nGenerate a stochastic field realisation time series of length tend given the noise model noise and spectral density J. The optional parameters atol, rtol control the accuracy of the power spectral density of the generated noise.\n\nArguments\n\ntend: The total evolution time.\nJ::AbstractSD: The environment spectral density.\nnoise::Noise: The noise model for the environment.\natol=0: (Optional) The absolute tolerance for the spectral density estimation. Default is 0.\nrtol=sqrt(eps()): (Optional) The relative tolerance for the spectral density estimation. Default is sqrt(eps()).\nmaxiters=Int(1e6): (Optional) The maximum number of iterations for the spectral density estimation. Default is 1e6.\ninterpolation=true: (Optional) Specifies whether to use linear interpolation for the stochastic field time series. Default is true.\n\nNote: The parameters used for generating the stochastic field are estimated using the estimate_bfield_parameters function. See the documentation for more details.\n\nReturns\n\nA time series of the stochastic field values.\n\n\n\n\n\n","category":"function"},{"location":"stochasticfield/#SpiDy.estimate_bfield_parameters","page":"Stochastic field","title":"SpiDy.estimate_bfield_parameters","text":"estimate_bfield_parameters(J::AbstractSD, noise::Noise; atol=0, rtol=sqrt(eps()), maxiters=Int(1e6))\n\nEstimate the minimum time step size Δt and minimum total evolution time tmin required to generate a stochastic field realisation time series based on the given noise model noise and spectral density J, such that the power spectral density of the generated noise matches the target power spectral density within absolute atol and relative tolerances rtol.\n\nArguments\n\nJ::AbstractSD: The environment spectral density.\nnoise::Noise: The noise model for the environment.\natol=0: (Optional) The absolute tolerance for the spectral density estimation. Default is 0.\nrtol=sqrt(eps()): (Optional) The relative tolerance for the spectral density estimation. Default is sqrt(eps()).\nmaxiters=Int(1e6): (Optional) The maximum number of iterations for the spectral density estimation. Default is 1e6.\n\nReturns\n\nThe minimum time step size Δt and minimum total evolution time tmin.\n\n\n\n\n\n","category":"function"},{"location":"couplingtensor/#Environment-coupling-tensor","page":"Spin-environment coupling tensor","title":"Environment coupling tensor","text":"","category":"section"},{"location":"couplingtensor/","page":"Spin-environment coupling tensor","title":"Spin-environment coupling tensor","text":"Coupling\nAnisoCoupling{TT<:AbstractMatrix{T} where {T<:Real}}\nIsoCoupling{TT<:Real}","category":"page"},{"location":"couplingtensor/#SpiDy.Coupling","page":"Spin-environment coupling tensor","title":"SpiDy.Coupling","text":"abstract type Coupling\n\nAbstract type used to represent different forms of the environment coupling tensor.\n\n\n\n\n\n","category":"type"},{"location":"couplingtensor/#SpiDy.AnisoCoupling","page":"Spin-environment coupling tensor","title":"SpiDy.AnisoCoupling","text":"struct AnisoCoupling{TT<:AbstractMatrix{T} where {T<:Real}} <: Coupling\n\nA subtype of Coupling used to represent generic anisotropic coupling between the spin and environment.\n\nFields\n\nC::TT: The coupling matrix, which must be a 3x3 matrix (of type Matrix{<:Real}).\n\nExamples\n\nFor a system with environment coupling where the y coupling is twice as large as the x, and the z three times as large, one can do:\n\njulia> C = [1.0 0.0 0.0; 0.0 2.0 0.0; 0.0 0.0 3.0]\n3×3 Matrix{Float64}:\n 1.0 0.0 0.0\n 0.0 2.0 0.0\n 0.0 0.0 3.0\n\njulia> coupling = AnisoCoupling(C)\nAnisoCoupling{Matrix{Float64}}([1.0 0.0 0.0; 0.0 2.0 0.0; 0.0 0.0 3.0])\n\nOne can define effective 2D couplings by setting all coefficients in one of the dimensions to zero:\n\njulia> C = [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 0.0]\n3x3 Matrix{Float64}\n 1.0 0.0 0.0\n 0.0 1.0 0.0\n 0.0 0.0 0.0\n\njulia> coupling_2d = AnisoCoupling(C)\nAnisoCoupling{Matrix{Float64}}([1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 0.0])\n\nSimilarly, one can define effective 1D couplings by setting two of the components to zero.\n\n\n\n\n\n","category":"type"},{"location":"couplingtensor/#SpiDy.IsoCoupling","page":"Spin-environment coupling tensor","title":"SpiDy.IsoCoupling","text":"struct IsoCoupling{TT<:Real} <: Coupling\n\nA subtype of Coupling used to represent isotropic coupling between spin and environment.\n\nFields\n\nC::Real: The coupling strength.\n\nExamples\n\njulia> coupling = IsoCoupling(2.5)\nIsoCoupling{Float64}(2.5)\n\n\n\n\n\n","category":"type"},{"location":"dynamics/#Dynamics","page":"Dynamics","title":"Dynamics","text":"","category":"section"},{"location":"dynamics/","page":"Dynamics","title":"Dynamics","text":"diffeqsolver","category":"page"},{"location":"dynamics/#SpiDy.diffeqsolver","page":"Dynamics","title":"SpiDy.diffeqsolver","text":"function diffeqsolver(s0, tspan, J::LorentzianSD, Jshared::LorentzianSD, bfields, bfieldshared, matrix::Coupling; JH=zero(I), S0=1/2, Bext=[0, 0, 1], saveat=[], save_fields=false, projection=true, alg=Tsit5(), atol=1e-3, rtol=1e-3)\n\nSolves the dynamics of a system of ineracting spins under the influence of both local (unique to each spin) and global (shared by all spins) stochastic noise from the environment.\n\nArguments\n\ns0: Array of length 3N specifying the initial conditions of the N spins. The order the initial consitions is first the Sx,Sy,Sz for the first spin, then for the second, and so on.\ntspan: The time span to solve the equations over, specified as a tuple (tstart, tend).\nJlist::Vector{LorentzianSD}: The list of spectral densities of the environment(s).\nbfield: An array of tuples of functions Array{Tuple{Function, Function, Function}} representing the time series of the noise for each environment.\nbcoupling::Vector{Vector{T}} T <: Real: A vector (of length the number of baths) of vectors (of length the number of spins), specifying if each bath couples to each spin.\nmatrix::Vector{TT} TT <: Coupling: A vector of Coupling structs specifying the spin-environment coupling matrix for each environment.\nJH=zero(I): (Optional) The spin-spin coupling matrix. Default is zero matrix (i.e. non-interacting spins).\nS0=1/2: (Optional) The spin quantum number. Default is 1/2.\nBext=[0, 0, 1]: (Optional) The external magnetic field vector. Default is [0, 0, 1] (normalised length pointing in the z direction).\nsaveat=[]: (Optional) An array of time points where the solution should be saved. Default is empty, which saves the solution at the time steps chosen by the integration algorithm.\nsave_fields=false: (Optional) If true, also return the auxiliary fields encoding the environment memory.\nprojection=false: (Optional) Specifies whether to project the spin vectors onto the unit sphere at each time step, hence forcing the numerical conservation of the spin length. Default is false.\nalg=Vern6(): (Optional) The differential equation solver algorithm. Default is Vern6(). See the DifferentialEquations.jl docs for choices.\natol=1e-6: (Optional) The absolute tolerance for the solver. Default is 1e-6.\nrtol=1e-6: (Optional) The relative tolerance for the solver. Default is 1e-6.\n\nNote: The LorentzianSD type is provided by the SpectralDensities.jl package.\n\nNote: Additional keyword arguments will be passed on to the ODE solver (see the DifferentialEquations.jl docs)\n\nReturns\n\nAn ODESolution struct from DifferentialEquations.jl containing the solution of the equations of motion.\n\n\n\n\n\nfunction diffeqsolver(s0, tspan, J::LorentzianSD, Jshared::LorentzianSD, bfields, bfieldshared, matrix::Coupling; JH=zero(I), S0=1/2, Bext=[0, 0, 1], saveat=[], save_fields=false, projection=true, alg=Tsit5(), atol=1e-3, rtol=1e-3)\n\nSolves the dynamics of a system of ineracting spins under the influence of either local (unique to each spin) or global (shared by all spins) stochastic noise from the environment.\n\nArguments\n\ns0: Array of length 3N specifying the initial conditions of the N spins. The order the initial consitions is first the Sx,Sy,Sz for the first spin, then for the second, and so on.\ntspan: The time span to solve the equations over, specified as a tuple (tstart, tend).\nJ::LorentzianSD: The spectral density of the noise acting on the spins (either local or shared depending on the value of bfields).\nbfields: For local baths, an array of tuples of functions Array{Tuple{Function, Function, Function}} representing the time series of the local stochastic field for each spin. For a global bath, a tuple of functions Tuple{Function, Function, Function} representing the time series of the global stochastic field shared by all the spins.\nmatrix::Coupling: The spin-environment coupling matrix.\nJH=zero(I): (Optional) The spin-spin coupling matrix. Default is zero matrix (i.e. non-interacting spins).\nS0=1/2: (Optional) The spin quantum number. Default is 1/2.\nBext=[0, 0, 1]: (Optional) The external magnetic field vector. Default is [0, 0, 1] (normalised length pointing in the z direction).\nsaveat=[]: (Optional) An array of time points where the solution should be saved. Default is empty, which saves the solution at the time steps chosen by the integration algorithm.\nsave_fields=false: (Optional) If true, also return the auxiliary fields encoding the environment memory.\nprojection=false: (Optional) Specifies whether to project the spin vectors onto the unit sphere at each time step, hence forcing the numerical conservation of the spin length. Default is false.\nalg=Vern6(): (Optional) The differential equation solver algorithm. Default is Vern6(). See the DifferentialEquations.jl docs for choices.\natol=1e-6: (Optional) The absolute tolerance for the solver. Default is 1e-6.\nrtol=1e-6: (Optional) The relative tolerance for the solver. Default is 1e-6.\n\nNote: The LorentzianSD type is provided by the SpectralDensities.jl package.\n\nNote: Additional keyword arguments will be passed on to the ODE solver (see the DifferentialEquations.jl docs)\n\nReturns\n\nAn ODESolution struct from DifferentialEquations.jl containing the solution of the equations of motion.\n\n\n\n\n\nfunction diffeqsolver(x0, p0, tspan, J::LorentzianSD, bfield, matrix::Coupling; JH=zero(I), Ω=1.0, counter_term=true, saveat=[], save_fields=false, alg=Tsit5(), atol=1e-3, rtol=1e-3)\n\nSolves the dynamics of a system of ineracting oscillators under the influence of either local (unique to each oscillator) or global (shared by all oscillators) stochastic noise from the environment.\n\nArguments\n\nx0: Array of length N specifying the initial position of the N oscillators.\np0: Array of length N specifying the initial momentum of the N oscillators.\ntspan: The time span to solve the equations over, specified as a tuple (tstart, tend).\nJ::LorentzianSD: The spectral density of the noise acting globally on the harmonic oscillators.\nbfield: A tuple of functions Tuple{Function, Function, Function} representing the time series of the global stochastic field shared by all the harmonic oscillators.\nmatrix::Coupling: The harmonic oscillators-environment coupling matrix.\nJH=zero(I): (Optional) The oscillator-oscillator coupling matrix. Default is zero matrix (i.e. non-interacting oscillators).\nΩ=1.0: (Optional) The natural angular frequency of the harmonic oscillators (currently the same for all). Default is 1.\ncounter_term=true: (Optional) Whether to include the counter-term or not. Default is true.\nsaveat=[]: (Optional) An array of time points where the solution should be saved. Default is empty, which saves the solution at the time steps chosen by the integration algorithm.\nsave_fields=false: (Optional) If true, also return the auxiliary fields encoding the environment memory.\nalg=Vern6(): (Optional) The differential equation solver algorithm. Default is Vern6(). See the DifferentialEquations.jl docs for choices.\natol=1e-6: (Optional) The absolute tolerance for the solver. Default is 1e-6.\nrtol=1e-6: (Optional) The relative tolerance for the solver. Default is 1e-6.\n\nNote: The LorentzianSD type is provided by the SpectralDensities.jl package.\n\nNote: Additional keyword arguments will be passed on to the ODE solver (see the DifferentialEquations.jl docs)\n\nReturns\n\nAn ODESolution struct from DifferentialEquations.jl containing the solution of the equations of motion.\n\n\n\n\n\n","category":"function"},{"location":"spectraldensity/#Spectral-density","page":"Spectral density","title":"Spectral density","text":"","category":"section"},{"location":"spectraldensity/","page":"Spectral density","title":"Spectral density","text":"Spectral densities are implemented using the SpectralDensities.jl package. Please refer to its documentation for details of how to use it. For SpiDy.jl, the key type is LorentzianSD, which is here used to characterise the spectral density of the environment.","category":"page"},{"location":"#SpiDy.jl-documentation","page":"Start with SpiDy.jl","title":"SpiDy.jl documentation","text":"","category":"section"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"pages = [\"Start with SpiDy.jl\" => \"index.md\",\n \"Units and parameter choice\" => \"units.md\",\n \"Noise\" => \"noise.md\",\n \"Spectral density\" => \"spectraldensity.md\",\n \"Stochastic field\" => \"stochasticfield.md\",\n \"Spin-environment coupling tensor\" => \"couplingtensor.md\",\n \"Spin-spin interactions\" => \"couplingfunctions.md\",\n \"Dynamics\" => \"dynamics.md]","category":"page"},{"location":"#Start-with-SpiDy.jl","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"","category":"section"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"SpiDy.jl is a Spin-Dynamics Julia package. The code is a generalization of the results obtained in the paper \"Quantum Brownian motion for magnets\" to account for arbitrary dimensional system-bath coupling. The system considered is a quantized three-dimensional spin + environment Hamiltonian. The code solves a set of differential equations for the spin vector where the damping accounts for memory, arbitrary noise and arbitrary statistics.","category":"page"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"The classical simulations in anisotropic coupling found in the pre-print \"Quantum-classical correspondence in spin-boson equilibrium states at arbitrary coupling\" have been generated using a very-early-version of this code.","category":"page"},{"location":"#Install-Julia","page":"Start with SpiDy.jl","title":"Install Julia","text":"","category":"section"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"If you are new to Julia, here is how to install it.","category":"page"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"If you are a Windows/Mac user, download Julia here and run the installer. On Mac, drag-and-drop the app to the Applications.","category":"page"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"If you are a Linux user, just open a terminal and use your package manager, e.g. on Debian-based distros run \"sudo apt-get install julia\", on RedHat-based distros run \"sudo dnf install julia\".","category":"page"},{"location":"#Install-SpiDy.jl","page":"Start with SpiDy.jl","title":"Install SpiDy.jl","text":"","category":"section"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"Following the Julia General Registry guidelines, the package can be installed as follows. (NB: the entire installation of SpiDy and its dependencies takes about 5 minutes on a bare-bones Julia environment.)","category":"page"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"Start Julia and enter in Pkg REPL mode by pressing ] then run the following,","category":"page"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"add https://github.com/quantum-exeter/SpiDy.jl","category":"page"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"or alternatively run the following lines in your code,","category":"page"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"using Pkg;\nPkg.add(url=\"https://github.com/quantum-exeter/SpiDy.jl\")","category":"page"},{"location":"#Run-SpiDy.jl","page":"Start with SpiDy.jl","title":"Run SpiDy.jl","text":"","category":"section"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"To run the code,","category":"page"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"save run_dynamics.jl and run_steadystate.jl in your preferred location (right click -> save as... should work to save the file)\nopen the terminal or command line\nrun the following command,","category":"page"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"julia \"path-to-your-file\"/run_dynamics.jl","category":"page"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"where \"path-to-your-file\" is the one where you saved your file. Replace run_dynamics.jl with run_steadystate.jl to run the one of your choice.","category":"page"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"NB: the code can exploit parallel computation. To do this, run your files as","category":"page"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"julia -t 6 \"path-to-your-file\"/run_dynamics.jl","category":"page"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"where you want to replace \"6\" with the number of threads that you wish to use. As a general idea, you do not want to use more than 80% of the number of threads you have available in your machine, e.g. if you have a 4-core CPU, you are likely to have 8 threads and you may want to run the parallelization as indicated above.","category":"page"},{"location":"#Units-and-choosing-parameters","page":"Start with SpiDy.jl","title":"Units and choosing parameters","text":"","category":"section"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"See the section \"Units and choosing parameters\" for a discussion on the choice of units implemented in SpiDy.jl and how to choose these parameters given a concrete real problem.","category":"page"},{"location":"#Index","page":"Start with SpiDy.jl","title":"Index","text":"","category":"section"},{"location":"","page":"Start with SpiDy.jl","title":"Start with SpiDy.jl","text":"","category":"page"}] +} diff --git a/v1.3.0/siteinfo.js b/v1.3.0/siteinfo.js new file mode 100644 index 0000000..08f3b4b --- /dev/null +++ b/v1.3.0/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v1.3.0"; diff --git a/v1.3.0/spectraldensity/index.html b/v1.3.0/spectraldensity/index.html new file mode 100644 index 0000000..4a9b478 --- /dev/null +++ b/v1.3.0/spectraldensity/index.html @@ -0,0 +1,2 @@ + +Spectral density · SpiDy.jl
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      Spectral density

      Spectral densities are implemented using the SpectralDensities.jl package. Please refer to its documentation for details of how to use it. For SpiDy.jl, the key type is LorentzianSD, which is here used to characterise the spectral density of the environment.

      diff --git a/v1.3.0/stochasticfield/index.html b/v1.3.0/stochasticfield/index.html new file mode 100644 index 0000000..8e0f49b --- /dev/null +++ b/v1.3.0/stochasticfield/index.html @@ -0,0 +1,2 @@ + +Stochastic field · SpiDy.jl
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      Stochastic field

      SpiDy.bfield — Function
      bfield(N, Δt, J::AbstractSD, noise::Noise; distro=Normal(0., 1/sqrt(Δt)), interpolation=true)

      Generate a stochastic field realisation time series (of length N and spacing Δt) based on the given noise model noise and spectral density J.

      Arguments

      • N: The number of time steps.
      • Δt: The time step size.
      • J::AbstractSD: The environment spectral density.
      • noise::Noise: The noise model for the environment.
      • distro=Normal(0., 1/sqrt(Δt)): (Optional) The distribution of noise samples. Default is a normal distribution with mean 0 and standard deviation 1/sqrt(Δt).
      • interpolation=true: (Optional) Specifies whether to use linear interpolation for the stochastic field time series. Default is true.

      Note: The AbstractSD type is provided by the SpectralDensities.jl package.

      Returns

      A time series of the stochastic field values.

      source
      bfield(tend, J::AbstractSD, noise::Noise; distro=Normal(0., 1/sqrt(Δt)), interpolation=true, atol=0, rtol=sqrt(eps()), maxiters=Int(1e6))

      Generate a stochastic field realisation time series of length tend given the noise model noise and spectral density J. The optional parameters atol, rtol control the accuracy of the power spectral density of the generated noise.

      Arguments

      • tend: The total evolution time.
      • J::AbstractSD: The environment spectral density.
      • noise::Noise: The noise model for the environment.
      • atol=0: (Optional) The absolute tolerance for the spectral density estimation. Default is 0.
      • rtol=sqrt(eps()): (Optional) The relative tolerance for the spectral density estimation. Default is sqrt(eps()).
      • maxiters=Int(1e6): (Optional) The maximum number of iterations for the spectral density estimation. Default is 1e6.
      • interpolation=true: (Optional) Specifies whether to use linear interpolation for the stochastic field time series. Default is true.

      Note: The parameters used for generating the stochastic field are estimated using the estimate_bfield_parameters function. See the documentation for more details.

      Returns

      A time series of the stochastic field values.

      source
      SpiDy.estimate_bfield_parameters — Function
      estimate_bfield_parameters(J::AbstractSD, noise::Noise; atol=0, rtol=sqrt(eps()), maxiters=Int(1e6))

      Estimate the minimum time step size Δt and minimum total evolution time tmin required to generate a stochastic field realisation time series based on the given noise model noise and spectral density J, such that the power spectral density of the generated noise matches the target power spectral density within absolute atol and relative tolerances rtol.

      Arguments

      • J::AbstractSD: The environment spectral density.
      • noise::Noise: The noise model for the environment.
      • atol=0: (Optional) The absolute tolerance for the spectral density estimation. Default is 0.
      • rtol=sqrt(eps()): (Optional) The relative tolerance for the spectral density estimation. Default is sqrt(eps()).
      • maxiters=Int(1e6): (Optional) The maximum number of iterations for the spectral density estimation. Default is 1e6.

      Returns

      The minimum time step size Δt and minimum total evolution time tmin.

      source
      diff --git a/v1.3.0/units/index.html b/v1.3.0/units/index.html new file mode 100644 index 0000000..0d3010d --- /dev/null +++ b/v1.3.0/units/index.html @@ -0,0 +1,23 @@ + +Units and parameter choice · SpiDy.jl
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      Units and choice of input parameters

      In this document we describe the choice of units implemented in SpiDy.jl (which follows the conventions utilised in NJP 24 033020 (2022)) and how to appropriately choose the parameters that the library takes as input.

      Equations of motion

      SpiDy.jl is designed to implement the equations of spins in presence of a bath of harmonic oscillators as derived in NJP 24 033020 (2022), which for a single spin $\mathbf{S}$ in presence of an external field $\mathbf{B}_\mathrm{ext}$ read

      \[\frac{\mathrm{d}\mathbf{S}}{\mathrm{d}t} = + \gamma_e\mathbf{S}\times\left(\mathbf{B}_\mathrm{ext} + \mathbf{b}(t) + \mathbf{V}(t)\right),\]

      where $\gamma_e$ is the electron gyromagnetic ratio, $b(t)$ is the environment induced thermal stochastic field, and

      \[\mathbf{V}(t) = \gamma_e\int_{-\infty}^{t}\mathrm{d}t' \, \mathbf{K}(t-t')\mathbf{S}(t'),\]

      where $\mathbf{K}(\tau)$ is a memory kernel accounting for the non-Markovian evolution of the spin (see NJP 24 033020 (2022) for more details). SpiDy focuses on the case of an environment with a Lorentzian spectral density, in which case these equations of motion can be rewritten as

      \[\begin{align} +\frac{\mathrm{d}\mathbf{S}}{\mathrm{d}t} &= + \gamma_e\mathbf{S}\times\left(\mathbf{B}_\mathrm{ext} + \mathbf{b} + \mathbf{V}\right), \\ +\frac{\mathrm{d}\mathbf{V}}{\mathrm{d}t} &= \mathbf{W}, \\ +\frac{\mathrm{d}\mathbf{W}}{\mathrm{d}t} &= \gamma_e A \mathbf{S} - \omega_0^2\mathbf{V} - \Gamma\mathbf{W}, +\end{align}\]

      where $A$, $\omega_0$, and $\Gamma$ parametrise the Lorentzian spectral density as

      \[J(\omega) = \frac{A\Gamma}{\pi} \frac{\omega}{(\omega_0^2 - \omega^2)^2 + \omega^2\Gamma^2},\]

      and the thermal stochastic $\mathbf{b}$ field is given by

      \[\mathbf{b}(t) = \int_{-\infty}^{+\infty}\mathrm{d}t' F(t-t') \xi(t'),\]

      with $\xi$ being white noise and

      \[F(\tau) = \frac{1}{2\pi}\int_{-\infty}^{+\infty}\mathrm{d}\omega + e^{-i\omega\tau} \sqrt{P(\omega)}.\]

      Here, $P(\omega)$ is the power spectral density of the environment, and it is given in terms of the Lorentzian spectral density $J(\omega)$ and the environment thermal noise $N(\omega)$ by $P(\omega) = \hbar\pi J(\omega) N(\omega)$. The noise $N(\omega)$ can be classical, "quantum", or "quantum" with no zero point fluctuations. For example, for the "quantum" case we have

      \[N_\mathrm{qu}(\omega) = \coth\left(\frac{\hbar\omega}{2k_\mathrm{B}T}\right).\]

      Note that in these equations above, all quantities have standard units.

      Units rescaling

      SpiDy.jl implements these equations in a unit-free way, following the conventions of NJP 24 033020 (2022). In summary, consider a spin of length $\hbar S_0$ is in presence of a reference magnetic field of magnitude $B_0$. We then define the Larmor frequency

      \[\omega_\mathrm{L} = |\gamma_e| B_0,\]

      with $\gamma_e$ the electron gyromagnetic ratio.

      SpiDy.jl then takes as input parameters for the simulation the following unit free parameters:

      • $S_0$: the spin length (in units of $\hbar$).
      • $\bar{B}_\mathrm{ext}$: external magnetic field.
      • $\bar{t}_\mathrm{end}$: final time of the evolution.
      • $\mathrm{d}\bar{t}$: time differential.
      • $\bar{\omega}_0$: peak frequency of the Lorentzian spectral density.
      • $\bar{\Gamma}$: width of the Lorentzian spectral density.
      • $\bar{\alpha}$: amplitude of the Lorentzian spectral density.
      • $\bar{T}$: the environment temperature.

      These unit-free quantities (denoted hereon by a bar on top) are related to the unitful quantities in the previous section by the following conversions:

      \[\begin{align} +\mathbf{B}_\mathrm{ext} &= B_0 \, \bar{B}_\mathrm{ext}, \\ +t_\mathrm{end} &= \omega_\mathrm{L}^{-1} \, \bar{t}_\mathrm{end}, \\ +\mathrm{d}t &= \omega_\mathrm{L}^{-1} \, \mathrm{d}\bar{t}, \\ +\omega_0 &= \omega_\mathrm{L} \, \bar{\omega}_0, \\ +\Gamma &= \omega_\mathrm{L} \, \bar{\Gamma}, \\ +\omega_0 &= \omega_\mathrm{L} \, \bar{\omega}_0, \\ +A &= \frac{B_0^2\omega_\mathrm{L}}{\hbar S_0} \, \bar{\alpha}, \\ +T &= \frac{\hbar\omega_\mathrm{L}}{k_\mathrm{B}} \, \bar{T}. +\end{align}\]

      Given these choices of rescaling and adimensionalisation and plugging them in the equations of motion of the previous section, one finally gets the equations being solved by SpiDy, that is

      \[\begin{align} +\frac{\mathrm{d}\bar{\mathbf{S}}}{\mathrm{d}\bar{t}} &= + \bar{\mathbf{S}}\times\left(\bar{\mathbf{B}}_\mathrm{ext} + \frac{1}{\sqrt{S_0}}\bar{\mathbf{b}} + \bar{\mathbf{V}}\right), \\ +\frac{\mathrm{d}\bar{\mathbf{V}}}{\mathrm{d}\bar{t}} &= \bar{\mathbf{W}}, \\ +\frac{\mathrm{d}\bar{\mathbf{W}}}{\mathrm{d}\bar{t}} &= \bar{\alpha}\bar{\mathbf{S}} - \bar{\omega}_0^2\bar{\mathbf{V}} - \bar{\Gamma}\bar{\mathbf{W}}, +\end{align}\]

      with environment Lorentzian spectral density

      \[\bar{J}(\bar{\omega}) = \frac{\bar{\alpha}\bar{\Gamma}}{\pi} \frac{\bar{\omega}}{(\bar{\omega}_0^2 - \bar{\omega}^2)^2 + \bar{\omega}^2\bar{\Gamma}^2},\]

      and thermal stochastic noise $\bar{\mathbf{b}}$ with power spectral density

      \[\bar{P}(\bar{\omega}) = \pi \bar{J}(\bar{\omega})\bar{N}(\bar{\omega}).\]

      For the "quantum" noise, the noise term is given by

      \[\bar{N}_\mathrm{qu}(\bar{\omega}) = \coth\left(\frac{\bar{\omega}}{2\bar{T}}\right),\]

      while for "classical" noise we have

      \[\bar{N}_\mathrm{cl}(\bar{\omega}) = \frac{2\bar{T}}{\bar{\omega}}.\]

      Finally, note that with these definitions above, the unit-free Gilbert damping is given by (see NJP 24 033020 (2022))

      \[\eta = \frac{\bar{\alpha}\bar{\Gamma}}{\bar{\omega}_0^4}.\]

      Units convention in old versions of SpiDy.jl

      Note that the unit conversion just explained, in line with NJP 24 033020 (2022), is correct for SpiDy.jl versions 1.2.0 and later.

      Older version of SpiDy.jl used a different convention, which unfortunately meant that a change of spin length $S_0$ implied a change in temperature and time-scale, therefore requiring redefining the temperature, the paramerts of the Loretnzian, evolution time, etc.

      The change in units convetion means that versions of SpiDy.jl before and after 1.2.0 will produce different results. This breaking change was made to bring the code into consistency with the article NJP 24 033020 (2022) and to make the mapping of parameters used in SpiDy.jl to real units much easier and more straightforward (see also next section).

      Finally, it is worth noting that the behaviour of SpiDy.jl in older versions can be exactly recovered by passing the option $S_0 = 1$ to the integrator, since in that case both units conventions agree.

      Extracting Lorentzian units from experimental data

      To be written. See also EPL 139 36002 (2022).

      diff --git a/versions.js b/versions.js index c9e3bd7..c5b6228 100644 --- a/versions.js +++ b/versions.js @@ -1,5 +1,6 @@ var DOC_VERSIONS = [ "stable", + "v1.3", "v1.2", "v1.1", "v1.0", @@ -7,5 +8,5 @@ var DOC_VERSIONS = [ "v0.1", "dev", ]; -var DOCUMENTER_NEWEST = "v1.2.1"; +var DOCUMENTER_NEWEST = "v1.3.0"; var DOCUMENTER_STABLE = "stable";