From b39a524112ecefcc8f50c00a7c9135017ddb8c6a Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Wed, 6 Nov 2024 14:11:29 +0000 Subject: [PATCH] build based on 8cbefdb --- previews/PR48/assets/documenter.js | 331 ++++++++++++++++++ previews/PR48/assets/logo.png | Bin 0 -> 246623 bytes previews/PR48/assets/search.js | 267 ++++++++++++++ previews/PR48/assets/style.css | 27 ++ .../PR48/assets/themes/documenter-dark.css | 7 + .../PR48/assets/themes/documenter-light.css | 9 + previews/PR48/assets/themeswap.js | 66 ++++ previews/PR48/assets/warner.js | 49 +++ previews/PR48/index.html | 3 + previews/PR48/reference/index.html | 14 + previews/PR48/search/index.html | 2 + previews/PR48/search_index.js | 3 + previews/PR48/siteinfo.js | 1 + previews/PR48/tutorial/index.html | 68 ++++ 14 files changed, 847 insertions(+) create mode 100644 previews/PR48/assets/documenter.js create mode 100644 previews/PR48/assets/logo.png create mode 100644 previews/PR48/assets/search.js create mode 100644 previews/PR48/assets/style.css create mode 100644 previews/PR48/assets/themes/documenter-dark.css create mode 100644 previews/PR48/assets/themes/documenter-light.css create mode 100644 previews/PR48/assets/themeswap.js create mode 100644 previews/PR48/assets/warner.js create mode 100644 previews/PR48/index.html create mode 100644 previews/PR48/reference/index.html create mode 100644 previews/PR48/search/index.html create mode 100644 previews/PR48/search_index.js create mode 100644 previews/PR48/siteinfo.js create mode 100644 previews/PR48/tutorial/index.html diff --git a/previews/PR48/assets/documenter.js b/previews/PR48/assets/documenter.js new file mode 100644 index 0000000..6adfbbb --- /dev/null +++ b/previews/PR48/assets/documenter.js @@ -0,0 +1,331 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fas", "fa-copy"); + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-times"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-times"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function() { + $('#documenter .docs-navbar').headroom({ + "tolerance": {"up": 10, "down": 10}, + }); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function() { + var settings = $('#documenter-settings'); + $('#documenter-settings-button').click(function(){ + settings.toggleClass('is-active'); + }); + // Close the dialog if X is clicked + $('#documenter-settings button.delete').click(function(){ + settings.removeClass('is-active'); + }); + // Close dialog if ESC is pressed + $(document).keyup(function(e) { + if (e.keyCode == 27) settings.removeClass('is-active'); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function() { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button") + sidebar_button.click(function(ev) { + ev.preventDefault(); + sidebar.toggleClass('visible'); + if (sidebar.hasClass('visible')) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind('click', function(ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + }); +}) + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function() { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css('max-width'), 10); + var L0 = e.width(); + if(L0 > L) { + var h0 = parseInt(e.css('font-size'), 10); + e.css('font-size', L * h0 / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on('orientationchange', resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function() { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if(typeof active !== 'undefined') { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +function set_theme(theme) { + var active = null; + var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function(x) { + target_href = version_selector_select.children("option:selected").get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if (typeof 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zm6dhtY~R`{Ks7bL&(BLI>bPpDgocK0pV?eHtj4e6mV(D8Cf*Et`yVnQD}Ty|kbl3k z{BZM9&Ijvn*76stYijE2>da9Ssh*{}efmaZoyROt8R2%YY_0CPNI?s?psL80pHM*3m6Z zz6ZAaaB?X)?}3UTycjqyAaJ-j+*vATAoIItzXufXFDMkM1ARTEw7tGf)(_;nFa<1k zdive8-^l$2Z?ZprFaFIO^71jUM1yO3+`O}KykSi}Y>L%?9{cm-8D3uP+9G&o&C+D% z$F9|&I+%yZbK6)mK}*x;c1dsY{ma>!p>0;l&3Dvjk93%Ds7^bgl@8=7BZHs8nk6Bw zBvHS5P6ykt$>hdcf@aI_{Knd(n*yqlomp0J6lZzrFT;tV`cpYxWOS~hkT2uzONw+s zl*h>Q>;nc%iEbnQjM==X_1c^F;%D?&c|%+mRHQ$RW>F&dFg?4ukPXSPa%GMMdL_;b@R4|qi$h5n`VfIVgF%U1RoBWULJb zVIkTmw~f};XiEDbv*d5FpBA}$>*Cgon-+Mkn2cGnUySWN{K2;Ti8qQ@+*>2T?ho0J zwe`eSjn#0&DV}CV@9*=*S + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('

  • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR48/assets/style.css b/previews/PR48/assets/style.css new file mode 100644 index 0000000..7f1fab0 --- 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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 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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 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.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 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form.docs-search>input.button{border-radius:290486px;padding-left:1em;padding-right:1em}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:0.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){border-radius:3px;font-size:.85em}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons 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Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return + }; + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return + }; + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement('meta'); + meta.name = 'robots'; + meta.content = 'noindex'; + + document.getElementsByTagName('head')[0].appendChild(meta); + }; + + const div = document.createElement('div'); + div.classList.add('outdated-warning-overlay'); + const closer = document.createElement('button'); + closer.classList.add('outdated-warning-closer', 'delete'); + closer.addEventListener('click', function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + '/../' + window.DOCUMENTER_STABLE; + div.innerHTML = 'This documentation is not for the latest stable release, but for either the development version or an older release.
    Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +}; + +if (document.readyState === 'loading') { + document.addEventListener('DOMContentLoaded', maybeAddWarning); +} else { + maybeAddWarning(); +}; diff --git a/previews/PR48/index.html b/previews/PR48/index.html new file mode 100644 index 0000000..6bc6784 --- /dev/null +++ b/previews/PR48/index.html @@ -0,0 +1,3 @@ + +Home · PartitionedVectors.jl
    Edit on GitHub

    PartitionedVectors.jl

    Compatibility

    Julia ≥ 1.6.

    How to install

    This module can be installed with the following command:

    pkg> add PartitionedVectors
+pkg> test PartitionedVectors

    Synopsis

    A PartitionedVector <: DenseVector <: AbstractVector wraps a PartitionedStructures.Elemental_pv, to make JuliaSmoothOptimizers modules able to exploit the partially separable structure.

    How to use

    Check the tutorial.

    How to Cite

    If you use PartitionedVectors.jl in your work, please cite using the format given in CITATION.bib.

    Bug reports and discussions

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

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

    diff --git a/previews/PR48/reference/index.html b/previews/PR48/reference/index.html new file mode 100644 index 0000000..5c96566 --- /dev/null +++ b/previews/PR48/reference/index.html @@ -0,0 +1,14 @@ + +Reference · PartitionedVectors.jl
    Edit on GitHub

    Reference

    ​

    Contents

    ​

    ​

    Index

    ​

    ​

    Base.getindex — Method
    element_vector = getindex(pv::PartitionedVector, i::Int)

    Return the i-th element of pv, e.g. the i-th element vector.

    source
    Base.setindex! — Method
    setindex!(pv::PartitionedVector, val::Elemental_elt_vec, index::Int)
+setindex!(pv::PartitionedVector{T}, val::T, index::Int) where T<:Number
+setindex!(pv::PartitionedVector{T}, val::Vector{T}, index::Int) where T<:Number

    Set pv[index] (i.e. the index-th element vector) to val.

    source
    LinearAlgebra.dot — Method
    dot(pv1::PartitionedVector{T}, pv2::PartitionedVector{T}; kwargs...) where {T}
+dot(pv1::PartitionedVector{T}, pv2::PartitionedVector{T}, ::Val{true}, ::Val{false}; kwargs...) where {T}
+dot(pv1::PartitionedVector{T}, pv2::PartitionedVector{T}, ::Val{false}, ::Val{true}; kwargs...) where {T}
+dot(pv1::PartitionedVector{T}, pv2::PartitionedVector{T}, ::Val{true}, ::Val{true}; kwargs...) where {T}
+dot(pv1::PartitionedVector{T}, pv2::PartitionedVector{T}, ::Val{false}, ::Val{false}; kwargs...) where {T}

    Compute the dot product between two partitioned vectors. Methods having Val{true} and Val{false} as parameters compute dedicated dot routines depending the usage of pv1, pv2. See the tutorial for more details about the usage of a PartitionedVector.

    source
    PartitionedVectors._filter — Method
    _filter(i::Int, arg::Tuple{})
+element_vector = _filter(i::Int, arg::PartitionedVector)
+_filter(i::Int, arg::Any)
+_filter(i::Int, args::Tuple)

    Pass through a Tuple to select the i-th element if necessary.

    source
    PartitionedVectors.build! — Method
    build!(pv::PartitionedVector)

    Set in place of pv.epv.v the Vector that pv represents. If pv.simulate=false, it aggregates contributions from elemental vectors. If pv.simulate=true, common variables among element vectors value the same. For each index 1 ≤ i ≤ n, , build! will take the first element containing i and sets pv.epv.v[i] to its value.

    source
    PartitionedVectors.find_pv — Method
    pv = find_pv(bc::Base.Broadcast.Broadcasted)
+pv = find_pv(x::PartitionedVector)
+pv = find_pv(x::PartitionedVector, a::Any)
+pv = find_pv(x::Any, a::Any)

    Pass through a Broadcasted tape to retrieve a PartitionedVector.

    source
    PartitionedVectors.partitionedMulOp! — Method
    partitionedMulOp!(epm::PS.Part_mat, Hv::PartitionedVector, pv_res::PartitionedVector, pv::PartitionedVector, α, β)

    Partitioned matrix-vector product for PartitionedVectors: Hv, res and v.

    source
    PartitionedVectors.partitionedMulOpVec! — Method
    partitionedMulOpVec!(epm::PS.Part_mat{T}, Hv::Vector{T}, res::Vector{T}, v::Vector{T}, α, β;

    Partitioned matrix-vector product for Vectors: Hv, res and v. Made to test LinearOperators.LinearOperator(epm::Part_mat{T}) (which relies on PartitionedVectors).

    source
    diff --git a/previews/PR48/search/index.html b/previews/PR48/search/index.html new file mode 100644 index 0000000..15dafb8 --- /dev/null +++ b/previews/PR48/search/index.html @@ -0,0 +1,2 @@ + +Search · PartitionedVectors.jl

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      diff --git a/previews/PR48/search_index.js b/previews/PR48/search_index.js new file mode 100644 index 0000000..f0cb5d3 --- /dev/null +++ b/previews/PR48/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"reference/#Reference","page":"Reference","title":"Reference","text":"","category":"section"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/#Contents","page":"Reference","title":"Contents","text":"","category":"section"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"Pages = [\"reference.md\"]","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/#Index","page":"Reference","title":"Index","text":"","category":"section"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"Pages = [\"reference.md\"]","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"​","category":"page"},{"location":"reference/","page":"Reference","title":"Reference","text":"Modules = [PartitionedVectors]","category":"page"},{"location":"reference/#PartitionedVectors.AbstractPartitionedVector","page":"Reference","title":"PartitionedVectors.AbstractPartitionedVector","text":"AbstractPartitionedVector{T} <: DenseVector{T}\n\nAbstract type for PartitionedVector<:AbstractPartitionedVector{T}. 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Focused suggestions and requests can also be opened as issues. Before opening a pull request, start an issue or a discussion on the topic, please.","category":"page"},{"location":"","page":"Home","title":"Home","text":"If you want to ask a question not suited for a bug report, feel free to start a discussion here. This forum is for general discussion about this repository and the JuliaSmoothOptimizers, so questions about any of our packages are welcome.","category":"page"},{"location":"tutorial/#PartitionedVectors.jl-Tutorial","page":"Tutorial","title":"PartitionedVectors.jl Tutorial","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"A PartitionedVector <: DenseVector <: AbstractVector wraps a PartitionedStructures.Elemental_pv, to make JuliaSmoothOptimizers modules able to exploit the partially separable structure. For now, PartitionedVector is the keystone to define PartiallySeparableNLPModels, and then to consequently:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"replace Vector in JSOSolvers.jl; \nreplace Vector in KrylovSolvers.jl;\nmake LinearOperators relying only on PartitionedVectors viable;\nfit the NLPModels interface (ex: NLPModels.obj(nlp::PartiallySeparableNLPModel, x::PartitionedVector) see PartiallySeparableNLPModels.jl for more details).","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Partitioned vectors usages are related to partially separable problems:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":" f(x) = sum_i=1^N f_i (U_i x) f_i R^n_i to R U_i in R^n_i times n n_i ll n","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"whose inherit partitioned derivatives:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":" nabla f(x) = sum_i=1^N U_i^top nabla f_i (U_i x) quad nabla^2 f(x) = sum_i=1^N U_i^top nabla^2 f_i (U_i x) U_i","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"where the set of U_i gathers all the information related to the partitioned structure. We consider U_i a linear application selecting the variable that parametrize the i-th element function f_i, each U_i is defined from a vector of integers. The partially separable function ","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"f(x) = f_1(x_1x_2x_3x_4) + f_2(x_3x_4x_5x_6) + f_3(x_5x_6x_7) + f_4(x_5x_6x_8)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"get the following U_i:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"U1 = [1, 2, 3, 4]\nU2 = [3, 4, 5, 6]\nU3 = [5, 6, 7]\nU4 = [5, 6, 8]\nUis = [U1, U2, U3, U4]","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"However, before defining a PartitionedVector, you must understand the two usages of PartitionedVectors:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"usage 1: store each element contribution hatv_i independently and aggregate them to form v = sum_i=1^N U_i^top hatv_i","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In optimization methods, you use it to store nabla f_i (U_i x), y_i = nabla f_i (U_i x_k+1) - nabla f_i (U_i x_k) or the result of a partitioned hessian-vector product which is a partitioned vector:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":" nabla^2 f(x_k) s approx B_k s = (sum_i=1^N U_i^top B_ki U_i ) s = sum_i=1^N U_i^top (B_ki U_i s) ","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"usage 2: represent simultaneously a vector x in mathbbR^n and the application of every U_i onto x: U_i x forall i.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"By construction, the elements parametrized by the same variables (for exemple U1 and U3 are parametrized by the third variable) share the same values. In optimization methods, it allows to store the current point x_k or step s_k, which always comes in handy to evaluate f_i(U_i x) nabla f_i(U_i x) or B_ki U_i s.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Any methods exploiting partially separable concepts will have to manipulate both usages at the same time, in particular the solvers from JSOSolvers.jl and Krylov.jl. By default, you can define a PartitionedVector just from Uis as","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using PartitionedVectors\npv = PartitionedVector(Uis)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"which will be of usage 1. If you want a vector for usage 2 you have to set simulate_vector optional argument to true","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"pv_vec = PartitionedVector(Uis; simulate_vector=true)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The distinction between both is about how they form a Vector from them. For example:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"pv .= pv_vec\npv == pv_vec","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"which means that elements from pv are of same value than those of pv_vec. However, Vector(pv) relies on build! satisfying the specified usage and consequently","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Vector(pv) != Vector(pv_vec)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"You can set a PartitionedVector of usage 2 from a Vector with","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"set!(pv_vec, rand(length(pv_vec))) ","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Warning: the application set!() on PartitionedVector of usage 1 doesn't have sense, and produces an error.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"PartitionedVectors.jl specify several methods from various modules. For operations that are not in place, the result will take usage 1.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Warning: you have to be careful when you mix both usages in a single operation, because the result may have no meaning. Keep in mind the result you expect for Vector(pv).","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Base.jl:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"elementary operations +, -, *, == for PartitionedVectors.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"pv + pv == 2 * pv\npv - pv == 0 * pv","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Moreover, it supports the broadcast for the same operations (unfortunately not in place for now).","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"pv .+ pv == 2 .* pv\npv .- pv == 0 .* pv","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Special case when both usages get the same Vector","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"pv .= 0\npv_vec .= pv\nVector(pv) == Vector(pv_vec)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"supports methods related to AbstractArrays such as: \nget_index, set_index! refers to the i-th element vector of pv\npv .= 1\npv[1]\npv2 = pv - 0.5 * pv\npv[1] = pv2[1]\npv[1] == pv[2]\nfirstindex, lastindex, size, length:\nfirstindex(pv) == 1\nlastindex(pv) == 4 \nsize(pv) == (4,)\nlength(pv) == 8\nnote that size and length differ, length refers to the biggest index (e.g. n) while size refers to the number of elements N.\ncopy, similar:\npvcopy = copy(pv)\npvsimilar = similar(pv)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"LinearAlgebra: both dot and norm rely on build!(::PartitionedVector) before applying dot or norm to the resulting Vector","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using LinearAlgebra\ndot(pv,pv) ≈ norm(pv)^2","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"In addition, PartitionedVectors.jl defines a:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"LinearOperator from a PartitionedMatrix (see PartitionedStructures.jl) relying on PartitionedVectors","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using PartitionedStructures, LinearOperators\nepm = PartitionedStructures.identity_epm(Uis)\nlo = LinearOperators.LinearOperator(epm)\nlo * pv","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Note: Matrix(lo) will produce an error, since the default implementation assumes a complete Vector-like behaviour.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"dedicated CGSolver from Krylov.jl to solve a partitioned linear system (from a partitioned LinearOperator).","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using Krylov # 0.9.0\nsolver = Krylov.CgSolver(pv)\n\npv_gradient = similar(pv)\n(N,) = size(pv)\nfor i = 1:N\n nie = pv_gradient[i].nie #size of a element vector\n pv_gradient[i] = rand(nie)\nend\n\nKrylov.solve!(solver, lo, -pv_gradient)","category":"page"}] +} diff --git a/previews/PR48/siteinfo.js b/previews/PR48/siteinfo.js new file mode 100644 index 0000000..d4d3f93 --- /dev/null +++ b/previews/PR48/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR48"; diff --git a/previews/PR48/tutorial/index.html b/previews/PR48/tutorial/index.html new file mode 100644 index 0000000..011db31 --- /dev/null +++ b/previews/PR48/tutorial/index.html @@ -0,0 +1,68 @@ + +Tutorial · PartitionedVectors.jl
      Edit on GitHub

      PartitionedVectors.jl Tutorial

      A PartitionedVector <: DenseVector <: AbstractVector wraps a PartitionedStructures.Elemental_pv, to make JuliaSmoothOptimizers modules able to exploit the partially separable structure. For now, PartitionedVector is the keystone to define PartiallySeparableNLPModels, and then to consequently:

      • replace Vector in JSOSolvers.jl;
      • replace Vector in KrylovSolvers.jl;
      • make LinearOperators relying only on PartitionedVectors viable;
      • fit the NLPModels interface (ex: NLPModels.obj(nlp::PartiallySeparableNLPModel, x::PartitionedVector) see PartiallySeparableNLPModels.jl for more details).

      Partitioned vectors usages are related to partially separable problems:

      \[ f(x) = \sum_{i=1}^N f_i (U_i x) , \; f_i : \R^{n_i} \to \R, \; U_i \in \R^{n_i \times n},\; n_i \ll n,\]

      whose inherit partitioned derivatives:

      \[ \nabla f(x) = \sum_{i=1}^N U_i^\top \nabla f_i (U_i x) \quad \nabla^2 f(x) = \sum_{i=1}^N U_i^\top \nabla^2 f_i (U_i x) U_i,\]

      where the set of $U_i$ gathers all the information related to the partitioned structure. We consider $U_i$ a linear application selecting the variable that parametrize the $i$-th element function $f_i$, each $U_i$ is defined from a vector of integers. The partially separable function

      \[f(x) = f_1(x_1,x_2,x_3,x_4) + f_2(x_3,x_4,x_5,x_6) + f_3(x_5,x_6,x_7) + f_4(x_5,x_6,x_8)\]

      get the following $U_i$:

      U1 = [1, 2, 3, 4]
+U2 = [3, 4, 5, 6]
+U3 = [5, 6, 7]
+U4 = [5, 6, 8]
+Uis = [U1, U2, U3, U4]
      4-element Vector{Vector{Int64}}:
+ [1, 2, 3, 4]
+ [3, 4, 5, 6]
+ [5, 6, 7]
+ [5, 6, 8]

      However, before defining a PartitionedVector, you must understand the two usages of PartitionedVectors:

      • usage 1: store each element contribution $\hat{v}_i$ independently and aggregate them to form $v = \sum_{i=1}^N U_i^\top \hat{v}_i$

      In optimization methods, you use it to store $\nabla f_i (U_i x)$, $y_i = \nabla f_i (U_i x_{k+1}) - \nabla f_i (U_i x_k)$ or the result of a partitioned hessian-vector product which is a partitioned vector:

      \[ \nabla^2 f(x_k) s \approx B_k s = (\sum_{i=1}^N U_i^\top B_{k,i} U_i ) s = \sum_{i=1}^N U_i^\top (B_{k,i} U_i s) .\]

      • usage 2: represent simultaneously a vector $x \in \mathbb{R}^n$ and the application of every $U_i$ onto $x$: $U_i x, \forall i$.

      By construction, the elements parametrized by the same variables (for exemple U1 and U3 are parametrized by the third variable) share the same values. In optimization methods, it allows to store the current point $x_k$ or step $s_k$, which always comes in handy to evaluate $f_i(U_i x), \nabla f_i(U_i x)$ or $B_{k,i} U_i s$.

      Any methods exploiting partially separable concepts will have to manipulate both usages at the same time, in particular the solvers from JSOSolvers.jl and Krylov.jl. By default, you can define a PartitionedVector just from Uis as

      using PartitionedVectors
+pv = PartitionedVector(Uis)
      PartitionedVector{Float64}
+[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

      which will be of usage 1. If you want a vector for usage 2 you have to set simulate_vector optional argument to true

      pv_vec = PartitionedVector(Uis; simulate_vector=true)
      PartitionedVector{Float64}
+[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

      The distinction between both is about how they form a Vector from them. For example:

      pv .= pv_vec
+pv == pv_vec

      which means that elements from pv are of same value than those of pv_vec. However, Vector(pv) relies on build! satisfying the specified usage and consequently

      Vector(pv) != Vector(pv_vec)

      You can set a PartitionedVector of usage 2 from a Vector with

      set!(pv_vec, rand(length(pv_vec)))
      PartitionedVector{Float64}
+[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

      Warning: the application set!() on PartitionedVector of usage 1 doesn't have sense, and produces an error.

      PartitionedVectors.jl specify several methods from various modules. For operations that are not in place, the result will take usage 1.

      Warning: you have to be careful when you mix both usages in a single operation, because the result may have no meaning. Keep in mind the result you expect for Vector(pv).

      Base.jl:

      • elementary operations +, -, *, == for PartitionedVectors.
      pv + pv == 2 * pv
+pv - pv == 0 * pv
      true

      Moreover, it supports the broadcast for the same operations (unfortunately not in place for now).

      pv .+ pv == 2 .* pv
+pv .- pv == 0 .* pv
      true

      Special case when both usages get the same Vector

      pv .= 0
+pv_vec .= pv
+Vector(pv) == Vector(pv_vec)
      true
      • supports methods related to AbstractArrays such as:
        • get_index, set_index! refers to the i-th element vector of pv
        pv .= 1
+pv[1]
        pv2 = pv - 0.5 * pv
+pv[1] = pv2[1]
+pv[1] == pv[2]
        • firstindex, lastindex, size, length:
        firstindex(pv) == 1
+lastindex(pv) == 4  
+size(pv) == (4,)
+length(pv) == 8
        note that size and length differ, length refers to the biggest index (e.g. $n$) while size refers to the number of elements $N$.
        • copy, similar:
        pvcopy = copy(pv)
+pvsimilar = similar(pv)

      LinearAlgebra: both dot and norm rely on build!(::PartitionedVector) before applying dot or norm to the resulting Vector

      using LinearAlgebra
+dot(pv,pv) ≈ norm(pv)^2
      true

      In addition, PartitionedVectors.jl defines a:

      • LinearOperator from a PartitionedMatrix (see PartitionedStructures.jl) relying on PartitionedVectors
      using PartitionedStructures, LinearOperators
+epm = PartitionedStructures.identity_epm(Uis)
+lo = LinearOperators.LinearOperator(epm)
+lo * pv
      PartitionedVector{Float64}
+[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

      Note: Matrix(lo) will produce an error, since the default implementation assumes a complete Vector-like behaviour.

      • dedicated CGSolver from Krylov.jl to solve a partitioned linear system (from a partitioned LinearOperator).
      using Krylov # 0.9.0
+solver = Krylov.CgSolver(pv)
+
+pv_gradient = similar(pv)
+(N,) = size(pv)
+for i = 1:N
+  nie = pv_gradient[i].nie #size of a element vector
+  pv_gradient[i] = rand(nie)
+end
+
+Krylov.solve!(solver, lo, -pv_gradient)
      ┌──────────────────┬──────────────────────────┬──────────────────┐
+│          CgSolver│                  nrows: 8│          ncols: 8│
+├──────────────────┼──────────────────────────┼──────────────────┤
+│Precision: Float64│         Architecture: GPU│Storage: 163 bytes│
+├──────────────────┼──────────────────────────┼──────────────────┤
+│         Attribute│                      Type│              Size│
+├──────────────────┼──────────────────────────┼──────────────────┤
+│                 m│                     Int64│           8 bytes│
+│                 n│                     Int64│           8 bytes│
+│                Δx│PartitionedVector{Float64}│          16 bytes│
+│                 x│PartitionedVector{Float64}│          16 bytes│
+│                 r│PartitionedVector{Float64}│          16 bytes│
+│                 p│PartitionedVector{Float64}│          16 bytes│
+│                Ap│PartitionedVector{Float64}│          16 bytes│
+│                 z│PartitionedVector{Float64}│          16 bytes│
+│        warm_start│                      Bool│            1 byte│
+│             stats│Krylov.SimpleStats{Float64}│          50 bytes│
+└──────────────────┴──────────────────────────┴──────────────────┘
+
+Simple stats
+ niter: 3
+ solved: true
+ inconsistent: false
+ residuals: []
+ Aresiduals: []
+ κ₂(A): []
+ status: solution good enough given atol and rtol
+