From 134c96f4716ad5cf9be3de6e506f529edb2583e1 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Mon, 15 Apr 2024 09:14:04 +0000 Subject: [PATCH] build based on 8b47c36 --- stable | 2 +- v1 | 2 +- v1.14 | 1 + v1.14.0/assets/documenter.js | 331 +++++++++++++++++++++ v1.14.0/assets/search.js | 267 +++++++++++++++++ v1.14.0/assets/themes/documenter-dark.css | 7 + v1.14.0/assets/themes/documenter-light.css | 9 + v1.14.0/assets/themeswap.js | 66 ++++ v1.14.0/assets/warner.js | 49 +++ v1.14.0/index.html | 60 ++++ v1.14.0/internals/index.html | 143 +++++++++ v1.14.0/reference/index.html | 177 +++++++++++ v1.14.0/search/index.html | 2 + v1.14.0/search_index.js | 3 + v1.14.0/siteinfo.js | 1 + versions.js | 3 +- 16 files changed, 1120 insertions(+), 3 deletions(-) create mode 120000 v1.14 create mode 100644 v1.14.0/assets/documenter.js create mode 100644 v1.14.0/assets/search.js create mode 100644 v1.14.0/assets/themes/documenter-dark.css create mode 100644 v1.14.0/assets/themes/documenter-light.css create mode 100644 v1.14.0/assets/themeswap.js create mode 100644 v1.14.0/assets/warner.js create mode 100644 v1.14.0/index.html create mode 100644 v1.14.0/internals/index.html create mode 100644 v1.14.0/reference/index.html create mode 100644 v1.14.0/search/index.html create mode 100644 v1.14.0/search_index.js create mode 100644 v1.14.0/siteinfo.js diff --git a/stable b/stable index e58d236a..071e9093 120000 --- a/stable +++ b/stable @@ -1 +1 @@ -v1.13.0 \ No newline at end of file +v1.14.0 \ No newline at end of file diff --git a/v1 b/v1 index e58d236a..071e9093 120000 --- a/v1 +++ b/v1 @@ -1 +1 @@ -v1.13.0 \ No newline at end of file +v1.14.0 \ No newline at end of file diff --git a/v1.14 b/v1.14 new file mode 120000 index 00000000..071e9093 --- /dev/null +++ b/v1.14 @@ -0,0 +1 @@ +v1.14.0 \ No newline at end of file diff --git a/v1.14.0/assets/documenter.js b/v1.14.0/assets/documenter.js new file mode 100644 index 00000000..6adfbbbf --- /dev/null +++ b/v1.14.0/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 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 = $(""); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}) + +}) diff --git a/v1.14.0/assets/search.js b/v1.14.0/assets/search.js new file mode 100644 index 00000000..c133f741 --- /dev/null +++ b/v1.14.0/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, 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/v1.14.0/assets/themes/documenter-dark.css b/v1.14.0/assets/themes/documenter-dark.css new file mode 100644 index 00000000..c94a294d --- /dev/null +++ b/v1.14.0/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ +@keyframes spinAround{from{transform:rotate(0deg)}to{transform:rotate(359deg)}}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark .button,.is-unselectable,html.theme--documenter-dark .modal-close,html.theme--documenter-dark .delete{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none}html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after,html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after{border:3px solid rgba(0,0,0,0);border-radius:2px;border-right:0;border-top:0;content:" 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content 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1055px){html.theme--documenter-dark .navbar>.container{display:block}html.theme--documenter-dark .navbar-brand .navbar-item,html.theme--documenter-dark .navbar-tabs .navbar-item{align-items:center;display:flex}html.theme--documenter-dark .navbar-link::after{display:none}html.theme--documenter-dark .navbar-menu{background-color:#375a7f;box-shadow:0 8px 16px rgba(10,10,10,0.1);padding:0.5rem 0}html.theme--documenter-dark .navbar-menu.is-active{display:block}html.theme--documenter-dark .navbar.is-fixed-bottom-touch,html.theme--documenter-dark .navbar.is-fixed-top-touch{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark .navbar.is-fixed-bottom-touch{bottom:0}html.theme--documenter-dark .navbar.is-fixed-bottom-touch.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--documenter-dark .navbar.is-fixed-top-touch{top:0}html.theme--documenter-dark .navbar.is-fixed-top .navbar-menu,html.theme--documenter-dark .navbar.is-fixed-top-touch 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a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#dbdee0}html.theme--documenter-dark .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#1abc9c}.navbar.is-spaced html.theme--documenter-dark .navbar-dropdown,html.theme--documenter-dark .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--documenter-dark .navbar-dropdown.is-right{left:auto;right:0}html.theme--documenter-dark .navbar-divider{display:block}html.theme--documenter-dark .navbar>.container .navbar-brand,html.theme--documenter-dark .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--documenter-dark .navbar>.container .navbar-menu,html.theme--documenter-dark .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop,html.theme--documenter-dark .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop{bottom:0}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--documenter-dark .navbar.is-fixed-top-desktop{top:0}html.theme--documenter-dark html.has-navbar-fixed-top-desktop,html.theme--documenter-dark body.has-navbar-fixed-top-desktop{padding-top:4rem}html.theme--documenter-dark html.has-navbar-fixed-bottom-desktop,html.theme--documenter-dark body.has-navbar-fixed-bottom-desktop{padding-bottom:4rem}html.theme--documenter-dark html.has-spaced-navbar-fixed-top,html.theme--documenter-dark body.has-spaced-navbar-fixed-top{padding-top:6rem}html.theme--documenter-dark html.has-spaced-navbar-fixed-bottom,html.theme--documenter-dark body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--documenter-dark a.navbar-item.is-active,html.theme--documenter-dark .navbar-link.is-active{color:#1abc9c}html.theme--documenter-dark a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--documenter-dark .pagination{font-size:15px;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.85em}html.theme--documenter-dark .pagination.is-medium{font-size:1.25rem}html.theme--documenter-dark .pagination.is-large{font-size:1.5rem}html.theme--documenter-dark .pagination.is-rounded .pagination-previous,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination .pagination-previous,html.theme--documenter-dark .pagination.is-rounded .pagination-next,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination .pagination-next{padding-left:1em;padding-right:1em;border-radius:290486px}html.theme--documenter-dark .pagination.is-rounded .pagination-link,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination .pagination-link{border-radius:290486px}html.theme--documenter-dark .pagination,html.theme--documenter-dark .pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link{border-color:#5e6d6f;color:#1abc9c;min-width:2.25em}html.theme--documenter-dark .pagination-previous:hover,html.theme--documenter-dark .pagination-next:hover,html.theme--documenter-dark .pagination-link:hover{border-color:#8c9b9d;color:#1dd2af}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus{border-color:#8c9b9d}html.theme--documenter-dark .pagination-previous:active,html.theme--documenter-dark .pagination-next:active,html.theme--documenter-dark .pagination-link:active{box-shadow:inset 0 1px 2px rgba(10,10,10,0.2)}html.theme--documenter-dark .pagination-previous[disabled],html.theme--documenter-dark 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ul.is-center{flex:none;justify-content:center;padding-left:0.75em;padding-right:0.75em}html.theme--documenter-dark .tabs ul.is-right{justify-content:flex-end;padding-left:0.75em}html.theme--documenter-dark .tabs .icon:first-child{margin-right:0.5em}html.theme--documenter-dark .tabs .icon:last-child{margin-left:0.5em}html.theme--documenter-dark .tabs.is-centered ul{justify-content:center}html.theme--documenter-dark .tabs.is-right ul{justify-content:flex-end}html.theme--documenter-dark .tabs.is-boxed a{border:1px solid transparent;border-radius:.4em .4em 0 0}html.theme--documenter-dark .tabs.is-boxed a:hover{background-color:#282f2f;border-bottom-color:#5e6d6f}html.theme--documenter-dark .tabs.is-boxed li.is-active a{background-color:#fff;border-color:#5e6d6f;border-bottom-color:rgba(0,0,0,0) !important}html.theme--documenter-dark .tabs.is-fullwidth li{flex-grow:1;flex-shrink:0}html.theme--documenter-dark .tabs.is-toggle a{border-color:#5e6d6f;border-style:solid;border-width:1px;margin-bottom:0;position:relative}html.theme--documenter-dark .tabs.is-toggle a:hover{background-color:#282f2f;border-color:#8c9b9d;z-index:2}html.theme--documenter-dark .tabs.is-toggle li+li{margin-left:-1px}html.theme--documenter-dark .tabs.is-toggle li:first-child a{border-radius:.4em 0 0 .4em}html.theme--documenter-dark .tabs.is-toggle li:last-child a{border-radius:0 .4em .4em 0}html.theme--documenter-dark .tabs.is-toggle li.is-active a{background-color:#1abc9c;border-color:#1abc9c;color:#fff;z-index:1}html.theme--documenter-dark .tabs.is-toggle ul{border-bottom:none}html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:first-child a{border-bottom-left-radius:290486px;border-top-left-radius:290486px;padding-left:1.25em}html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:last-child a{border-bottom-right-radius:290486px;border-top-right-radius:290486px;padding-right:1.25em}html.theme--documenter-dark 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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/v1.14.0/assets/warner.js b/v1.14.0/assets/warner.js new file mode 100644 index 00000000..5531c885 --- /dev/null +++ b/v1.14.0/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. 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    Edit on GitHub

    OffsetArrays.jl

    OffsetArrays provides Julia users with arrays that have arbitrary indices, similar to those found in some other programming languages like Fortran. Below is the basic usage found in the README, followed by a couple of short examples illustrating circumstances in which OffsetArrays can be useful. For a lengthier discussion, see this blog post.

    Usage

    You can construct such arrays as follows:

    OA = OffsetArray(A, axis1, axis2, ...)

    where you want OA to have axes (axis1, axis2, ...) and be indexed by values that fall within these axis ranges.

    julia> using OffsetArrays
    julia> A = Float64.(reshape(1:15, 3, 5))3×5 Matrix{Float64}:
+ 1.0  4.0  7.0  10.0  13.0
+ 2.0  5.0  8.0  11.0  14.0
+ 3.0  6.0  9.0  12.0  15.0
    julia> OA = OffsetArray(A, -1:1, 0:4) # OA will have axes (-1:1, 0:4)3×5 OffsetArray(::Matrix{Float64}, -1:1, 0:4) with eltype Float64 with indices -1:1×0:4:
+ 1.0  4.0  7.0  10.0  13.0
+ 2.0  5.0  8.0  11.0  14.0
+ 3.0  6.0  9.0  12.0  15.0
    julia> OA = OffsetArray(A, CartesianIndex(-1, 0):CartesianIndex(1, 4))3×5 OffsetArray(::Matrix{Float64}, -1:1, 0:4) with eltype Float64 with indices -1:1×0:4:
+ 1.0  4.0  7.0  10.0  13.0
+ 2.0  5.0  8.0  11.0  14.0
+ 3.0  6.0  9.0  12.0  15.0
    julia> OA[-1,0], OA[1,4](1.0, 15.0)

    You could also pass integers as offsets, where 0 means no offsets are applied:

    julia> OA = OffsetArray(A, -2, -1)3×5 OffsetArray(::Matrix{Float64}, -1:1, 0:4) with eltype Float64 with indices -1:1×0:4:
+ 1.0  4.0  7.0  10.0  13.0
+ 2.0  5.0  8.0  11.0  14.0
+ 3.0  6.0  9.0  12.0  15.0

    When you create a new OffsetArray on the top of another OffsetArray, the offsets are accumulated:

    julia> OOA = OffsetArray(OA, 2, 1)3×5 OffsetArray(::Matrix{Float64}, 1:3, 1:5) with eltype Float64 with indices 1:3×1:5:
+ 1.0  4.0  7.0  10.0  13.0
+ 2.0  5.0  8.0  11.0  14.0
+ 3.0  6.0  9.0  12.0  15.0

    For the special cases that you want to compensate the offset back to the ordinary 1-based array, you can use OffsetArrays.no_offset_view(A). Furthermore, you could use Base.require_one_based_indexing if you want to ensure the array does not have offsets.

    julia> OffsetArrays.no_offset_view(OA)3×5 Matrix{Float64}:
+ 1.0  4.0  7.0  10.0  13.0
+ 2.0  5.0  8.0  11.0  14.0
+ 3.0  6.0  9.0  12.0  15.0
    julia> Base.require_one_based_indexing(ans)true
    julia> Base.require_one_based_indexing(OA)ERROR: ArgumentError: offset arrays are not supported but got an array with index other than 1

    OffsetArrays.Origin can be convenient if you want to directly specify the origin of the output OffsetArray, it will automatically compute the corresponding offsets. For example:

    julia> OffsetArray(A, OffsetArrays.Origin(-1, -1))3×5 OffsetArray(::Matrix{Float64}, -1:1, -1:3) with eltype Float64 with indices -1:1×-1:3:
+ 1.0  4.0  7.0  10.0  13.0
+ 2.0  5.0  8.0  11.0  14.0
+ 3.0  6.0  9.0  12.0  15.0
    julia> OffsetArray(OA, OffsetArrays.Origin(-1, -1))3×5 OffsetArray(::Matrix{Float64}, -1:1, -1:3) with eltype Float64 with indices -1:1×-1:3:
+ 1.0  4.0  7.0  10.0  13.0
+ 2.0  5.0  8.0  11.0  14.0
+ 3.0  6.0  9.0  12.0  15.0

    An equivalent — but possibly more convenient — way to specify the origin of an array is

    julia> OffsetArrays.Origin(-1, -1)(A)3×5 OffsetArray(::Matrix{Float64}, -1:1, -1:3) with eltype Float64 with indices -1:1×-1:3:
+ 1.0  4.0  7.0  10.0  13.0
+ 2.0  5.0  8.0  11.0  14.0
+ 3.0  6.0  9.0  12.0  15.0

    Sometimes, it will be convenient to shift the center coordinate of the given array to (0, 0, ...), OffsetArrays.centered is a helper for this very purpose:

    julia> Ao = OffsetArrays.centered(A)3×5 OffsetArray(::Matrix{Float64}, -1:1, -2:2) with eltype Float64 with indices -1:1×-2:2:
+ 1.0  4.0  7.0  10.0  13.0
+ 2.0  5.0  8.0  11.0  14.0
+ 3.0  6.0  9.0  12.0  15.0
    julia> Ao[0, 0] == 8.0true

    and OffsetArrays.center tells you the center coordinate of given array:

    julia> c = OffsetArrays.center(A)(2, 3)
    julia> A[c...] == 8.0true

    Example: Relativistic Notation

    Suppose we have a position vector r = [:x, :y, :z] which is naturally one-based, ie. r[1] == :x, r[2] == :y, r[3] == :z and we also want to construct a relativistic position vector which includes time as the 0th component. This can be done with OffsetArrays like

    julia> r = [:x, :y, :z];
+
+julia> x = OffsetVector([:t, r...], 0:3)
+4-element OffsetArray(::Vector{Symbol}, 0:3) with eltype Symbol with indices 0:3:
+ :t
+ :x
+ :y
+ :z
+
+julia> x[0]
+:t
+
+julia> x[1:3]
+3-element Vector{Symbol}:
+ :x
+ :y
+ :z

    Example: Polynomials

    Suppose one wants to represent the Laurent polynomial

    \[6/x + 5 - 2*x + 3*x^2 + x^3\]

    The coefficients of this polynomial are a naturally -1 based list, since the nth element of the list (counting from -1) 6, 5, -2, 3, 1 is the coefficient corresponding to the nth power of x. This Laurent polynomial can be evaluated at say x = 2 as follows.

    julia> coeffs = OffsetVector([6, 5, -2, 3, 1], -1:3)
+5-element OffsetArray(::Vector{Int64}, -1:3) with eltype Int64 with indices -1:3:
+  6
+  5
+ -2
+  3
+  1
+
+julia> polynomial(x, coeffs) = sum(coeffs[n]*x^n for n in eachindex(coeffs))
+polynomial (generic function with 1 method)
+
+julia> polynomial(2.0, coeffs)
+24.0

    Notice our use of the eachindex function which does not assume that the given array starts at 1.

    diff --git a/v1.14.0/internals/index.html b/v1.14.0/internals/index.html new file mode 100644 index 00000000..b47433f8 --- /dev/null +++ b/v1.14.0/internals/index.html @@ -0,0 +1,143 @@ + +For developers · OffsetArrays
    Edit on GitHub

    For developers

    Writing code that supports OffsetArrays is generally fairly straightforward. The majority of cases can be handled with these tips:

    • replace many uses of size with axes
    • replace 1:length(A) with eachindex(A), or if you need an integer index with LinearIndices(A)
    • replace explicit allocations like Array{Int}(undef, size(B)) with similar(Array{Int}, axes(B))

    More information can be found in Julia's developer documentation. The most subtle issues tend to arise around the axes, and further detail specific to OffsetArrays.jl follows below.

    Internals

    How does OffsetArrays work? The fundamental principle is very simple: an OffsetArray is just a wrapper around a "parent" array, together with an index offset:

    julia> oa = OffsetArray([1 2; 3 4], 0:1, 5:6)
+2×2 OffsetArray(::Matrix{Int64}, 0:1, 5:6) with eltype Int64 with indices 0:1×5:6:
+ 1  2
+ 3  4
+
+julia> parent(oa)
+2×2 Matrix{Int64}:
+ 1  2
+ 3  4
+
+julia> oa.offsets
+(-1, 4)

    So parent(oa) is the original array we constructed it with, and oa.offsets is a tuple, each entry encoding the index-shift to be applied along the corresponding axis. When you index oa[i,j], it "translates" the i,j indexes back to the parent array's indexes and then returns the value in the parent.

    The axes of OffsetArrays

    The internal of offset computing is achieved by IdOffsetRange type:

    julia> ax = axes(oa, 2)
+OffsetArrays.IdOffsetRange(values=5:6, indices=5:6)

    This has a similar design to Base.IdentityUnitRange that ax[x] == x always holds.

    julia> ax[5]
+5
+julia> ax[1]
+ERROR: BoundsError: attempt to access 2-element OffsetArrays.IdOffsetRange{Int64, Base.OneTo{Int64}} with indices 5:6 at index [1]
+[...]

    This property makes sure that they tend to be their own axes:

    julia> axes(ax)
+(OffsetArrays.IdOffsetRange(values=5:6, indices=5:6),)
+
+julia> axes(ax[ax])
+(OffsetArrays.IdOffsetRange(values=5:6, indices=5:6),)

    This example of indexing is idempotent. This is a useful characteristic for ensuring the "fundamental axiom" of generalized indexing, that a[ax][i] == a[ax[i]]:

    julia> oa2 = OffsetArray([5, 10, 15, 20], 0:3)
+4-element OffsetArray(::Vector{Int64}, 0:3) with eltype Int64 with indices 0:3:
+  5
+ 10
+ 15
+ 20
+
+julia> ax2 = axes(oa2, 1)
+OffsetArrays.IdOffsetRange(values=0:3, indices=0:3)
+
+julia> oa2[2]
+15
+
+julia> oa2[ax2][2]
+15
+
+julia> oa2[ax2[2]]
+15

    IdOffsetRanges apply the offset both to the values and the indices of the range, and otherwise preserve the parent range.

    Warning

    There are circumstances where constructing a specific type of IdOffsetRange cannot be supported without changing the axes of the range (see OffsetArrays.IdOffsetRange.) In the future, this package will distinguish between construction and conversion:

    • construction (aka, coercion) will always succeed, even if it has to change the axes of the result (Examples: RangeType(rng), typeof(rng1)(rng2))
    • conversion will succeed only if it can preserve both the values and the axes (Examples: convert(RangeType, rng), oftype(rng1, rng2))

    While these behave equivalently now (conversion currently performs coercion), developers are encouraged to "future-proof" their code by choosing the behavior appropriate for each usage.

    Wrapping other offset array types

    An OffsetArray may wrap any subtype of AbstractArray, including ones that do not use 1-based indexing. Such arrays however need to satisfy the fundamental axiom of idempotent indexing for things to work correctly. In other words, an axis of an offset array needs to have the same values as its own axis. This property is built into OffsetArrays if the parent uses 1-based indexing, but it's up to the user to ensure the correctness in case a type is to be wrapped that uses offset indices.

    We demonstrate this through an example by creating a custom 0-based range type that we wrap in an OffsetArray:

    julia> struct ZeroBasedRange{T,A<:AbstractRange{T}} <: AbstractRange{T}
+           a :: A
+           function ZeroBasedRange(a::AbstractRange{T}) where {T}
+               @assert !Base.has_offset_axes(a)
+               new{T, typeof(a)}(a)
+           end
+       end;
+
+julia> Base.parent(A::ZeroBasedRange) = A.a;
+
+julia> Base.first(A::ZeroBasedRange) = first(A.a);
+
+julia> Base.length(A::ZeroBasedRange) = length(A.a);
+
+julia> Base.last(A::ZeroBasedRange) = last(A.a);
+
+julia> Base.size(A::ZeroBasedRange) = size(A.a);
+
+julia> Base.axes(A::ZeroBasedRange) = map(x -> 0:x-1, size(A.a));
+
+julia> Base.getindex(A::ZeroBasedRange, i::Int) = A.a[i + 1];
+
+julia> Base.step(A::ZeroBasedRange) = step(A.a);
+
+julia> function Base.show(io::IO, A::ZeroBasedRange)
+           show(io, A.a)
+           print(io, " with indices $(axes(A,1))")
+       end;

    This definition of a ZeroBasedRange appears to have the correct indices, for example:

    julia> z = ZeroBasedRange(1:4)
+1:4 with indices 0:3
+
+julia> z[0]
+1
+
+julia> z[3]
+4

    However this does not use idempotent indexing, as the axis of a ZeroBasedRange is not its own axis.

    julia> axes(z, 1)
+0:3
+
+julia> axes(axes(z, 1), 1)
+Base.OneTo(4)

    This will lead to complications in certain functions –- for example LinearIndices –- that tends to implicitly assume idempotent indexing. In this case the LinearIndices of z will not match its axis.

    julia> LinearIndices(z)
+4-element LinearIndices{1, Tuple{UnitRange{Int64}}}:
+ 1
+ 2
+ 3
+ 4

    Wrapping such a type in an OffsetArray might lead to unexpected bugs.

    julia> zo = OffsetArray(z, 1);
+
+julia> axes(zo, 1)
+OffsetArrays.IdOffsetRange(values=1:4, indices=2:5)
+
+julia> Array(zo)
+ERROR: BoundsError: attempt to access 4-element UnitRange{Int64} at index [5]
+[...]

    The Array conversion errors despite zo having 1-based indices. The function axes(zo, 1) hints at the underlying problem –- the values and the indices of the axis are different. We may check that the axis of zo is not its own axis:

    julia> axes(zo, 1)
+OffsetArrays.IdOffsetRange(values=1:4, indices=2:5)
+
+julia> axes(axes(zo, 1), 1)
+OffsetArrays.IdOffsetRange(values=2:5, indices=2:5)

    In this case the bug may be fixed by defining the axes of a ZeroBasedRange to be idempotent, for example using the OffsetArrays.IdentityUnitRange wrapper:

    julia> Base.axes(A::ZeroBasedRange) = map(x -> OffsetArrays.IdentityUnitRange(0:x-1), size(A.a))
+
+julia> axes(zo, 1)
+OffsetArrays.IdOffsetRange(values=1:4, indices=1:4)

    With this new definition, the values and indices of the axis are identical, which makes indexing idempotent. The conversion to an Array works as expected now:

    julia> Array(zo)
+4-element Vector{Int64}:
+ 1
+ 2
+ 3
+ 4

    Caveats

    Because IdOffsetRange behaves quite differently to the normal UnitRange type, there are some cases that you should be aware of, especially when you are working with multi-dimensional arrays.

    One such cases is getindex:

    julia> Ao = zeros(-3:3, -3:3); Ao[:] .= 1:49;
+
+julia> Ao[-3:0, :] |> axes # the first dimension does not preserve offsets
+(OffsetArrays.IdOffsetRange(values=1:4, indices=1:4), OffsetArrays.IdOffsetRange(values=-3:3, indices=-3:3))
+
+julia> Ao[-3:0, -3:3] |> axes # neither dimensions preserve offsets
+(Base.OneTo(4), Base.OneTo(7))
+
+julia> Ao[axes(Ao)...] |> axes # offsets are preserved
+(OffsetArrays.IdOffsetRange(values=-3:3, indices=-3:3), OffsetArrays.IdOffsetRange(values=-3:3, indices=-3:3))
+
+julia> Ao[:] |> axes # This is linear indexing
+(Base.OneTo(49),)

    Note that if you pass a UnitRange, the offsets in corresponding dimension will not be preserved. This might look weird at first, but since it follows the a[ax][i] == a[ax[i]] rule, it is not a bug.

    julia> I = -3:0; # UnitRange always starts at index 1
+
+julia> Ao[I, 0][1] == Ao[I[1], 0]
+true
+
+julia> ax = axes(Ao, 1) # ax starts at index -3
+OffsetArrays.IdOffsetRange(values=-3:3, indices=-3:3)
+
+julia> Ao[ax, 0][1] == Ao[ax[1], 0]
+true

    Using custom axis types

    While a wide variety of AbstractUnitRanges provided by Base may be used as indices to construct an OffsetArray, at times it might be convenient to define custom types. The OffsetArray constructor accepts any type that may be converted to an AbstractUnitRange. This proceeds through a two-step process. Let's assume that the constructor called is OffsetArray(A, indstup), where indstup is a Tuple of indices.

    1. At the first step, the constructor calls to_indices(A, axes(A), indstup) to lower indstup to a Tuple of AbstractUnitRanges. This step converts –- among other things –- Colons to axis ranges. Custom types may extend Base.to_indices(A, axes(A), indstup) with the desired conversion of indstup to Tuple{Vararg{AbstractUnitRange{Int}}} if this is feasible.

    2. At the second step, the result obtained from the previous step treated again to convert it to a Tuple of AbstractUnitRanges to handle cases where the first step doesn't achieve this. An additional customization option may be specified at this stage: a type may be converted either to a single AbstractUnitRange{Int}, or to a Tuple of them. A type might specify which of these two behaviours is desired by extending OffsetArrays.AxisConversionStyle. An example of a type that is acted upon at this stage is CartesianIndices, which is converted to a Tuple of AbstractUnitRanges.

    For example, here are a couple of custom type that facilitate zero-based indexing:

    julia> struct ZeroBasedIndexing end
+
+julia> Base.to_indices(A, inds, ::Tuple{ZeroBasedIndexing}) = map(x -> 0:length(x)-1, inds)
+
+julia> a = zeros(3, 3);
+
+julia> oa = OffsetArray(a, ZeroBasedIndexing());
+
+julia> axes(oa)
+(OffsetArrays.IdOffsetRange(values=0:2, indices=0:2), OffsetArrays.IdOffsetRange(values=0:2, indices=0:2))

    In this example we had to define the action of to_indices as the type ZeroBasedIndexing did not have a familiar hierarchy. Things are even simpler if we subtype AbstractUnitRange, in which case we need to define first and length for the custom range to be able to use it as an axis:

    julia> struct ZeroTo <: AbstractUnitRange{Int}
+       n :: Int
+       ZeroTo(n) = new(n < 0 ? -1 : n)
+       end
+
+julia> Base.first(::ZeroTo) = 0
+
+julia> Base.length(r::ZeroTo) = r.n + 1
+
+julia> oa = OffsetArray(zeros(2,2), ZeroTo(1), ZeroTo(1));
+
+julia> axes(oa)
+(OffsetArrays.IdOffsetRange(values=0:1, indices=0:1), OffsetArrays.IdOffsetRange(values=0:1, indices=0:1))

    Note that zero-based indexing may also be achieved using the pre-defined type OffsetArrays.Origin.

    diff --git a/v1.14.0/reference/index.html b/v1.14.0/reference/index.html new file mode 100644 index 00000000..a12516d4 --- /dev/null +++ b/v1.14.0/reference/index.html @@ -0,0 +1,177 @@ + +Reference · OffsetArrays
    Edit on GitHub

    Reference

    OffsetArrays.OffsetArray — Type
    OffsetArray(A, indices...)

    Return an AbstractArray that shares element type and size with the first argument but uses the supplied indices to infer its axes. If all the indices are AbstractUnitRanges then these are directly used as the axis span along each dimension. Refer to the examples below for other permissible types.

    Alternatively it's possible to specify the coordinates of one corner of the array and have the axes be computed automatically from the size of A. This constructor makes it convenient to shift to an arbitrary starting index along each axis, for example to a zero-based indexing scheme followed by arrays in languages such as C and Python. See Origin and the examples below for this usage.

    Example: offsets

    There are two types of indices: integers and ranges-like types.

    Integers are recognized as offsets, where 0 means no offsets are applied:

    julia> A = OffsetArray(reshape(1:6, 2, 3), -1, -2)
+2×3 OffsetArray(reshape(::UnitRange{Int64}, 2, 3), 0:1, -1:1) with eltype Int64 with indices 0:1×-1:1:
+ 1  3  5
+ 2  4  6
+
+julia> A[0, 1]
+5

    Examples of range-like types are: UnitRange (e.g, -1:2), CartesianIndices, and Colon() (or concisely :). A UnitRange specifies the axis span along one particular dimension, CartesianIndices specify the axis spans along multiple dimensions, and a Colon is a placeholder that specifies that the OffsetArray shares its axis with its parent along that dimension.

    julia> OffsetArray(reshape(1:6, 2, 3), 0:1, -1:1)
+2×3 OffsetArray(reshape(::UnitRange{Int64}, 2, 3), 0:1, -1:1) with eltype Int64 with indices 0:1×-1:1:
+ 1  3  5
+ 2  4  6
+
+julia> OffsetArray(reshape(1:6, 2, 3), :, -1:1) # : as a placeholder to indicate that no offset is to be applied to the first dimension
+2×3 OffsetArray(reshape(::UnitRange{Int64}, 2, 3), 1:2, -1:1) with eltype Int64 with indices 1:2×-1:1:
+ 1  3  5
+ 2  4  6

    Use CartesianIndices to specify the coordinates of two diagonally opposite corners:

    julia> OffsetArray(reshape(1:6, 2, 3), CartesianIndex(0, -1):CartesianIndex(1, 1))
+2×3 OffsetArray(reshape(::UnitRange{Int64}, 2, 3), 0:1, -1:1) with eltype Int64 with indices 0:1×-1:1:
+ 1  3  5
+ 2  4  6

    Integers and range-like types may not be combined in the same call:

    julia> OffsetArray(reshape(1:6, 2, 3), 0, -1:1)
+ERROR: [...]

    Example: origin

    OffsetArrays.Origin may be used to specify the origin of the OffsetArray. The term origin here refers to the corner with the lowest values of coordinates, such as the left edge for an AbstractVector, the bottom left corner for an AbstractMatrix and so on. The coordinates of the origin sets the starting index of the array along each dimension.

    julia> a = [1 2; 3 4];
+
+julia> OffsetArray(a, OffsetArrays.Origin(0, 1))
+2×2 OffsetArray(::Matrix{Int64}, 0:1, 1:2) with eltype Int64 with indices 0:1×1:2:
+ 1  2
+ 3  4
+
+julia> OffsetArray(a, OffsetArrays.Origin(0)) # set the origin to zero along each dimension
+2×2 OffsetArray(::Matrix{Int64}, 0:1, 0:1) with eltype Int64 with indices 0:1×0:1:
+ 1  2
+ 3  4
    source
    OffsetArrays.Origin — Type
    Origin(indices...)
+Origin(origin::Tuple)
+Origin(origin::CartesianIndex)

    A helper type to construct OffsetArray with a given origin. This is not exported.

    The origin of an array is defined as the tuple of the first index along each axis, i.e., first.(axes(A)).

    Example

    julia> a = [1 2; 3 4];
+
+julia> using OffsetArrays: Origin
+
+julia> OffsetArray(a, Origin(0, 1))
+2×2 OffsetArray(::Matrix{Int64}, 0:1, 1:2) with eltype Int64 with indices 0:1×1:2:
+ 1  2
+ 3  4
+
+julia> OffsetArray(a, Origin(0)) # short notation for `Origin(0, 0)`
+2×2 OffsetArray(::Matrix{Int64}, 0:1, 0:1) with eltype Int64 with indices 0:1×0:1:
+ 1  2
+ 3  4

    An Origin object is callable, and it may shift the origin of an array to the specified point.

    julia> b = Origin(0)(a) # shift the origin of the array to (0,0)
+2×2 OffsetArray(::Matrix{Int64}, 0:1, 0:1) with eltype Int64 with indices 0:1×0:1:
+ 1  2
+ 3  4

    The type Origin, when called with an AbstractArray as the argument, will return an instance corresponding ot the origin of the array.

    julia> origin_b = Origin(b) # retrieve the origin of the array as an Origin instance
+Origin(0, 0)
+
+julia> origin_b(ones(2,2)) # shift the origin of another array to that of b, in this case to (0,0)
+2×2 OffsetArray(::Matrix{Float64}, 0:1, 0:1) with eltype Float64 with indices 0:1×0:1:
+ 1.0  1.0
+ 1.0  1.0
    Tip

    One may broadcast an Origin instance over multiple arrays to shift them all to the same origin.

    julia> using OffsetArrays: Origin
+
+julia> a = [1 2; 3 4]; # origin at (1,1)
+
+julia> b = Origin(2,3)(a); # origin at (2,3)
+
+julia> c = Origin(4)(a); # origin at (4,4)
+
+julia> ao, bo, co = Origin(0).((a, b, c)); # shift all origins to (0,0)
+
+julia> first.(axes(ao)) == first.(axes(bo)) == first.(axes(co)) == (0,0)
+true
+
+julia> ao, bo, co = Origin(b).((a, b, c)); # shift all origins to that of b
+
+julia> first.(axes(ao)) == first.(axes(bo)) == first.(axes(co)) == (2,3)
+true
+
+julia> ao, bo, co = OffsetArray.((a, b, c), Origin(b)); # another way to do the same
+
+julia> first.(axes(ao)) == first.(axes(bo)) == first.(axes(co)) == (2,3)
+true
    source
    OffsetArrays.IdOffsetRange — Type
    ro = IdOffsetRange(r::AbstractUnitRange, offset=0)

    Construct an "identity offset range". Numerically, collect(ro) == collect(r) .+ offset, with the additional property that axes(ro, 1) = axes(r, 1) .+ offset. When r starts at 1, then ro[i] == i and even ro[ro] == ro, i.e., it's the "identity," which is the origin of the "Id" in IdOffsetRange.

    Examples

    The most common case is shifting a range that starts at 1 (either 1:n or Base.OneTo(n)):

    julia> using OffsetArrays: IdOffsetRange
+
+julia> ro = IdOffsetRange(1:3, -2)
+IdOffsetRange(values=-1:1, indices=-1:1)
+
+julia> axes(ro, 1)
+IdOffsetRange(values=-1:1, indices=-1:1)
+
+julia> ro[-1]
+-1
+
+julia> ro[3]
+ERROR: BoundsError: attempt to access 3-element OffsetArrays.IdOffsetRange{Int64, UnitRange{Int64}} with indices -1:1 at index [3]

    If the range doesn't start at 1, the values may be different from the indices:

    julia> ro = IdOffsetRange(11:13, -2)
+IdOffsetRange(values=9:11, indices=-1:1)
+
+julia> axes(ro, 1)     # 11:13 is indexed by 1:3, and the offset is also applied to the axes
+IdOffsetRange(values=-1:1, indices=-1:1)
+
+julia> ro[-1]
+9
+
+julia> ro[3]
+ERROR: BoundsError: attempt to access 3-element OffsetArrays.IdOffsetRange{Int64, UnitRange{Int64}} with indices -1:1 at index [3]

    Extended help

    Construction/coercion preserves the (shifted) values of the input range, but may modify the indices if required by the specified types. For example,

    r = OffsetArrays.IdOffsetRange{Int,UnitRange{Int}}(3:4)

    has r[1] == 3 and r[2] == 4, whereas

    r = OffsetArrays.IdOffsetRange{Int,Base.OneTo{Int}}(3:4)

    has r[3] == 3 and r[4] == 4, and r[1] would throw a BoundsError. In this latter case, a shift in the axes was needed because Base.OneTo ranges must start with value 1.

    Warning

    In the future, conversion will preserve both the values and the indices, throwing an error when this is not achievable. For instance,

    r = convert(OffsetArrays.IdOffsetRange{Int,UnitRange{Int}}, 3:4)

    has r[1] == 3 and r[2] == 4 and would satisfy r == 3:4, whereas

    julia> convert(OffsetArrays.IdOffsetRange{Int,Base.OneTo{Int}}, 3:4)    # future behavior, not present behavior
+ERROR: ArgumentError: first element must be 1, got 3

    where the error will arise because the result could not have the same axes as the input.

    An important corollary is that typeof(r1)(r2) and oftype(r1, r2) will behave differently: the first coerces r2 to be of the type of r1, whereas the second converts. Developers are urged to future-proof their code by choosing the behavior appropriate for each usage.

    source
    OffsetArrays.no_offset_view — Function
    no_offset_view(A)

    Return an AbstractArray that shares structure and underlying data with the argument, but uses 1-based indexing. May just return the argument when applicable. Not exported.

    The default implementation uses OffsetArrays, but other types should use something more specific to remove a level of indirection when applicable.

    julia> A = [1 3 5; 2 4 6];
+
+julia> O = OffsetArray(A, 0:1, -1:1)
+2×3 OffsetArray(::Matrix{Int64}, 0:1, -1:1) with eltype Int64 with indices 0:1×-1:1:
+ 1  3  5
+ 2  4  6
+
+julia> OffsetArrays.no_offset_view(O)[1,1] = -9
+-9
+
+julia> A
+2×3 Matrix{Int64}:
+ -9  3  5
+  2  4  6
    source
    OffsetArrays.AxisConversionStyle — Type
    OffsetArrays.AxisConversionStyle(typeof(indices))

    AxisConversionStyle declares if indices should be converted to a single AbstractUnitRange{Int} or to a Tuple{Vararg{AbstractUnitRange{Int}}} while flattening custom types into indices. This method is called after to_indices(A::Array, axes(A), indices) to provide further information in case to_indices does not return a Tuple of AbstractUnitRange{Int}.

    Custom index types should extend AxisConversionStyle and return either OffsetArray.SingleRange(), which is the default, or OffsetArray.TupleOfRanges(). In the former case, the type T should define Base.convert(::Type{AbstractUnitRange{Int}}, ::T), whereas in the latter it should define Base.convert(::Type{Tuple{Vararg{AbstractUnitRange{Int}}}}, ::T).

    An example of the latter is CartesianIndices, which is converted to a Tuple of AbstractUnitRange{Int} while flattening the indices.

    Example

    julia> struct NTupleOfUnitRanges{N}
+           x ::NTuple{N, UnitRange{Int}}
+       end
+
+julia> Base.to_indices(A, inds, t::Tuple{NTupleOfUnitRanges{N}}) where {N} = t;
+
+julia> OffsetArrays.AxisConversionStyle(::Type{NTupleOfUnitRanges{N}}) where {N} = OffsetArrays.TupleOfRanges();
+
+julia> Base.convert(::Type{Tuple{Vararg{AbstractUnitRange{Int}}}}, t::NTupleOfUnitRanges) = t.x;
+
+julia> a = zeros(3, 3);
+
+julia> inds = NTupleOfUnitRanges((3:5, 2:4));
+
+julia> oa = OffsetArray(a, inds);
+
+julia> axes(oa, 1) == 3:5
+true
+
+julia> axes(oa, 2) == 2:4
+true
    source
    OffsetArrays.center — Function
    center(A, [r::RoundingMode=RoundDown])::Dims

    Return the center coordinate of given array A. If size(A, k) is even, a rounding procedure will be applied with mode r.

    OffsetArrays 1.9

    This method requires at least OffsetArrays 1.9.

    Examples

    julia> A = reshape(collect(1:9), 3, 3)
+3×3 Matrix{Int64}:
+ 1  4  7
+ 2  5  8
+ 3  6  9
+
+julia> c = OffsetArrays.center(A)
+(2, 2)
+
+julia> A[c...]
+5
+
+julia> Ao = OffsetArray(A, -2, -2); # axes (-1:1, -1:1)
+
+julia> c = OffsetArrays.center(Ao)
+(0, 0)
+
+julia> Ao[c...]
+5

    To shift the center coordinate of the given array to (0, 0, ...), you can use centered.

    source
    OffsetArrays.centered — Function
    centered(A, cp=center(A)) -> Ao

    Shift the center coordinate/point cp of array A to (0, 0, ..., 0). Internally, this is equivalent to OffsetArray(A, .-cp).

    OffsetArrays 1.9

    This method requires at least OffsetArrays 1.9.

    Examples

    julia> A = reshape(collect(1:9), 3, 3)
+3×3 Matrix{Int64}:
+ 1  4  7
+ 2  5  8
+ 3  6  9
+
+julia> Ao = OffsetArrays.centered(A); # axes (-1:1, -1:1)
+
+julia> Ao[0, 0]
+5
+
+julia> Ao = OffsetArray(A, OffsetArrays.Origin(0)); # axes (0:2, 0:2)
+
+julia> Aoo = OffsetArrays.centered(Ao); # axes (-1:1, -1:1)
+
+julia> Aoo[0, 0]
+5

    Users are allowed to pass cp to change how "center point" is interpreted, but the meaning of the output array should be reinterpreted as well. For instance, if cp = map(last, axes(A)) then this function no longer shifts the center point but instead the bottom-right point to (0, 0, ..., 0). A commonly usage of cp is to change the rounding behavior when the array is of even size at some dimension:

    julia> A = reshape(collect(1:4), 2, 2) # Ideally the center should be (1.5, 1.5) but OffsetArrays only support integer offsets
+2×2 Matrix{Int64}:
+ 1  3
+ 2  4
+
+julia> OffsetArrays.centered(A, OffsetArrays.center(A, RoundUp)) # set (2, 2) as the center point
+2×2 OffsetArray(::Matrix{Int64}, -1:0, -1:0) with eltype Int64 with indices -1:0×-1:0:
+ 1  3
+ 2  4
+
+julia> OffsetArrays.centered(A, OffsetArrays.center(A, RoundDown)) # set (1, 1) as the center point
+2×2 OffsetArray(::Matrix{Int64}, 0:1, 0:1) with eltype Int64 with indices 0:1×0:1:
+ 1  3
+ 2  4

    See also center.

    source
    diff --git a/v1.14.0/search/index.html b/v1.14.0/search/index.html new file mode 100644 index 00000000..ea23de28 --- /dev/null +++ b/v1.14.0/search/index.html @@ -0,0 +1,2 @@ + +Search · OffsetArrays

    Loading search...

      diff --git a/v1.14.0/search_index.js b/v1.14.0/search_index.js new file mode 100644 index 00000000..079a861a --- /dev/null +++ b/v1.14.0/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":"OffsetArray\nOffsetVector\nOffsetMatrix\nOffsetArrays.Origin\nOffsetArrays.IdOffsetRange\nOffsetArrays.no_offset_view\nOffsetArrays.AxisConversionStyle\nOffsetArrays.center\nOffsetArrays.centered","category":"page"},{"location":"reference/#OffsetArrays.OffsetArray","page":"Reference","title":"OffsetArrays.OffsetArray","text":"OffsetArray(A, indices...)\n\nReturn an AbstractArray that shares element type and size with the first argument but uses the supplied indices to infer its axes. If all the indices are AbstractUnitRanges then these are directly used as the axis span along each dimension. Refer to the examples below for other permissible types.\n\nAlternatively it's possible to specify the coordinates of one corner of the array and have the axes be computed automatically from the size of A. This constructor makes it convenient to shift to an arbitrary starting index along each axis, for example to a zero-based indexing scheme followed by arrays in languages such as C and Python. See Origin and the examples below for this usage.\n\nExample: offsets\n\nThere are two types of indices: integers and ranges-like types.\n\nIntegers are recognized as offsets, where 0 means no offsets are applied:\n\njulia> A = OffsetArray(reshape(1:6, 2, 3), -1, -2)\n2×3 OffsetArray(reshape(::UnitRange{Int64}, 2, 3), 0:1, -1:1) with eltype Int64 with indices 0:1×-1:1:\n 1 3 5\n 2 4 6\n\njulia> A[0, 1]\n5\n\nExamples of range-like types are: UnitRange (e.g, -1:2), CartesianIndices, and Colon() (or concisely :). A UnitRange specifies the axis span along one particular dimension, CartesianIndices specify the axis spans along multiple dimensions, and a Colon is a placeholder that specifies that the OffsetArray shares its axis with its parent along that dimension.\n\njulia> OffsetArray(reshape(1:6, 2, 3), 0:1, -1:1)\n2×3 OffsetArray(reshape(::UnitRange{Int64}, 2, 3), 0:1, -1:1) with eltype Int64 with indices 0:1×-1:1:\n 1 3 5\n 2 4 6\n\njulia> OffsetArray(reshape(1:6, 2, 3), :, -1:1) # : as a placeholder to indicate that no offset is to be applied to the first dimension\n2×3 OffsetArray(reshape(::UnitRange{Int64}, 2, 3), 1:2, -1:1) with eltype Int64 with indices 1:2×-1:1:\n 1 3 5\n 2 4 6\n\nUse CartesianIndices to specify the coordinates of two diagonally opposite corners:\n\njulia> OffsetArray(reshape(1:6, 2, 3), CartesianIndex(0, -1):CartesianIndex(1, 1))\n2×3 OffsetArray(reshape(::UnitRange{Int64}, 2, 3), 0:1, -1:1) with eltype Int64 with indices 0:1×-1:1:\n 1 3 5\n 2 4 6\n\nIntegers and range-like types may not be combined in the same call:\n\njulia> OffsetArray(reshape(1:6, 2, 3), 0, -1:1)\nERROR: [...]\n\nExample: origin\n\nOffsetArrays.Origin may be used to specify the origin of the OffsetArray. The term origin here refers to the corner with the lowest values of coordinates, such as the left edge for an AbstractVector, the bottom left corner for an AbstractMatrix and so on. The coordinates of the origin sets the starting index of the array along each dimension.\n\njulia> a = [1 2; 3 4];\n\njulia> OffsetArray(a, OffsetArrays.Origin(0, 1))\n2×2 OffsetArray(::Matrix{Int64}, 0:1, 1:2) with eltype Int64 with indices 0:1×1:2:\n 1 2\n 3 4\n\njulia> OffsetArray(a, OffsetArrays.Origin(0)) # set the origin to zero along each dimension\n2×2 OffsetArray(::Matrix{Int64}, 0:1, 0:1) with eltype Int64 with indices 0:1×0:1:\n 1 2\n 3 4\n\n\n\n\n\n","category":"type"},{"location":"reference/#OffsetArrays.OffsetVector","page":"Reference","title":"OffsetArrays.OffsetVector","text":"OffsetVector(v, index)\n\nType alias and convenience constructor for one-dimensional OffsetArrays.\n\n\n\n\n\n","category":"type"},{"location":"reference/#OffsetArrays.OffsetMatrix","page":"Reference","title":"OffsetArrays.OffsetMatrix","text":"OffsetMatrix(A, index1, index2)\n\nType alias and convenience constructor for two-dimensional OffsetArrays.\n\n\n\n\n\n","category":"type"},{"location":"reference/#OffsetArrays.Origin","page":"Reference","title":"OffsetArrays.Origin","text":"Origin(indices...)\nOrigin(origin::Tuple)\nOrigin(origin::CartesianIndex)\n\nA helper type to construct OffsetArray with a given origin. This is not exported.\n\nThe origin of an array is defined as the tuple of the first index along each axis, i.e., first.(axes(A)).\n\nExample\n\njulia> a = [1 2; 3 4];\n\njulia> using OffsetArrays: Origin\n\njulia> OffsetArray(a, Origin(0, 1))\n2×2 OffsetArray(::Matrix{Int64}, 0:1, 1:2) with eltype Int64 with indices 0:1×1:2:\n 1 2\n 3 4\n\njulia> OffsetArray(a, Origin(0)) # short notation for `Origin(0, 0)`\n2×2 OffsetArray(::Matrix{Int64}, 0:1, 0:1) with eltype Int64 with indices 0:1×0:1:\n 1 2\n 3 4\n\nAn Origin object is callable, and it may shift the origin of an array to the specified point.\n\njulia> b = Origin(0)(a) # shift the origin of the array to (0,0)\n2×2 OffsetArray(::Matrix{Int64}, 0:1, 0:1) with eltype Int64 with indices 0:1×0:1:\n 1 2\n 3 4\n\nThe type Origin, when called with an AbstractArray as the argument, will return an instance corresponding ot the origin of the array.\n\njulia> origin_b = Origin(b) # retrieve the origin of the array as an Origin instance\nOrigin(0, 0)\n\njulia> origin_b(ones(2,2)) # shift the origin of another array to that of b, in this case to (0,0)\n2×2 OffsetArray(::Matrix{Float64}, 0:1, 0:1) with eltype Float64 with indices 0:1×0:1:\n 1.0 1.0\n 1.0 1.0\n\ntip: Tip\nOne may broadcast an Origin instance over multiple arrays to shift them all to the same origin.julia> using OffsetArrays: Origin\n\njulia> a = [1 2; 3 4]; # origin at (1,1)\n\njulia> b = Origin(2,3)(a); # origin at (2,3)\n\njulia> c = Origin(4)(a); # origin at (4,4)\n\njulia> ao, bo, co = Origin(0).((a, b, c)); # shift all origins to (0,0)\n\njulia> first.(axes(ao)) == first.(axes(bo)) == first.(axes(co)) == (0,0)\ntrue\n\njulia> ao, bo, co = Origin(b).((a, b, c)); # shift all origins to that of b\n\njulia> first.(axes(ao)) == first.(axes(bo)) == first.(axes(co)) == (2,3)\ntrue\n\njulia> ao, bo, co = OffsetArray.((a, b, c), Origin(b)); # another way to do the same\n\njulia> first.(axes(ao)) == first.(axes(bo)) == first.(axes(co)) == (2,3)\ntrue\n\n\n\n\n\n","category":"type"},{"location":"reference/#OffsetArrays.IdOffsetRange","page":"Reference","title":"OffsetArrays.IdOffsetRange","text":"ro = IdOffsetRange(r::AbstractUnitRange, offset=0)\n\nConstruct an \"identity offset range\". Numerically, collect(ro) == collect(r) .+ offset, with the additional property that axes(ro, 1) = axes(r, 1) .+ offset. When r starts at 1, then ro[i] == i and even ro[ro] == ro, i.e., it's the \"identity,\" which is the origin of the \"Id\" in IdOffsetRange.\n\nExamples\n\nThe most common case is shifting a range that starts at 1 (either 1:n or Base.OneTo(n)):\n\njulia> using OffsetArrays: IdOffsetRange\n\njulia> ro = IdOffsetRange(1:3, -2)\nIdOffsetRange(values=-1:1, indices=-1:1)\n\njulia> axes(ro, 1)\nIdOffsetRange(values=-1:1, indices=-1:1)\n\njulia> ro[-1]\n-1\n\njulia> ro[3]\nERROR: BoundsError: attempt to access 3-element OffsetArrays.IdOffsetRange{Int64, UnitRange{Int64}} with indices -1:1 at index [3]\n\nIf the range doesn't start at 1, the values may be different from the indices:\n\njulia> ro = IdOffsetRange(11:13, -2)\nIdOffsetRange(values=9:11, indices=-1:1)\n\njulia> axes(ro, 1) # 11:13 is indexed by 1:3, and the offset is also applied to the axes\nIdOffsetRange(values=-1:1, indices=-1:1)\n\njulia> ro[-1]\n9\n\njulia> ro[3]\nERROR: BoundsError: attempt to access 3-element OffsetArrays.IdOffsetRange{Int64, UnitRange{Int64}} with indices -1:1 at index [3]\n\nExtended help\n\nConstruction/coercion preserves the (shifted) values of the input range, but may modify the indices if required by the specified types. For example,\n\nr = OffsetArrays.IdOffsetRange{Int,UnitRange{Int}}(3:4)\n\nhas r[1] == 3 and r[2] == 4, whereas\n\nr = OffsetArrays.IdOffsetRange{Int,Base.OneTo{Int}}(3:4)\n\nhas r[3] == 3 and r[4] == 4, and r[1] would throw a BoundsError. In this latter case, a shift in the axes was needed because Base.OneTo ranges must start with value 1.\n\nwarning: Warning\nIn the future, conversion will preserve both the values and the indices, throwing an error when this is not achievable. For instance,r = convert(OffsetArrays.IdOffsetRange{Int,UnitRange{Int}}, 3:4)has r[1] == 3 and r[2] == 4 and would satisfy r == 3:4, whereasjulia> convert(OffsetArrays.IdOffsetRange{Int,Base.OneTo{Int}}, 3:4) # future behavior, not present behavior\nERROR: ArgumentError: first element must be 1, got 3where the error will arise because the result could not have the same axes as the input.An important corollary is that typeof(r1)(r2) and oftype(r1, r2) will behave differently: the first coerces r2 to be of the type of r1, whereas the second converts. Developers are urged to future-proof their code by choosing the behavior appropriate for each usage.\n\n\n\n\n\n","category":"type"},{"location":"reference/#OffsetArrays.no_offset_view","page":"Reference","title":"OffsetArrays.no_offset_view","text":"no_offset_view(A)\n\nReturn an AbstractArray that shares structure and underlying data with the argument, but uses 1-based indexing. May just return the argument when applicable. Not exported.\n\nThe default implementation uses OffsetArrays, but other types should use something more specific to remove a level of indirection when applicable.\n\njulia> A = [1 3 5; 2 4 6];\n\njulia> O = OffsetArray(A, 0:1, -1:1)\n2×3 OffsetArray(::Matrix{Int64}, 0:1, -1:1) with eltype Int64 with indices 0:1×-1:1:\n 1 3 5\n 2 4 6\n\njulia> OffsetArrays.no_offset_view(O)[1,1] = -9\n-9\n\njulia> A\n2×3 Matrix{Int64}:\n -9 3 5\n 2 4 6\n\n\n\n\n\n","category":"function"},{"location":"reference/#OffsetArrays.AxisConversionStyle","page":"Reference","title":"OffsetArrays.AxisConversionStyle","text":"OffsetArrays.AxisConversionStyle(typeof(indices))\n\nAxisConversionStyle declares if indices should be converted to a single AbstractUnitRange{Int} or to a Tuple{Vararg{AbstractUnitRange{Int}}} while flattening custom types into indices. This method is called after to_indices(A::Array, axes(A), indices) to provide further information in case to_indices does not return a Tuple of AbstractUnitRange{Int}.\n\nCustom index types should extend AxisConversionStyle and return either OffsetArray.SingleRange(), which is the default, or OffsetArray.TupleOfRanges(). In the former case, the type T should define Base.convert(::Type{AbstractUnitRange{Int}}, ::T), whereas in the latter it should define Base.convert(::Type{Tuple{Vararg{AbstractUnitRange{Int}}}}, ::T).\n\nAn example of the latter is CartesianIndices, which is converted to a Tuple of AbstractUnitRange{Int} while flattening the indices.\n\nExample\n\njulia> struct NTupleOfUnitRanges{N}\n x ::NTuple{N, UnitRange{Int}}\n end\n\njulia> Base.to_indices(A, inds, t::Tuple{NTupleOfUnitRanges{N}}) where {N} = t;\n\njulia> OffsetArrays.AxisConversionStyle(::Type{NTupleOfUnitRanges{N}}) where {N} = OffsetArrays.TupleOfRanges();\n\njulia> Base.convert(::Type{Tuple{Vararg{AbstractUnitRange{Int}}}}, t::NTupleOfUnitRanges) = t.x;\n\njulia> a = zeros(3, 3);\n\njulia> inds = NTupleOfUnitRanges((3:5, 2:4));\n\njulia> oa = OffsetArray(a, inds);\n\njulia> axes(oa, 1) == 3:5\ntrue\n\njulia> axes(oa, 2) == 2:4\ntrue\n\n\n\n\n\n","category":"type"},{"location":"reference/#OffsetArrays.center","page":"Reference","title":"OffsetArrays.center","text":"center(A, [r::RoundingMode=RoundDown])::Dims\n\nReturn the center coordinate of given array A. If size(A, k) is even, a rounding procedure will be applied with mode r.\n\ncompat: OffsetArrays 1.9\nThis method requires at least OffsetArrays 1.9.\n\nExamples\n\njulia> A = reshape(collect(1:9), 3, 3)\n3×3 Matrix{Int64}:\n 1 4 7\n 2 5 8\n 3 6 9\n\njulia> c = OffsetArrays.center(A)\n(2, 2)\n\njulia> A[c...]\n5\n\njulia> Ao = OffsetArray(A, -2, -2); # axes (-1:1, -1:1)\n\njulia> c = OffsetArrays.center(Ao)\n(0, 0)\n\njulia> Ao[c...]\n5\n\nTo shift the center coordinate of the given array to (0, 0, ...), you can use centered.\n\n\n\n\n\n","category":"function"},{"location":"reference/#OffsetArrays.centered","page":"Reference","title":"OffsetArrays.centered","text":"centered(A, cp=center(A)) -> Ao\n\nShift the center coordinate/point cp of array A to (0, 0, ..., 0). Internally, this is equivalent to OffsetArray(A, .-cp).\n\ncompat: OffsetArrays 1.9\nThis method requires at least OffsetArrays 1.9.\n\nExamples\n\njulia> A = reshape(collect(1:9), 3, 3)\n3×3 Matrix{Int64}:\n 1 4 7\n 2 5 8\n 3 6 9\n\njulia> Ao = OffsetArrays.centered(A); # axes (-1:1, -1:1)\n\njulia> Ao[0, 0]\n5\n\njulia> Ao = OffsetArray(A, OffsetArrays.Origin(0)); # axes (0:2, 0:2)\n\njulia> Aoo = OffsetArrays.centered(Ao); # axes (-1:1, -1:1)\n\njulia> Aoo[0, 0]\n5\n\nUsers are allowed to pass cp to change how \"center point\" is interpreted, but the meaning of the output array should be reinterpreted as well. For instance, if cp = map(last, axes(A)) then this function no longer shifts the center point but instead the bottom-right point to (0, 0, ..., 0). A commonly usage of cp is to change the rounding behavior when the array is of even size at some dimension:\n\njulia> A = reshape(collect(1:4), 2, 2) # Ideally the center should be (1.5, 1.5) but OffsetArrays only support integer offsets\n2×2 Matrix{Int64}:\n 1 3\n 2 4\n\njulia> OffsetArrays.centered(A, OffsetArrays.center(A, RoundUp)) # set (2, 2) as the center point\n2×2 OffsetArray(::Matrix{Int64}, -1:0, -1:0) with eltype Int64 with indices -1:0×-1:0:\n 1 3\n 2 4\n\njulia> OffsetArrays.centered(A, OffsetArrays.center(A, RoundDown)) # set (1, 1) as the center point\n2×2 OffsetArray(::Matrix{Int64}, 0:1, 0:1) with eltype Int64 with indices 0:1×0:1:\n 1 3\n 2 4\n\nSee also center.\n\n\n\n\n\n","category":"function"},{"location":"#OffsetArrays.jl","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"","category":"section"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"OffsetArrays provides Julia users with arrays that have arbitrary indices, similar to those found in some other programming languages like Fortran. Below is the basic usage found in the README, followed by a couple of short examples illustrating circumstances in which OffsetArrays can be useful. For a lengthier discussion, see this blog post.","category":"page"},{"location":"#Usage","page":"OffsetArrays.jl","title":"Usage","text":"","category":"section"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"You can construct such arrays as follows:","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"OA = OffsetArray(A, axis1, axis2, ...)","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"where you want OA to have axes (axis1, axis2, ...) and be indexed by values that fall within these axis ranges.","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"using OffsetArrays\n\nA = Float64.(reshape(1:15, 3, 5))\n\nOA = OffsetArray(A, -1:1, 0:4) # OA will have axes (-1:1, 0:4)\n\nOA = OffsetArray(A, CartesianIndex(-1, 0):CartesianIndex(1, 4))\n\nOA[-1,0], OA[1,4]","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"You could also pass integers as offsets, where 0 means no offsets are applied:","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"OA = OffsetArray(A, -2, -1)","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"When you create a new OffsetArray on the top of another OffsetArray, the offsets are accumulated:","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"OOA = OffsetArray(OA, 2, 1)","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"For the special cases that you want to compensate the offset back to the ordinary 1-based array, you can use OffsetArrays.no_offset_view(A). Furthermore, you could use Base.require_one_based_indexing if you want to ensure the array does not have offsets.","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"OffsetArrays.no_offset_view(OA)\n\nBase.require_one_based_indexing(ans)\n\nBase.require_one_based_indexing(OA)","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"OffsetArrays.Origin can be convenient if you want to directly specify the origin of the output OffsetArray, it will automatically compute the corresponding offsets. For example:","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"OffsetArray(A, OffsetArrays.Origin(-1, -1))\nOffsetArray(OA, OffsetArrays.Origin(-1, -1))","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"An equivalent — but possibly more convenient — way to specify the origin of an array is","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"OffsetArrays.Origin(-1, -1)(A)","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"Sometimes, it will be convenient to shift the center coordinate of the given array to (0, 0, ...), OffsetArrays.centered is a helper for this very purpose:","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"Ao = OffsetArrays.centered(A)\nAo[0, 0] == 8.0","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"and OffsetArrays.center tells you the center coordinate of given array:","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"c = OffsetArrays.center(A)\nA[c...] == 8.0","category":"page"},{"location":"#Example:-Relativistic-Notation","page":"OffsetArrays.jl","title":"Example: Relativistic Notation","text":"","category":"section"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"Suppose we have a position vector r = [:x, :y, :z] which is naturally one-based, ie. r[1] == :x, r[2] == :y, r[3] == :z and we also want to construct a relativistic position vector which includes time as the 0th component. This can be done with OffsetArrays like","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"julia> r = [:x, :y, :z];\n\njulia> x = OffsetVector([:t, r...], 0:3)\n4-element OffsetArray(::Vector{Symbol}, 0:3) with eltype Symbol with indices 0:3:\n :t\n :x\n :y\n :z\n\njulia> x[0]\n:t\n\njulia> x[1:3]\n3-element Vector{Symbol}:\n :x\n :y\n :z","category":"page"},{"location":"#Example:-Polynomials","page":"OffsetArrays.jl","title":"Example: Polynomials","text":"","category":"section"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"Suppose one wants to represent the Laurent polynomial","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"6x + 5 - 2*x + 3*x^2 + x^3","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"The coefficients of this polynomial are a naturally -1 based list, since the nth element of the list (counting from -1) 6, 5, -2, 3, 1 is the coefficient corresponding to the nth power of x. This Laurent polynomial can be evaluated at say x = 2 as follows.","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"julia> coeffs = OffsetVector([6, 5, -2, 3, 1], -1:3)\n5-element OffsetArray(::Vector{Int64}, -1:3) with eltype Int64 with indices -1:3:\n 6\n 5\n -2\n 3\n 1\n\njulia> polynomial(x, coeffs) = sum(coeffs[n]*x^n for n in eachindex(coeffs))\npolynomial (generic function with 1 method)\n\njulia> polynomial(2.0, coeffs)\n24.0","category":"page"},{"location":"","page":"OffsetArrays.jl","title":"OffsetArrays.jl","text":"Notice our use of the eachindex function which does not assume that the given array starts at 1.","category":"page"},{"location":"internals/#For-developers","page":"For developers","title":"For developers","text":"","category":"section"},{"location":"internals/","page":"For developers","title":"For developers","text":"Writing code that supports OffsetArrays is generally fairly straightforward. The majority of cases can be handled with these tips:","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"replace many uses of size with axes\nreplace 1:length(A) with eachindex(A), or if you need an integer index with LinearIndices(A)\nreplace explicit allocations like Array{Int}(undef, size(B)) with similar(Array{Int}, axes(B))","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"More information can be found in Julia's developer documentation. The most subtle issues tend to arise around the axes, and further detail specific to OffsetArrays.jl follows below.","category":"page"},{"location":"internals/#Internals","page":"For developers","title":"Internals","text":"","category":"section"},{"location":"internals/","page":"For developers","title":"For developers","text":"How does OffsetArrays work? The fundamental principle is very simple: an OffsetArray is just a wrapper around a \"parent\" array, together with an index offset:","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> oa = OffsetArray([1 2; 3 4], 0:1, 5:6)\n2×2 OffsetArray(::Matrix{Int64}, 0:1, 5:6) with eltype Int64 with indices 0:1×5:6:\n 1 2\n 3 4\n\njulia> parent(oa)\n2×2 Matrix{Int64}:\n 1 2\n 3 4\n\njulia> oa.offsets\n(-1, 4)","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"So parent(oa) is the original array we constructed it with, and oa.offsets is a tuple, each entry encoding the index-shift to be applied along the corresponding axis. When you index oa[i,j], it \"translates\" the i,j indexes back to the parent array's indexes and then returns the value in the parent.","category":"page"},{"location":"internals/#The-axes-of-OffsetArrays","page":"For developers","title":"The axes of OffsetArrays","text":"","category":"section"},{"location":"internals/","page":"For developers","title":"For developers","text":"The internal of offset computing is achieved by IdOffsetRange type:","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> ax = axes(oa, 2)\nOffsetArrays.IdOffsetRange(values=5:6, indices=5:6)","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"This has a similar design to Base.IdentityUnitRange that ax[x] == x always holds.","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> ax[5]\n5\njulia> ax[1]\nERROR: BoundsError: attempt to access 2-element OffsetArrays.IdOffsetRange{Int64, Base.OneTo{Int64}} with indices 5:6 at index [1]\n[...]","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"This property makes sure that they tend to be their own axes:","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> axes(ax)\n(OffsetArrays.IdOffsetRange(values=5:6, indices=5:6),)\n\njulia> axes(ax[ax])\n(OffsetArrays.IdOffsetRange(values=5:6, indices=5:6),)","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"This example of indexing is idempotent. This is a useful characteristic for ensuring the \"fundamental axiom\" of generalized indexing, that a[ax][i] == a[ax[i]]:","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> oa2 = OffsetArray([5, 10, 15, 20], 0:3)\n4-element OffsetArray(::Vector{Int64}, 0:3) with eltype Int64 with indices 0:3:\n 5\n 10\n 15\n 20\n\njulia> ax2 = axes(oa2, 1)\nOffsetArrays.IdOffsetRange(values=0:3, indices=0:3)\n\njulia> oa2[2]\n15\n\njulia> oa2[ax2][2]\n15\n\njulia> oa2[ax2[2]]\n15","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"IdOffsetRanges apply the offset both to the values and the indices of the range, and otherwise preserve the parent range.","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"warning: Warning\nThere are circumstances where constructing a specific type of IdOffsetRange cannot be supported without changing the axes of the range (see OffsetArrays.IdOffsetRange.) In the future, this package will distinguish between construction and conversion:construction (aka, coercion) will always succeed, even if it has to change the axes of the result (Examples: RangeType(rng), typeof(rng1)(rng2))\nconversion will succeed only if it can preserve both the values and the axes (Examples: convert(RangeType, rng), oftype(rng1, rng2))While these behave equivalently now (conversion currently performs coercion), developers are encouraged to \"future-proof\" their code by choosing the behavior appropriate for each usage.","category":"page"},{"location":"internals/#Wrapping-other-offset-array-types","page":"For developers","title":"Wrapping other offset array types","text":"","category":"section"},{"location":"internals/","page":"For developers","title":"For developers","text":"An OffsetArray may wrap any subtype of AbstractArray, including ones that do not use 1-based indexing. Such arrays however need to satisfy the fundamental axiom of idempotent indexing for things to work correctly. In other words, an axis of an offset array needs to have the same values as its own axis. This property is built into OffsetArrays if the parent uses 1-based indexing, but it's up to the user to ensure the correctness in case a type is to be wrapped that uses offset indices.","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"We demonstrate this through an example by creating a custom 0-based range type that we wrap in an OffsetArray:","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> struct ZeroBasedRange{T,A<:AbstractRange{T}} <: AbstractRange{T}\n a :: A\n function ZeroBasedRange(a::AbstractRange{T}) where {T}\n @assert !Base.has_offset_axes(a)\n new{T, typeof(a)}(a)\n end\n end;\n\njulia> Base.parent(A::ZeroBasedRange) = A.a;\n\njulia> Base.first(A::ZeroBasedRange) = first(A.a);\n\njulia> Base.length(A::ZeroBasedRange) = length(A.a);\n\njulia> Base.last(A::ZeroBasedRange) = last(A.a);\n\njulia> Base.size(A::ZeroBasedRange) = size(A.a);\n\njulia> Base.axes(A::ZeroBasedRange) = map(x -> 0:x-1, size(A.a));\n\njulia> Base.getindex(A::ZeroBasedRange, i::Int) = A.a[i + 1];\n\njulia> Base.step(A::ZeroBasedRange) = step(A.a);\n\njulia> function Base.show(io::IO, A::ZeroBasedRange)\n show(io, A.a)\n print(io, \" with indices $(axes(A,1))\")\n end;","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"This definition of a ZeroBasedRange appears to have the correct indices, for example:","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> z = ZeroBasedRange(1:4)\n1:4 with indices 0:3\n\njulia> z[0]\n1\n\njulia> z[3]\n4","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"However this does not use idempotent indexing, as the axis of a ZeroBasedRange is not its own axis.","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> axes(z, 1)\n0:3\n\njulia> axes(axes(z, 1), 1)\nBase.OneTo(4)","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"This will lead to complications in certain functions –- for example LinearIndices –- that tends to implicitly assume idempotent indexing. In this case the LinearIndices of z will not match its axis.","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> LinearIndices(z)\n4-element LinearIndices{1, Tuple{UnitRange{Int64}}}:\n 1\n 2\n 3\n 4","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"Wrapping such a type in an OffsetArray might lead to unexpected bugs.","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> zo = OffsetArray(z, 1);\n\njulia> axes(zo, 1)\nOffsetArrays.IdOffsetRange(values=1:4, indices=2:5)\n\njulia> Array(zo)\nERROR: BoundsError: attempt to access 4-element UnitRange{Int64} at index [5]\n[...]","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"The Array conversion errors despite zo having 1-based indices. The function axes(zo, 1) hints at the underlying problem –- the values and the indices of the axis are different. We may check that the axis of zo is not its own axis:","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> axes(zo, 1)\nOffsetArrays.IdOffsetRange(values=1:4, indices=2:5)\n\njulia> axes(axes(zo, 1), 1)\nOffsetArrays.IdOffsetRange(values=2:5, indices=2:5)","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"In this case the bug may be fixed by defining the axes of a ZeroBasedRange to be idempotent, for example using the OffsetArrays.IdentityUnitRange wrapper:","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> Base.axes(A::ZeroBasedRange) = map(x -> OffsetArrays.IdentityUnitRange(0:x-1), size(A.a))\n\njulia> axes(zo, 1)\nOffsetArrays.IdOffsetRange(values=1:4, indices=1:4)","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"With this new definition, the values and indices of the axis are identical, which makes indexing idempotent. The conversion to an Array works as expected now:","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> Array(zo)\n4-element Vector{Int64}:\n 1\n 2\n 3\n 4","category":"page"},{"location":"internals/#Caveats","page":"For developers","title":"Caveats","text":"","category":"section"},{"location":"internals/","page":"For developers","title":"For developers","text":"Because IdOffsetRange behaves quite differently to the normal UnitRange type, there are some cases that you should be aware of, especially when you are working with multi-dimensional arrays.","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"One such cases is getindex:","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> Ao = zeros(-3:3, -3:3); Ao[:] .= 1:49;\n\njulia> Ao[-3:0, :] |> axes # the first dimension does not preserve offsets\n(OffsetArrays.IdOffsetRange(values=1:4, indices=1:4), OffsetArrays.IdOffsetRange(values=-3:3, indices=-3:3))\n\njulia> Ao[-3:0, -3:3] |> axes # neither dimensions preserve offsets\n(Base.OneTo(4), Base.OneTo(7))\n\njulia> Ao[axes(Ao)...] |> axes # offsets are preserved\n(OffsetArrays.IdOffsetRange(values=-3:3, indices=-3:3), OffsetArrays.IdOffsetRange(values=-3:3, indices=-3:3))\n\njulia> Ao[:] |> axes # This is linear indexing\n(Base.OneTo(49),)","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"Note that if you pass a UnitRange, the offsets in corresponding dimension will not be preserved. This might look weird at first, but since it follows the a[ax][i] == a[ax[i]] rule, it is not a bug.","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> I = -3:0; # UnitRange always starts at index 1\n\njulia> Ao[I, 0][1] == Ao[I[1], 0]\ntrue\n\njulia> ax = axes(Ao, 1) # ax starts at index -3\nOffsetArrays.IdOffsetRange(values=-3:3, indices=-3:3)\n\njulia> Ao[ax, 0][1] == Ao[ax[1], 0]\ntrue","category":"page"},{"location":"internals/#Using-custom-axis-types","page":"For developers","title":"Using custom axis types","text":"","category":"section"},{"location":"internals/","page":"For developers","title":"For developers","text":"While a wide variety of AbstractUnitRanges provided by Base may be used as indices to construct an OffsetArray, at times it might be convenient to define custom types. The OffsetArray constructor accepts any type that may be converted to an AbstractUnitRange. This proceeds through a two-step process. Let's assume that the constructor called is OffsetArray(A, indstup), where indstup is a Tuple of indices.","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"At the first step, the constructor calls to_indices(A, axes(A), indstup) to lower indstup to a Tuple of AbstractUnitRanges. This step converts –- among other things –- Colons to axis ranges. Custom types may extend Base.to_indices(A, axes(A), indstup) with the desired conversion of indstup to Tuple{Vararg{AbstractUnitRange{Int}}} if this is feasible.\nAt the second step, the result obtained from the previous step treated again to convert it to a Tuple of AbstractUnitRanges to handle cases where the first step doesn't achieve this. An additional customization option may be specified at this stage: a type may be converted either to a single AbstractUnitRange{Int}, or to a Tuple of them. A type might specify which of these two behaviours is desired by extending OffsetArrays.AxisConversionStyle. An example of a type that is acted upon at this stage is CartesianIndices, which is converted to a Tuple of AbstractUnitRanges.","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"For example, here are a couple of custom type that facilitate zero-based indexing:","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> struct ZeroBasedIndexing end\n\njulia> Base.to_indices(A, inds, ::Tuple{ZeroBasedIndexing}) = map(x -> 0:length(x)-1, inds)\n\njulia> a = zeros(3, 3);\n\njulia> oa = OffsetArray(a, ZeroBasedIndexing());\n\njulia> axes(oa)\n(OffsetArrays.IdOffsetRange(values=0:2, indices=0:2), OffsetArrays.IdOffsetRange(values=0:2, indices=0:2))","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"In this example we had to define the action of to_indices as the type ZeroBasedIndexing did not have a familiar hierarchy. Things are even simpler if we subtype AbstractUnitRange, in which case we need to define first and length for the custom range to be able to use it as an axis:","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"julia> struct ZeroTo <: AbstractUnitRange{Int}\n n :: Int\n ZeroTo(n) = new(n < 0 ? -1 : n)\n end\n\njulia> Base.first(::ZeroTo) = 0\n\njulia> Base.length(r::ZeroTo) = r.n + 1\n\njulia> oa = OffsetArray(zeros(2,2), ZeroTo(1), ZeroTo(1));\n\njulia> axes(oa)\n(OffsetArrays.IdOffsetRange(values=0:1, indices=0:1), OffsetArrays.IdOffsetRange(values=0:1, indices=0:1))","category":"page"},{"location":"internals/","page":"For developers","title":"For developers","text":"Note that zero-based indexing may also be achieved using the pre-defined type OffsetArrays.Origin.","category":"page"}] +} diff --git a/v1.14.0/siteinfo.js b/v1.14.0/siteinfo.js new file mode 100644 index 00000000..32f65c4e --- /dev/null +++ b/v1.14.0/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v1.14.0"; diff --git a/versions.js b/versions.js index b43ca556..e668e7d5 100644 --- a/versions.js +++ b/versions.js @@ -1,5 +1,6 @@ var DOC_VERSIONS = [ "stable", + "v1.14", "v1.13", "v1.12", "v1.11", @@ -16,5 +17,5 @@ var DOC_VERSIONS = [ "v1.0", "dev", ]; -var DOCUMENTER_NEWEST = "v1.13.0"; +var DOCUMENTER_NEWEST = "v1.14.0"; var DOCUMENTER_STABLE = "stable";