diff --git a/.github/.DS_Store b/.github/.DS_Store
new file mode 100644
index 0000000..abe0673
Binary files /dev/null and b/.github/.DS_Store differ
diff --git a/docs/.DS_Store b/docs/.DS_Store
new file mode 100644
index 0000000..74e6c6d
Binary files /dev/null and b/docs/.DS_Store differ
diff --git a/docs/build/.documenter-siteinfo.json b/docs/build/.documenter-siteinfo.json
new file mode 100644
index 0000000..84645e1
--- /dev/null
+++ b/docs/build/.documenter-siteinfo.json
@@ -0,0 +1 @@
+{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-04-16T16:09:24","documenter_version":"1.4.0"}}
\ No newline at end of file
diff --git a/docs/build/assets/documenter.js b/docs/build/assets/documenter.js
new file mode 100644
index 0000000..c6562b5
--- /dev/null
+++ b/docs/build/assets/documenter.js
@@ -0,0 +1,1050 @@
+// Generated by Documenter.jl
+requirejs.config({
+  paths: {
+    'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
+    'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
+    'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min',
+    'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
+    'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
+    'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+    'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min',
+    'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min',
+    'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min',
+  },
+  shim: {
+  "highlight-julia": {
+    "deps": [
+      "highlight"
+    ]
+  },
+  "katex-auto-render": {
+    "deps": [
+      "katex"
+    ]
+  },
+  "headroom-jquery": {
+    "deps": [
+      "jquery",
+      "headroom"
+    ]
+  },
+  "highlight-julia-repl": {
+    "deps": [
+      "highlight"
+    ]
+  }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+  renderMathInElement(
+    document.body,
+    {
+  "delimiters": [
+    {
+      "left": "$",
+      "right": "$",
+      "display": false
+    },
+    {
+      "left": "$$",
+      "right": "$$",
+      "display": true
+    },
+    {
+      "left": "\\[",
+      "right": "\\]",
+      "display": true
+    }
+  ]
+}
+
+  );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) {
+$(document).ready(function() {
+    hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let timer = 0;
+var isExpanded = true;
+
+$(document).on("click", ".docstring header", function () {
+  let articleToggleTitle = "Expand docstring";
+
+  debounce(() => {
+    if ($(this).siblings("section").is(":visible")) {
+      $(this)
+        .find(".docstring-article-toggle-button")
+        .removeClass("fa-chevron-down")
+        .addClass("fa-chevron-right");
+    } else {
+      $(this)
+        .find(".docstring-article-toggle-button")
+        .removeClass("fa-chevron-right")
+        .addClass("fa-chevron-down");
+
+      articleToggleTitle = "Collapse docstring";
+    }
+
+    $(this)
+      .find(".docstring-article-toggle-button")
+      .prop("title", articleToggleTitle);
+    $(this).siblings("section").slideToggle();
+  });
+});
+
+$(document).on("click", ".docs-article-toggle-button", function (event) {
+  let articleToggleTitle = "Expand docstring";
+  let navArticleToggleTitle = "Expand all docstrings";
+  let animationSpeed = event.noToggleAnimation ? 0 : 400;
+
+  debounce(() => {
+    if (isExpanded) {
+      $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down");
+      $(".docstring-article-toggle-button")
+        .removeClass("fa-chevron-down")
+        .addClass("fa-chevron-right");
+
+      isExpanded = false;
+
+      $(".docstring section").slideUp(animationSpeed);
+    } else {
+      $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
+      $(".docstring-article-toggle-button")
+        .removeClass("fa-chevron-right")
+        .addClass("fa-chevron-down");
+
+      isExpanded = true;
+      articleToggleTitle = "Collapse docstring";
+      navArticleToggleTitle = "Collapse all docstrings";
+
+      $(".docstring section").slideDown(animationSpeed);
+    }
+
+    $(this).prop("title", navArticleToggleTitle);
+    $(".docstring-article-toggle-button").prop("title", articleToggleTitle);
+  });
+});
+
+function debounce(callback, timeout = 300) {
+  if (Date.now() - timer > timeout) {
+    callback();
+  }
+
+  clearTimeout(timer);
+
+  timer = Date.now();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+  for (const el of document.getElementsByTagName("pre")) {
+    const button = document.createElement("button");
+    button.classList.add("copy-button", "fa-solid", "fa-copy");
+    button.setAttribute("aria-label", "Copy this code block");
+    button.setAttribute("title", "Copy");
+
+    el.appendChild(button);
+
+    const success = function () {
+      button.classList.add("success", "fa-check");
+      button.classList.remove("fa-copy");
+    };
+
+    const failure = function () {
+      button.classList.add("error", "fa-xmark");
+      button.classList.remove("fa-copy");
+    };
+
+    button.addEventListener("click", function () {
+      copyToClipboard(el.innerText).then(success, failure);
+
+      setTimeout(function () {
+        button.classList.add("fa-copy");
+        button.classList.remove("success", "fa-check", "fa-xmark");
+      }, 5000);
+    });
+  }
+}
+
+function copyToClipboard(text) {
+  // clipboard API is only available in secure contexts
+  if (window.navigator && window.navigator.clipboard) {
+    return window.navigator.clipboard.writeText(text);
+  } else {
+    return new Promise(function (resolve, reject) {
+      try {
+        const el = document.createElement("textarea");
+        el.textContent = text;
+        el.style.position = "fixed";
+        el.style.opacity = 0;
+        document.body.appendChild(el);
+        el.select();
+        document.execCommand("copy");
+
+        resolve();
+      } catch (err) {
+        reject(err);
+      } finally {
+        document.body.removeChild(el);
+      }
+    });
+  }
+}
+
+if (document.readyState === "loading") {
+  document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+  addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function () {
+  $("#documenter .docs-navbar").headroom({
+    tolerance: { up: 10, down: 10 },
+  });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+  let meta = $("div[data-docstringscollapsed]").data();
+
+  if (meta?.docstringscollapsed) {
+    $("#documenter-article-toggle-button").trigger({
+      type: "click",
+      noToggleAnimation: true,
+    });
+  }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+/*
+To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+PSEUDOCODE:
+
+Searching happens automatically as the user types or adjusts the selected filters.
+To preserve responsiveness, as much as possible of the slow parts of the search are done
+in a web worker. Searching and result generation are done in the worker, and filtering and
+DOM updates are done in the main thread. The filters are in the main thread as they should
+be very quick to apply. This lets filters be changed without re-searching with minisearch
+(which is possible even if filtering is on the worker thread) and also lets filters be
+changed _while_ the worker is searching and without message passing (neither of which are
+possible if filtering is on the worker thread)
+
+SEARCH WORKER:
+
+Import minisearch
+
+Build index
+
+On message from main thread
+  run search
+  find the first 200 unique results from each category, and compute their divs for display
+    note that this is necessary and sufficient information for the main thread to find the
+    first 200 unique results from any given filter set
+  post results to main thread
+
+MAIN:
+
+Launch worker
+
+Declare nonconstant globals (worker_is_running,  last_search_text, unfiltered_results)
+
+On text update
+  if worker is not running, launch_search()
+
+launch_search
+  set worker_is_running to true, set last_search_text to the search text
+  post the search query to worker
+
+on message from worker
+  if last_search_text is not the same as the text in the search field,
+    the latest search result is not reflective of the latest search query, so update again
+    launch_search()
+  otherwise
+    set worker_is_running to false
+
+  regardless, display the new search results to the user
+  save the unfiltered_results as a global
+  update_search()
+
+on filter click
+  adjust the filter selection
+  update_search()
+
+update_search
+  apply search filters by looping through the unfiltered_results and finding the first 200
+    unique results that match the filters
+
+  Update the DOM
+*/
+
+/////// SEARCH WORKER ///////
+
+function worker_function(documenterSearchIndex, documenterBaseURL, filters) {
+  importScripts(
+    "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js"
+  );
+
+  let data = documenterSearchIndex.map((x, key) => {
+    x["id"] = key; // minisearch requires a unique for each object
+    return x;
+  });
+
+  // list below is the lunr 2.1.3 list minus the intersect with names(Base)
+  // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+  // ideally we'd just filter the original list but it's not available as a variable
+  const stopWords = new Set([
+    "a",
+    "able",
+    "about",
+    "across",
+    "after",
+    "almost",
+    "also",
+    "am",
+    "among",
+    "an",
+    "and",
+    "are",
+    "as",
+    "at",
+    "be",
+    "because",
+    "been",
+    "but",
+    "by",
+    "can",
+    "cannot",
+    "could",
+    "dear",
+    "did",
+    "does",
+    "either",
+    "ever",
+    "every",
+    "from",
+    "got",
+    "had",
+    "has",
+    "have",
+    "he",
+    "her",
+    "hers",
+    "him",
+    "his",
+    "how",
+    "however",
+    "i",
+    "if",
+    "into",
+    "it",
+    "its",
+    "just",
+    "least",
+    "like",
+    "likely",
+    "may",
+    "me",
+    "might",
+    "most",
+    "must",
+    "my",
+    "neither",
+    "no",
+    "nor",
+    "not",
+    "of",
+    "off",
+    "often",
+    "on",
+    "or",
+    "other",
+    "our",
+    "own",
+    "rather",
+    "said",
+    "say",
+    "says",
+    "she",
+    "should",
+    "since",
+    "so",
+    "some",
+    "than",
+    "that",
+    "the",
+    "their",
+    "them",
+    "then",
+    "there",
+    "these",
+    "they",
+    "this",
+    "tis",
+    "to",
+    "too",
+    "twas",
+    "us",
+    "wants",
+    "was",
+    "we",
+    "were",
+    "what",
+    "when",
+    "who",
+    "whom",
+    "why",
+    "will",
+    "would",
+    "yet",
+    "you",
+    "your",
+  ]);
+
+  let index = new MiniSearch({
+    fields: ["title", "text"], // fields to index for full-text search
+    storeFields: ["location", "title", "text", "category", "page"], // fields to return with results
+    processTerm: (term) => {
+      let word = stopWords.has(term) ? null : term;
+      if (word) {
+        // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+        word = word
+          .replace(/^[^a-zA-Z0-9@!]+/, "")
+          .replace(/[^a-zA-Z0-9@!]+$/, "");
+
+        word = word.toLowerCase();
+      }
+
+      return word ?? null;
+    },
+    // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not
+    // find anything if searching for "add!", only for the entire qualification
+    tokenize: (string) => string.split(/[\s\-\.]+/),
+    // options which will be applied during the search
+    searchOptions: {
+      prefix: true,
+      boost: { title: 100 },
+      fuzzy: 2,
+    },
+  });
+
+  index.addAll(data);
+
+  /**
+   *  Used to map characters to HTML entities.
+   * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+   */
+  const htmlEscapes = {
+    "&": "&",
+    "<": "&lt;",
+    ">": "&gt;",
+    '"': "&quot;",
+    "'": "&#39;",
+  };
+
+  /**
+   * Used to match HTML entities and HTML characters.
+   * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+   */
+  const reUnescapedHtml = /[&<>"']/g;
+  const reHasUnescapedHtml = RegExp(reUnescapedHtml.source);
+
+  /**
+   * Escape function from lodash
+   * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+   */
+  function escape(string) {
+    return string && reHasUnescapedHtml.test(string)
+      ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr])
+      : string || "";
+  }
+
+  /**
+   * Make the result component given a minisearch result data object and the value
+   * of the search input as queryString. To view the result object structure, refer:
+   * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+   *
+   * @param {object} result
+   * @param {string} querystring
+   * @returns string
+   */
+  function make_search_result(result, querystring) {
+    let search_divider = `<div class="search-divider w-100"></div>`;
+    let display_link =
+      result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+      (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+    if (result.page !== "") {
+      display_link += ` (${result.page})`;
+    }
+
+    let textindex = new RegExp(`${querystring}`, "i").exec(result.text);
+    let text =
+      textindex !== null
+        ? result.text.slice(
+            Math.max(textindex.index - 100, 0),
+            Math.min(
+              textindex.index + querystring.length + 100,
+              result.text.length
+            )
+          )
+        : ""; // cut-off text before and after from the match
+
+    text = text.length ? escape(text) : "";
+
+    let display_result = text.length
+      ? "..." +
+        text.replace(
+          new RegExp(`${escape(querystring)}`, "i"), // For first occurrence
+          '<span class="search-result-highlight py-1">$&</span>'
+        ) +
+        "..."
+      : ""; // highlights the match
+
+    let in_code = false;
+    if (!["page", "section"].includes(result.category.toLowerCase())) {
+      in_code = true;
+    }
+
+    // We encode the full url to escape some special characters which can lead to broken links
+    let result_div = `
+        <a href="${encodeURI(
+          documenterBaseURL + "/" + result.location
+        )}" class="search-result-link w-100 is-flex is-flex-direction-column gap-2 px-4 py-2">
+          <div class="w-100 is-flex is-flex-wrap-wrap is-justify-content-space-between is-align-items-flex-start">
+            <div class="search-result-title has-text-weight-bold ${
+              in_code ? "search-result-code-title" : ""
+            }">${escape(result.title)}</div>
+            <div class="property-search-result-badge">${result.category}</div>
+          </div>
+          <p>
+            ${display_result}
+          </p>
+          <div
+            class="has-text-left"
+            style="font-size: smaller;"
+            title="${result.location}"
+          >
+            <i class="fas fa-link"></i> ${display_link}
+          </div>
+        </a>
+        ${search_divider}
+      `;
+
+    return result_div;
+  }
+
+  self.onmessage = function (e) {
+    let query = e.data;
+    let results = index.search(query, {
+      filter: (result) => {
+        // Only return relevant results
+        return result.score >= 1;
+      },
+    });
+
+    // Pre-filter to deduplicate and limit to 200 per category to the extent
+    // possible without knowing what the filters are.
+    let filtered_results = [];
+    let counts = {};
+    for (let filter of filters) {
+      counts[filter] = 0;
+    }
+    let present = {};
+
+    for (let result of results) {
+      cat = result.category;
+      cnt = counts[cat];
+      if (cnt < 200) {
+        id = cat + "---" + result.location;
+        if (present[id]) {
+          continue;
+        }
+        present[id] = true;
+        filtered_results.push({
+          location: result.location,
+          category: cat,
+          div: make_search_result(result, query),
+        });
+      }
+    }
+
+    postMessage(filtered_results);
+  };
+}
+
+// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript!
+const filters = [
+  ...new Set(documenterSearchIndex["docs"].map((x) => x.category)),
+];
+const worker_str =
+  "(" +
+  worker_function.toString() +
+  ")(" +
+  JSON.stringify(documenterSearchIndex["docs"]) +
+  "," +
+  JSON.stringify(documenterBaseURL) +
+  "," +
+  JSON.stringify(filters) +
+  ")";
+const worker_blob = new Blob([worker_str], { type: "text/javascript" });
+const worker = new Worker(URL.createObjectURL(worker_blob));
+
+/////// SEARCH MAIN ///////
+
+// Whether the worker is currently handling a search. This is a boolean
+// as the worker only ever handles 1 or 0 searches at a time.
+var worker_is_running = false;
+
+// The last search text that was sent to the worker. This is used to determine
+// if the worker should be launched again when it reports back results.
+var last_search_text = "";
+
+// The results of the last search. This, in combination with the state of the filters
+// in the DOM, is used compute the results to display on calls to update_search.
+var unfiltered_results = [];
+
+// Which filter is currently selected
+var selected_filter = "";
+
+$(document).on("input", ".documenter-search-input", function (event) {
+  if (!worker_is_running) {
+    launch_search();
+  }
+});
+
+function launch_search() {
+  worker_is_running = true;
+  last_search_text = $(".documenter-search-input").val();
+  worker.postMessage(last_search_text);
+}
+
+worker.onmessage = function (e) {
+  if (last_search_text !== $(".documenter-search-input").val()) {
+    launch_search();
+  } else {
+    worker_is_running = false;
+  }
+
+  unfiltered_results = e.data;
+  update_search();
+};
+
+$(document).on("click", ".search-filter", function () {
+  if ($(this).hasClass("search-filter-selected")) {
+    selected_filter = "";
+  } else {
+    selected_filter = $(this).text().toLowerCase();
+  }
+
+  // This updates search results and toggles classes for UI:
+  update_search();
+});
+
+/**
+ * Make/Update the search component
+ */
+function update_search() {
+  let querystring = $(".documenter-search-input").val();
+
+  if (querystring.trim()) {
+    if (selected_filter == "") {
+      results = unfiltered_results;
+    } else {
+      results = unfiltered_results.filter((result) => {
+        return selected_filter == result.category.toLowerCase();
+      });
+    }
+
+    let search_result_container = ``;
+    let modal_filters = make_modal_body_filters();
+    let search_divider = `<div class="search-divider w-100"></div>`;
+
+    if (results.length) {
+      let links = [];
+      let count = 0;
+      let search_results = "";
+
+      for (var i = 0, n = results.length; i < n && count < 200; ++i) {
+        let result = results[i];
+        if (result.location && !links.includes(result.location)) {
+          search_results += result.div;
+          count++;
+          links.push(result.location);
+        }
+      }
+
+      if (count == 1) {
+        count_str = "1 result";
+      } else if (count == 200) {
+        count_str = "200+ results";
+      } else {
+        count_str = count + " results";
+      }
+      let result_count = `<div class="is-size-6">${count_str}</div>`;
+
+      search_result_container = `
+            <div class="is-flex is-flex-direction-column gap-2 is-align-items-flex-start">
+                ${modal_filters}
+                ${search_divider}
+                ${result_count}
+                <div class="is-clipped w-100 is-flex is-flex-direction-column gap-2 is-align-items-flex-start has-text-justified mt-1">
+                  ${search_results}
+                </div>
+            </div>
+        `;
+    } else {
+      search_result_container = `
+           <div class="is-flex is-flex-direction-column gap-2 is-align-items-flex-start">
+               ${modal_filters}
+               ${search_divider}
+               <div class="is-size-6">0 result(s)</div>
+            </div>
+            <div class="has-text-centered my-5 py-5">No result found!</div>
+       `;
+    }
+
+    if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+      $(".search-modal-card-body").removeClass("is-justify-content-center");
+    }
+
+    $(".search-modal-card-body").html(search_result_container);
+  } else {
+    if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+      $(".search-modal-card-body").addClass("is-justify-content-center");
+    }
+
+    $(".search-modal-card-body").html(`
+      <div class="has-text-centered my-5 py-5">Type something to get started!</div>
+    `);
+  }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @returns string
+ */
+function make_modal_body_filters() {
+  let str = filters
+    .map((val) => {
+      if (selected_filter == val.toLowerCase()) {
+        return `<a href="javascript:;" class="search-filter search-filter-selected"><span>${val}</span></a>`;
+      } else {
+        return `<a href="javascript:;" class="search-filter"><span>${val}</span></a>`;
+      }
+    })
+    .join("");
+
+  return `
+        <div class="is-flex gap-2 is-flex-wrap-wrap is-justify-content-flex-start is-align-items-center search-filters">
+            <span class="is-size-6">Filters:</span>
+            ${str}
+        </div>`;
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// 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
+  $(document).keyup(function (e) {
+    if (e.keyCode == 27) settings.removeClass("is-active");
+  });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+  let search_modal_header = `
+    <header class="modal-card-head gap-2 is-align-items-center is-justify-content-space-between w-100 px-3">
+      <div class="field mb-0 w-100">
+        <p class="control has-icons-right">
+          <input class="input documenter-search-input" type="text" placeholder="Search" />
+          <span class="icon is-small is-right has-text-primary-dark">
+            <i class="fas fa-magnifying-glass"></i>
+          </span>
+        </p>
+      </div>
+      <div class="icon is-size-4 is-clickable close-search-modal">
+        <i class="fas fa-times"></i>
+      </div>
+    </header>
+  `;
+
+  let initial_search_body = `
+    <div class="has-text-centered my-5 py-5">Type something to get started!</div>
+  `;
+
+  let search_modal_footer = `
+    <footer class="modal-card-foot">
+      <span>
+        <kbd class="search-modal-key-hints">Ctrl</kbd> +
+        <kbd class="search-modal-key-hints">/</kbd> to search
+      </span>
+      <span class="ml-3"> <kbd class="search-modal-key-hints">esc</kbd> to close </span>
+    </footer>
+  `;
+
+  $(document.body).append(
+    `
+      <div class="modal" id="search-modal">
+        <div class="modal-background"></div>
+        <div class="modal-card search-min-width-50 search-min-height-100 is-justify-content-center">
+          ${search_modal_header}
+          <section class="modal-card-body is-flex is-flex-direction-column is-justify-content-center gap-4 search-modal-card-body">
+            ${initial_search_body}
+          </section>
+          ${search_modal_footer}
+        </div>
+      </div>
+    `
+  );
+
+  document.querySelector(".docs-search-query").addEventListener("click", () => {
+    openModal();
+  });
+
+  document
+    .querySelector(".close-search-modal")
+    .addEventListener("click", () => {
+      closeModal();
+    });
+
+  $(document).on("click", ".search-result-link", function () {
+    closeModal();
+  });
+
+  document.addEventListener("keydown", (event) => {
+    if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+      openModal();
+    } else if (event.key === "Escape") {
+      closeModal();
+    }
+
+    return false;
+  });
+
+  // Functions to open and close a modal
+  function openModal() {
+    let searchModal = document.querySelector("#search-modal");
+
+    searchModal.classList.add("is-active");
+    document.querySelector(".documenter-search-input").focus();
+  }
+
+  function closeModal() {
+    let searchModal = document.querySelector("#search-modal");
+    let initial_search_body = `
+      <div class="has-text-centered my-5 py-5">Type something to get started!</div>
+    `;
+
+    searchModal.classList.remove("is-active");
+    document.querySelector(".documenter-search-input").blur();
+
+    if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+      $(".search-modal-card-body").addClass("is-justify-content-center");
+    }
+
+    $(".documenter-search-input").val("");
+    $(".search-modal-card-body").html(initial_search_body);
+  }
+
+  document
+    .querySelector("#search-modal .modal-background")
+    .addEventListener("click", () => {
+      closeModal();
+    });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function () {
+  var sidebar = $("#documenter > .docs-sidebar");
+  var sidebar_button = $("#documenter-sidebar-button");
+  sidebar_button.click(function (ev) {
+    ev.preventDefault();
+    sidebar.toggleClass("visible");
+    if (sidebar.hasClass("visible")) {
+      // Makes sure that the current menu item is visible in the sidebar.
+      $("#documenter .docs-menu a.is-active").focus();
+    }
+  });
+  $("#documenter > .docs-main").bind("click", function (ev) {
+    if ($(ev.target).is(sidebar_button)) {
+      return;
+    }
+    if (sidebar.hasClass("visible")) {
+      sidebar.removeClass("visible");
+    }
+  });
+});
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function () {
+  e = $("#documenter .docs-autofit");
+  function resize() {
+    var L = parseInt(e.css("max-width"), 10);
+    var L0 = e.width();
+    if (L0 > L) {
+      var h0 = parseInt(e.css("font-size"), 10);
+      e.css("font-size", (L * h0) / L0);
+      // TODO: make sure it survives resizes?
+    }
+  }
+  // call once and then register events
+  resize();
+  $(window).resize(resize);
+  $(window).on("orientationchange", resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function () {
+  var sidebar = $("#documenter .docs-menu").get(0);
+  var active = $("#documenter .docs-menu .is-active").get(0);
+  if (typeof active !== "undefined") {
+    sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+  }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+  // onchange callback
+  $("#documenter-themepicker").change(function themepick_callback(ev) {
+    var themename = $("#documenter-themepicker option:selected").attr("value");
+    if (themename === "auto") {
+      // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+      window.localStorage.removeItem("documenter-theme");
+    } else {
+      // set_theme(themename);
+      window.localStorage.setItem("documenter-theme", themename);
+    }
+    // We re-use the global function from themeswap.js to actually do the swapping.
+    set_theme_from_local_storage();
+  });
+
+  // Make sure that the themepicker displays the correct theme when the theme is retrieved
+  // from localStorage
+  if (typeof window.localStorage !== "undefined") {
+    var theme = window.localStorage.getItem("documenter-theme");
+    if (theme !== null) {
+      $("#documenter-themepicker option").each(function (i, e) {
+        e.selected = e.value === theme;
+      });
+    }
+  }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function () {
+  // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+  // siteinfo.js file, we just return immediately and not display the version selector.
+  if (
+    typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+    DOCUMENTER_VERSION_SELECTOR_DISABLED
+  ) {
+    return;
+  }
+
+  var version_selector = $("#documenter .docs-version-selector");
+  var version_selector_select = $("#documenter .docs-version-selector select");
+
+  version_selector_select.change(function (x) {
+    target_href = version_selector_select
+      .children("option:selected")
+      .get(0).value;
+    window.location.href = target_href;
+  });
+
+  // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+  if (
+    typeof DOCUMENTER_CURRENT_VERSION !== "undefined" &&
+    $("#version-selector > option").length == 0
+  ) {
+    var option = $(
+      "<option value='#' selected='selected'>" +
+        DOCUMENTER_CURRENT_VERSION +
+        "</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 = $(
+          "<option value='" + version_url + "'>" + each + "</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/docs/build/assets/themes/documenter-dark.css b/docs/build/assets/themes/documenter-dark.css
new file mode 100644
index 0000000..53889fb
--- /dev/null
+++ b/docs/build/assets/themes/documenter-dark.css
@@ -0,0 +1,7 @@
+html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,html.theme--documenter-dark .is-focused.pagination-previous,html.theme--documenter-dark .is-focused.pagination-next,html.theme--documenter-dark .is-focused.pagination-link,html.theme--documenter-dark .is-focused.pagination-ellipsis,html.theme--documenter-dark .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--documenter-dark .is-focused.button,html.theme--documenter-dark .pagination-previous:active,html.theme--documenter-dark .pagination-next:active,html.theme--documenter-dark .pagination-link:active,html.theme--documenter-dark .pagination-ellipsis:active,html.theme--documenter-dark .file-cta:active,html.theme--documenter-dark .file-name:active,html.theme--documenter-dark .select select:active,html.theme--documenter-dark .textarea:active,html.theme--documenter-dark .input:active,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:active,html.theme--documenter-dark .button:active,html.theme--documenter-dark .is-active.pagination-previous,html.theme--documenter-dark .is-active.pagination-next,html.theme--documenter-dark .is-active.pagination-link,html.theme--documenter-dark .is-active.pagination-ellipsis,html.theme--documenter-dark .is-active.file-cta,html.theme--documenter-dark .is-active.file-name,html.theme--documenter-dark .select select.is-active,html.theme--documenter-dark .is-active.textarea,html.theme--documenter-dark .is-active.input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-active,html.theme--documenter-dark .is-active.button{outline:none}html.theme--documenter-dark .pagination-previous[disabled],html.theme--documenter-dark .pagination-next[disabled],html.theme--documenter-dark .pagination-link[disabled],html.theme--documenter-dark .pagination-ellipsis[disabled],html.theme--documenter-dark .file-cta[disabled],html.theme--documenter-dark .file-name[disabled],html.theme--documenter-dark .select select[disabled],html.theme--documenter-dark .textarea[disabled],html.theme--documenter-dark .input[disabled],html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input[disabled],html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark fieldset[disabled] .pagination-previous,fieldset[disabled] html.theme--documenter-dark .pagination-next,html.theme--documenter-dark fieldset[disabled] .pagination-next,fieldset[disabled] html.theme--documenter-dark .pagination-link,html.theme--documenter-dark fieldset[disabled] .pagination-link,fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis,fieldset[disabled] html.theme--documenter-dark .file-cta,html.theme--documenter-dark fieldset[disabled] .file-cta,fieldset[disabled] html.theme--documenter-dark .file-name,html.theme--documenter-dark fieldset[disabled] .file-name,fieldset[disabled] html.theme--documenter-dark .select select,fieldset[disabled] html.theme--documenter-dark .textarea,fieldset[disabled] html.theme--documenter-dark .input,fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark fieldset[disabled] .select select,html.theme--documenter-dark .select fieldset[disabled] select,html.theme--documenter-dark fieldset[disabled] .textarea,html.theme--documenter-dark fieldset[disabled] .input,html.theme--documenter-dark fieldset[disabled] #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark #documenter .docs-sidebar fieldset[disabled] form.docs-search>input,fieldset[disabled] html.theme--documenter-dark .button,html.theme--documenter-dark fieldset[disabled] .button{cursor:not-allowed}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{-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:" ";display:block;height:0.625em;margin-top:-0.4375em;pointer-events:none;position:absolute;top:50%;transform:rotate(-45deg);transform-origin:center;width:0.625em}html.theme--documenter-dark .admonition:not(:last-child),html.theme--documenter-dark .tabs:not(:last-child),html.theme--documenter-dark .pagination:not(:last-child),html.theme--documenter-dark .message:not(:last-child),html.theme--documenter-dark .level:not(:last-child),html.theme--documenter-dark .breadcrumb:not(:last-child),html.theme--documenter-dark .block:not(:last-child),html.theme--documenter-dark .title:not(:last-child),html.theme--documenter-dark .subtitle:not(:last-child),html.theme--documenter-dark .table-container:not(:last-child),html.theme--documenter-dark .table:not(:last-child),html.theme--documenter-dark .progress:not(:last-child),html.theme--documenter-dark .notification:not(:last-child),html.theme--documenter-dark .content:not(:last-child),html.theme--documenter-dark .box:not(:last-child){margin-bottom:1.5rem}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;-moz-appearance:none;-webkit-appearance:none;background-color:rgba(10,10,10,0.2);border:none;border-radius:9999px;cursor:pointer;pointer-events:auto;display:inline-block;flex-grow:0;flex-shrink:0;font-size:0;height:20px;max-height:20px;max-width:20px;min-height:20px;min-width:20px;outline:none;position:relative;vertical-align:top;width:20px}html.theme--documenter-dark .modal-close::before,html.theme--documenter-dark .delete::before,html.theme--documenter-dark .modal-close::after,html.theme--documenter-dark .delete::after{background-color:#fff;content:"";display:block;left:50%;position:absolute;top:50%;transform:translateX(-50%) translateY(-50%) rotate(45deg);transform-origin:center center}html.theme--documenter-dark .modal-close::before,html.theme--documenter-dark .delete::before{height:2px;width:50%}html.theme--documenter-dark .modal-close::after,html.theme--documenter-dark .delete::after{height:50%;width:2px}html.theme--documenter-dark .modal-close:hover,html.theme--documenter-dark .delete:hover,html.theme--documenter-dark .modal-close:focus,html.theme--documenter-dark .delete:focus{background-color:rgba(10,10,10,0.3)}html.theme--documenter-dark .modal-close:active,html.theme--documenter-dark .delete:active{background-color:rgba(10,10,10,0.4)}html.theme--documenter-dark .is-small.modal-close,html.theme--documenter-dark #documenter .docs-sidebar 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+  Author: @ericwbailey
+  Maintainer: @ericwbailey
+
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.button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter 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#documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter 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img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--documenter-dark .image.is-3by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--documenter-dark .image.is-2by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--documenter-dark .image.is-2by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--documenter-dark .image.is-3by5 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--documenter-dark .image.is-3by5 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--documenter-dark .image.is-9by16 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--documenter-dark .image.is-9by16 .has-ratio,html.theme--documenter-dark #documenter 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.docs-logo>img.is-5by4{padding-top:80%}html.theme--documenter-dark .image.is-4by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--documenter-dark .image.is-3by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--documenter-dark .image.is-5by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--documenter-dark .image.is-16by9,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--documenter-dark .image.is-2by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--documenter-dark .image.is-3by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--documenter-dark .image.is-4by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--documenter-dark .image.is-3by4,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--documenter-dark .image.is-2by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--documenter-dark .image.is-3by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--documenter-dark .image.is-9by16,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--documenter-dark .image.is-1by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--documenter-dark .image.is-1by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by3{padding-top:300%}html.theme--documenter-dark .image.is-16x16,html.theme--documenter-dark #documenter .docs-sidebar 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new file mode 100644
index 0000000..2f168c7
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+++ b/docs/build/assets/themes/documenter-light.css
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+  Description: Original highlight.js style
+  Author: (c) Ivan Sagalaev <maniac@softwaremaniacs.org>
+  Maintainer: @highlightjs/core-team
+  Website: https://highlightjs.org/
+  License: see project LICENSE
+  Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem}
diff --git a/docs/build/assets/themeswap.js b/docs/build/assets/themeswap.js
new file mode 100644
index 0000000..9f5eebe
--- /dev/null
+++ b/docs/build/assets/themeswap.js
@@ -0,0 +1,84 @@
+// Small function to quickly swap out themes. Gets put into the <head> tag..
+function set_theme_from_local_storage() {
+  // Initialize the theme to null, which means default
+  var theme = null;
+  // If the browser supports the localstorage and is not disabled then try to get the
+  // documenter theme
+  if (window.localStorage != null) {
+    // Get the user-picked theme from localStorage. May be `null`, which means the default
+    // theme.
+    theme = window.localStorage.getItem("documenter-theme");
+  }
+  // Check if the users preference is for dark color scheme
+  var darkPreference =
+    window.matchMedia("(prefers-color-scheme: dark)").matches === true;
+  // Initialize a few variables for the loop:
+  //
+  //  - active: will contain the index of the theme that should be active. Note that there
+  //    is no guarantee that localStorage contains sane values. If `active` stays `null`
+  //    we either could not find the theme or it is the default (primary) theme anyway.
+  //    Either way, we then need to stick to the primary theme.
+  //
+  //  - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+  //    that are not the currently active theme)
+  var active = null;
+  var disabled = [];
+  var primaryLightTheme = null;
+  var primaryDarkTheme = null;
+  for (var i = 0; i < document.styleSheets.length; i++) {
+    var ss = document.styleSheets[i];
+    // The <link> 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.
+    if (ss.ownerNode.getAttribute("data-theme-primary") !== null) {
+      primaryLightTheme = themename;
+    }
+    // Check if the theme is primary dark theme so that we could store its name in darkTheme
+    if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) {
+      primaryDarkTheme = themename;
+    }
+    // If we find a matching theme (and it's not the default), we'll set active to non-null
+    if (themename === theme) active = i;
+    // Store the style sheets of inactive themes so that we could disable them
+    if (themename !== theme) disabled.push(ss);
+  }
+  var activeTheme = null;
+  if (active !== null) {
+    // If we did find an active theme, we'll (1) add the theme--$(theme) class to <html>
+    document.getElementsByTagName("html")[0].className = "theme--" + theme;
+    activeTheme = theme;
+  } else {
+    // If we did _not_ find an active theme, then we need to fall back to the primary theme
+    // which can either be dark or light, depending on the user's OS preference.
+    var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme;
+    // In case it somehow happens that the relevant primary theme was not found in the
+    // preceding loop, we abort without doing anything.
+    if (activeTheme === null) {
+      console.error("Unable to determine primary theme.");
+      return;
+    }
+    // When switching to the primary light theme, then we must not have a class name
+    // for the <html> tag. That's only for non-primary or the primary dark theme.
+    if (darkPreference) {
+      document.getElementsByTagName("html")[0].className =
+        "theme--" + activeTheme;
+    } else {
+      document.getElementsByTagName("html")[0].className = "";
+    }
+  }
+  for (var i = 0; i < document.styleSheets.length; i++) {
+    var ss = document.styleSheets[i];
+    // The <link> tag of each style sheet is expected to have a data-theme-name attribute
+    // which must contain the name of the theme. The names in localStorage much match this.
+    var themename = ss.ownerNode.getAttribute("data-theme-name");
+    // attribute not set => non-theme stylesheet => ignore
+    if (themename === null) continue;
+    // we'll disable all the stylesheets, except for the active one
+    ss.disabled = !(themename == activeTheme);
+  }
+}
+set_theme_from_local_storage();
diff --git a/docs/build/assets/warner.js b/docs/build/assets/warner.js
new file mode 100644
index 0000000..3f6f5d0
--- /dev/null
+++ b/docs/build/assets/warner.js
@@ -0,0 +1,52 @@
+function maybeAddWarning() {
+  // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+  // in siteinfo.js.
+  // If either of these are undefined something went horribly wrong, so we abort.
+  if (
+    window.DOCUMENTER_NEWEST === undefined ||
+    window.DOCUMENTER_CURRENT_VERSION === undefined ||
+    window.DOCUMENTER_STABLE === undefined
+  ) {
+    return;
+  }
+
+  // Current version is not a version number, so we can't tell if it's the newest version. Abort.
+  if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) {
+    return;
+  }
+
+  // Current version is newest version, so no need to add a warning.
+  if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) {
+    return;
+  }
+
+  // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs.
+  if (document.body.querySelector('meta[name="robots"]') === null) {
+    const meta = document.createElement("meta");
+    meta.name = "robots";
+    meta.content = "noindex";
+
+    document.getElementsByTagName("head")[0].appendChild(meta);
+  }
+
+  const div = document.createElement("div");
+  div.classList.add("outdated-warning-overlay");
+  const closer = document.createElement("button");
+  closer.classList.add("outdated-warning-closer", "delete");
+  closer.addEventListener("click", function () {
+    document.body.removeChild(div);
+  });
+  const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE;
+  div.innerHTML =
+    'This documentation is not for the latest stable release, but for either the development version or an older release.<br><a href="' +
+    href +
+    '">Click here to go to the documentation for the latest stable release.</a>';
+  div.appendChild(closer);
+  document.body.appendChild(div);
+}
+
+if (document.readyState === "loading") {
+  document.addEventListener("DOMContentLoaded", maybeAddWarning);
+} else {
+  maybeAddWarning();
+}
diff --git a/docs/build/index.html b/docs/build/index.html
new file mode 100644
index 0000000..82b8f76
--- /dev/null
+++ b/docs/build/index.html
@@ -0,0 +1,6 @@
+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · AtomisticQoIs.jl</title><meta name="title" content="Home · AtomisticQoIs.jl"/><meta property="og:title" content="Home · AtomisticQoIs.jl"/><meta property="twitter:title" content="Home · AtomisticQoIs.jl"/><meta name="description" content="Documentation for AtomisticQoIs.jl."/><meta property="og:description" content="Documentation for AtomisticQoIs.jl."/><meta property="twitter:description" content="Documentation for AtomisticQoIs.jl."/><meta property="og:url" content="https://cesmix-mit.github.io/AtomisticQoIs.jl/index.html"/><meta property="twitter:url" content="https://cesmix-mit.github.io/AtomisticQoIs.jl/index.html"/><link rel="canonical" href="https://cesmix-mit.github.io/AtomisticQoIs.jl/index.html"/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="search_index.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="index.html">AtomisticQoIs.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li class="is-active"><a class="tocitem" href="index.html">Home</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select 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id="documenter-page"><h1 id="AtomisticQoIs"><a class="docs-heading-anchor" href="#AtomisticQoIs">AtomisticQoIs</a><a id="AtomisticQoIs-1"></a><a class="docs-heading-anchor-permalink" href="#AtomisticQoIs" title="Permalink"></a></h1><p>Documentation for <a href="https://github.com/cesmix-mit/AtomisticQoIs.jl">AtomisticQoIs</a>.</p><ul><li><a href="index.html#AtomisticQoIs.AtomisticQoIs"><code>AtomisticQoIs.AtomisticQoIs</code></a></li><li><a href="index.html#AtomisticQoIs.GaussQuadrature"><code>AtomisticQoIs.GaussQuadrature</code></a></li><li><a href="index.html#AtomisticQoIs.GibbsQoI"><code>AtomisticQoIs.GibbsQoI</code></a></li><li><a href="index.html#AtomisticQoIs.HMC"><code>AtomisticQoIs.HMC</code></a></li><li><a href="index.html#AtomisticQoIs.ISMC"><code>AtomisticQoIs.ISMC</code></a></li><li><a href="index.html#AtomisticQoIs.ISMCMC"><code>AtomisticQoIs.ISMCMC</code></a></li><li><a href="index.html#AtomisticQoIs.ISMixSamples"><code>AtomisticQoIs.ISMixSamples</code></a></li><li><a href="index.html#AtomisticQoIs.ISSamples"><code>AtomisticQoIs.ISSamples</code></a></li><li><a href="index.html#AtomisticQoIs.Integrator"><code>AtomisticQoIs.Integrator</code></a></li><li><a href="index.html#AtomisticQoIs.MALA"><code>AtomisticQoIs.MALA</code></a></li><li><a href="index.html#AtomisticQoIs.MCMC"><code>AtomisticQoIs.MCMC</code></a></li><li><a href="index.html#AtomisticQoIs.MCSamples"><code>AtomisticQoIs.MCSamples</code></a></li><li><a href="index.html#AtomisticQoIs.MonteCarlo"><code>AtomisticQoIs.MonteCarlo</code></a></li><li><a href="index.html#AtomisticQoIs.NUTS"><code>AtomisticQoIs.NUTS</code></a></li><li><a href="index.html#AtomisticQoIs.QoI"><code>AtomisticQoIs.QoI</code></a></li><li><a href="index.html#AtomisticQoIs.EffSampleSize-Tuple{Vector}"><code>AtomisticQoIs.EffSampleSize</code></a></li><li><a href="index.html#AtomisticQoIs.EffSampleSize-Tuple{GibbsQoI, Vector}"><code>AtomisticQoIs.EffSampleSize</code></a></li><li><a href="index.html#AtomisticQoIs.ISWeightDiagnostic-Tuple{Vector}"><code>AtomisticQoIs.ISWeightDiagnostic</code></a></li><li><a href="index.html#AtomisticQoIs.ISWeightVariance-Tuple{Vector}"><code>AtomisticQoIs.ISWeightVariance</code></a></li><li><a href="index.html#AtomisticQoIs.MCSE-Tuple{GibbsQoI, Vector}"><code>AtomisticQoIs.MCSE</code></a></li><li><a href="index.html#AtomisticQoIs.MCSEbm-Tuple{GibbsQoI, Vector}"><code>AtomisticQoIs.MCSEbm</code></a></li><li><a href="index.html#AtomisticQoIs.MCSEobm-Tuple{GibbsQoI, Vector}"><code>AtomisticQoIs.MCSEobm</code></a></li><li><a href="index.html#AtomisticQoIs.compute_metrics-Tuple{Vector, Vector, Vector}"><code>AtomisticQoIs.compute_metrics</code></a></li><li><a href="index.html#AtomisticQoIs.expectation_is_stable-Tuple{Vector, Function, Gibbs, Distribution}"><code>AtomisticQoIs.expectation_is_stable</code></a></li><li><a href="index.html#AtomisticQoIs.gaussquad-Tuple{Integer, Function, Vararg{Any}}"><code>AtomisticQoIs.gaussquad</code></a></li><li><a href="index.html#AtomisticQoIs.gaussquad_2D-Tuple{Integer, Function, Vararg{Any}}"><code>AtomisticQoIs.gaussquad_2D</code></a></li><li><a href="index.html#AtomisticQoIs.grad_expectation-Tuple{Union{Real, Vector{&lt;:Real}}, GibbsQoI, Integrator}"><code>AtomisticQoIs.grad_expectation</code></a></li><li><a href="index.html#AtomisticQoIs.hasapproxnormconst-Tuple{Gibbs}"><code>AtomisticQoIs.hasapproxnormconst</code></a></li><li><a href="index.html#AtomisticQoIs.hasupdf-Tuple{Gibbs}"><code>AtomisticQoIs.hasupdf</code></a></li><li><a href="index.html#AtomisticQoIs.sample-Tuple{Function, Function, Union{HMC, MALA}, Int64, Real}"><code>AtomisticQoIs.sample</code></a></li><li><a href="index.html#AtomisticQoIs.sample-Tuple{Function, Function, NUTS, Int64, Vector{&lt;:Real}}"><code>AtomisticQoIs.sample</code></a></li><li><a href="index.html#AtomisticQoIs.sample-Tuple{Function, Function, NUTS, Int64, Real}"><code>AtomisticQoIs.sample</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.AtomisticQoIs" href="#AtomisticQoIs.AtomisticQoIs"><code>AtomisticQoIs.AtomisticQoIs</code></a> — <span class="docstring-category">Module</span></header><section><div><p>AtomisticQoIs</p><p>Author: Joanna Zou &lt;jjzou@mit.edu&gt; Version: 0.1.0 Year: 2024 Notes: A Julia library for computing expectation-valued quantities of interest (QoIs) from molecular dynamics simulation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/AtomisticQoIs.jl#L1-L10">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.GaussQuadrature" href="#AtomisticQoIs.GaussQuadrature"><code>AtomisticQoIs.GaussQuadrature</code></a> — <span class="docstring-category">Type</span></header><section><div><p>struct GaussQuadrature &lt;: QuadIntegrator</p><p>Contains parameters for 1D or 2D Gauss quadrature integration.</p><p><strong>Arguments</strong></p><ul><li><code>ξ :: Union{Vector{&lt;:Real}, Vector{&lt;:Vector}}</code>  : quadrature points</li><li><code>w :: Union{Vector{&lt;:Real}, Vector{&lt;:Vector}}</code>  : quadrature weights</li><li><code>d :: Real</code>                                     : dimension</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Integrators/quadrature.jl#L4-L13">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.GibbsQoI" href="#AtomisticQoIs.GibbsQoI"><code>AtomisticQoIs.GibbsQoI</code></a> — <span class="docstring-category">Type</span></header><section><div><p>@kwdef mutable struct GibbsQoI &lt;: QoI</p><p>Defines the struct for computing the quantity of interest (QoI) as the expected value of a function h over Gibbs measure p given input parameters θ, e. g. E_p[h(θ)]</p><p><strong>Arguments</strong></p><ul><li><code>h :: Function</code>   : function to evaluate expectation, receiving inputs (x,θ)</li><li><code>p :: Gibbs</code>      : Gibbs (invariant) distribution with θ == nothing (undefined parameters)</li><li><code>∇h :: Union{Function, Nothing} = nothing</code>   : gradient of h (if nothing, gradient is computed using AutoDiff)</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/QoI/gibbs_qoi.jl#L3-L14">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.HMC" href="#AtomisticQoIs.HMC"><code>AtomisticQoIs.HMC</code></a> — <span class="docstring-category">Type</span></header><section><div><p>struct HMC &lt;: Sampler</p><p>Defines the struct with parameters of the Hamiltonian Monte Carlo algorithm for sampling.</p><p><strong>Arguments</strong></p><ul><li><code>L :: Int</code>        : time length of integrating Hamiltonian&#39;s equations</li><li><code>ϵ :: Real</code>       : step size</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Sampling/hmc.jl#L1-L10">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.ISMC" href="#AtomisticQoIs.ISMC"><code>AtomisticQoIs.ISMC</code></a> — <span class="docstring-category">Type</span></header><section><div><p>struct ISMC &lt;: ISIntegrator</p><p>Contains parameters for Importance Sampling (IS) integration using MC samples from a biasing distribution. This method is implemented when the biasing distribution g can be analytically sampled using rand().</p><p><strong>Arguments</strong></p><ul><li><code>g :: Distribution</code>      : biasing distribution</li><li><code>n :: Int</code>               : number of samples</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Integrators/importance_sampling.jl#L3-L12">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.ISMCMC" href="#AtomisticQoIs.ISMCMC"><code>AtomisticQoIs.ISMCMC</code></a> — <span class="docstring-category">Type</span></header><section><div><p>struct ISMCMC &lt;: ISIntegrator</p><p>Contains parameters for Importance Sampling (IS) integration using MCMC samples from a biasing distribution. This method is implemented when the biasing distribution g cannot be analytically sampled.</p><p><strong>Arguments</strong></p><ul><li><code>g :: Distribution</code>      : biasing distribution</li><li><code>n :: Int</code>               : number of samples</li><li><code>sampler :: Sampler</code>     : type of sampler (see <code>Sampler</code>)</li><li><code>ρ0 :: Distribution</code>     : prior distribution of the state</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Integrators/importance_sampling.jl#L18-L29">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.ISMixSamples" href="#AtomisticQoIs.ISMixSamples"><code>AtomisticQoIs.ISMixSamples</code></a> — <span class="docstring-category">Type</span></header><section><div><p>struct ISMixSamples &lt;: ISIntegrator</p><p>Contains parameters for Importance Sampling (IS) integration using samples from a mixture biasing distribution. The mixture weights are computed based on a kernel distance metric of the parameter with respect to parameters of the mixture component distributions. This method is implemented with the user providing samples from each component mixture distribution. </p><p><strong>Arguments</strong></p><ul><li><code>g :: MixtureModel</code>        : mixture biasing distribution</li><li><code>n :: Int</code>                 : number of samples</li><li><code>knl :: Kernel</code>            : kernel function to compute mixture weights</li><li><code>xsamp :: Vector</code>          : Vector of sample sets from each component distribution</li><li><code>normint :: Integrator</code>    : Integrator for the approximating the normalizing constant of each component distribution</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Integrators/importance_sampling.jl#L67-L81">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.ISSamples" href="#AtomisticQoIs.ISSamples"><code>AtomisticQoIs.ISSamples</code></a> — <span class="docstring-category">Type</span></header><section><div><p>struct ISSamples &lt;: ISIntegrator</p><p>Contains pre-defined Monte Carlo samples from the biasing distribution to evaluate in integration. This method is implemented with the user providing samples from the biasing distribution. </p><p><strong>Arguments</strong></p><ul><li><code>g :: Distribution</code>                               : biasing distribution</li><li><code>xsamp :: Vector</code>                                 : fixed set of samples</li><li><code>normint :: Union{Integrator, Nothing}</code>           : integrator for computing normalizing constant of biasing distribution (required for mixture models)</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Integrators/importance_sampling.jl#L38-L49">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.Integrator" href="#AtomisticQoIs.Integrator"><code>AtomisticQoIs.Integrator</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">Integrator
+
+A struct of abstract type Integrator computes the expectation of a function h(x, θ) with respect to an invariant measure p(x, θ).</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Integrators/integrators.jl#L1-L6">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.MALA" href="#AtomisticQoIs.MALA"><code>AtomisticQoIs.MALA</code></a> — <span class="docstring-category">Type</span></header><section><div><p>struct MALA &lt;: Sampler</p><p>Defines the struct with parameters of the Metropolis-Adjusted Langevin Algorithm (MALA) for sampling.</p><p><strong>Arguments</strong></p><ul><li><code>L :: Int</code>        : time length between evaluating accept/reject criterion</li><li><code>ϵ :: Real</code>       : step size</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Sampling/mala.jl#L1-L10">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.MCMC" href="#AtomisticQoIs.MCMC"><code>AtomisticQoIs.MCMC</code></a> — <span class="docstring-category">Type</span></header><section><div><p>struct MCMC &lt;: MCIntegrator</p><p>Contains parameters for Monte Carlo (MC) integration using MCMC samples. This method is implemented when the distribution cannot be analytically sampled.</p><p><strong>Arguments</strong></p><ul><li><code>n :: Int</code>               : number of samples</li><li><code>sampler :: Sampler</code>     : type of sampler (see <code>Sampler</code>)</li><li><code>ρ0 :: Distribution</code>     : prior distribution of the state</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Integrators/monte_carlo.jl#L17-L27">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.MCSamples" href="#AtomisticQoIs.MCSamples"><code>AtomisticQoIs.MCSamples</code></a> — <span class="docstring-category">Type</span></header><section><div><p>struct MCSamples &lt;: MCIntegrator</p><p>Contains pre-defined Monte Carlo samples to evaluate in integration. This method is implemented with the user providing samples from the distribution.</p><p><strong>Arguments</strong></p><ul><li><code>xsamp :: Vector</code>    : fixed set of samples</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Integrators/monte_carlo.jl#L35-L43">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.MonteCarlo" href="#AtomisticQoIs.MonteCarlo"><code>AtomisticQoIs.MonteCarlo</code></a> — <span class="docstring-category">Type</span></header><section><div><p>struct MonteCarlo &lt;: MCIntegrator</p><p>Contains parameters for Monte Carlo (MC) integration using MC samples. This method may only be implemented when the distribution can be analytically sampled using rand().</p><p><strong>Arguments</strong></p><ul><li><code>n :: Int</code>   : number of samples</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Integrators/monte_carlo.jl#L3-L11">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.NUTS" href="#AtomisticQoIs.NUTS"><code>AtomisticQoIs.NUTS</code></a> — <span class="docstring-category">Type</span></header><section><div><p>struct NUTS &lt;: Sampler</p><p>Defines the struct with parameters of the No-U-Turn-Sampler algorithm for sampling.</p><p><strong>Arguments</strong></p><ul><li><code>ϵ :: Union{&lt;:Real, Nothing}</code>        : step size</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Sampling/nuts.jl#L1-L8">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.QoI" href="#AtomisticQoIs.QoI"><code>AtomisticQoIs.QoI</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">QoI
+
+A struct of abstract type QoI computes the expectation of a function h(x, θ) with respect to an invariant measure p(x, θ).</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/QoI/qoi.jl#L1-L6">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.EffSampleSize-Tuple{GibbsQoI, Vector}" href="#AtomisticQoIs.EffSampleSize-Tuple{GibbsQoI, Vector}"><code>AtomisticQoIs.EffSampleSize</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function EffSampleSize(q::GibbsQoI, xsamp::Vector)</p><p>Computes the effective sample size of a set of nMC samples from an MCMC chain. </p><p><strong>Arguments</strong></p><ul><li><code>q :: GibbsQoI</code>     : Gibbs QoI struct</li><li><code>xsamp :: Vector</code>   : nMC-vector of x-samples</li></ul><p><strong>Outputs</strong></p><ul><li><code>ESS :: Float64</code>    : effective sample size (where 1 &lt; ESS &lt; nMC)</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Diagnostics/sampling_metrics.jl#L66-L77">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.EffSampleSize-Tuple{Vector}" href="#AtomisticQoIs.EffSampleSize-Tuple{Vector}"><code>AtomisticQoIs.EffSampleSize</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function EffSampleSize(hsamp::Vector)</p><p>Computes the effective sample size of a set of nMC samples from an MCMC chain. </p><p><strong>Arguments</strong></p><ul><li><code>hsamp :: Vector</code>   : nMC-vector of d-dimensional function evaluation h</li></ul><p><strong>Outputs</strong></p><ul><li><code>ESS :: Float64</code>    : effective sample size (where 1 &lt; ESS &lt; nMC)</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Diagnostics/sampling_metrics.jl#L84-L94">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.ISWeightDiagnostic-Tuple{Vector}" href="#AtomisticQoIs.ISWeightDiagnostic-Tuple{Vector}"><code>AtomisticQoIs.ISWeightDiagnostic</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function ISWeightDiagnostic(wsamp::Vector)</p><p>Returns a diagnostic value for importance sampling weights using an unnormalized biasing distribution. The importance sampling estimate is reliable when the diagnostic is less than 5. </p><p><strong>Arguments</strong></p><ul><li><code>wsamp :: Vector</code>   : nMC-vector of 1-dim. weights</li></ul><p><strong>Outputs</strong></p><ul><li><code>diagnostic :: Float64</code>    : diagnostic value (want &lt; 5)</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Diagnostics/sampling_metrics.jl#L145-L154">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.ISWeightVariance-Tuple{Vector}" href="#AtomisticQoIs.ISWeightVariance-Tuple{Vector}"><code>AtomisticQoIs.ISWeightVariance</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function ISWeightVariance(wsamp::Vector)</p><p>Returns the variance of importance sampling weights. </p><p><strong>Arguments</strong></p><ul><li><code>wsamp :: Vector</code>   : nMC-vector of weights</li></ul><p><strong>Outputs</strong></p><ul><li><code>var(wsamp) :: Float64</code>    : variance of weights</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Diagnostics/sampling_metrics.jl#L105-L115">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.MCSE-Tuple{GibbsQoI, Vector}" href="#AtomisticQoIs.MCSE-Tuple{GibbsQoI, Vector}"><code>AtomisticQoIs.MCSE</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function MCSE(q::GibbsQoI, xsamp::Vector)</p><p>Estimates the Monte Carlo standard error (se = std(h(x))/√n) using an empirical estimate of standard deviation.</p><p><strong>Arguments</strong></p><ul><li><code>q :: GibbsQoI</code>     : Gibbs QoI struct</li><li><code>xsamp :: Vector</code>   : vector of samples</li></ul><p><strong>Outputs</strong></p><ul><li><code>se :: Float64</code>     : Monte Carlo standard error</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Diagnostics/sampling_metrics.jl#L2-L13">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.MCSEbm-Tuple{GibbsQoI, Vector}" href="#AtomisticQoIs.MCSEbm-Tuple{GibbsQoI, Vector}"><code>AtomisticQoIs.MCSEbm</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function MCSEbm(q::GibbsQoI, xsamp::Vector)</p><p>Estimates the Monte Carlo standard error (se = std(h(x))/√n) using the batch means (BM) method.</p><p><strong>Arguments</strong></p><ul><li><code>q :: GibbsQoI</code>     : Gibbs QoI struct</li><li><code>xsamp :: Vector</code>   : vector of samples</li></ul><p><strong>Outputs</strong></p><ul><li><code>se :: Float64</code>     : Monte Carlo standard error</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Diagnostics/sampling_metrics.jl#L22-L33">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.MCSEobm-Tuple{GibbsQoI, Vector}" href="#AtomisticQoIs.MCSEobm-Tuple{GibbsQoI, Vector}"><code>AtomisticQoIs.MCSEobm</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function MCSEbm(q::GibbsQoI, xsamp::Vector)</p><p>Estimates the Monte Carlo standard error (se = std(h(x))/√n) using the overlapping batch means (OBM) method.</p><p><strong>Arguments</strong></p><ul><li><code>q :: GibbsQoI</code>     : Gibbs QoI struct</li><li><code>xsamp :: Vector</code>   : vector of samples</li></ul><p><strong>Outputs</strong></p><ul><li><code>se :: Float64</code>     : Monte Carlo standard error</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Diagnostics/sampling_metrics.jl#L44-L55">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.compute_metrics-Tuple{Vector, Vector, Vector}" href="#AtomisticQoIs.compute_metrics-Tuple{Vector, Vector, Vector}"><code>AtomisticQoIs.compute_metrics</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function compute_metrics(θ::Vector, h::Vector, w::Vector)</p><p>Computes importance sampling diagnostic metrics, including variance of IS weights (&quot;wvar&quot;), ESS of IS weights (&quot;wESS&quot;), and diagnostic measure (&quot;wdiag&quot;).</p><p><strong>Arguments</strong></p><ul><li><code>θ :: Vector</code>                 : vector of parameters</li><li><code>h :: Vector</code>                 : evaluations of summand function h(x) at samples</li><li><code>w :: Vector</code>                 : evaluations of importance sampling weights at samples</li></ul><p><strong>Outputs</strong></p><ul><li><code>metrics :: Dict{String, Vector}</code>        : dictionary of importance sampling diagnostics</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Diagnostics/diagnostics.jl#L5-L18">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.expectation_is_stable-Tuple{Vector, Function, Gibbs, Distribution}" href="#AtomisticQoIs.expectation_is_stable-Tuple{Vector, Function, Gibbs, Distribution}"><code>AtomisticQoIs.expectation_is_stable</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function expectation<em>is</em>stable(xsamp::Vector, ϕ::Function, f::Gibbs, g::Distribution; normint=nothing)</p><p>Helper function for computing stable importance sampling weights (using log formulation).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/QoI/gibbs_qoi.jl#L236-L241">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.gaussquad-Tuple{Integer, Function, Vararg{Any}}" href="#AtomisticQoIs.gaussquad-Tuple{Integer, Function, Vararg{Any}}"><code>AtomisticQoIs.gaussquad</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function gaussquad(nquad::Integer, gaussbasis::Function, args...; limits::Vector=[-1,1])</p><p>Computes 1D Gauss quadrature points with a change of domain to limits=[ll, ul].</p><p><strong>Arguments</strong></p><ul><li><code>nquad::Integer</code>          : number of quadrature points</li><li><code>gaussbasis::Function</code>    : polynomial basis function from FastGaussQuadrature (gausslegendre, gaussjacobi, etc.)</li><li><code>args...</code>                 : additional arguments for the gaussbasis() function</li><li><code>limits::Vector</code>          : defines lower and upper limits for rescaling</li></ul><p><strong>Outputs</strong></p><ul><li><code>ξ :: Vector{&lt;:Real}</code>     : quadrature points ranging [ll, ul]</li><li><code>w :: Vector{&lt;:Real}</code>     : quadrature weights</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Integrators/quadrature.jl#L24-L38">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.gaussquad_2D-Tuple{Integer, Function, Vararg{Any}}" href="#AtomisticQoIs.gaussquad_2D-Tuple{Integer, Function, Vararg{Any}}"><code>AtomisticQoIs.gaussquad_2D</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function gaussquad_2D(nquad::Integer, gaussbasis::Function, args...; limits::Vector=[-1,1])</p><p>Computes 2D (symmetric) Gauss quadrature points with a change of domain to limits=[ll, ul].</p><p><strong>Arguments</strong></p><ul><li><code>nquad::Integer</code>          : number of quadrature points</li><li><code>gaussbasis::Function</code>    : polynomial basis function from FastGaussQuadrature (gausslegendre, gaussjacobi, etc.)</li><li><code>args...</code>                 : additional arguments for the gaussbasis() function</li><li><code>limits::Vector</code>          : defines lower and upper limits for rescaling</li></ul><p><strong>Outputs</strong></p><ul><li><code>ξ :: Vector{&lt;:Real}</code>     : quadrature points ranging [ll, ul]</li><li><code>w :: Vector{&lt;:Real}</code>     : quadrature weights</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Integrators/quadrature.jl#L46-L60">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.grad_expectation-Tuple{Union{Real, Vector{&lt;:Real}}, GibbsQoI, Integrator}" href="#AtomisticQoIs.grad_expectation-Tuple{Union{Real, Vector{&lt;:Real}}, GibbsQoI, Integrator}"><code>AtomisticQoIs.grad_expectation</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function grad_expectation(θ::Union{Real, Vector{&lt;:Real}}, qoi::GibbsQoI, integrator::Integrator; gradh::Union{Function, Nothing}=nothing)</p><p>Computes the gradient of the QoI with respect to the parameters θ, e. g. ∇θ E_p[h(θ)]. See <code>expectation</code> for more information.</p><p><strong>Arguments</strong></p><ul><li><code>θ :: Union{Real, Vector{&lt;:Real}}</code>    : parameters to evaluate expectation</li><li><code>qoi :: QoI</code>                          : QoI object containing h and p</li><li><code>integrator :: Integrator</code>            : struct specifying method of integration</li><li><code>gradh :: Union{Function, Nothing}</code>   : gradient of qoi.h; if nothing, compute with ForwardDiff</li></ul><p><strong>Outputs</strong></p><ul><li><code>expec_estimator :: Vector{&lt;:Real}</code>   : estimate of vector-valued gradient of the expectation</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/QoI/gibbs_qoi.jl#L151-L167">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.hasapproxnormconst-Tuple{Gibbs}" href="#AtomisticQoIs.hasapproxnormconst-Tuple{Gibbs}"><code>AtomisticQoIs.hasapproxnormconst</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function hasapproxnormconst(d::Distribution)</p><p>Returns &#39;true&#39; if distribution d requires an approximation of its normalizing constant.</p><p><strong>Arguments</strong></p><ul><li><code>d :: Distribution</code>    : distribution to check</li></ul><p><strong>Outputs</strong></p><ul><li><code>flag :: Bool</code>        : true or false</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Distributions/distributions.jl#L21-L31">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.hasupdf-Tuple{Gibbs}" href="#AtomisticQoIs.hasupdf-Tuple{Gibbs}"><code>AtomisticQoIs.hasupdf</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function hasupdf(d::Distribution)</p><p>Returns &#39;true&#39; if distribution d has an unnormalized pdf function (updf(), logupdf()).</p><p><strong>Arguments</strong></p><ul><li><code>d :: Distribution</code>    : distribution to check</li></ul><p><strong>Outputs</strong></p><ul><li><code>flag :: Bool</code>        : true or false</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Distributions/distributions.jl#L5-L16">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.sample-Tuple{Function, Function, NUTS, Int64, Real}" href="#AtomisticQoIs.sample-Tuple{Function, Function, NUTS, Int64, Real}"><code>AtomisticQoIs.sample</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function sample(lπ::Function, gradlπ::Function, sampler::NUTS, n::Int64, x0::Real)</p><p>Draw samples from target distribution π(x) using the No-U-Turn Sampler (NUTS) for scalar-valued support (x::Real).</p><p><strong>Arguments</strong></p><ul><li><code>lπ :: Function</code>        : log likelihood of target π</li><li><code>gradlπ :: Function</code>    : gradient of log likelihood of π</li><li><code>sampler :: HMC</code>        : Sampler struct specifying sampling algorithm</li><li><code>n :: Int64</code>            : number of samples</li><li><code>x0 :: Real</code>            : initial state</li></ul><p><strong>Outputs</strong></p><ul><li><code>samples :: Vector</code>     : vector of samples from π</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Sampling/nuts.jl#L57-L72">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.sample-Tuple{Function, Function, NUTS, Int64, Vector{&lt;:Real}}" href="#AtomisticQoIs.sample-Tuple{Function, Function, NUTS, Int64, Vector{&lt;:Real}}"><code>AtomisticQoIs.sample</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function sample(lπ::Function, gradlπ::Function, sampler::NUTS, n::Int64, x0::Vector{&lt;:Real})</p><p>Draw samples from target distribution π(x) using the No-U-Turn Sampler (NUTS) from the AdvancedHMC package. Assumes multi-dimensional support (x::Vector).</p><p><strong>Arguments</strong></p><ul><li><code>lπ :: Function</code>              : log likelihood of target π</li><li><code>gradlπ :: Function</code>          : gradient of log likelihood of π</li><li><code>sampler :: HMC</code>              : Sampler struct specifying sampling algorithm</li><li><code>n :: Int64</code>                  : number of samples</li><li><code>x0 :: Vector{&lt;:Real}</code>        : initial state</li></ul><p><strong>Outputs</strong></p><ul><li><code>samples::Vector{Vector}</code>     : vector of samples from π</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Sampling/nuts.jl#L19-L34">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="AtomisticQoIs.sample-Tuple{Function, Function, Union{HMC, MALA}, Int64, Real}" href="#AtomisticQoIs.sample-Tuple{Function, Function, Union{HMC, MALA}, Int64, Real}"><code>AtomisticQoIs.sample</code></a> — <span class="docstring-category">Method</span></header><section><div><p>function sample(lπ::Function, gradlπ::Function, sampler::Union{HMC,MALA}, n::Int64, x0::Real)</p><p>Draw samples from target distribution π(x) for scalar-valued support (x::Real).</p><p><strong>Arguments</strong></p><ul><li><code>lπ :: Function</code>                      : log likelihood of target π</li><li><code>gradlπ :: Function</code>                  : gradient of log likelihood of π</li><li><code>sampler :: Union{HMC,MALA}</code>          : Sampler struct specifying sampling algorithm</li><li><code>n :: Int64</code>                          : number of samples</li><li><code>x0 :: Real</code>                          : initial state</li></ul><p><strong>Outputs</strong></p><ul><li><code>samples :: Vector</code>                   : vector of samples from π</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/cesmix-mit/AtomisticQoIs.jl/blob/766a4dbd22e31949c5ef2403f17e66df477255dd/src/Sampling/sampling.jl#L8-L23">source</a></section></article></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.0 on <span class="colophon-date" title="Tuesday 16 April 2024 16:09">Tuesday 16 April 2024</span>. 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+[{"location":"index.html","page":"Home","title":"Home","text":"CurrentModule = AtomisticQoIs","category":"page"},{"location":"index.html#AtomisticQoIs","page":"Home","title":"AtomisticQoIs","text":"","category":"section"},{"location":"index.html","page":"Home","title":"Home","text":"Documentation for AtomisticQoIs.","category":"page"},{"location":"index.html","page":"Home","title":"Home","text":"","category":"page"},{"location":"index.html","page":"Home","title":"Home","text":"Modules = [AtomisticQoIs]","category":"page"},{"location":"index.html#AtomisticQoIs.AtomisticQoIs","page":"Home","title":"AtomisticQoIs.AtomisticQoIs","text":"AtomisticQoIs\n\nAuthor: Joanna Zou <jjzou@mit.edu> Version: 0.1.0 Year: 2024 Notes: A Julia library for computing expectation-valued quantities of interest (QoIs) from molecular dynamics simulation.\n\n\n\n\n\n","category":"module"},{"location":"index.html#AtomisticQoIs.GaussQuadrature","page":"Home","title":"AtomisticQoIs.GaussQuadrature","text":"struct GaussQuadrature <: QuadIntegrator\n\nContains parameters for 1D or 2D Gauss quadrature integration.\n\nArguments\n\nξ :: Union{Vector{<:Real}, Vector{<:Vector}}  : quadrature points\nw :: Union{Vector{<:Real}, Vector{<:Vector}}  : quadrature weights\nd :: Real                                     : dimension\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.GibbsQoI","page":"Home","title":"AtomisticQoIs.GibbsQoI","text":"@kwdef mutable struct GibbsQoI <: QoI\n\nDefines the struct for computing the quantity of interest (QoI) as the expected value of a function h over Gibbs measure p given input parameters θ, e. g. E_p[h(θ)]\n\nArguments\n\nh :: Function   : function to evaluate expectation, receiving inputs (x,θ)\np :: Gibbs      : Gibbs (invariant) distribution with θ == nothing (undefined parameters)\n∇h :: Union{Function, Nothing} = nothing   : gradient of h (if nothing, gradient is computed using AutoDiff)\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.HMC","page":"Home","title":"AtomisticQoIs.HMC","text":"struct HMC <: Sampler\n\nDefines the struct with parameters of the Hamiltonian Monte Carlo algorithm for sampling.\n\nArguments\n\nL :: Int        : time length of integrating Hamiltonian's equations\nϵ :: Real       : step size\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.ISMC","page":"Home","title":"AtomisticQoIs.ISMC","text":"struct ISMC <: ISIntegrator\n\nContains parameters for Importance Sampling (IS) integration using MC samples from a biasing distribution. This method is implemented when the biasing distribution g can be analytically sampled using rand().\n\nArguments\n\ng :: Distribution      : biasing distribution\nn :: Int               : number of samples\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.ISMCMC","page":"Home","title":"AtomisticQoIs.ISMCMC","text":"struct ISMCMC <: ISIntegrator\n\nContains parameters for Importance Sampling (IS) integration using MCMC samples from a biasing distribution. This method is implemented when the biasing distribution g cannot be analytically sampled.\n\nArguments\n\ng :: Distribution      : biasing distribution\nn :: Int               : number of samples\nsampler :: Sampler     : type of sampler (see Sampler)\nρ0 :: Distribution     : prior distribution of the state\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.ISMixSamples","page":"Home","title":"AtomisticQoIs.ISMixSamples","text":"struct ISMixSamples <: ISIntegrator\n\nContains parameters for Importance Sampling (IS) integration using samples from a mixture biasing distribution. The mixture weights are computed based on a kernel distance metric of the parameter with respect to parameters of the mixture component distributions. This method is implemented with the user providing samples from each component mixture distribution. \n\nArguments\n\ng :: MixtureModel        : mixture biasing distribution\nn :: Int                 : number of samples\nknl :: Kernel            : kernel function to compute mixture weights\nxsamp :: Vector          : Vector of sample sets from each component distribution\nnormint :: Integrator    : Integrator for the approximating the normalizing constant of each component distribution\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.ISSamples","page":"Home","title":"AtomisticQoIs.ISSamples","text":"struct ISSamples <: ISIntegrator\n\nContains pre-defined Monte Carlo samples from the biasing distribution to evaluate in integration. This method is implemented with the user providing samples from the biasing distribution. \n\nArguments\n\ng :: Distribution                               : biasing distribution\nxsamp :: Vector                                 : fixed set of samples\nnormint :: Union{Integrator, Nothing}           : integrator for computing normalizing constant of biasing distribution (required for mixture models)\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.Integrator","page":"Home","title":"AtomisticQoIs.Integrator","text":"Integrator\n\nA struct of abstract type Integrator computes the expectation of a function h(x, θ) with respect to an invariant measure p(x, θ).\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.MALA","page":"Home","title":"AtomisticQoIs.MALA","text":"struct MALA <: Sampler\n\nDefines the struct with parameters of the Metropolis-Adjusted Langevin Algorithm (MALA) for sampling.\n\nArguments\n\nL :: Int        : time length between evaluating accept/reject criterion\nϵ :: Real       : step size\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.MCMC","page":"Home","title":"AtomisticQoIs.MCMC","text":"struct MCMC <: MCIntegrator\n\nContains parameters for Monte Carlo (MC) integration using MCMC samples. This method is implemented when the distribution cannot be analytically sampled.\n\nArguments\n\nn :: Int               : number of samples\nsampler :: Sampler     : type of sampler (see Sampler)\nρ0 :: Distribution     : prior distribution of the state\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.MCSamples","page":"Home","title":"AtomisticQoIs.MCSamples","text":"struct MCSamples <: MCIntegrator\n\nContains pre-defined Monte Carlo samples to evaluate in integration. This method is implemented with the user providing samples from the distribution.\n\nArguments\n\nxsamp :: Vector    : fixed set of samples\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.MonteCarlo","page":"Home","title":"AtomisticQoIs.MonteCarlo","text":"struct MonteCarlo <: MCIntegrator\n\nContains parameters for Monte Carlo (MC) integration using MC samples. This method may only be implemented when the distribution can be analytically sampled using rand().\n\nArguments\n\nn :: Int   : number of samples\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.NUTS","page":"Home","title":"AtomisticQoIs.NUTS","text":"struct NUTS <: Sampler\n\nDefines the struct with parameters of the No-U-Turn-Sampler algorithm for sampling.\n\nArguments\n\nϵ :: Union{<:Real, Nothing}        : step size\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.QoI","page":"Home","title":"AtomisticQoIs.QoI","text":"QoI\n\nA struct of abstract type QoI computes the expectation of a function h(x, θ) with respect to an invariant measure p(x, θ).\n\n\n\n\n\n","category":"type"},{"location":"index.html#AtomisticQoIs.EffSampleSize-Tuple{GibbsQoI, Vector}","page":"Home","title":"AtomisticQoIs.EffSampleSize","text":"function EffSampleSize(q::GibbsQoI, xsamp::Vector)\n\nComputes the effective sample size of a set of nMC samples from an MCMC chain. \n\nArguments\n\nq :: GibbsQoI     : Gibbs QoI struct\nxsamp :: Vector   : nMC-vector of x-samples\n\nOutputs\n\nESS :: Float64    : effective sample size (where 1 < ESS < nMC)\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.EffSampleSize-Tuple{Vector}","page":"Home","title":"AtomisticQoIs.EffSampleSize","text":"function EffSampleSize(hsamp::Vector)\n\nComputes the effective sample size of a set of nMC samples from an MCMC chain. \n\nArguments\n\nhsamp :: Vector   : nMC-vector of d-dimensional function evaluation h\n\nOutputs\n\nESS :: Float64    : effective sample size (where 1 < ESS < nMC)\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.ISWeightDiagnostic-Tuple{Vector}","page":"Home","title":"AtomisticQoIs.ISWeightDiagnostic","text":"function ISWeightDiagnostic(wsamp::Vector)\n\nReturns a diagnostic value for importance sampling weights using an unnormalized biasing distribution. The importance sampling estimate is reliable when the diagnostic is less than 5. \n\nArguments\n\nwsamp :: Vector   : nMC-vector of 1-dim. weights\n\nOutputs\n\ndiagnostic :: Float64    : diagnostic value (want < 5)\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.ISWeightVariance-Tuple{Vector}","page":"Home","title":"AtomisticQoIs.ISWeightVariance","text":"function ISWeightVariance(wsamp::Vector)\n\nReturns the variance of importance sampling weights. \n\nArguments\n\nwsamp :: Vector   : nMC-vector of weights\n\nOutputs\n\nvar(wsamp) :: Float64    : variance of weights\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.MCSE-Tuple{GibbsQoI, Vector}","page":"Home","title":"AtomisticQoIs.MCSE","text":"function MCSE(q::GibbsQoI, xsamp::Vector)\n\nEstimates the Monte Carlo standard error (se = std(h(x))/√n) using an empirical estimate of standard deviation.\n\nArguments\n\nq :: GibbsQoI     : Gibbs QoI struct\nxsamp :: Vector   : vector of samples\n\nOutputs\n\nse :: Float64     : Monte Carlo standard error\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.MCSEbm-Tuple{GibbsQoI, Vector}","page":"Home","title":"AtomisticQoIs.MCSEbm","text":"function MCSEbm(q::GibbsQoI, xsamp::Vector)\n\nEstimates the Monte Carlo standard error (se = std(h(x))/√n) using the batch means (BM) method.\n\nArguments\n\nq :: GibbsQoI     : Gibbs QoI struct\nxsamp :: Vector   : vector of samples\n\nOutputs\n\nse :: Float64     : Monte Carlo standard error\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.MCSEobm-Tuple{GibbsQoI, Vector}","page":"Home","title":"AtomisticQoIs.MCSEobm","text":"function MCSEbm(q::GibbsQoI, xsamp::Vector)\n\nEstimates the Monte Carlo standard error (se = std(h(x))/√n) using the overlapping batch means (OBM) method.\n\nArguments\n\nq :: GibbsQoI     : Gibbs QoI struct\nxsamp :: Vector   : vector of samples\n\nOutputs\n\nse :: Float64     : Monte Carlo standard error\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.compute_metrics-Tuple{Vector, Vector, Vector}","page":"Home","title":"AtomisticQoIs.compute_metrics","text":"function compute_metrics(θ::Vector, h::Vector, w::Vector)\n\nComputes importance sampling diagnostic metrics, including variance of IS weights (\"wvar\"), ESS of IS weights (\"wESS\"), and diagnostic measure (\"wdiag\").\n\nArguments\n\nθ :: Vector                 : vector of parameters\nh :: Vector                 : evaluations of summand function h(x) at samples\nw :: Vector                 : evaluations of importance sampling weights at samples\n\nOutputs\n\nmetrics :: Dict{String, Vector}        : dictionary of importance sampling diagnostics\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.expectation_is_stable-Tuple{Vector, Function, Gibbs, Distribution}","page":"Home","title":"AtomisticQoIs.expectation_is_stable","text":"function expectationisstable(xsamp::Vector, ϕ::Function, f::Gibbs, g::Distribution; normint=nothing)\n\nHelper function for computing stable importance sampling weights (using log formulation).\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.gaussquad-Tuple{Integer, Function, Vararg{Any}}","page":"Home","title":"AtomisticQoIs.gaussquad","text":"function gaussquad(nquad::Integer, gaussbasis::Function, args...; limits::Vector=[-1,1])\n\nComputes 1D Gauss quadrature points with a change of domain to limits=[ll, ul].\n\nArguments\n\nnquad::Integer          : number of quadrature points\ngaussbasis::Function    : polynomial basis function from FastGaussQuadrature (gausslegendre, gaussjacobi, etc.)\nargs...                 : additional arguments for the gaussbasis() function\nlimits::Vector          : defines lower and upper limits for rescaling\n\nOutputs\n\nξ :: Vector{<:Real}     : quadrature points ranging [ll, ul]\nw :: Vector{<:Real}     : quadrature weights\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.gaussquad_2D-Tuple{Integer, Function, Vararg{Any}}","page":"Home","title":"AtomisticQoIs.gaussquad_2D","text":"function gaussquad_2D(nquad::Integer, gaussbasis::Function, args...; limits::Vector=[-1,1])\n\nComputes 2D (symmetric) Gauss quadrature points with a change of domain to limits=[ll, ul].\n\nArguments\n\nnquad::Integer          : number of quadrature points\ngaussbasis::Function    : polynomial basis function from FastGaussQuadrature (gausslegendre, gaussjacobi, etc.)\nargs...                 : additional arguments for the gaussbasis() function\nlimits::Vector          : defines lower and upper limits for rescaling\n\nOutputs\n\nξ :: Vector{<:Real}     : quadrature points ranging [ll, ul]\nw :: Vector{<:Real}     : quadrature weights\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.grad_expectation-Tuple{Union{Real, Vector{<:Real}}, GibbsQoI, Integrator}","page":"Home","title":"AtomisticQoIs.grad_expectation","text":"function grad_expectation(θ::Union{Real, Vector{<:Real}}, qoi::GibbsQoI, integrator::Integrator; gradh::Union{Function, Nothing}=nothing)\n\nComputes the gradient of the QoI with respect to the parameters θ, e. g. ∇θ E_p[h(θ)]. See expectation for more information.\n\nArguments\n\nθ :: Union{Real, Vector{<:Real}}    : parameters to evaluate expectation\nqoi :: QoI                          : QoI object containing h and p\nintegrator :: Integrator            : struct specifying method of integration\ngradh :: Union{Function, Nothing}   : gradient of qoi.h; if nothing, compute with ForwardDiff\n\nOutputs\n\nexpec_estimator :: Vector{<:Real}   : estimate of vector-valued gradient of the expectation\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.hasapproxnormconst-Tuple{Gibbs}","page":"Home","title":"AtomisticQoIs.hasapproxnormconst","text":"function hasapproxnormconst(d::Distribution)\n\nReturns 'true' if distribution d requires an approximation of its normalizing constant.\n\nArguments\n\nd :: Distribution    : distribution to check\n\nOutputs\n\nflag :: Bool        : true or false\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.hasupdf-Tuple{Gibbs}","page":"Home","title":"AtomisticQoIs.hasupdf","text":"function hasupdf(d::Distribution)\n\nReturns 'true' if distribution d has an unnormalized pdf function (updf(), logupdf()).\n\nArguments\n\nd :: Distribution    : distribution to check\n\nOutputs\n\nflag :: Bool        : true or false\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.sample-Tuple{Function, Function, NUTS, Int64, Real}","page":"Home","title":"AtomisticQoIs.sample","text":"function sample(lπ::Function, gradlπ::Function, sampler::NUTS, n::Int64, x0::Real)\n\nDraw samples from target distribution π(x) using the No-U-Turn Sampler (NUTS) for scalar-valued support (x::Real).\n\nArguments\n\nlπ :: Function        : log likelihood of target π\ngradlπ :: Function    : gradient of log likelihood of π\nsampler :: HMC        : Sampler struct specifying sampling algorithm\nn :: Int64            : number of samples\nx0 :: Real            : initial state\n\nOutputs\n\nsamples :: Vector     : vector of samples from π\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.sample-Tuple{Function, Function, NUTS, Int64, Vector{<:Real}}","page":"Home","title":"AtomisticQoIs.sample","text":"function sample(lπ::Function, gradlπ::Function, sampler::NUTS, n::Int64, x0::Vector{<:Real})\n\nDraw samples from target distribution π(x) using the No-U-Turn Sampler (NUTS) from the AdvancedHMC package. Assumes multi-dimensional support (x::Vector).\n\nArguments\n\nlπ :: Function              : log likelihood of target π\ngradlπ :: Function          : gradient of log likelihood of π\nsampler :: HMC              : Sampler struct specifying sampling algorithm\nn :: Int64                  : number of samples\nx0 :: Vector{<:Real}        : initial state\n\nOutputs\n\nsamples::Vector{Vector}     : vector of samples from π\n\n\n\n\n\n","category":"method"},{"location":"index.html#AtomisticQoIs.sample-Tuple{Function, Function, Union{HMC, MALA}, Int64, Real}","page":"Home","title":"AtomisticQoIs.sample","text":"function sample(lπ::Function, gradlπ::Function, sampler::Union{HMC,MALA}, n::Int64, x0::Real)\n\nDraw samples from target distribution π(x) for scalar-valued support (x::Real).\n\nArguments\n\nlπ :: Function                      : log likelihood of target π\ngradlπ :: Function                  : gradient of log likelihood of π\nsampler :: Union{HMC,MALA}          : Sampler struct specifying sampling algorithm\nn :: Int64                          : number of samples\nx0 :: Real                          : initial state\n\nOutputs\n\nsamples :: Vector                   : vector of samples from π\n\n\n\n\n\n","category":"method"}]
+}
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+var DOC_VERSIONS = [
+];