From 7b9320f76104adf8720331b648225302cc36beeb Mon Sep 17 00:00:00 2001
From: yjunechoe <jchoe001@gmail.com>
Date: Sun, 22 Sep 2024 19:51:17 -0400
Subject: [PATCH] kronecker() aside

---
 .../row-relational-operations.Rmd             |   29 +
 .../row-relational-operations.html            |  131 +-
 .../figure-html5/final-gapminder-plot-1.png   |  Bin 18806 -> 19953 bytes
 .../header-attrs-2.27/header-attrs.js         |   12 +
 .../panelset-0.3.0/panelset.css               |  291 +
 .../panelset-0.3.0/panelset.js                |  826 ++
 docs/blog.html                                | 7224 ++++++++---------
 docs/blog.xml                                 | 1851 ++++-
 .../index.html                                |  100 +-
 .../figure-html5/final-gapminder-plot-1.png   |  Bin 18806 -> 19953 bytes
 .../header-attrs-2.21/header-attrs.js         |   12 +
 .../panelset-0.2.6/panelset.css               |  227 +
 .../panelset-0.2.6/panelset.js                |  325 +
 docs/posts/posts.json                         |   44 +-
 docs/site_libs/panelset-0.3.0/panelset.css    |  291 +
 docs/site_libs/panelset-0.3.0/panelset.js     |  826 ++
 docs/sitemap.xml                              |    8 +-
 17 files changed, 8503 insertions(+), 3694 deletions(-)
 create mode 100644 _posts/2023-06-11-row-relational-operations/row-relational-operations_files/header-attrs-2.27/header-attrs.js
 create mode 100644 _posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.3.0/panelset.css
 create mode 100644 _posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.3.0/panelset.js
 create mode 100644 docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/header-attrs-2.21/header-attrs.js
 create mode 100644 docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.2.6/panelset.css
 create mode 100644 docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.2.6/panelset.js
 create mode 100644 docs/site_libs/panelset-0.3.0/panelset.css
 create mode 100644 docs/site_libs/panelset-0.3.0/panelset.js

diff --git a/_posts/2023-06-11-row-relational-operations/row-relational-operations.Rmd b/_posts/2023-06-11-row-relational-operations/row-relational-operations.Rmd
index 2d889af5..429d8831 100644
--- a/_posts/2023-06-11-row-relational-operations/row-relational-operations.Rmd
+++ b/_posts/2023-06-11-row-relational-operations/row-relational-operations.Rmd
@@ -637,6 +637,35 @@ We find that the lessons of working with row indices from `slice()` translated t
 
 </details>
 
+### Aside: `kronecker()` as `as.vector(outer())`
+
+Following from the `slice()` + `outer()` strategy demoed above, imagine if we wanted to filter for `"Luke Skywalker"` and 4 other characters that are neighbors in the `height` and `mass` values.
+
+```{r}
+dplyr::starwars[, 1:3]
+```
+
+In row-relational terms, "filtering neighboring values" just means "filtering rows after arranging by the values we care about". We can express this using `slice()` and `outer()` as:
+
+```{r}
+starwars %>% 
+  select(name, mass, height) %>% 
+  arrange(mass, height) %>% 
+  slice( as.vector(outer(-2:2, which(name == "Luke Skywalker"), `+`)) )
+```
+
+I raised this example on an unrelated thread on the [R4DS/DSLC slack](https://fosstodon.org/@DSLC), where Anthony Durrant pointed me to `kronecker()` as a version of `outer()` that unlist before returning the output.
+
+So in examples involving `outer()` to generate row indices in `slice()`, we can also use `kronecker()` instead to save a call to a flattening function like `as.vector()`:
+
+```{r}
+starwars %>% 
+  select(name, mass, height) %>% 
+  arrange(mass, height) %>% 
+  slice( kronecker(-2:2, which(name == "Luke Skywalker"), `+`) )
+```
+
+
 ### Windowed min/max/median (etc.)
 
 Let's say we have this small time series data, and we want to calculate a **lagged 3-window moving minimum** for the `val` column:
diff --git a/_posts/2023-06-11-row-relational-operations/row-relational-operations.html b/_posts/2023-06-11-row-relational-operations/row-relational-operations.html
index 7ba40fb3..3981ff9d 100644
--- a/_posts/2023-06-11-row-relational-operations/row-relational-operations.html
+++ b/_posts/2023-06-11-row-relational-operations/row-relational-operations.html
@@ -21,7 +21,7 @@
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 pre > code.sourceCode { white-space: pre; position: relative; }
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+pre > code.sourceCode > span { line-height: 1.25; }
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 .sourceCode { overflow: visible; }
 code.sourceCode > span { color: inherit; text-decoration: inherit; }
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 }
 @media print {
 pre > code.sourceCode { white-space: pre-wrap; }
-pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
+pre > code.sourceCode > span { display: inline-block; text-indent: -5em; padding-left: 5em; }
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@@ -94,8 +94,8 @@
 
 
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-  <meta property="article:created" itemprop="dateCreated" content="2023-06-11"/>
+  <meta property="article:published" itemprop="datePublished" content="2024-09-22"/>
+  <meta property="article:created" itemprop="dateCreated" content="2024-09-22"/>
   <meta name="article:author" content="June Choe"/>
 
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@@ -1094,6 +1111,12 @@
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@@ -1198,12 +1222,13 @@
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@@ -1481,9 +1506,9 @@
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@@ -1509,7 +1534,7 @@
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 <script id="distill-front-matter" type="text/json">
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+{"title":"Row relational operations with slice()","description":"A love letter to dplyr::slice() and a gallery of usecases","authors":[{"author":"June Choe","authorURL":"#","affiliation":"University of Pennsylvania Linguistics","affiliationURL":"https://live-sas-www-ling.pantheon.sas.upenn.edu/","orcidID":"0000-0002-0701-921X"}],"publishedDate":"2024-09-22T00:00:00.000-04:00","citationText":"Choe, 2024"}
 </script>
 
 <!--/radix_placeholder_front_matter-->
@@ -1520,6 +1545,7 @@
 
 <div class="d-title">
 <h1>Row relational operations with slice()</h1>
+
 <!--radix_placeholder_categories-->
 <div class="dt-tags">
 <div class="dt-tag">data wrangling</div>
@@ -1532,7 +1558,7 @@ <h1>Row relational operations with slice()</h1>
 <div class="d-byline">
   June Choe  (University of Pennsylvania Linguistics)<a href="https://live-sas-www-ling.pantheon.sas.upenn.edu/" class="uri">https://live-sas-www-ling.pantheon.sas.upenn.edu/</a>
   
-<br/>2023-06-11
+<br/>2024-09-22
 </div>
 
 <div class="d-article">
@@ -1553,6 +1579,7 @@ <h3>Contents</h3>
 <li><a href="#subset-a-selection-of-rows-the-following-row" id="toc-subset-a-selection-of-rows-the-following-row">Subset a selection of rows + the following row</a></li>
 <li><a href="#subset-a-selection-of-rows-multiple-following-rows" id="toc-subset-a-selection-of-rows-multiple-following-rows">Subset a selection of rows + multiple following rows</a></li>
 <li><a href="#filter-and-encode-neighboring-rows" id="toc-filter-and-encode-neighboring-rows">Filter (and encode) neighboring rows</a></li>
+<li><a href="#aside-kronecker-as-as.vectorouter" id="toc-aside-kronecker-as-as.vectorouter">Aside: <code>kronecker()</code> as <code>as.vector(outer())</code></a></li>
 <li><a href="#windowed-minmaxmedian-etc." id="toc-windowed-minmaxmedian-etc.">Windowed min/max/median (etc.)</a></li>
 <li><a href="#evenly-distributed-row-shuffling-of-balanced-categories" id="toc-evenly-distributed-row-shuffling-of-balanced-categories">Evenly distributed row shuffling of balanced categories</a></li>
 <li><a href="#inserting-a-new-row-at-specific-intervals" id="toc-inserting-a-new-row-at-specific-intervals">Inserting a new row at specific intervals</a></li>
@@ -1586,7 +1613,7 @@ <h3 id="basic-usage">Basic usage</h3>
    4 Darth Vader           202   136
    5 Leia Organa           150    49
    6 Owen Lars             178   120
-   7 Beru Whitesun lars    165    75
+   7 Beru Whitesun Lars    165    75
    8 R5-D4                  97    32
    9 Biggs Darklighter     183    84
   10 Obi-Wan Kenobi        182    77</code></pre>
@@ -1714,7 +1741,7 @@ <h4 id="row-ordering">3) Row ordering</h4>
    5 Luke Skywalker        172    77
    6 R5-D4                  97    32
    7 C-3PO                 167    75
-   8 Beru Whitesun lars    165    75
+   8 Beru Whitesun Lars    165    75
    9 Biggs Darklighter     183    84
   10 R2-D2                  96    32</code></pre>
 </div>
@@ -1733,7 +1760,7 @@ <h4 id="row-ordering">3) Row ordering</h4>
    4 Darth Vader           202   136
    5 Luke Skywalker        172    77
    6 Owen Lars             178   120
-   7 Beru Whitesun lars    165    75
+   7 Beru Whitesun Lars    165    75
    8 R5-D4                  97    32
    9 Biggs Darklighter     183    84
   10 Obi-Wan Kenobi        182    77</code></pre>
@@ -1750,7 +1777,7 @@ <h4 id="row-ordering">3) Row ordering</h4>
    1 Obi-Wan Kenobi        182    77
    2 Biggs Darklighter     183    84
    3 R5-D4                  97    32
-   4 Beru Whitesun lars    165    75
+   4 Beru Whitesun Lars    165    75
    5 Owen Lars             178   120
    6 Leia Organa           150    49
    7 Darth Vader           202   136
@@ -1817,7 +1844,7 @@ <h4 id="slice-as-arrange"><code>slice()</code> as <code>arrange()</code></h4>
    1 R2-D2                  96    32
    2 R5-D4                  97    32
    3 Leia Organa           150    49
-   4 Beru Whitesun lars    165    75
+   4 Beru Whitesun Lars    165    75
    5 C-3PO                 167    75
    6 Luke Skywalker        172    77
    7 Owen Lars             178   120
@@ -1837,7 +1864,7 @@ <h4 id="slice-as-arrange"><code>slice()</code> as <code>arrange()</code></h4>
    1 R2-D2                  96    32
    2 R5-D4                  97    32
    3 Leia Organa           150    49
-   4 Beru Whitesun lars    165    75
+   4 Beru Whitesun Lars    165    75
    5 C-3PO                 167    75
    6 Luke Skywalker        172    77
    7 Owen Lars             178   120
@@ -1865,7 +1892,7 @@ <h4 id="slice-as-arrange"><code>slice()</code> as <code>arrange()</code></h4>
    1 R2-D2                  96    32
    2 R5-D4                  97    32
    3 Leia Organa           150    49
-   4 Beru Whitesun lars    165    75
+   4 Beru Whitesun Lars    165    75
    5 C-3PO                 167    75
    6 Luke Skywalker        172    77
    7 Owen Lars             178   120
@@ -1981,7 +2008,7 @@ <h3 id="repeat-rows-in-place">Repeat rows (in place)</h3>
    6 Leia Organa           150    49
    7 Leia Organa           150    49
    8 Owen Lars             178   120
-   9 Beru Whitesun lars    165    75
+   9 Beru Whitesun Lars    165    75
   10 R5-D4                  97    32
   11 Biggs Darklighter     183    84
   12 Obi-Wan Kenobi        182    77</code></pre>
@@ -2012,7 +2039,7 @@ <h3 id="repeat-rows-in-place">Repeat rows (in place)</h3>
    9 Leia Organa           150    49
   10 Leia Organa           150    49
   11 Owen Lars             178   120
-  12 Beru Whitesun lars    165    75
+  12 Beru Whitesun Lars    165    75
   13 R5-D4                  97    32
   14 Biggs Darklighter     183    84
   15 Obi-Wan Kenobi        182    77</code></pre>
@@ -2037,7 +2064,7 @@ <h3 id="repeat-rows-in-place">Repeat rows (in place)</h3>
    9 Leia Organa           150    49
   10 Leia Organa           150    49
   11 Owen Lars             178   120
-  12 Beru Whitesun lars    165    75
+  12 Beru Whitesun Lars    165    75
   13 R5-D4                  97    32
   14 Biggs Darklighter     183    84
   15 Obi-Wan Kenobi        182    77</code></pre>
@@ -2570,6 +2597,62 @@ <h3 id="filter-and-encode-neighboring-rows">Filter (and encode) neighboring rows
 </div>
 <p>We find that the lessons of working with row indices from <code>slice()</code> translated to solving this complex <code>mutate()</code> problem - neat!</p>
 </details>
+<h3 id="aside-kronecker-as-as.vectorouter">Aside: <code>kronecker()</code> as <code>as.vector(outer())</code></h3>
+<p>Following from the <code>slice()</code> + <code>outer()</code> strategy demoed above, imagine if we wanted to filter for <code>"Luke Skywalker"</code> and 4 other characters that are neighbors in the <code>height</code> and <code>mass</code> values.</p>
+<div class="layout-chunk" data-layout="l-body">
+<div class="sourceCode">
+<pre class="sourceCode r"><code class="sourceCode r"><span><span class='fu'>dplyr</span><span class='fu'>::</span><span class='va'><a href='https://dplyr.tidyverse.org/reference/starwars.html'>starwars</a></span><span class='op'>[</span>, <span class='fl'>1</span><span class='op'>:</span><span class='fl'>3</span><span class='op'>]</span></span></code></pre>
+</div>
+<pre><code>  # A tibble: 87 × 3
+     name               height  mass
+     &lt;chr&gt;               &lt;int&gt; &lt;dbl&gt;
+   1 Luke Skywalker        172    77
+   2 C-3PO                 167    75
+   3 R2-D2                  96    32
+   4 Darth Vader           202   136
+   5 Leia Organa           150    49
+   6 Owen Lars             178   120
+   7 Beru Whitesun Lars    165    75
+   8 R5-D4                  97    32
+   9 Biggs Darklighter     183    84
+  10 Obi-Wan Kenobi        182    77
+  # ℹ 77 more rows</code></pre>
+</div>
+<p>In row-relational terms, “filtering neighboring values” just means “filtering rows after arranging by the values we care about”. We can express this using <code>slice()</code> and <code>outer()</code> as:</p>
+<div class="layout-chunk" data-layout="l-body">
+<div class="sourceCode">
+<pre class="sourceCode r"><code class="sourceCode r"><span><span class='va'>starwars</span> <span class='op'><a href='https://magrittr.tidyverse.org/reference/pipe.html'>%&gt;%</a></span> </span>
+<span>  <span class='fu'><a href='https://dplyr.tidyverse.org/reference/select.html'>select</a></span><span class='op'>(</span><span class='va'>name</span>, <span class='va'>mass</span>, <span class='va'>height</span><span class='op'>)</span> <span class='op'><a href='https://magrittr.tidyverse.org/reference/pipe.html'>%&gt;%</a></span> </span>
+<span>  <span class='fu'><a href='https://dplyr.tidyverse.org/reference/arrange.html'>arrange</a></span><span class='op'>(</span><span class='va'>mass</span>, <span class='va'>height</span><span class='op'>)</span> <span class='op'><a href='https://magrittr.tidyverse.org/reference/pipe.html'>%&gt;%</a></span> </span>
+<span>  <span class='fu'><a href='https://dplyr.tidyverse.org/reference/slice.html'>slice</a></span><span class='op'>(</span> <span class='fu'><a href='https://rdrr.io/r/base/vector.html'>as.vector</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/outer.html'>outer</a></span><span class='op'>(</span><span class='op'>-</span><span class='fl'>2</span><span class='op'>:</span><span class='fl'>2</span>, <span class='fu'><a href='https://rdrr.io/r/base/which.html'>which</a></span><span class='op'>(</span><span class='va'>name</span> <span class='op'>==</span> <span class='st'>"Luke Skywalker"</span><span class='op'>)</span>, <span class='va'>`+`</span><span class='op'>)</span><span class='op'>)</span> <span class='op'>)</span></span></code></pre>
+</div>
+<pre><code>  # A tibble: 5 × 3
+    name            mass height
+    &lt;chr&gt;          &lt;dbl&gt;  &lt;int&gt;
+  1 Palpatine       75      170
+  2 Wedge Antilles  77      170
+  3 Luke Skywalker  77      172
+  4 Obi-Wan Kenobi  77      182
+  5 Boba Fett       78.2    183</code></pre>
+</div>
+<p>I raised this example on an unrelated thread on the <a href="https://fosstodon.org/@DSLC">R4DS/DSLC slack</a>, where Anthony Durrant pointed me to <code>kronecker()</code> as a version of <code>outer()</code> that unlist before returning the output.</p>
+<p>So in examples involving <code>outer()</code> to generate row indices in <code>slice()</code>, we can also use <code>kronecker()</code> instead to save a call to a flattening function like <code>as.vector()</code>:</p>
+<div class="layout-chunk" data-layout="l-body">
+<div class="sourceCode">
+<pre class="sourceCode r"><code class="sourceCode r"><span><span class='va'>starwars</span> <span class='op'><a href='https://magrittr.tidyverse.org/reference/pipe.html'>%&gt;%</a></span> </span>
+<span>  <span class='fu'><a href='https://dplyr.tidyverse.org/reference/select.html'>select</a></span><span class='op'>(</span><span class='va'>name</span>, <span class='va'>mass</span>, <span class='va'>height</span><span class='op'>)</span> <span class='op'><a href='https://magrittr.tidyverse.org/reference/pipe.html'>%&gt;%</a></span> </span>
+<span>  <span class='fu'><a href='https://dplyr.tidyverse.org/reference/arrange.html'>arrange</a></span><span class='op'>(</span><span class='va'>mass</span>, <span class='va'>height</span><span class='op'>)</span> <span class='op'><a href='https://magrittr.tidyverse.org/reference/pipe.html'>%&gt;%</a></span> </span>
+<span>  <span class='fu'><a href='https://dplyr.tidyverse.org/reference/slice.html'>slice</a></span><span class='op'>(</span> <span class='fu'><a href='https://rdrr.io/r/base/kronecker.html'>kronecker</a></span><span class='op'>(</span><span class='op'>-</span><span class='fl'>2</span><span class='op'>:</span><span class='fl'>2</span>, <span class='fu'><a href='https://rdrr.io/r/base/which.html'>which</a></span><span class='op'>(</span><span class='va'>name</span> <span class='op'>==</span> <span class='st'>"Luke Skywalker"</span><span class='op'>)</span>, <span class='va'>`+`</span><span class='op'>)</span> <span class='op'>)</span></span></code></pre>
+</div>
+<pre><code>  # A tibble: 5 × 3
+    name            mass height
+    &lt;chr&gt;          &lt;dbl&gt;  &lt;int&gt;
+  1 Palpatine       75      170
+  2 Wedge Antilles  77      170
+  3 Luke Skywalker  77      172
+  4 Obi-Wan Kenobi  77      182
+  5 Boba Fett       78.2    183</code></pre>
+</div>
 <h3 id="windowed-minmaxmedian-etc.">Windowed min/max/median (etc.)</h3>
 <p>Let’s say we have this small time series data, and we want to calculate a <strong>lagged 3-window moving minimum</strong> for the <code>val</code> column:</p>
 <div class="layout-chunk" data-layout="l-body">
@@ -3446,7 +3529,7 @@ <h3 id="evenly-distributed-row-shuffling-of-unequal-categories">Evenly distribut
 <h2 id="conclusion">Conclusion</h2>
 <p>When I started drafting this blog post, I thought I’d come with a principled taxonomy of row-relational operations. Ha. This was a lot trickier to think through than I thought.</p>
 <p>But I hope that this gallery of esoteric use-cases for <code>slice()</code> inspires you to use it more, and to think about “tidy” solutions to seemingly “untidy” problems.</p>
-<div class="sourceCode" id="cb109"><pre class="sourceCode r distill-force-highlighting-css"><code class="sourceCode r"></code></pre></div>
+<div class="sourceCode" id="cb112"><pre class="sourceCode r distill-force-highlighting-css"><code class="sourceCode r"></code></pre></div>
 <section id="footnotes" class="footnotes footnotes-end-of-document" role="doc-endnotes">
 <hr />
 <ol>
diff --git a/_posts/2023-06-11-row-relational-operations/row-relational-operations_files/figure-html5/final-gapminder-plot-1.png b/_posts/2023-06-11-row-relational-operations/row-relational-operations_files/figure-html5/final-gapminder-plot-1.png
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diff --git a/_posts/2023-06-11-row-relational-operations/row-relational-operations_files/header-attrs-2.27/header-attrs.js b/_posts/2023-06-11-row-relational-operations/row-relational-operations_files/header-attrs-2.27/header-attrs.js
new file mode 100644
index 00000000..dd57d92e
--- /dev/null
+++ b/_posts/2023-06-11-row-relational-operations/row-relational-operations_files/header-attrs-2.27/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
diff --git a/_posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.3.0/panelset.css b/_posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.3.0/panelset.css
new file mode 100644
index 00000000..b1d32552
--- /dev/null
+++ b/_posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.3.0/panelset.css
@@ -0,0 +1,291 @@
+/*
+* Prefixed by https://autoprefixer.github.io
+* PostCSS: v8.4.14,
+* Autoprefixer: v10.4.7
+* Browsers: >0.3%,last 2 versions,not dead
+*/
+
+.panelset {
+  width: 100%;
+  position: relative;
+  --_tabs-separator-color: var(--panel-tabs-separator-color, var(--panel-tabs-border-bottom, #ddd));
+  --_tabs-separator-width: var(--panel-tabs-separator-width, 2px);
+  --_tabs-separator: var(--_tabs-separator-width) solid var(--_tabs-separator-color);
+  --_tabs-sideways-max-width: var(--panel-tabs-sideways-max-width, 25%);
+  --_tabs-spacing: var(--panel-tabs-spacing, 0);
+
+  --_foreground: var(--panel-tab-foreground, currentColor);
+  --_background: var(--panel-tab-background, unset);
+  --_active-foreground: var(--panel-tab-active-foreground, currentColor);
+  --_active-background: var(--panel-tab-active-background, unset);
+  --_hover-foreground: var(--panel-tab-hover-foreground, currentColor);
+  --_hover-background: var(--panel-tab-hover-background, unset);
+
+  --_border-color: var(--panel-tab-border-color, transparent);
+  --_border-top-color: var(--panel-tab-border-top-color, var(--_border-color));
+  --_border-bottom-color: var(--panel-tab-border-bottom-color, var(--_border-color));
+  --_border-width: var(--_tabs-separator-width) 0;
+  --_border-radius: var(--panel-tab-border-radius, 0);
+
+  --_active-border-color: var(--panel-tab-active-border-color, currentColor);
+  --_active-border-top-color: var(--panel-tab-active-border-top-color, var(--_active-border-color));
+  --_active-border-bottom-color: var(--panel-tab-active-border-bottom-color, var(--_active-border-color));
+
+  --_hover-border-top-color: var(--panel-tab-hover-border-top-color, transparent);
+  --_hover-border-bottom-color: var(--panel-tab-hover-border-bottom-color, currentColor);
+
+  --_focus-ring: var(
+    --panel-tab-focus-ring,
+    solid var(--bs-focus-ring-color, var(--_active-border-color)) var(--bs-focus-ring-width, 2px)
+  );
+
+  --_inactive-opacity: var(--panel-tab-inactive-opacity, 0.5);
+  --_font-family: var(--panel-tab-font-family, inherit);
+  --_transition-duration: var(--panel-tab-transition-duration, 0.5s);
+}
+
+.panelset * {
+  box-sizing: border-box;
+}
+
+.panelset .panel-tabs {
+  display: flex;
+  flex-wrap: wrap;
+  flex-direction: row;
+  justify-content: start;
+  align-items: center;
+  overflow: visible;
+  padding: 0;
+  gap: var(--_tabs-spacing);
+  border-bottom: var(--_tabs-separator);
+}
+
+.panelset .panel-tabs * {
+  transition: opacity var(--_transition-duration) ease;
+}
+
+.panelset .panel-tabs .panel-tab {
+  min-height: 50px;
+  display: flex;
+  justify-content: center;
+  align-items: center;
+  padding: 0.5em 1em;
+  font-family: var(--_font-family);
+  opacity: var(--_inactive-opacity);
+  border-width: var(--_border-width);
+  border-style: solid;
+  border-radius: var(--_border-radius);
+  border-top-color: var(--_border-top-color);
+  border-bottom-color: var(--_border-bottom-color);
+  margin-bottom: calc(-1 * var(--_tabs-separator-width));
+  color: var(--_foreground);
+  background-color: var(--_background);
+  list-style: none;
+  z-index: 5;
+}
+
+.panelset .panel-tabs .panel-tab > a {
+  color: currentColor;
+  text-decoration: none;
+  border: none;
+  width: 100%;
+  height: 100%;
+}
+
+.panelset .panel-tabs .panel-tab > a:focus {
+  outline: none;
+  text-decoration: none;
+  border: none;
+}
+
+.panelset .panel-tabs .panel-tab > a:hover {
+  text-decoration: none;
+  border: none;
+}
+
+.panelset .panel-tabs .panel-tab:hover {
+  opacity: 1;
+  cursor: pointer;
+  z-index: 10;
+}
+
+.panelset .panel-tabs .panel-tab:hover {
+  --_border-top-color: var(--_hover-border-top-color);
+  --_border-bottom-color: var(--_hover-border-bottom-color);
+  --_foreground: var(--_hover-foreground);
+  --_background: var(--_hover-background);
+}
+
+.panelset .panel-tabs .panel-tab.panel-tab-active {
+  --_foreground: var(--_active-foreground);
+  --_background: var(--_active-background);
+  --_border-top-color: var(--_active-border-top-color);
+  --_border-bottom-color: var(--_active-border-bottom-color);
+  opacity: 1;
+}
+
+.panelset .panel-tabs .panel-tab:focus {
+  outline: none;
+}
+
+.panelset .panel-tabs .panel-tab:focus > a {
+  outline: var(--_focus-ring);
+  outline-offset: 2px;
+}
+
+.panelset .panel-tabs .panel-tab:focus[tabindex="-1"] > a {
+  outline: none;
+}
+
+.panelset .panel {
+  display: none;
+}
+
+.panelset .panel-active {
+  display: block;
+}
+
+.panelset .panel > :first-child,
+.panelset .panel > section:first-child > :first-child {
+  margin-top: 0;
+}
+
+/* ---- Sideways Panelset ---- */
+
+@media (min-width: 480px) {
+  .panelset[aria-orientation="vertical"] {
+    display: flex;
+    flex-direction: row;
+    margin-bottom: 1rem;
+  }
+
+  .panelset[aria-orientation="vertical"] .panel-tabs {
+    box-shadow: none;
+    flex-direction: column;
+    align-items: stretch;
+    margin: 0;
+    margin-right: 1em;
+    border-right: var(--_tabs-separator);
+    border-bottom: unset;
+    max-width: var(--_tabs-sideways-max-width);
+  }
+
+  .panelset[aria-orientation="vertical"] .panel {
+    max-width: calc(100% - var(--_tabs-sideways-max-width) - 1em);
+  }
+
+  .panelset[aria-orientation="vertical"] .panel-tabs .panel-tab {
+    border-top: unset;
+    border-bottom: unset;
+    padding-left: 0;
+  }
+
+  .panelset[aria-orientation="vertical"]:not(.right) .panel-tabs .panel-tab {
+    text-align: left;
+    border-right: var(--_tabs-separator-width) solid var(--_border-bottom-color);
+    margin-right: calc(-1 * var(--_tabs-separator-width));
+  }
+
+  .panelset[aria-orientation="vertical"].right .panel-tabs .panel-tab {
+    text-align: right;
+    border-left: var(--_tabs-separator-width) solid var(--_border-bottom-color);
+    margin-left: calc(-1 * var(--_tabs-separator-width));
+  }
+
+  .panelset[aria-orientation="vertical"].right {
+    flex-direction: row-reverse;
+    justify-content: space-between;
+  }
+
+  .panelset[aria-orientation="vertical"].right .panel-tabs {
+    margin-right: 0;
+    margin-left: 1em;
+    border-right: unset;
+    border-left: var(--_tabs-separator);
+  }
+
+  .panelset[aria-orientation="vertical"].right .panel-tabs .panel-tab {
+    padding-left: 1em;
+    width: 100%;
+  }
+
+  .panelset[aria-orientation="vertical"].right .panel-tabs .panel-tab a {
+    text-align: right;
+  }
+}
+
+/*
+  This next part repeats the same CSS inside the @media query above but with
+  remarkjs-specific classes to ensure that sideways panelsets are always used.
+  In the future, we could use CSS nesting instead once it's availble.
+*/
+
+.remark-container .panelset[aria-orientation="vertical"] {
+  display: flex;
+  flex-direction: row;
+}
+
+.remark-container .panelset[aria-orientation="vertical"] .panel-tabs {
+  box-shadow: none;
+  flex-direction: column;
+  align-items: stretch;
+  margin: 0;
+  margin-right: 1em;
+  border-right: var(--_tabs-separator);
+  border-bottom: unset;
+  max-width: var(--_tabs-sideways-max-width);
+}
+
+.remark-container .panelset[aria-orientation="vertical"] .panel {
+  max-width: calc(100% - var(--_tabs-sideways-max-width) - 1em);
+}
+
+.remark-container .panelset[aria-orientation="vertical"] .panel-tabs .panel-tab {
+  border-top: unset;
+  border-bottom: unset;
+  padding-left: 0;
+}
+
+.remark-container .panelset[aria-orientation="vertical"]:not(.right) .panel-tabs .panel-tab {
+  text-align: left;
+  border-right: var(--_tabs-separator-width) solid var(--_border-bottom-color);
+  margin-right: calc(-1 * var(--_tabs-separator-width));
+}
+
+.remark-container .panelset[aria-orientation="vertical"].right .panel-tabs .panel-tab {
+  text-align: right;
+  border-left: var(--_tabs-separator-width) solid var(--_border-bottom-color);
+  margin-left: calc(-1 * var(--_tabs-separator-width));
+}
+
+.remark-container .panelset[aria-orientation="vertical"].right {
+  flex-direction: row-reverse;
+  justify-content: space-between;
+}
+
+.remark-container .panelset[aria-orientation="vertical"].right .panel-tabs {
+  margin-right: 0;
+  margin-left: 1em;
+  border-right: unset;
+  border-left: var(--_tabs-separator);
+}
+
+.remark-container .panelset[aria-orientation="vertical"].right .panel-tabs .panel-tab {
+  padding-left: 1em;
+  width: 100%;
+}
+
+.remark-container .panelset[aria-orientation="vertical"].right .panel-tabs .panel-tab a {
+  text-align: right;
+}
+
+/* Other remarkjs (xaringan) specific styles */
+.remark-container .panelset .panel-tabs .panel-tab:focus > a {
+  /* The outline isn't needed, since navigation is always <- or -> */
+  outline: none;
+}
+
+/* Reveal (Quarto) specific styles */
+.reveal .panelset .panel-tabs {
+  margin-left: 0;
+}
diff --git a/_posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.3.0/panelset.js b/_posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.3.0/panelset.js
new file mode 100644
index 00000000..31b8c294
--- /dev/null
+++ b/_posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.3.0/panelset.js
@@ -0,0 +1,826 @@
+/* Panelset
+ * Tab panels for web projects created from markdown with Quarto and R Markdown.
+ *
+ * https://pkg.garrickadenbuie.com/xaringanExtra/#/panelset
+ *
+ * Copyright (c) 2019-2024 Garrick Aden-Buie
+ *
+ * This software is released under the MIT License.
+ * https://opensource.org/licenses/MIT
+ */
+
+/* VERSION: 0.3.0 */
+
+/* global slideshow */
+;(function () {
+  const ready = function (fn) {
+    /* MIT License Copyright (c) 2016 Nuclei */
+    /* https://github.com/nuclei/readyjs */
+    const completed = () => {
+      document.removeEventListener('DOMContentLoaded', completed)
+      window.removeEventListener('load', completed)
+      fn()
+    }
+    if (document.readyState !== 'loading') {
+      setTimeout(fn)
+    } else {
+      document.addEventListener('DOMContentLoaded', completed)
+      window.addEventListener('load', completed)
+    }
+  }
+
+  ready(function () {
+    ;[...document.querySelectorAll('.panel-name')].map(el =>
+      el.textContent.trim()
+    )
+
+    function inRevealjs () {
+      return typeof window.Reveal !== 'undefined'
+    }
+
+    function inRemarkjs () {
+      return typeof window.remark !== 'undefined'
+    }
+
+    function inRemarkSlide (el) {
+      return inRemarkjs() && el.closest('.remark-slide')
+    }
+
+    const panelIds = {}
+    let panelsetIdx = 0
+    const panelsetIds = []
+
+    /**
+     * Generates a unique panelset ID.
+     * @param {string} id - The optional ID to be used as a base for the panelset ID.
+     * @returns {string} - The generated unique panelset ID.
+     */
+    const uniquePanelsetId = id => {
+      const panelsetNumber = () => (++panelsetIdx).toString().padStart(3, '0')
+
+      if (typeof id === 'undefined' || id === '') {
+        id = 'panelset_' + panelsetNumber()
+      } else if (panelsetIds.includes(id)) {
+        id = id + '_' + panelsetNumber()
+      }
+
+      panelsetIds.push(id)
+      return id
+    }
+
+    /**
+     * Generates a unique panel ID based on the provided name, by appending an
+     * increasing integer to the name to make it unique.
+     *
+     * @param {string} name - The name to generate the panel ID from.
+     * @returns {string} The unique panel ID.
+     */
+    const uniquePanelId = name => {
+      name = encodeURIComponent(name.toLowerCase().replace(/[\s]/g, '-'))
+      if (Object.keys(panelIds).includes(name)) {
+        name += ++panelIds[name]
+      } else {
+        panelIds[name] = 1
+      }
+      return name
+    }
+
+    /**
+     * Identifies the panel name based on the given item, taking into account
+     * the various ways that panel names can be specified in R Markdown, Quarto,
+     * or revealjs.
+     *
+     * @param {HTMLElement} item - The item to identify the panel name from.
+     * @returns {string} The identified panel name or undefined if no name can
+     * be identified.
+     */
+    const identifyPanelName = item => {
+      let name = 'Panel'
+
+      // If the item doesn't have a parent element, then we've already processed
+      // it, probably because we're in an Rmd, and it's been removed from the DOM
+      if (!item.parentElement) {
+        return
+      }
+
+      if (item.matches('.panel')) {
+        if (item.dataset.name) return item.dataset.name
+        if (item.getAttribute('name')) return item.getAttribute('name')
+      }
+
+      // In R Markdown when header-attrs.js is present, we may have found a
+      // section header but the class attributes won't be duplicated on the <hX> tag
+      if (
+        (item.tagName === 'SECTION' || item.classList.contains('section')) &&
+        /^H[1-6]/.test(item.children[0].tagName)
+      ) {
+        name = item.children[0].textContent
+        item.classList.remove('panel-name')
+        item.removeChild(item.children[0])
+        return name
+      }
+
+      const nameDiv = item.querySelector('.panel-name')
+      if (!nameDiv) return name
+
+      // In remarkjs the .panel-name span might be in a paragraph tag
+      // and if the <p> is empty, we'll remove it
+      if (
+        nameDiv.tagName === 'SPAN' &&
+        nameDiv.parentNode.tagName === 'P' &&
+        nameDiv.textContent === nameDiv.parentNode.textContent
+      ) {
+        name = nameDiv.textContent
+        item.removeChild(nameDiv.parentNode)
+        return name
+      }
+
+      // If none of the above, remove the nameDiv and return the name
+      name = nameDiv.textContent
+      nameDiv.parentNode.removeChild(nameDiv)
+      return name
+    }
+
+    function getElementAttributes (el) {
+      return {
+        classes: Array.from(el.classList)
+          .filter(c => !/^level\d$/.test(c))
+          .toString(),
+        style: el.style.cssText,
+        dataset: el.dataset
+      }
+    }
+
+    /**
+     * Processes an original section of content and prepare data for the content
+     * panel the item will become.
+     *
+     * @param {HTMLElement} item - The panel item to process.
+     * @returns {Object|null} - An object containing the panel's name, content,
+     * id, active status, and other attributes. Returns null if the panel name
+     * cannot be identified.
+     */
+    const processPanelItem = item => {
+      const name = identifyPanelName(item)
+      if (!name) {
+        return null
+      }
+      return {
+        name,
+        content: item.children,
+        id: uniquePanelId(name),
+        active:
+          item.dataset &&
+          ['', 'true'].includes(item.dataset.active?.toLowerCase()),
+        ...getElementAttributes(item)
+      }
+    }
+
+    /**
+     * Retrieves the current panel from the URL parameters.
+     * @param {string} panelsetId - The ID of the panelset.
+     * @returns {string|null} - The current panel ID or null if not in the URL.
+     */
+    const getCurrentPanelFromUrl = panelsetId => {
+      const params = new URLSearchParams(window.location.search)
+      return params.get(panelsetId)
+    }
+
+    /**
+     * Returns the initial selected panel ID based on the provided panels and
+     * the ID of the corresponding panelset. The active panel is chosen
+     * following:
+     *
+     * 1. If the panselset appears in the URL, use the panel ID from the URL.
+     * 2. If there is an active panel, use the ID of the first active panel.
+     * 3. Use the ID of the first panel in the array.
+     *
+     * Note that groups are not considered here. If the panelset is part of a
+     * group, the group state will be updated after the initial panelset is
+     * created.
+     *
+     * @param {Array} panels - The array of panel objects.
+     * @param {string} panelsetId - The ID of the panelset specified in the URL.
+     * @returns {string} - The ID of the initial selected panel.
+     */
+    function getInitSelectedPanel (panels, panelsetId) {
+      const panelIds = panels.map(p => p.id)
+
+      const panelSelectedUrl = getCurrentPanelFromUrl(panelsetId)
+      if (panelSelectedUrl && panelIds.includes(panelSelectedUrl)) {
+        return panelSelectedUrl
+      }
+
+      const panelsActive = panels.filter(p => p.active)
+      if (panelsActive.length) {
+        return panelsActive[0].id
+      }
+
+      return panels[0].id
+    }
+
+    /**
+     * Creates a panel set element with header tabs and corresponding content
+     * sections.
+     *
+     * @param {Array} panels - An array of panel objects.
+     * @param {Object} options - An object containing optional parameters for
+     * the panel set.
+     * @param {string} options.id - The ID of the panel set element.
+     * @param {string} options.classes - Additional CSS classes to be applied to
+     * the panel set element.
+     * @param {string} options.style - Inline CSS styles to be applied to the
+     * panel set element.
+     * @param {Object} options.dataset - Custom data attributes to be added to
+     * the panel set element.
+     * @returns {HTMLElement} - The created panel set element.
+     */
+    const reflowPanelSet = (panels, { id, classes, style, dataset }) => {
+      const res = document.createElement('div')
+      res.classList = 'panelset' + (classes ? ' ' + classes : '')
+      res.id = uniquePanelsetId(id)
+      res.style.cssText = style
+      if (dataset) {
+        Object.keys(dataset).forEach(key => {
+          res.dataset[key] = dataset[key]
+        })
+      }
+
+      const panelSelected = getInitSelectedPanel(panels, res.id)
+
+      // create header row
+      const headerRow = document.createElement('ul')
+      headerRow.className = 'panel-tabs'
+      headerRow.setAttribute('role', 'tablist')
+      panels
+        .map((p, idx) => {
+          const thisPanelIsActive = panelSelected === p.id
+
+          const panelHeaderItem = document.createElement('li')
+          panelHeaderItem.id = res.id + '_' + p.id // #panelsetid_panelid
+          panelHeaderItem.className = 'panel-tab'
+          panelHeaderItem.setAttribute('role', 'tab')
+          if (thisPanelIsActive) {
+            panelHeaderItem.tabIndex = 0
+          }
+          panelHeaderItem.classList.toggle(
+            'panel-tab-active',
+            thisPanelIsActive
+          )
+          panelHeaderItem.setAttribute('aria-selected', thisPanelIsActive)
+
+          if (p.dataset) {
+            Object.keys(p.dataset).forEach(key => {
+              panelHeaderItem.dataset[key] = p.dataset[key]
+            })
+          }
+
+          const panelHeaderLink = document.createElement('a')
+          panelHeaderLink.href =
+            '?' + res.id + '=' + p.id + '#' + panelHeaderItem.id
+          panelHeaderLink.setAttribute('onclick', 'return false;')
+          panelHeaderLink.tabIndex = -1 // list item is tabable, not link
+          panelHeaderLink.innerHTML = p.name
+          panelHeaderLink.setAttribute('aria-controls', p.id)
+
+          panelHeaderItem.appendChild(panelHeaderLink)
+          return panelHeaderItem
+        })
+        .forEach(el => headerRow.appendChild(el))
+
+      res.appendChild(headerRow)
+
+      panels
+        .map((p, idx) => {
+          const thisPanelIsActive = panelSelected === p.id
+          const panelTag = inRevealjs() ? 'div' : 'section'
+          const panelContent = document.createElement(panelTag)
+          panelContent.classList = p.classes ? 'panel ' + p.classes : 'panel'
+          panelContent.style.cssText = p.style
+          panelContent.classList.toggle('panel-active', thisPanelIsActive)
+          panelContent.id = p.id
+          // https://www.w3.org/WAI/ARIA/apg/patterns/tabs/examples/tabs-automatic/
+          panelContent.setAttribute('role', 'tabpanel')
+          panelContent.setAttribute('aria-labelledby', p.id)
+          panelContent.tabIndex = 0
+          Array.from(p.content).forEach(el => panelContent.appendChild(el))
+          return panelContent
+        })
+        .forEach(el => res.appendChild(el))
+
+      return res
+    }
+
+    /*
+     * Update selected panel for panelset or delete panelset from query string
+     *
+     * @param panelset Panelset ID to update in the search params @param panel
+     * Panel ID of selected panel in panelset, or null to delete from search
+     * params @param params Current params object, or params from
+     * window.location.search
+     */
+
+    /**
+     * Updates the search parameters with the specified panelset and panel
+     * values. If a panel is provided, it sets the panelset and panel in the
+     * search parameters. If no panel is provided, it removes the panelset from
+     * the search parameters.
+     *
+     * @param {string} panelsetId - The ID of the panelset.
+     * @param {string} [panelId] - The ID of the panel (optional).
+     * @param {URLSearchParams} [params=new
+     * URLSearchParams(window.location.search)] - The search parameters object
+     * (optional).
+     * @returns {URLSearchParams} - The updated search parameters object.
+     */
+    function updateSearchParams (
+      panelsetId,
+      panelId,
+      params = new URLSearchParams(window.location.search)
+    ) {
+      if (panelId) {
+        params.set(panelsetId, panelId)
+      } else {
+        params.delete(panelsetId)
+      }
+      return params
+    }
+
+    /*
+     * Update the URL to match params
+     */
+    const updateUrl = params => {
+      if (typeof params === 'undefined') return
+      params = params.toString() ? '?' + params.toString() : ''
+      const { pathname, hash } = window.location
+      const uri = pathname + params + hash
+      window.history.replaceState(uri, '', uri)
+    }
+
+    /**
+     * Handles the click event on a panel tab within a panelset.
+     * @param {HTMLElement} clicked - The clicked element.
+     */
+    function handleClickedPanel (clicked) {
+      const panelset = clicked.closest('.panelset')
+      if (!panelset) return
+
+      clicked = clicked.closest('.panel-tab')
+      if (!clicked) return
+
+      togglePanel(panelset, clicked)
+    }
+
+    /**
+     * Handles keydown events for the `.panel-tabs` element within a panelset.
+     * This performs two actions: toggling the panel via space or enter and
+     * moving to the next or previous panel via arrow keys, depending on the
+     * panelset orientation.
+     *
+     * @see https://www.w3.org/WAI/ARIA/apg/patterns/tabs/examples/tabs-automatic/
+     *
+     * @param {HTMLElement} panelset - The panelset element.
+     * @param {KeyboardEvent} ev - The keydown event.
+     */
+    function handlePanelTabsKeydown (panelset, ev) {
+      const target = ev.currentTarget.querySelector('.panel-tab-active')
+
+      function stopEvent () {
+        ev.preventDefault()
+        if (inRemarkjs() || inRevealjs()) {
+          ev.stopPropagation()
+        }
+      }
+
+      if (ev.code === 'Space' || ev.code === 'Enter') {
+        togglePanel(panelset, ev.target)
+        stopEvent()
+        return
+      }
+
+      let direction
+
+      if (panelset.getAttribute('aria-orientation') === 'vertical') {
+        if (ev.code === 'ArrowUp') direction = 'prev'
+        if (ev.code === 'ArrowDown') direction = 'next'
+      }
+
+      if (
+        inRemarkSlide(panelset) ||
+        inRevealjs() ||
+        panelset.getAttribute('aria-orientation') === 'horizontal'
+      ) {
+        if (ev.code === 'ArrowLeft') direction = 'prev'
+        if (ev.code === 'ArrowRight') direction = 'next'
+      }
+
+      if (!direction) return
+
+      const newActive = toggleSibling(panelset, target, direction)
+      if (newActive) stopEvent()
+      return newActive
+    }
+
+    /**
+     * Finds a panel by name within a panelset. `name` is compared with the
+     * panel tab text content, case-insensitive and trimmed.
+     *
+     * @param {HTMLElement} panelset - The panelset element.
+     * @param {string} name - The name of the panel tab to find.
+     * @returns {HTMLElement|undefined} - The matching panel element, or
+     * undefined if not found.
+     */
+    function findPanelByName (panelset, name) {
+      const matches = Array.from(
+        panelset.querySelectorAll(':scope > .panel-tabs > .panel-tab')
+      ).filter(p => p.innerText.toLowerCase().trim() === name)
+
+      if (!matches) {
+        console.error(
+          `No panel with name "${name}" found in panelset ${panelset.id}`,
+          { panelset, name }
+        )
+        return
+      }
+
+      if (matches > 1) {
+        console.warn(
+          `Multiple panels with name "${name}" found in panelset ${panelset.id}`,
+          { panelset, name }
+        )
+      }
+      return matches[0]
+    }
+
+    /**
+     * Toggles the visibility of a panel in a panelset.
+     *
+     * @param {HTMLElement} panelset - The panelset element containing the
+     * panels.
+     * @param {HTMLElement|string} target - The target panel or panel name to
+     * toggle.
+     * @param {'string'} [update='all'] - The update mode for the
+     * panelset. Possible values are 'all', 'group', or 'url'.
+     */
+    function togglePanel (panelset, target, update = 'all', tabIndex = 0) {
+      // target is a .panel-tab element or a panel name
+      if (!(target instanceof window.HTMLElement)) {
+        target = findPanelByName(panelset, target)
+        if (!target) return
+      }
+
+      const tabs = panelset.querySelectorAll(
+        ':scope > .panel-tabs > .panel-tab'
+      )
+      const panels = panelset.querySelectorAll(':scope > .panel')
+
+      const targetPanelId = target.children[0].getAttribute('aria-controls')
+
+      // Set tab state
+      Array.from(tabs).forEach(t => {
+        t.classList.remove('panel-tab-active')
+        t.setAttribute('aria-selected', false)
+        t.removeAttribute('tabindex')
+      })
+
+      target.classList.add('panel-tab-active')
+      target.setAttribute('aria-selected', true)
+      target.tabIndex = tabIndex
+
+      Array.from(panels).forEach(p => {
+        const isActive = p.id === targetPanelId
+        p.classList.toggle('panel-active', isActive)
+        p.hidden = !isActive
+      })
+
+      // emit window resize event to trick html widgets into fitting to the panel width
+      window.dispatchEvent(new window.Event('resize'))
+
+      if (['all', 'group'].includes(update) && panelset.dataset.group) {
+        const group = panelset.dataset.group
+        const panel = target.innerText.toLowerCase().trim()
+
+        setStoredPanelGroupState(group, panel)
+
+        panelset.dispatchEvent(
+          new window.CustomEvent('panelset:group', {
+            bubbles: true,
+            detail: { group, panel }
+          })
+        )
+      }
+
+      // update query string
+      if (['all', 'url'].includes(update)) {
+        const params = updateSearchParams(panelset.id, targetPanelId)
+        updateUrl(params)
+      }
+    }
+
+    /**
+     * Toggles the sibling panel in the specified direction.
+     *
+     * @param {HTMLElement} panelset - The panelset element.
+     * @param {HTMLElement} target - The target panel element.
+     * @param {"next" | "prev"} [direction="next"] - The direction to toggle the
+     * sibling panel. Possible values are "next" and "prev".
+     */
+    function toggleSibling (panelset, target, direction = 'next') {
+      let sibling
+      switch (direction) {
+        case 'next':
+          sibling = target.nextSibling
+          break
+        case 'prev':
+          sibling = target.previousSibling
+          break
+      }
+
+      if (!sibling) return
+      const update = parseInt(target.tabIndex) < 0 ? 'url' : 'all'
+      togglePanel(panelset, sibling, update, target.tabIndex)
+      sibling.focus()
+      return sibling
+    }
+
+    /**
+     * Initializes a panel set from the original markup into a full panelset.
+     * This includes creating the panel tabs, rearranging content, adding event
+     * listeners, and synchronizing with a panel set group.
+     *
+     * @param {HTMLElement} panelset - The `.panelset` element to initialize.
+     * @returns {HTMLElement} - The new panelset element.
+     */
+    const initPanelSet = panelset => {
+      let panels = Array.from(panelset.querySelectorAll(':scope > .panel, :scope > .cell > .panel'))
+
+      const pandocSectionSelector = ':is(section, .section)[class*="level"]'
+      if (!panels.length) {
+        // we're in tabset-alike R Markdown or Quarto
+        const getSectionLevel = el => {
+          const levels = [...el.classList].filter(s => s.match(/^level/))
+          return levels.length ? levels[0].replace('level', '') : levels
+        }
+
+        // {.panelset} applied to a section heading
+        let panelsetLevel = getSectionLevel(panelset)
+
+        if (!panelsetLevel.length) {
+          // {.panelset} applied as a fenced div around subsections
+          const subSections = panelset.querySelectorAll(pandocSectionSelector)
+          if (!subSections.length) return
+
+          panelsetLevel = Array.from(subSections)
+            .map(getSectionLevel)
+            .map(x => parseInt(x))
+            .reduce((acc, x) => Math.min(acc, x), Infinity)
+
+          panelsetLevel = +panelsetLevel - 1
+        }
+
+        // move children that aren't inside a section up above the panelset
+        Array.from(panelset.children).forEach(function (el) {
+          if (el.matches(pandocSectionSelector)) return
+          panelset.parentElement.insertBefore(el, panelset)
+        })
+
+        // panels are all .sections with .level<panelsetLevel + 1>
+        const panelLevel = +panelsetLevel + 1
+        panels = Array.from(
+          panelset.querySelectorAll(`:is(section, .section).level${panelLevel}`)
+        )
+      }
+
+      if (!panels.length) return
+
+      // create content panels
+      const contents = panels.map(processPanelItem).filter(o => o !== null)
+
+      // create panelset
+      const panelsetAttrs = getElementAttributes(panelset)
+      const newPanelSet = reflowPanelSet(contents, {
+        id: panelset.id,
+        ...panelsetAttrs
+      })
+      newPanelSet.classList = panelset.classList
+
+      // set orientation
+      const isVertical = panelset.matches(
+        '.sideways, .vertical, [aria-orientation="vertical"]'
+      )
+      newPanelSet.setAttribute(
+        'aria-orientation',
+        isVertical ? 'vertical' : 'horizontal'
+      )
+
+      panelset.parentNode.insertBefore(newPanelSet, panelset)
+      panelset.parentNode.removeChild(panelset)
+
+      // click and touch events
+      const panelTabs = newPanelSet.querySelector('.panel-tabs')
+      ;['click', 'touchend'].forEach(eventType => {
+        panelTabs.addEventListener(eventType, function (ev) {
+          handleClickedPanel(ev.target)
+          ev.stopPropagation()
+        })
+      })
+      panelTabs.addEventListener('touchmove', function (ev) {
+        ev.preventDefault()
+      })
+
+      // key events
+      newPanelSet
+        .querySelector('.panel-tabs')
+        .addEventListener('keydown', ev => {
+          handlePanelTabsKeydown(newPanelSet, ev)
+        })
+
+      // synchronize with the panelset group
+      if (newPanelSet.dataset.group) {
+        window.addEventListener('panelset:group', ev => {
+          if (ev.target === newPanelSet) return
+          if (ev.detail.group !== newPanelSet.dataset.group) return
+          togglePanel(newPanelSet, ev.detail.panel, 'url')
+        })
+
+        const groupData = getStoredPanelSettings()
+        const currentPanelFromUrl = getCurrentPanelFromUrl(newPanelSet.id)
+
+        if (!currentPanelFromUrl && groupData[newPanelSet.dataset.group]) {
+          togglePanel(newPanelSet, groupData[newPanelSet.dataset.group], null)
+        }
+      }
+
+      return newPanelSet
+    }
+
+    const localStorageKey = 'panelset-data'
+
+    /**
+     * Retrieves or creates the stored panel settings from local storage.
+     * @returns {{['string']: 'string'} | {}} The stored panel settings, as an
+     * empty object or an object with group names as keys and the currently
+     * activated panel names as values.
+     */
+    function getStoredPanelSettings () {
+      const data = window.localStorage.getItem(localStorageKey)
+      if (!data) {
+        window.localStorage.setItem(localStorageKey, '{}')
+        return {}
+      }
+      if (data) {
+        return JSON.parse(data)
+      }
+    }
+
+    function setStoredPanelSettings (data) {
+      window.localStorage.setItem(localStorageKey, JSON.stringify(data))
+    }
+
+    /**
+     * Sets the stored panel group state in local storage. The group `name` is
+     * used as a key and is globally checked across pages in the same domain.
+     *
+     * @param {string} name - The name of the panel group.
+     * @param {any} value - The value to set for the panel group.
+     */
+    function setStoredPanelGroupState (name, value) {
+      const data = getStoredPanelSettings()
+      data[name] = value
+      setStoredPanelSettings(data)
+    }
+
+    // initialize panels
+    document
+      .querySelectorAll('[data-panelset="true"]')
+      .forEach(el => {
+        const isCell = el.classList.contains('cell')
+        const hasParentPanelset = el.parentElement.classList.contains('panelset')
+        if (!isCell || !hasParentPanelset) {
+          // We let `data-panelset="true"` create a new panelset, unless it's on
+          // a code cell that's already inside a panelset, in which case the
+          // panels will be folded into the parent panelset.
+          el.classList.add('panelset')
+        }
+      })
+
+    const panelsets = { atomic: [], nested: [] }
+    Array.from(document.querySelectorAll('.panelset')).forEach(el => {
+      if (el.querySelector('.panelset')) {
+        // push nested panelsets to the start of the list (inner -> outer)
+        panelsets.nested.unshift(el)
+      } else {
+        // put panelsets without nested panelsets at the beginning
+        panelsets.atomic.push(el)
+      }
+    })
+
+    // initialize atomic panelsets first, then nested panelsets
+    panelsets.atomic.forEach(initPanelSet)
+    panelsets.nested.forEach(initPanelSet)
+
+    if (inRemarkjs()) {
+      const getVisibleActivePanelInfo = () => {
+        const slidePanels = document.querySelectorAll(
+          '.remark-visible .panel-tab-active'
+        )
+
+        if (!slidePanels.length) return null
+
+        return slidePanels.map(panel => {
+          return {
+            panel,
+            panelId: panel.children[0].getAttribute('aria-controls'),
+            panelSetId: panel.parentNode.parentNode.id
+          }
+        })
+      }
+
+      slideshow.on('hideSlide', slide => {
+        // clear focus if we had a panel-tab selected
+        document.activeElement.blur()
+
+        // clear search query for panelsets in current slide
+        const params = [
+          ...document.querySelectorAll('.remark-visible .panelset')
+        ].reduce(function (params, panelset) {
+          return updateSearchParams(panelset.id, null, params)
+        }, new URLSearchParams(window.location.search))
+
+        updateUrl(params)
+      })
+
+      slideshow.on('afterShowSlide', slide => {
+        const slidePanels = getVisibleActivePanelInfo()
+
+        if (slidePanels) {
+          // only first panel gets focus
+          slidePanels[0].panel.focus()
+          // but still update the url to reflect all active panels
+          const params = slidePanels.reduce(function (
+            params,
+            { panelId, panelSetId }
+          ) {
+            return updateSearchParams(panelSetId, panelId, params)
+          },
+          new URLSearchParams(window.location.search))
+          updateUrl(params)
+        }
+      })
+    }
+
+    if (inRevealjs()) {
+      window.Reveal.on('slidechanged', function ({ currentSlide, previousSlide, ...data }) {
+        // clear focus from any active panel-tab in the previous slide
+        const previousActive = previousSlide.querySelector('.panelset .panel-tab:focus')
+        if (previousActive) {
+          previousActive.blur()
+          previousActive.removeAttribute('tabindex')
+        }
+
+        const previousPanelsets = previousSlide.querySelectorAll('.panelset')
+        if (previousPanelsets.length) {
+          // clear search query for panelsets in previous slide
+          const params = [
+            ...previousSlide.querySelectorAll('.panelset')
+          ].reduce(function (params, panelset) {
+            return updateSearchParams(panelset.id, null, params)
+          }, new URLSearchParams(window.location.search))
+
+          updateUrl(params)
+        }
+
+        const firstPanelset = currentSlide.querySelector('.panelset')
+        if (!firstPanelset) return
+
+        const panelIdFromUrl = getCurrentPanelFromUrl(firstPanelset.id)
+        const panelFromUrl = !panelIdFromUrl
+          ? null
+          : firstPanelset
+            .querySelector(`[aria-controls="${panelIdFromUrl}"]`)
+            ?.parentElement
+
+        const firstPanel = panelIdFromUrl
+          ? panelFromUrl
+          : firstPanelset.querySelector('.panel-tab-active')
+
+        if (!firstPanel) return
+        firstPanel.setAttribute('tabindex', '-1')
+        firstPanel.focus()
+
+        // update url for all panels on this slide
+        const params = [
+          ...currentSlide.querySelectorAll('.panelset')
+        ].reduce(function (params, panelset) {
+          return updateSearchParams(
+            panelset.id,
+            panelset.querySelector('.panel-active').id,
+            params
+          )
+        }, new URLSearchParams(window.location.search))
+
+        updateUrl(params)
+      })
+    }
+  })
+})()
diff --git a/docs/blog.html b/docs/blog.html
index 3daf1b4e..bce2ce71 100644
--- a/docs/blog.html
+++ b/docs/blog.html
@@ -1,3612 +1,3612 @@
-<!DOCTYPE html>
-
-<html xmlns="http://www.w3.org/1999/xhtml" lang="" xml:lang="">
-
-<head>
-  <meta charset="utf-8"/>
-  <meta name="viewport" content="width=device-width, initial-scale=1"/>
-  <meta http-equiv="X-UA-Compatible" content="IE=Edge,chrome=1"/>
-  <meta name="generator" content="distill" />
-  <link rel="alternate" type="application/rss+xml" href="https://yjunechoe.github.io/blog.xml" />
-
-  <style type="text/css">
-  /* Hide doc at startup (prevent jankiness while JS renders/transforms) */
-  body {
-    visibility: hidden;
-  }
-  </style>
-
- <!--radix_placeholder_import_source-->
- <!--/radix_placeholder_import_source-->
-
-<style type="text/css">code{white-space: pre;}</style>
-<style type="text/css" data-origin="pandoc">
-pre > code.sourceCode { white-space: pre; position: relative; }
-pre > code.sourceCode > span { line-height: 1.25; }
-pre > code.sourceCode > span:empty { height: 1.2em; }
-.sourceCode { overflow: visible; }
-code.sourceCode > span { color: inherit; text-decoration: inherit; }
-div.sourceCode { margin: 1em 0; }
-pre.sourceCode { margin: 0; }
-@media screen {
-div.sourceCode { overflow: auto; }
-}
-@media print {
-pre > code.sourceCode { white-space: pre-wrap; }
-pre > code.sourceCode > span { display: inline-block; text-indent: -5em; padding-left: 5em; }
-}
-pre.numberSource code
-  { counter-reset: source-line 0; }
-pre.numberSource code > span
-  { position: relative; left: -4em; counter-increment: source-line; }
-pre.numberSource code > span > a:first-child::before
-  { content: counter(source-line);
-    position: relative; left: -1em; text-align: right; vertical-align: baseline;
-    border: none; display: inline-block;
-    -webkit-touch-callout: none; -webkit-user-select: none;
-    -khtml-user-select: none; -moz-user-select: none;
-    -ms-user-select: none; user-select: none;
-    padding: 0 4px; width: 4em;
-    color: #aaaaaa;
-  }
-pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa;  padding-left: 4px; }
-div.sourceCode
-  {  background-color: #f8f8f8; }
-@media screen {
-pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
-}
-code span.al { color: #ef2929; } /* Alert */
-code span.an { color: #8f5902; font-weight: bold; font-style: italic; } /* Annotation */
-code span.at { color: #204a87; } /* Attribute */
-code span.bn { color: #0000cf; } /* BaseN */
-code span.cf { color: #204a87; font-weight: bold; } /* ControlFlow */
-code span.ch { color: #4e9a06; } /* Char */
-code span.cn { color: #8f5902; } /* Constant */
-code span.co { color: #8f5902; font-style: italic; } /* Comment */
-code span.cv { color: #8f5902; font-weight: bold; font-style: italic; } /* CommentVar */
-code span.do { color: #8f5902; font-weight: bold; font-style: italic; } /* Documentation */
-code span.dt { color: #204a87; } /* DataType */
-code span.dv { color: #0000cf; } /* DecVal */
-code span.er { color: #a40000; font-weight: bold; } /* Error */
-code span.ex { } /* Extension */
-code span.fl { color: #0000cf; } /* Float */
-code span.fu { color: #204a87; font-weight: bold; } /* Function */
-code span.im { } /* Import */
-code span.in { color: #8f5902; font-weight: bold; font-style: italic; } /* Information */
-code span.kw { color: #204a87; font-weight: bold; } /* Keyword */
-code span.op { color: #ce5c00; font-weight: bold; } /* Operator */
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-
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-  <meta property="og:title" content="June Choe: Blog Posts"/>
-  <meta property="og:type" content="article"/>
-  <meta property="og:locale" content="en_US"/>
-  <meta property="og:site_name" content="June Choe"/>
-
-  <!--  https://dev.twitter.com/cards/types/summary -->
-  <meta property="twitter:card" content="summary"/>
-  <meta property="twitter:title" content="June Choe: Blog Posts"/>
-  <meta property="twitter:site" content="@yjunechoe"/>
-
-  <!--/radix_placeholder_meta_tags-->
-  <!--radix_placeholder_rmarkdown_metadata-->
-
-  <script type="text/json" id="radix-rmarkdown-metadata">
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-  <!--/radix_placeholder_rmarkdown_metadata-->
-  <!--radix_placeholder_navigation_in_header-->
-  <meta name="distill:offset" content=""/>
-
-  <script type="application/javascript">
-
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-
-    window.document.addEventListener("DOMContentLoaded", function (event) {
-
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-      var header = $('header').get(0);
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-  .distill-site-nav a {
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-    text-decoration: none;
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-  .distill-site-nav a:hover {
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-    .distill-site-nav {
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-  }
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-  .distill-site-header {
-
-  }
-
-  .distill-site-footer {
-
-  }
-
-
-  /* Site Header */
-
-  .distill-site-header {
-    width: 100%;
-    box-sizing: border-box;
-    z-index: 3;
-  }
-
-  .distill-site-header .nav-left {
-    display: inline-block;
-    margin-left: 8px;
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-  .distill-site-header .nav-right {
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-    margin-right: 8px;
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-  .distill-site-header a,
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-    text-align: center;
-    padding: 14px 10px 14px 10px;
-  }
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-  .distill-site-header .title {
-    font-size: 18px;
-    min-width: 150px;
-  }
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-  .distill-site-header .logo {
-    padding: 0;
-  }
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-  .distill-site-header .logo img {
-    display: none;
-    max-height: 20px;
-    width: auto;
-    margin-bottom: -4px;
-  }
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-  .distill-site-header .nav-image img {
-    max-height: 18px;
-    width: auto;
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-    margin-bottom: -3px;
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-    .distill-site-header .logo img {
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-      margin-left: 20px;
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-    .distill-site-header .nav-right {
-      margin-right: 20px;
-    }
-    .distill-site-header .title {
-      padding-left: 12px;
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-
-
-  .distill-site-header .nav-toggle {
-    display: none;
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-
-  .nav-dropdown {
-    display: inline-block;
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-  .nav-dropdown .nav-dropbtn {
-    border: none;
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-    color: rgba(255, 255, 255, 0.8);
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-    font-family: inherit;
-    font-size: inherit;
-    font-weight: inherit;
-    margin: 0;
-    margin-top: 1px;
-    z-index: 2;
-  }
-
-  .nav-dropdown-content {
-    display: none;
-    position: absolute;
-    background-color: white;
-    min-width: 200px;
-    border: 1px solid rgba(0,0,0,0.15);
-    border-radius: 4px;
-    box-shadow: 0px 8px 16px 0px rgba(0,0,0,0.1);
-    z-index: 1;
-    margin-top: 2px;
-    white-space: nowrap;
-    padding-top: 4px;
-    padding-bottom: 4px;
-  }
-
-  .nav-dropdown-content hr {
-    margin-top: 4px;
-    margin-bottom: 4px;
-    border: none;
-    border-bottom: 1px solid rgba(0, 0, 0, 0.1);
-  }
-
-  .nav-dropdown-active {
-    display: block;
-  }
-
-  .nav-dropdown-content a, .nav-dropdown-content .nav-dropdown-header {
-    color: black;
-    padding: 6px 24px;
-    text-decoration: none;
-    display: block;
-    text-align: left;
-  }
-
-  .nav-dropdown-content .nav-dropdown-header {
-    display: block;
-    padding: 5px 24px;
-    padding-bottom: 0;
-    text-transform: uppercase;
-    font-size: 14px;
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-    color: white;
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-    background-color: #ddd;
-    color: black;
-  }
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-  .nav-right .nav-dropdown-content {
-    margin-left: -45%;
-    right: 0;
-  }
-
-  @media screen and (max-width: 768px) {
-    .distill-site-header a, .distill-site-header .nav-dropdown  {display: none;}
-    .distill-site-header a.nav-toggle {
-      float: right;
-      display: block;
-    }
-    .distill-site-header .title {
-      margin-left: 0;
-    }
-    .distill-site-header .nav-right {
-      margin-right: 0;
-    }
-    .distill-site-header {
-      overflow: hidden;
-    }
-    .nav-right .nav-dropdown-content {
-      margin-left: 0;
-    }
-  }
-
-
-  @media screen and (max-width: 768px) {
-    .distill-site-header.responsive {position: relative; min-height: 500px; }
-    .distill-site-header.responsive a.nav-toggle {
-      position: absolute;
-      right: 0;
-      top: 0;
-    }
-    .distill-site-header.responsive a,
-    .distill-site-header.responsive .nav-dropdown {
-      display: block;
-      text-align: left;
-    }
-    .distill-site-header.responsive .nav-left,
-    .distill-site-header.responsive .nav-right {
-      width: 100%;
-    }
-    .distill-site-header.responsive .nav-dropdown {float: none;}
-    .distill-site-header.responsive .nav-dropdown-content {position: relative;}
-    .distill-site-header.responsive .nav-dropdown .nav-dropbtn {
-      display: block;
-      width: 100%;
-      text-align: left;
-    }
-  }
-
-  /* Site Footer */
-
-  .distill-site-footer {
-    width: 100%;
-    overflow: hidden;
-    box-sizing: border-box;
-    z-index: 3;
-    margin-top: 30px;
-    padding-top: 30px;
-    padding-bottom: 30px;
-    text-align: center;
-  }
-
-  /* Headroom */
-
-  d-title {
-    padding-top: 6rem;
-  }
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-    d-title {
-      padding-top: 4rem;
-    }
-  }
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-    position: fixed;
-    top: 0;
-    left: 0;
-    right: 0;
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-    transition: all .4s ease-in-out;
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-    top: -100px;
-  }
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-    top: 0;
-  }
-
-  /* adjust viewport for navbar height */
-  /* helps vertically center bootstrap (non-distill) content */
-  .min-vh-100 {
-    min-height: calc(100vh - 100px) !important;
-  }
-
-  </style>
-
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-  <link href="site_libs/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"/>
-  <link href="site_libs/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"/>
-  <script src="site_libs/headroom-0.9.4/headroom.min.js"></script>
-  <script src="site_libs/autocomplete-0.37.1/autocomplete.min.js"></script>
-  <script src="site_libs/fuse-6.4.1/fuse.min.js"></script>
-
-  <script type="application/javascript">
-
-  function getMeta(metaName) {
-    var metas = document.getElementsByTagName('meta');
-    for (let i = 0; i < metas.length; i++) {
-      if (metas[i].getAttribute('name') === metaName) {
-        return metas[i].getAttribute('content');
-      }
-    }
-    return '';
-  }
-
-  function offsetURL(url) {
-    var offset = getMeta('distill:offset');
-    return offset ? offset + '/' + url : url;
-  }
-
-  function createFuseIndex() {
-
-    // create fuse index
-    var options = {
-      keys: [
-        { name: 'title', weight: 20 },
-        { name: 'categories', weight: 15 },
-        { name: 'description', weight: 10 },
-        { name: 'contents', weight: 5 },
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-      ignoreLocation: true,
-      threshold: 0
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-    var fuse = new window.Fuse([], options);
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-          return Promise.reject(
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-                        response.status)
-          );
-        }
-      });
-  }
-
-  window.document.addEventListener("DOMContentLoaded", function (event) {
-
-    // get search element (bail if we don't have one)
-    var searchEl = window.document.getElementById('distill-search');
-    if (!searchEl)
-      return;
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-      .then(function(fuse) {
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-              return html;
-            }
-          }
-        }]).on('autocomplete:selected', function(event, suggestion) {
-          window.location.href = offsetURL(suggestion.path);
-        });
-        // remove inline display style on autocompleter (we want to
-        // manage responsive display via css)
-        $('.algolia-autocomplete').css("display", "");
-      })
-      .catch(function(error) {
-        console.log(error);
-      });
-
-  });
-
-  </script>
-
-  <style type="text/css">
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-  .nav-search {
-    font-size: x-small;
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-
-  /* Algolioa Autocomplete */
-
-  .algolia-autocomplete {
-    display: inline-block;
-    margin-left: 10px;
-    vertical-align: sub;
-    background-color: white;
-    color: black;
-    padding: 6px;
-    padding-top: 8px;
-    padding-bottom: 0;
-    border-radius: 6px;
-    border: 1px #0F2E3D solid;
-    width: 180px;
-  }
-
-
-  @media screen and (max-width: 768px) {
-    .distill-site-nav .algolia-autocomplete {
-      display: none;
-      visibility: hidden;
-    }
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-      display: inline-block;
-      visibility: visible;
-    }
-    .distill-site-nav.responsive .algolia-autocomplete .aa-dropdown-menu {
-      margin-left: 0;
-      width: 400px;
-      max-height: 400px;
-    }
-  }
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-    outline: none;
-    border: none;
-  }
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-  .algolia-autocomplete .aa-hint {
-    color: #999;
-  }
-  .algolia-autocomplete .aa-dropdown-menu {
-    width: 550px;
-    max-height: 70vh;
-    overflow-x: visible;
-    overflow-y: scroll;
-    padding: 5px;
-    margin-top: 3px;
-    margin-left: -150px;
-    background-color: #fff;
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-    border: 1px solid #999;
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-    cursor: pointer;
-    padding: 5px 4px;
-    border-bottom: 1px solid #eee;
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-  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion:last-of-type {
-    border-bottom: none;
-    margin-bottom: 2px;
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-    font-size: 1rem;
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-    margin-block-end: 5px;
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-    display: inline-block;
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-    margin-right: 4%;
-  }
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-    display: inline-block;
-    width: 15%;
-  }
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-  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item-preview img {
-    height: 3em;
-    width: auto;
-    display: none;
-  }
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-  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item-preview img[src] {
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-    background-color: #eee;
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-  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion em {
-    font-weight: bold;
-    font-style: normal;
-  }
-
-  </style>
-
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-  <!--radix_placeholder_distill-->
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-  <style type="text/css">
-
-  body {
-    background-color: white;
-  }
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-  .pandoc-table {
-    width: 100%;
-  }
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-  .pandoc-table>caption {
-    margin-bottom: 10px;
-  }
-
-  .pandoc-table th:not([align]) {
-    text-align: left;
-  }
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-  .pagedtable-footer {
-    font-size: 15px;
-  }
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-  d-byline .byline {
-    grid-template-columns: 2fr 2fr;
-  }
-
-  d-byline .byline h3 {
-    margin-block-start: 1.5em;
-  }
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-  d-byline .byline .authors-affiliations h3 {
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-  .authors-affiliations .orcid-id {
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-    height:16px;
-    margin-left: 4px;
-    margin-right: 4px;
-    vertical-align: middle;
-    padding-bottom: 2px;
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-    margin-top: 1em;
-    grid-column: text;
-  }
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-  .dt-tags .dt-tag {
-    text-decoration: none;
-    display: inline-block;
-    color: rgba(0,0,0,0.6);
-    padding: 0em 0.4em;
-    margin-right: 0.5em;
-    margin-bottom: 0.4em;
-    font-size: 70%;
-    border: 1px solid rgba(0,0,0,0.2);
-    border-radius: 3px;
-    text-transform: uppercase;
-    font-weight: 500;
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-  d-article table.gt_table td,
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-    border-bottom: none;
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-  .html-widget {
-    margin-bottom: 2.0em;
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-  .l-screen-inset {
-    padding-right: 16px;
-  }
-
-  .l-screen .caption {
-    margin-left: 10px;
-  }
-
-  .shaded {
-    background: rgb(247, 247, 247);
-    padding-top: 20px;
-    padding-bottom: 20px;
-    border-top: 1px solid rgba(0, 0, 0, 0.1);
-    border-bottom: 1px solid rgba(0, 0, 0, 0.1);
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-
-  .shaded .html-widget {
-    margin-bottom: 0;
-    border: 1px solid rgba(0, 0, 0, 0.1);
-  }
-
-  .shaded .shaded-content {
-    background: white;
-  }
-
-  .text-output {
-    margin-top: 0;
-    line-height: 1.5em;
-  }
-
-  .hidden {
-    display: none !important;
-  }
-
-  hr.section-separator {
-    border: none;
-    border-top: 1px solid rgba(0, 0, 0, 0.1);
-    margin: 0px;
-  }
-
-
-  d-byline {
-    border-top: none;
-  }
-
-  d-article {
-    padding-top: 2.5rem;
-    padding-bottom: 30px;
-    border-top: none;
-  }
-
-  d-appendix {
-    padding-top: 30px;
-  }
-
-  d-article>p>img {
-    width: 100%;
-  }
-
-  d-article h2 {
-    margin: 1rem 0 1.5rem 0;
-  }
-
-  d-article h3 {
-    margin-top: 1.5rem;
-  }
-
-  d-article iframe {
-    border: 1px solid rgba(0, 0, 0, 0.1);
-    margin-bottom: 2.0em;
-    width: 100%;
-  }
-
-  /* Tweak code blocks */
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-  d-article div.sourceCode code,
-  d-article pre code {
-    font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
-  }
-
-  d-article pre,
-  d-article div.sourceCode,
-  d-article div.sourceCode pre {
-    overflow: auto;
-  }
-
-  d-article div.sourceCode {
-    background-color: white;
-  }
-
-  d-article div.sourceCode pre {
-    padding-left: 10px;
-    font-size: 12px;
-    border-left: 2px solid rgba(0,0,0,0.1);
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-  d-article pre {
-    font-size: 12px;
-    color: black;
-    background: none;
-    margin-top: 0;
-    text-align: left;
-    white-space: pre;
-    word-spacing: normal;
-    word-break: normal;
-    word-wrap: normal;
-    line-height: 1.5;
-
-    -moz-tab-size: 4;
-    -o-tab-size: 4;
-    tab-size: 4;
-
-    -webkit-hyphens: none;
-    -moz-hyphens: none;
-    -ms-hyphens: none;
-    hyphens: none;
-  }
-
-  d-article pre a {
-    border-bottom: none;
-  }
-
-  d-article pre a:hover {
-    border-bottom: none;
-    text-decoration: underline;
-  }
-
-  d-article details {
-    grid-column: text;
-    margin-bottom: 0.8em;
-  }
-
-  @media(min-width: 768px) {
-
-  d-article pre,
-  d-article div.sourceCode,
-  d-article div.sourceCode pre {
-    overflow: visible !important;
-  }
-
-  d-article div.sourceCode pre {
-    padding-left: 18px;
-    font-size: 14px;
-  }
-
-  /* tweak for Pandoc numbered line within distill */
-  d-article pre.numberSource code > span {
-      left: -2em;
-  }
-
-  d-article pre {
-    font-size: 14px;
-  }
-
-  }
-
-  figure img.external {
-    background: white;
-    border: 1px solid rgba(0, 0, 0, 0.1);
-    box-shadow: 0 1px 8px rgba(0, 0, 0, 0.1);
-    padding: 18px;
-    box-sizing: border-box;
-  }
-
-  /* CSS for d-contents */
-
-  .d-contents {
-    grid-column: text;
-    color: rgba(0,0,0,0.8);
-    font-size: 0.9em;
-    padding-bottom: 1em;
-    margin-bottom: 1em;
-    padding-bottom: 0.5em;
-    margin-bottom: 1em;
-    padding-left: 0.25em;
-    justify-self: start;
-  }
-
-  @media(min-width: 1000px) {
-    .d-contents.d-contents-float {
-      height: 0;
-      grid-column-start: 1;
-      grid-column-end: 4;
-      justify-self: center;
-      padding-right: 3em;
-      padding-left: 2em;
-    }
-  }
-
-  .d-contents nav h3 {
-    font-size: 18px;
-    margin-top: 0;
-    margin-bottom: 1em;
-  }
-
-  .d-contents li {
-    list-style-type: none
-  }
-
-  .d-contents nav > ul {
-    padding-left: 0;
-  }
-
-  .d-contents ul {
-    padding-left: 1em
-  }
-
-  .d-contents nav ul li {
-    margin-top: 0.6em;
-    margin-bottom: 0.2em;
-  }
-
-  .d-contents nav a {
-    font-size: 13px;
-    border-bottom: none;
-    text-decoration: none
-    color: rgba(0, 0, 0, 0.8);
-  }
-
-  .d-contents nav a:hover {
-    text-decoration: underline solid rgba(0, 0, 0, 0.6)
-  }
-
-  .d-contents nav > ul > li > a {
-    font-weight: 600;
-  }
-
-  .d-contents nav > ul > li > ul {
-    font-weight: inherit;
-  }
-
-  .d-contents nav > ul > li > ul > li {
-    margin-top: 0.2em;
-  }
-
-
-  .d-contents nav ul {
-    margin-top: 0;
-    margin-bottom: 0.25em;
-  }
-
-  .d-article-with-toc h2:nth-child(2) {
-    margin-top: 0;
-  }
-
-
-  /* Figure */
-
-  .figure {
-    position: relative;
-    margin-bottom: 2.5em;
-    margin-top: 1.5em;
-  }
-
-  .figure .caption {
-    color: rgba(0, 0, 0, 0.6);
-    font-size: 12px;
-    line-height: 1.5em;
-  }
-
-  .figure img.external {
-    background: white;
-    border: 1px solid rgba(0, 0, 0, 0.1);
-    box-shadow: 0 1px 8px rgba(0, 0, 0, 0.1);
-    padding: 18px;
-    box-sizing: border-box;
-  }
-
-  .figure .caption a {
-    color: rgba(0, 0, 0, 0.6);
-  }
-
-  .figure .caption b,
-  .figure .caption strong, {
-    font-weight: 600;
-    color: rgba(0, 0, 0, 1.0);
-  }
-
-  /* Citations */
-
-  d-article .citation {
-    color: inherit;
-    cursor: inherit;
-  }
-
-  div.hanging-indent{
-    margin-left: 1em; text-indent: -1em;
-  }
-
-  /* Citation hover box */
-
-  .tippy-box[data-theme~=light-border] {
-    background-color: rgba(250, 250, 250, 0.95);
-  }
-
-  .tippy-content > p {
-    margin-bottom: 0;
-    padding: 2px;
-  }
-
-
-  /* Tweak 1000px media break to show more text */
-
-  @media(min-width: 1000px) {
-    .base-grid,
-    distill-header,
-    d-title,
-    d-abstract,
-    d-article,
-    d-appendix,
-    distill-appendix,
-    d-byline,
-    d-footnote-list,
-    d-citation-list,
-    distill-footer {
-      grid-template-columns: [screen-start] 1fr [page-start kicker-start] 80px [middle-start] 50px [text-start kicker-end] 65px 65px 65px 65px 65px 65px 65px 65px [text-end gutter-start] 65px [middle-end] 65px [page-end gutter-end] 1fr [screen-end];
-      grid-column-gap: 16px;
-    }
-
-    .grid {
-      grid-column-gap: 16px;
-    }
-
-    d-article {
-      font-size: 1.06rem;
-      line-height: 1.7em;
-    }
-    figure .caption, .figure .caption, figure figcaption {
-      font-size: 13px;
-    }
-  }
-
-  @media(min-width: 1180px) {
-    .base-grid,
-    distill-header,
-    d-title,
-    d-abstract,
-    d-article,
-    d-appendix,
-    distill-appendix,
-    d-byline,
-    d-footnote-list,
-    d-citation-list,
-    distill-footer {
-      grid-template-columns: [screen-start] 1fr [page-start kicker-start] 60px [middle-start] 60px [text-start kicker-end] 60px 60px 60px 60px 60px 60px 60px 60px [text-end gutter-start] 60px [middle-end] 60px [page-end gutter-end] 1fr [screen-end];
-      grid-column-gap: 32px;
-    }
-
-    .grid {
-      grid-column-gap: 32px;
-    }
-  }
-
-
-  /* Get the citation styles for the appendix (not auto-injected on render since
-     we do our own rendering of the citation appendix) */
-
-  d-appendix .citation-appendix,
-  .d-appendix .citation-appendix {
-    font-size: 11px;
-    line-height: 15px;
-    border-left: 1px solid rgba(0, 0, 0, 0.1);
-    padding-left: 18px;
-    border: 1px solid rgba(0,0,0,0.1);
-    background: rgba(0, 0, 0, 0.02);
-    padding: 10px 18px;
-    border-radius: 3px;
-    color: rgba(150, 150, 150, 1);
-    overflow: hidden;
-    margin-top: -12px;
-    white-space: pre-wrap;
-    word-wrap: break-word;
-  }
-
-  /* Include appendix styles here so they can be overridden */
-
-  d-appendix {
-    contain: layout style;
-    font-size: 0.8em;
-    line-height: 1.7em;
-    margin-top: 60px;
-    margin-bottom: 0;
-    border-top: 1px solid rgba(0, 0, 0, 0.1);
-    color: rgba(0,0,0,0.5);
-    padding-top: 60px;
-    padding-bottom: 48px;
-  }
-
-  d-appendix h3 {
-    grid-column: page-start / text-start;
-    font-size: 15px;
-    font-weight: 500;
-    margin-top: 1em;
-    margin-bottom: 0;
-    color: rgba(0,0,0,0.65);
-  }
-
-  d-appendix h3 + * {
-    margin-top: 1em;
-  }
-
-  d-appendix ol {
-    padding: 0 0 0 15px;
-  }
-
-  @media (min-width: 768px) {
-    d-appendix ol {
-      padding: 0 0 0 30px;
-      margin-left: -30px;
-    }
-  }
-
-  d-appendix li {
-    margin-bottom: 1em;
-  }
-
-  d-appendix a {
-    color: rgba(0, 0, 0, 0.6);
-  }
-
-  d-appendix > * {
-    grid-column: text;
-  }
-
-  d-appendix > d-footnote-list,
-  d-appendix > d-citation-list,
-  d-appendix > distill-appendix {
-    grid-column: screen;
-  }
-
-  /* Include footnote styles here so they can be overridden */
-
-  d-footnote-list {
-    contain: layout style;
-  }
-
-  d-footnote-list > * {
-    grid-column: text;
-  }
-
-  d-footnote-list a.footnote-backlink {
-    color: rgba(0,0,0,0.3);
-    padding-left: 0.5em;
-  }
-
-
-
-  /* Anchor.js */
-
-  .anchorjs-link {
-    /*transition: all .25s linear; */
-    text-decoration: none;
-    border-bottom: none;
-  }
-  *:hover > .anchorjs-link {
-    margin-left: -1.125em !important;
-    text-decoration: none;
-    border-bottom: none;
-  }
-
-  /* Social footer */
-
-  .social_footer {
-    margin-top: 30px;
-    margin-bottom: 0;
-    color: rgba(0,0,0,0.67);
-  }
-
-  .disqus-comments {
-    margin-right: 30px;
-  }
-
-  .disqus-comment-count {
-    border-bottom: 1px solid rgba(0, 0, 0, 0.4);
-    cursor: pointer;
-  }
-
-  #disqus_thread {
-    margin-top: 30px;
-  }
-
-  .article-sharing a {
-    border-bottom: none;
-    margin-right: 8px;
-  }
-
-  .article-sharing a:hover {
-    border-bottom: none;
-  }
-
-  .sidebar-section.subscribe {
-    font-size: 12px;
-    line-height: 1.6em;
-  }
-
-  .subscribe p {
-    margin-bottom: 0.5em;
-  }
-
-
-  .article-footer .subscribe {
-    font-size: 15px;
-    margin-top: 45px;
-  }
-
-
-  .sidebar-section.custom {
-    font-size: 12px;
-    line-height: 1.6em;
-  }
-
-  .custom p {
-    margin-bottom: 0.5em;
-  }
-
-  /* Styles for listing layout (hide title) */
-  .layout-listing d-title, .layout-listing .d-title {
-    display: none;
-  }
-
-  /* Styles for posts lists (not auto-injected) */
-
-
-  .posts-with-sidebar {
-    padding-left: 45px;
-    padding-right: 45px;
-  }
-
-  .posts-list .description h2,
-  .posts-list .description p {
-    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen, Ubuntu, Cantarell, "Fira Sans", "Droid Sans", "Helvetica Neue", Arial, sans-serif;
-  }
-
-  .posts-list .description h2 {
-    font-weight: 700;
-    border-bottom: none;
-    padding-bottom: 0;
-  }
-
-  .posts-list h2.post-tag {
-    border-bottom: 1px solid rgba(0, 0, 0, 0.2);
-    padding-bottom: 12px;
-  }
-  .posts-list {
-    margin-top: 60px;
-    margin-bottom: 24px;
-  }
-
-  .posts-list .post-preview {
-    text-decoration: none;
-    overflow: hidden;
-    display: block;
-    border-bottom: 1px solid rgba(0, 0, 0, 0.1);
-    padding: 24px 0;
-  }
-
-  .post-preview-last {
-    border-bottom: none !important;
-  }
-
-  .posts-list .posts-list-caption {
-    grid-column: screen;
-    font-weight: 400;
-  }
-
-  .posts-list .post-preview h2 {
-    margin: 0 0 6px 0;
-    line-height: 1.2em;
-    font-style: normal;
-    font-size: 24px;
-  }
-
-  .posts-list .post-preview p {
-    margin: 0 0 12px 0;
-    line-height: 1.4em;
-    font-size: 16px;
-  }
-
-  .posts-list .post-preview .thumbnail {
-    box-sizing: border-box;
-    margin-bottom: 24px;
-    position: relative;
-    max-width: 500px;
-  }
-  .posts-list .post-preview img {
-    width: 100%;
-    display: block;
-  }
-
-  .posts-list .metadata {
-    font-size: 12px;
-    line-height: 1.4em;
-    margin-bottom: 18px;
-  }
-
-  .posts-list .metadata > * {
-    display: inline-block;
-  }
-
-  .posts-list .metadata .publishedDate {
-    margin-right: 2em;
-  }
-
-  .posts-list .metadata .dt-authors {
-    display: block;
-    margin-top: 0.3em;
-    margin-right: 2em;
-  }
-
-  .posts-list .dt-tags {
-    display: block;
-    line-height: 1em;
-  }
-
-  .posts-list .dt-tags .dt-tag {
-    display: inline-block;
-    color: rgba(0,0,0,0.6);
-    padding: 0.3em 0.4em;
-    margin-right: 0.2em;
-    margin-bottom: 0.4em;
-    font-size: 60%;
-    border: 1px solid rgba(0,0,0,0.2);
-    border-radius: 3px;
-    text-transform: uppercase;
-    font-weight: 500;
-  }
-
-  .posts-list img {
-    opacity: 1;
-  }
-
-  .posts-list img[data-src] {
-    opacity: 0;
-  }
-
-  .posts-more {
-    clear: both;
-  }
-
-
-  .posts-sidebar {
-    font-size: 16px;
-  }
-
-  .posts-sidebar h3 {
-    font-size: 16px;
-    margin-top: 0;
-    margin-bottom: 0.5em;
-    font-weight: 400;
-    text-transform: uppercase;
-  }
-
-  .sidebar-section {
-    margin-bottom: 30px;
-  }
-
-  .categories ul {
-    list-style-type: none;
-    margin: 0;
-    padding: 0;
-  }
-
-  .categories li {
-    color: rgba(0, 0, 0, 0.8);
-    margin-bottom: 0;
-  }
-
-  .categories li>a {
-    border-bottom: none;
-  }
-
-  .categories li>a:hover {
-    border-bottom: 1px solid rgba(0, 0, 0, 0.4);
-  }
-
-  .categories .active {
-    font-weight: 600;
-  }
-
-  .categories .category-count {
-    color: rgba(0, 0, 0, 0.4);
-  }
-
-
-  @media(min-width: 768px) {
-    .posts-list .post-preview h2 {
-      font-size: 26px;
-    }
-    .posts-list .post-preview .thumbnail {
-      float: right;
-      width: 30%;
-      margin-bottom: 0;
-    }
-    .posts-list .post-preview .description {
-      float: left;
-      width: 45%;
-    }
-    .posts-list .post-preview .metadata {
-      float: left;
-      width: 20%;
-      margin-top: 8px;
-    }
-    .posts-list .post-preview p {
-      margin: 0 0 12px 0;
-      line-height: 1.5em;
-      font-size: 16px;
-    }
-    .posts-with-sidebar .posts-list {
-      float: left;
-      width: 75%;
-    }
-    .posts-with-sidebar .posts-sidebar {
-      float: right;
-      width: 20%;
-      margin-top: 60px;
-      padding-top: 24px;
-      padding-bottom: 24px;
-    }
-  }
-
-
-  /* Improve display for browsers without grid (IE/Edge <= 15) */
-
-  .downlevel {
-    line-height: 1.6em;
-    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen, Ubuntu, Cantarell, "Fira Sans", "Droid Sans", "Helvetica Neue", Arial, sans-serif;
-    margin: 0;
-  }
-
-  .downlevel .d-title {
-    padding-top: 6rem;
-    padding-bottom: 1.5rem;
-  }
-
-  .downlevel .d-title h1 {
-    font-size: 50px;
-    font-weight: 700;
-    line-height: 1.1em;
-    margin: 0 0 0.5rem;
-  }
-
-  .downlevel .d-title p {
-    font-weight: 300;
-    font-size: 1.2rem;
-    line-height: 1.55em;
-    margin-top: 0;
-  }
-
-  .downlevel .d-byline {
-    padding-top: 0.8em;
-    padding-bottom: 0.8em;
-    font-size: 0.8rem;
-    line-height: 1.8em;
-  }
-
-  .downlevel .section-separator {
-    border: none;
-    border-top: 1px solid rgba(0, 0, 0, 0.1);
-  }
-
-  .downlevel .d-article {
-    font-size: 1.06rem;
-    line-height: 1.7em;
-    padding-top: 1rem;
-    padding-bottom: 2rem;
-  }
-
-
-  .downlevel .d-appendix {
-    padding-left: 0;
-    padding-right: 0;
-    max-width: none;
-    font-size: 0.8em;
-    line-height: 1.7em;
-    margin-bottom: 0;
-    color: rgba(0,0,0,0.5);
-    padding-top: 40px;
-    padding-bottom: 48px;
-  }
-
-  .downlevel .footnotes ol {
-    padding-left: 13px;
-  }
-
-  .downlevel .base-grid,
-  .downlevel .distill-header,
-  .downlevel .d-title,
-  .downlevel .d-abstract,
-  .downlevel .d-article,
-  .downlevel .d-appendix,
-  .downlevel .distill-appendix,
-  .downlevel .d-byline,
-  .downlevel .d-footnote-list,
-  .downlevel .d-citation-list,
-  .downlevel .distill-footer,
-  .downlevel .appendix-bottom,
-  .downlevel .posts-container {
-    padding-left: 40px;
-    padding-right: 40px;
-  }
-
-  @media(min-width: 768px) {
-    .downlevel .base-grid,
-    .downlevel .distill-header,
-    .downlevel .d-title,
-    .downlevel .d-abstract,
-    .downlevel .d-article,
-    .downlevel .d-appendix,
-    .downlevel .distill-appendix,
-    .downlevel .d-byline,
-    .downlevel .d-footnote-list,
-    .downlevel .d-citation-list,
-    .downlevel .distill-footer,
-    .downlevel .appendix-bottom,
-    .downlevel .posts-container {
-    padding-left: 150px;
-    padding-right: 150px;
-    max-width: 900px;
-  }
-  }
-
-  .downlevel pre code {
-    display: block;
-    border-left: 2px solid rgba(0, 0, 0, .1);
-    padding: 0 0 0 20px;
-    font-size: 14px;
-  }
-
-  .downlevel code, .downlevel pre {
-    color: black;
-    background: none;
-    font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
-    text-align: left;
-    white-space: pre;
-    word-spacing: normal;
-    word-break: normal;
-    word-wrap: normal;
-    line-height: 1.5;
-
-    -moz-tab-size: 4;
-    -o-tab-size: 4;
-    tab-size: 4;
-
-    -webkit-hyphens: none;
-    -moz-hyphens: none;
-    -ms-hyphens: none;
-    hyphens: none;
-  }
-
-  .downlevel .posts-list .post-preview {
-    color: inherit;
-  }
-
-
-
-  </style>
-
-  <script type="application/javascript">
-
-  function is_downlevel_browser() {
-    if (bowser.isUnsupportedBrowser({ msie: "12", msedge: "16"},
-                                   window.navigator.userAgent)) {
-      return true;
-    } else {
-      return window.load_distill_framework === undefined;
-    }
-  }
-
-  // show body when load is complete
-  function on_load_complete() {
-
-    // add anchors
-    if (window.anchors) {
-      window.anchors.options.placement = 'left';
-      window.anchors.add('d-article > h2, d-article > h3, d-article > h4, d-article > h5');
-    }
-
-
-    // set body to visible
-    document.body.style.visibility = 'visible';
-
-    // force redraw for leaflet widgets
-    if (window.HTMLWidgets) {
-      var maps = window.HTMLWidgets.findAll(".leaflet");
-      $.each(maps, function(i, el) {
-        var map = this.getMap();
-        map.invalidateSize();
-        map.eachLayer(function(layer) {
-          if (layer instanceof L.TileLayer)
-            layer.redraw();
-        });
-      });
-    }
-
-    // trigger 'shown' so htmlwidgets resize
-    $('d-article').trigger('shown');
-  }
-
-  function init_distill() {
-
-    init_common();
-
-    // create front matter
-    var front_matter = $('<d-front-matter></d-front-matter>');
-    $('#distill-front-matter').wrap(front_matter);
-
-    // create d-title
-    $('.d-title').changeElementType('d-title');
-
-    // separator
-    var separator = '<hr class="section-separator" style="clear: both"/>';
-    // prepend separator above appendix
-    $('.d-byline').before(separator);
-    $('.d-article').before(separator);
-
-    // create d-byline
-    var byline = $('<d-byline></d-byline>');
-    $('.d-byline').replaceWith(byline);
-
-    // create d-article
-    var article = $('<d-article></d-article>');
-    $('.d-article').wrap(article).children().unwrap();
-
-    // move posts container into article
-    $('.posts-container').appendTo($('d-article'));
-
-    // create d-appendix
-    $('.d-appendix').changeElementType('d-appendix');
-
-    // flag indicating that we have appendix items
-    var appendix = $('.appendix-bottom').children('h3').length > 0;
-
-    // replace footnotes with <d-footnote>
-    $('.footnote-ref').each(function(i, val) {
-      appendix = true;
-      var href = $(this).attr('href');
-      var id = href.replace('#', '');
-      var fn = $('#' + id);
-      var fn_p = $('#' + id + '>p');
-      fn_p.find('.footnote-back').remove();
-      var text = fn_p.html();
-      var dtfn = $('<d-footnote></d-footnote>');
-      dtfn.html(text);
-      $(this).replaceWith(dtfn);
-    });
-    // remove footnotes
-    $('.footnotes').remove();
-
-    // move refs into #references-listing
-    $('#references-listing').replaceWith($('#refs'));
-
-    $('h1.appendix, h2.appendix').each(function(i, val) {
-      $(this).changeElementType('h3');
-    });
-    $('h3.appendix').each(function(i, val) {
-      var id = $(this).attr('id');
-      $('.d-contents a[href="#' + id + '"]').parent().remove();
-      appendix = true;
-      $(this).nextUntil($('h1, h2, h3')).addBack().appendTo($('d-appendix'));
-    });
-
-    // show d-appendix if we have appendix content
-    $("d-appendix").css('display', appendix ? 'grid' : 'none');
-
-    // localize layout chunks to just output
-    $('.layout-chunk').each(function(i, val) {
-
-      // capture layout
-      var layout = $(this).attr('data-layout');
-
-      // apply layout to markdown level block elements
-      var elements = $(this).children().not('details, div.sourceCode, pre, script');
-      elements.each(function(i, el) {
-        var layout_div = $('<div class="' + layout + '"></div>');
-        if (layout_div.hasClass('shaded')) {
-          var shaded_content = $('<div class="shaded-content"></div>');
-          $(this).wrap(shaded_content);
-          $(this).parent().wrap(layout_div);
-        } else {
-          $(this).wrap(layout_div);
-        }
-      });
-
-
-      // unwrap the layout-chunk div
-      $(this).children().unwrap();
-    });
-
-    // remove code block used to force  highlighting css
-    $('.distill-force-highlighting-css').parent().remove();
-
-    // remove empty line numbers inserted by pandoc when using a
-    // custom syntax highlighting theme, except when numbering line
-    // in code chunk
-    $('pre:not(.numberLines) code.sourceCode a:empty').remove();
-
-    // load distill framework
-    load_distill_framework();
-
-    // wait for window.distillRunlevel == 4 to do post processing
-    function distill_post_process() {
-
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-        return;
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-      // hide author/affiliations entirely if we have no authors
-      var front_matter = JSON.parse($("#distill-front-matter").html());
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-      if (!have_authors)
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-      // article with toc class
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-      // strip links that point to #
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-      // add orcid ids
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-        var orcid_id = front_matter.authors[i].orcidID;
-        var author_name = front_matter.authors[i].author
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-          var a = $('<a></a>');
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-          var img = $('<img></img>');
-          img.addClass('orcid-id');
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-          a.append(img);
-          $(this).append(a);
-        }
-      });
-
-      // hide elements of author/affiliations grid that have no value
-      function hide_byline_column(caption) {
-        $('d-byline').find('h3:contains("' + caption + '")').parent().css('visibility', 'hidden');
-      }
-
-      // affiliations
-      var have_affiliations = false;
-      for (var i = 0; i<front_matter.authors.length; ++i) {
-        var author = front_matter.authors[i];
-        if (author.affiliation !== "&nbsp;") {
-          have_affiliations = true;
-          break;
-        }
-      }
-      if (!have_affiliations)
-        $('d-byline').find('h3:contains("Affiliations")').css('visibility', 'hidden');
-
-      // published date
-      if (!front_matter.publishedDate)
-        hide_byline_column("Published");
-
-      // document object identifier
-      var doi = $('d-byline').find('h3:contains("DOI")');
-      var doi_p = doi.next().empty();
-      if (!front_matter.doi) {
-        // if we have a citation and valid citationText then link to that
-        if ($('#citation').length > 0 && front_matter.citationText) {
-          doi.html('Citation');
-          $('<a href="#citation"></a>')
-            .text(front_matter.citationText)
-            .appendTo(doi_p);
-        } else {
-          hide_byline_column("DOI");
-        }
-      } else {
-        $('<a></a>')
-           .attr('href', "https://doi.org/" + front_matter.doi)
-           .html(front_matter.doi)
-           .appendTo(doi_p);
-      }
-
-       // change plural form of authors/affiliations
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-      }
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-      // remove d-appendix and d-footnote-list local styles
-      $('d-appendix > style:first-child').remove();
-      $('d-footnote-list > style:first-child').remove();
-
-      // move appendix-bottom entries to the bottom
-      $('.appendix-bottom').appendTo('d-appendix').children().unwrap();
-      $('.appendix-bottom').remove();
-
-      // hoverable references
-      $('span.citation[data-cites]').each(function() {
-        const citeChild = $(this).children()[0]
-        // Do not process if @xyz has been used without escaping and without bibliography activated
-        // https://github.com/rstudio/distill/issues/466
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-
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-          var fn = citeChild
-          $(this).html(fn.shadowRoot.querySelector("sup"))
-          $(this).id = fn.id
-          fn.remove()
-        }
-        var refs = $(this).attr('data-cites').split(" ");
-        var refHtml = refs.map(function(ref) {
-          // Could use CSS.escape too here, we insure backward compatibility in navigator
-          return "<p>" + $('div[id="ref-' + ref + '"]').html() + "</p>";
-        }).join("\n");
-        window.tippy(this, {
-          allowHTML: true,
-          content: refHtml,
-          maxWidth: 500,
-          interactive: true,
-          interactiveBorder: 10,
-          theme: 'light-border',
-          placement: 'bottom-start'
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-      });
-
-      // fix footnotes in tables (#411)
-      // replacing broken distill.pub feature
-      $('table d-footnote').each(function() {
-        // we replace internal showAtNode methode which is triggered when hovering a footnote
-        this.hoverBox.showAtNode = function(node) {
-          // ported from https://github.com/distillpub/template/pull/105/files
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-              let x = elem.offsetLeft;
-              let y = elem.offsetTop;
-              // Traverse upwards until an `absolute` element is found or `elem`
-              // becomes null.
-              while (elem = elem.offsetParent && elem.style.position != 'absolute') {
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-                  y += elem.offsetTop;
-              }
-
-              return { left: x, top: y };
-          }
-          // https://developer.mozilla.org/en-US/docs/Web/API/HTMLElement/offsetTop
-          const bbox = node.getBoundingClientRect();
-          const offset = calcOffset(node);
-          this.show([offset.left + bbox.width, offset.top + bbox.height]);
-        }
-      })
-
-      // clear polling timer
-      clearInterval(tid);
-
-      // show body now that everything is ready
-      on_load_complete();
-    }
-
-    var tid = setInterval(distill_post_process, 50);
-    distill_post_process();
-
-  }
-
-  function init_downlevel() {
-
-    init_common();
-
-     // insert hr after d-title
-    $('.d-title').after($('<hr class="section-separator"/>'));
-
-    // check if we have authors
-    var front_matter = JSON.parse($("#distill-front-matter").html());
-    var have_authors = front_matter.authors && front_matter.authors.length > 0;
-
-    // manage byline/border
-    if (!have_authors)
-      $('.d-byline').remove();
-    $('.d-byline').after($('<hr class="section-separator"/>'));
-    $('.d-byline a').remove();
-
-    // remove toc
-    $('.d-contents').remove();
-
-    // move appendix elements
-    $('h1.appendix, h2.appendix').each(function(i, val) {
-      $(this).changeElementType('h3');
-    });
-    $('h3.appendix').each(function(i, val) {
-      $(this).nextUntil($('h1, h2, h3')).addBack().appendTo($('.d-appendix'));
-    });
-
-
-    // inject headers into references and footnotes
-    var refs_header = $('<h3></h3>');
-    refs_header.text('References');
-    $('#refs').prepend(refs_header);
-
-    var footnotes_header = $('<h3></h3');
-    footnotes_header.text('Footnotes');
-    $('.footnotes').children('hr').first().replaceWith(footnotes_header);
-
-    // move appendix-bottom entries to the bottom
-    $('.appendix-bottom').appendTo('.d-appendix').children().unwrap();
-    $('.appendix-bottom').remove();
-
-    // remove appendix if it's empty
-    if ($('.d-appendix').children().length === 0)
-      $('.d-appendix').remove();
-
-    // prepend separator above appendix
-    $('.d-appendix').before($('<hr class="section-separator" style="clear: both"/>'));
-
-    // trim code
-    $('pre>code').each(function(i, val) {
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-    });
-
-    // move posts-container right before article
-    $('.posts-container').insertBefore($('.d-article'));
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-    $('body').addClass('downlevel');
-
-    on_load_complete();
-  }
-
-
-  function init_common() {
-
-    // jquery plugin to change element types
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-        var attrs = {};
-
-        $.each(this[0].attributes, function(idx, attr) {
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-
-        this.replaceWith(function() {
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-        });
-      };
-    })(jQuery);
-
-    // prevent underline for linked images
-    $('a > img').parent().css({'border-bottom' : 'none'});
-
-    // mark non-body figures created by knitr chunks as 100% width
-    $('.layout-chunk').each(function(i, val) {
-      var figures = $(this).find('img, .html-widget');
-      // ignore leaflet img layers (#106)
-      figures = figures.filter(':not(img[class*="leaflet"])')
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-        figures.css('width', '100%');
-      } else {
-        figures.css('max-width', '100%');
-        figures.filter("[width]").each(function(i, val) {
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-        });
-
-      }
-    });
-
-    // auto-append index.html to post-preview links in file: protocol
-    // and in rstudio ide preview
-    $('.post-preview').each(function(i, val) {
-      if (window.location.protocol === "file:")
-        $(this).attr('href', $(this).attr('href') + "index.html");
-    });
-
-    // get rid of index.html references in header
-    if (window.location.protocol !== "file:") {
-      $('.distill-site-header a[href]').each(function(i,val) {
-        $(this).attr('href', $(this).attr('href').replace(/^index[.]html/, "./"));
-      });
-    }
-
-    // add class to pandoc style tables
-    $('tr.header').parent('thead').parent('table').addClass('pandoc-table');
-    $('.kable-table').children('table').addClass('pandoc-table');
-
-    // add figcaption style to table captions
-    $('caption').parent('table').addClass("figcaption");
-
-    // initialize posts list
-    if (window.init_posts_list)
-      window.init_posts_list();
-
-    // implmement disqus comment link
-    $('.disqus-comment-count').click(function() {
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-      $('#disqus_thread').toggleClass('hidden');
-      if (!$('#disqus_thread').hasClass('hidden')) {
-        var offset = $(this).offset();
-        $(window).resize();
-        $('html, body').animate({
-          scrollTop: offset.top - 35
-        });
-      }
-    });
-  }
-
-  document.addEventListener('DOMContentLoaded', function() {
-    if (is_downlevel_browser())
-      init_downlevel();
-    else
-      window.addEventListener('WebComponentsReady', init_distill);
-  });
-
-  </script>
-
-  <!--/radix_placeholder_distill-->
-  <script src="site_libs/header-attrs-2.27/header-attrs.js"></script>
-  <script src="site_libs/popper-2.6.0/popper.min.js"></script>
-  <link href="site_libs/tippy-6.2.7/tippy.css" rel="stylesheet" />
-  <link href="site_libs/tippy-6.2.7/tippy-light-border.css" rel="stylesheet" />
-  <script src="site_libs/tippy-6.2.7/tippy.umd.min.js"></script>
-  <script src="site_libs/anchor-4.2.2/anchor.min.js"></script>
-  <script src="site_libs/bowser-1.9.3/bowser.min.js"></script>
-  <script src="site_libs/webcomponents-2.0.0/webcomponents.js"></script>
-  <script src="site_libs/distill-2.2.21/template.v2.js"></script>
-  <!--radix_placeholder_site_in_header-->
-  <script type="text/javascript" cookie-consent="tracking" async src="https://www.googletagmanager.com/gtag/js?id=UA-178413324-1"></script>
-  <script type="text/javascript" cookie-consent="tracking">
-  window.dataLayer = window.dataLayer || [];
-  function gtag(){dataLayer.push(arguments);}
-  gtag('js', new Date());
-  gtag('config', 'UA-178413324-1');
-  </script>
-  <style type="text/css">
-  /* ---------- Global Styles ---------- */
-
-  @import url('https://fonts.googleapis.com/css?family=Atkinson+Hyperlegible&display=swap');
-  @import url('https://fonts.googleapis.com/css?family=Roboto+Mono&display=swap');
-  @import url('https://fonts.googleapis.com/css?family=Roboto+Slab&display=swap');
-  @import url('https://fonts.googleapis.com/css?family=Roboto&display=swap');
-  @import url('https://fonts.googleapis.com/css?family=Fira+Mono&display=swap');
-
-  html, body, p {
-    
-    font-family: 'Atkinson Hyperlegible';
-    font-weight: 400;
-    line-height: 1.7; 
-    font-size: 1em;
-    color: #333333;
-    font-style: normal;
-    
-  }
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-  h2, h3 {
-    font-family: 'Roboto Slab'
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-  d-article h4 {
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-    text-align: center;
-    margin-top: 0.5em;
-    padding: 5px 0px;
-    outline: 1px solid black;
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-  d-article h5 {
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-    margin-bottom: 0.5em;
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-  em {
-    margin-right: 3px;
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-  div.opener {
-    text-align: justify;
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-
-  /* Small caps */
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-  .sc {
-    font-variant: small-caps;
-    letter-spacing: 0.1em;
-  }
-
-
-  /* ---------- Index Page Styles ---------- */
-
-
-  /* Name time */
-
-  div.nav-left.title {
-    font-family: 'Roboto Slab';
-  }
-
-
-  /* Search bar */
-
-  .angolia-autocomplete {
-    width: 300px;
-  }
-
-  .nav-search {
-      font-size: inherit;
-  }
-
-  /* Publication Date */
-
-  .publishedDate {
-    font-size: 1.1em;
-  }
-
-
-  /* Post Description */
-
-  .posts-list .description h2 {
-    font-family: 'Roboto Slab';
-  }
-
-  .description p {
-    font-style: italic;
-    padding-top: 5px;
-  }
-
-
-  /* Tags */
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-  .posts-list .dt-tags {
-    margin-top: 10px;
-    margin-right: 10px;
-  }
-
-
-  .posts-list .dt-tags .dt-tag {
-    font-family: 'Roboto Slab';
-    font-weight: bold;
-    letter-spacing: 1px;
-    background-color: #565656;
-    color: white;
-  }
-
-  /* Top & Bot bars */
-
-  .distill-site-nav {
-    background-color: #262c2f;
-  }
-
-  .distill-site-footer p {
-    color: white;
-  }
-
-
-
-  /* Post published date medatada */
-  .posts-list .metadata .publishedDate{
-    font-family: 'Roboto Mono';
-  }
-
-
-  /* Post list caption */
-  .posts-list .posts-list-caption{
-    font-family: 'Fira Mono';
-    border-bottom: 5px solid #f3f3f3;
-    padding-bottom: 2rem;
-  }
-
-
-  /* Sidebar Categories */
-  .posts-sidebar {
-    font-family: 'Fira Mono';
-  }
-
-  .sidebar-section h3 {
-    font-size: 22px;
-    margin-bottom: 20px;
-  }
-
-
-  /* ---------- Article Styles ---------- */
-
-
-  /* Title */
-
-  d-title {
-    padding-bottom: 0;
-  }
-
-  d-title h1 {
-    font-family: 'Roboto Slab';
-    line-height: 1.3;
-  }
-
-  d-title p {
-    font-weight: 600;
-  }
-
-
-  /* General */
-
-  d-article > h2 {
-    margin: 2.5rem 0 1.5rem 0;
-    border-bottom: 2px solid black;
-  }
-
-  div.l-body + h2 {
-    margin-top: 0px;
-  }
-
-  d-article > h3 {
-    margin-top: 1em;
-    font-size: 28px;
-    padding-bottom: 10px;
-    border-bottom: 2px solid lightgrey;
-  }
-
-  d-article ol {
-    padding-bottom: 15px;
-  }
-
-  /* Aside */
-
-  aside {
-    margin-left: 20px;
-    width: 200px;
-    font-family: 'Roboto Slab';
-  }
-
-  div.sourceCode + aside {
-    margin-top: 1.5em;
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-
-  aside code {
-    font-weight: 600;
-  }
-
-  /* Details */
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-  }
-
-  details {
-    background-color: #008bff0f;
-    outline: 2px solid #38566F;
-    padding: 1rem;
-  }
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-  d-article details[open] summary {
-    margin-bottom: 1em;
-  }
-
-  /* Block Quotes */
-
-  d-article blockquote {
-    border-left: 5px solid rgba(0, 0, 0, 0.2);
-    padding-left: 1em;
-  }
-
-  blockquote p {
-    margin-bottom: 0;
-  }
-
-
-  /* Footnote margins */
-  d-footnote {
-    margin-left: -.2em;
-    margin-right: .1em;
-  }
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-  /* Footnote Image */
-
-  d-footnote-list ol li img {
-    width: 700px;
-  }
-
-  d-footnote img {
-    width: 660px;
-    padding: 10px;
-  }
-
-
-  /* -------- Layout Helpers -------- */
-
-  /* 2-column Even */
-
-  .pull-left {
-    float: left;
-    width: 47%;
-  }
-
-  .pull-right {
-    float: right;
-    width: 47%;
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-
-  /* 2-column Left-skew */
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-<h2>Plot Makeover #2</h2>
-<div class="dt-tags">
-<div class="dt-tag">plot makeover</div>
-<div class="dt-tag">data visualization</div>
-<div class="dt-tag">ggplot2</div>
-</div>
-<p>Making a dodged-stacked hybrid bar plot in {ggplot2}</p>
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-<a href="posts/2020-11-03-tidytuesday-2020-week-45/" class="post-preview">
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-<div class="publishedDate">Nov. 3, 2020</div>
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-<div class="dt-tag">ggplot2</div>
-<div class="dt-tag">data visualization</div>
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-<p>Waffle chart of IKEA furnitures in stock</p>
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-<a href="posts/2020-10-28-tidytuesday-2020-week-44/" class="post-preview">
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-<div class="publishedDate">Oct. 28, 2020</div>
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-<p>Patched animation of the location and cumulative capacity of wind turbines in Canada</p>
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-<div class="publishedDate">Oct. 22, 2020</div>
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-<img data-src="posts/2020-10-22-analysis-of-everycolorbots-tweets/preview.png"/>
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-<p>And why you should avoid neon colors</p>
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-<div class="publishedDate">Oct. 13, 2020</div>
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-<h2>Designing guiding aesthetics</h2>
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-<div class="dt-tag">data visualization</div>
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-<p>The fine line between creativity and noise</p>
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-<div class="publishedDate">Sept. 27, 2020</div>
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-<h2>Demystifying stat_ layers in {ggplot2}</h2>
-<div class="dt-tags">
-<div class="dt-tag">data visualization</div>
-<div class="dt-tag">ggplot2</div>
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-</div>
-<p>The motivation behind stat, the distinction between stat and geom, and a case study of stat_summary()</p>
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-<div class="publishedDate">Sept. 23, 2020</div>
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-<h2>TidyTuesday 2020 week 39</h2>
-<div class="dt-tags">
-<div class="dt-tag">ggplot2</div>
-<div class="dt-tag">data visualization</div>
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-<p>Stacked area plot of the heights of Himalayan peaks attempted over the last century</p>
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-<a href="posts/2020-09-20-plot-makeover-1/" class="post-preview">
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-<div class="publishedDate">Sept. 20, 2020</div>
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-<img data-src="posts/2020-09-20-plot-makeover-1/plot-makeover-1_files/figure-html5/after_bar_plot-1.png"/>
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-<div class="description">
-<h2>Plot Makeover #1</h2>
-<div class="dt-tags">
-<div class="dt-tag">plot makeover</div>
-<div class="dt-tag">data visualization</div>
-<div class="dt-tag">ggplot2</div>
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-<p>Flattening a faceted grid for strictly horizontal comparisons</p>
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-<h2>TidyTuesday 2020 week 38</h2>
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-<p>Visualizing two decades of primary and secondary education spending with {gt}</p>
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-<p>A small collection of my favorite fonts for data visualization</p>
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-<p>An animation of the main characters in Avatar</p>
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-<p>Some notes on lesser known functions/functionalities that combine common chain of {dplyr} verbs.</p>
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-<h2>TidyTuesday 2020 Week 32</h2>
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-<p>A dumbbell chart visualization of energy production trends among European countries</p>
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+pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa;  padding-left: 4px; }
+div.sourceCode
+  {  background-color: #f8f8f8; }
+@media screen {
+pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
+}
+code span.al { color: #ef2929; } /* Alert */
+code span.an { color: #8f5902; font-weight: bold; font-style: italic; } /* Annotation */
+code span.at { color: #204a87; } /* Attribute */
+code span.bn { color: #0000cf; } /* BaseN */
+code span.cf { color: #204a87; font-weight: bold; } /* ControlFlow */
+code span.ch { color: #4e9a06; } /* Char */
+code span.cn { color: #8f5902; } /* Constant */
+code span.co { color: #8f5902; font-style: italic; } /* Comment */
+code span.cv { color: #8f5902; font-weight: bold; font-style: italic; } /* CommentVar */
+code span.do { color: #8f5902; font-weight: bold; font-style: italic; } /* Documentation */
+code span.dt { color: #204a87; } /* DataType */
+code span.dv { color: #0000cf; } /* DecVal */
+code span.er { color: #a40000; font-weight: bold; } /* Error */
+code span.ex { } /* Extension */
+code span.fl { color: #0000cf; } /* Float */
+code span.fu { color: #204a87; font-weight: bold; } /* Function */
+code span.im { } /* Import */
+code span.in { color: #8f5902; font-weight: bold; font-style: italic; } /* Information */
+code span.kw { color: #204a87; font-weight: bold; } /* Keyword */
+code span.op { color: #ce5c00; font-weight: bold; } /* Operator */
+code span.ot { color: #8f5902; } /* Other */
+code span.pp { color: #8f5902; font-style: italic; } /* Preprocessor */
+code span.sc { color: #ce5c00; font-weight: bold; } /* SpecialChar */
+code span.ss { color: #4e9a06; } /* SpecialString */
+code span.st { color: #4e9a06; } /* String */
+code span.va { color: #000000; } /* Variable */
+code span.vs { color: #4e9a06; } /* VerbatimString */
+code span.wa { color: #8f5902; font-weight: bold; font-style: italic; } /* Warning */
+</style>
+
+
+  <!--radix_placeholder_meta_tags-->
+  <title>June Choe: Blog Posts</title>
+
+
+  <link rel="icon" type="image/png" href="static/img/icon.png"/>
+
+
+  <!--  https://developers.facebook.com/docs/sharing/webmasters#markup -->
+  <meta property="og:title" content="June Choe: Blog Posts"/>
+  <meta property="og:type" content="article"/>
+  <meta property="og:locale" content="en_US"/>
+  <meta property="og:site_name" content="June Choe"/>
+
+  <!--  https://dev.twitter.com/cards/types/summary -->
+  <meta property="twitter:card" content="summary"/>
+  <meta property="twitter:title" content="June Choe: Blog Posts"/>
+  <meta property="twitter:site" content="@yjunechoe"/>
+
+  <!--/radix_placeholder_meta_tags-->
+  <!--radix_placeholder_rmarkdown_metadata-->
+
+  <script type="text/json" id="radix-rmarkdown-metadata">
+  {"type":"list","attributes":{"names":{"type":"character","attributes":{},"value":["title","site","listing","link-citations"]}},"value":[{"type":"character","attributes":{},"value":["Blog Posts"]},{"type":"character","attributes":{},"value":["distill::distill_website"]},{"type":"character","attributes":{},"value":["posts"]},{"type":"logical","attributes":{},"value":[true]}]}
+  </script>
+  <!--/radix_placeholder_rmarkdown_metadata-->
+  <!--radix_placeholder_navigation_in_header-->
+  <meta name="distill:offset" content=""/>
+
+  <script type="application/javascript">
+
+    window.headroom_prevent_pin = false;
+
+    window.document.addEventListener("DOMContentLoaded", function (event) {
+
+      // initialize headroom for banner
+      var header = $('header').get(0);
+      var headerHeight = header.offsetHeight;
+      var headroom = new Headroom(header, {
+        tolerance: 5,
+        onPin : function() {
+          if (window.headroom_prevent_pin) {
+            window.headroom_prevent_pin = false;
+            headroom.unpin();
+          }
+        }
+      });
+      headroom.init();
+      if(window.location.hash)
+        headroom.unpin();
+      $(header).addClass('headroom--transition');
+
+      // offset scroll location for banner on hash change
+      // (see: https://github.com/WickyNilliams/headroom.js/issues/38)
+      window.addEventListener("hashchange", function(event) {
+        window.scrollTo(0, window.pageYOffset - (headerHeight + 25));
+      });
+
+      // responsive menu
+      $('.distill-site-header').each(function(i, val) {
+        var topnav = $(this);
+        var toggle = topnav.find('.nav-toggle');
+        toggle.on('click', function() {
+          topnav.toggleClass('responsive');
+        });
+      });
+
+      // nav dropdowns
+      $('.nav-dropbtn').click(function(e) {
+        $(this).next('.nav-dropdown-content').toggleClass('nav-dropdown-active');
+        $(this).parent().siblings('.nav-dropdown')
+           .children('.nav-dropdown-content').removeClass('nav-dropdown-active');
+      });
+      $("body").click(function(e){
+        $('.nav-dropdown-content').removeClass('nav-dropdown-active');
+      });
+      $(".nav-dropdown").click(function(e){
+        e.stopPropagation();
+      });
+    });
+  </script>
+
+  <style type="text/css">
+
+  /* Theme (user-documented overrideables for nav appearance) */
+
+  .distill-site-nav {
+    color: rgba(255, 255, 255, 0.8);
+    background-color: #0F2E3D;
+    font-size: 15px;
+    font-weight: 300;
+  }
+
+  .distill-site-nav a {
+    color: inherit;
+    text-decoration: none;
+  }
+
+  .distill-site-nav a:hover {
+    color: white;
+  }
+
+  @media print {
+    .distill-site-nav {
+      display: none;
+    }
+  }
+
+  .distill-site-header {
+
+  }
+
+  .distill-site-footer {
+
+  }
+
+
+  /* Site Header */
+
+  .distill-site-header {
+    width: 100%;
+    box-sizing: border-box;
+    z-index: 3;
+  }
+
+  .distill-site-header .nav-left {
+    display: inline-block;
+    margin-left: 8px;
+  }
+
+  @media screen and (max-width: 768px) {
+    .distill-site-header .nav-left {
+      margin-left: 0;
+    }
+  }
+
+
+  .distill-site-header .nav-right {
+    float: right;
+    margin-right: 8px;
+  }
+
+  .distill-site-header a,
+  .distill-site-header .title {
+    display: inline-block;
+    text-align: center;
+    padding: 14px 10px 14px 10px;
+  }
+
+  .distill-site-header .title {
+    font-size: 18px;
+    min-width: 150px;
+  }
+
+  .distill-site-header .logo {
+    padding: 0;
+  }
+
+  .distill-site-header .logo img {
+    display: none;
+    max-height: 20px;
+    width: auto;
+    margin-bottom: -4px;
+  }
+
+  .distill-site-header .nav-image img {
+    max-height: 18px;
+    width: auto;
+    display: inline-block;
+    margin-bottom: -3px;
+  }
+
+
+
+  @media screen and (min-width: 1000px) {
+    .distill-site-header .logo img {
+      display: inline-block;
+    }
+    .distill-site-header .nav-left {
+      margin-left: 20px;
+    }
+    .distill-site-header .nav-right {
+      margin-right: 20px;
+    }
+    .distill-site-header .title {
+      padding-left: 12px;
+    }
+  }
+
+
+  .distill-site-header .nav-toggle {
+    display: none;
+  }
+
+  .nav-dropdown {
+    display: inline-block;
+    position: relative;
+  }
+
+  .nav-dropdown .nav-dropbtn {
+    border: none;
+    outline: none;
+    color: rgba(255, 255, 255, 0.8);
+    padding: 16px 10px;
+    background-color: transparent;
+    font-family: inherit;
+    font-size: inherit;
+    font-weight: inherit;
+    margin: 0;
+    margin-top: 1px;
+    z-index: 2;
+  }
+
+  .nav-dropdown-content {
+    display: none;
+    position: absolute;
+    background-color: white;
+    min-width: 200px;
+    border: 1px solid rgba(0,0,0,0.15);
+    border-radius: 4px;
+    box-shadow: 0px 8px 16px 0px rgba(0,0,0,0.1);
+    z-index: 1;
+    margin-top: 2px;
+    white-space: nowrap;
+    padding-top: 4px;
+    padding-bottom: 4px;
+  }
+
+  .nav-dropdown-content hr {
+    margin-top: 4px;
+    margin-bottom: 4px;
+    border: none;
+    border-bottom: 1px solid rgba(0, 0, 0, 0.1);
+  }
+
+  .nav-dropdown-active {
+    display: block;
+  }
+
+  .nav-dropdown-content a, .nav-dropdown-content .nav-dropdown-header {
+    color: black;
+    padding: 6px 24px;
+    text-decoration: none;
+    display: block;
+    text-align: left;
+  }
+
+  .nav-dropdown-content .nav-dropdown-header {
+    display: block;
+    padding: 5px 24px;
+    padding-bottom: 0;
+    text-transform: uppercase;
+    font-size: 14px;
+    color: #999999;
+    white-space: nowrap;
+  }
+
+  .nav-dropdown:hover .nav-dropbtn {
+    color: white;
+  }
+
+  .nav-dropdown-content a:hover {
+    background-color: #ddd;
+    color: black;
+  }
+
+  .nav-right .nav-dropdown-content {
+    margin-left: -45%;
+    right: 0;
+  }
+
+  @media screen and (max-width: 768px) {
+    .distill-site-header a, .distill-site-header .nav-dropdown  {display: none;}
+    .distill-site-header a.nav-toggle {
+      float: right;
+      display: block;
+    }
+    .distill-site-header .title {
+      margin-left: 0;
+    }
+    .distill-site-header .nav-right {
+      margin-right: 0;
+    }
+    .distill-site-header {
+      overflow: hidden;
+    }
+    .nav-right .nav-dropdown-content {
+      margin-left: 0;
+    }
+  }
+
+
+  @media screen and (max-width: 768px) {
+    .distill-site-header.responsive {position: relative; min-height: 500px; }
+    .distill-site-header.responsive a.nav-toggle {
+      position: absolute;
+      right: 0;
+      top: 0;
+    }
+    .distill-site-header.responsive a,
+    .distill-site-header.responsive .nav-dropdown {
+      display: block;
+      text-align: left;
+    }
+    .distill-site-header.responsive .nav-left,
+    .distill-site-header.responsive .nav-right {
+      width: 100%;
+    }
+    .distill-site-header.responsive .nav-dropdown {float: none;}
+    .distill-site-header.responsive .nav-dropdown-content {position: relative;}
+    .distill-site-header.responsive .nav-dropdown .nav-dropbtn {
+      display: block;
+      width: 100%;
+      text-align: left;
+    }
+  }
+
+  /* Site Footer */
+
+  .distill-site-footer {
+    width: 100%;
+    overflow: hidden;
+    box-sizing: border-box;
+    z-index: 3;
+    margin-top: 30px;
+    padding-top: 30px;
+    padding-bottom: 30px;
+    text-align: center;
+  }
+
+  /* Headroom */
+
+  d-title {
+    padding-top: 6rem;
+  }
+
+  @media print {
+    d-title {
+      padding-top: 4rem;
+    }
+  }
+
+  .headroom {
+    z-index: 1000;
+    position: fixed;
+    top: 0;
+    left: 0;
+    right: 0;
+  }
+
+  .headroom--transition {
+    transition: all .4s ease-in-out;
+  }
+
+  .headroom--unpinned {
+    top: -100px;
+  }
+
+  .headroom--pinned {
+    top: 0;
+  }
+
+  /* adjust viewport for navbar height */
+  /* helps vertically center bootstrap (non-distill) content */
+  .min-vh-100 {
+    min-height: calc(100vh - 100px) !important;
+  }
+
+  </style>
+
+  <script src="site_libs/jquery-3.6.0/jquery-3.6.0.min.js"></script>
+  <link href="site_libs/font-awesome-6.4.2/css/all.min.css" rel="stylesheet"/>
+  <link href="site_libs/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet"/>
+  <script src="site_libs/headroom-0.9.4/headroom.min.js"></script>
+  <script src="site_libs/autocomplete-0.37.1/autocomplete.min.js"></script>
+  <script src="site_libs/fuse-6.4.1/fuse.min.js"></script>
+
+  <script type="application/javascript">
+
+  function getMeta(metaName) {
+    var metas = document.getElementsByTagName('meta');
+    for (let i = 0; i < metas.length; i++) {
+      if (metas[i].getAttribute('name') === metaName) {
+        return metas[i].getAttribute('content');
+      }
+    }
+    return '';
+  }
+
+  function offsetURL(url) {
+    var offset = getMeta('distill:offset');
+    return offset ? offset + '/' + url : url;
+  }
+
+  function createFuseIndex() {
+
+    // create fuse index
+    var options = {
+      keys: [
+        { name: 'title', weight: 20 },
+        { name: 'categories', weight: 15 },
+        { name: 'description', weight: 10 },
+        { name: 'contents', weight: 5 },
+      ],
+      ignoreLocation: true,
+      threshold: 0
+    };
+    var fuse = new window.Fuse([], options);
+
+    // fetch the main search.json
+    return fetch(offsetURL('search.json'))
+      .then(function(response) {
+        if (response.status == 200) {
+          return response.json().then(function(json) {
+            // index main articles
+            json.articles.forEach(function(article) {
+              fuse.add(article);
+            });
+            // download collections and index their articles
+            return Promise.all(json.collections.map(function(collection) {
+              return fetch(offsetURL(collection)).then(function(response) {
+                if (response.status === 200) {
+                  return response.json().then(function(articles) {
+                    articles.forEach(function(article) {
+                      fuse.add(article);
+                    });
+                  })
+                } else {
+                  return Promise.reject(
+                    new Error('Unexpected status from search index request: ' +
+                              response.status)
+                  );
+                }
+              });
+            })).then(function() {
+              return fuse;
+            });
+          });
+
+        } else {
+          return Promise.reject(
+            new Error('Unexpected status from search index request: ' +
+                        response.status)
+          );
+        }
+      });
+  }
+
+  window.document.addEventListener("DOMContentLoaded", function (event) {
+
+    // get search element (bail if we don't have one)
+    var searchEl = window.document.getElementById('distill-search');
+    if (!searchEl)
+      return;
+
+    createFuseIndex()
+      .then(function(fuse) {
+
+        // make search box visible
+        searchEl.classList.remove('hidden');
+
+        // initialize autocomplete
+        var options = {
+          autoselect: true,
+          hint: false,
+          minLength: 2,
+        };
+        window.autocomplete(searchEl, options, [{
+          source: function(query, callback) {
+            const searchOptions = {
+              isCaseSensitive: false,
+              shouldSort: true,
+              minMatchCharLength: 2,
+              limit: 10,
+            };
+            var results = fuse.search(query, searchOptions);
+            callback(results
+              .map(function(result) { return result.item; })
+            );
+          },
+          templates: {
+            suggestion: function(suggestion) {
+              var img = suggestion.preview && Object.keys(suggestion.preview).length > 0
+                ? `<img src="${offsetURL(suggestion.preview)}"</img>`
+                : '';
+              var html = `
+                <div class="search-item">
+                  <h3>${suggestion.title}</h3>
+                  <div class="search-item-description">
+                    ${suggestion.description || ''}
+                  </div>
+                  <div class="search-item-preview">
+                    ${img}
+                  </div>
+                </div>
+              `;
+              return html;
+            }
+          }
+        }]).on('autocomplete:selected', function(event, suggestion) {
+          window.location.href = offsetURL(suggestion.path);
+        });
+        // remove inline display style on autocompleter (we want to
+        // manage responsive display via css)
+        $('.algolia-autocomplete').css("display", "");
+      })
+      .catch(function(error) {
+        console.log(error);
+      });
+
+  });
+
+  </script>
+
+  <style type="text/css">
+
+  .nav-search {
+    font-size: x-small;
+  }
+
+  /* Algolioa Autocomplete */
+
+  .algolia-autocomplete {
+    display: inline-block;
+    margin-left: 10px;
+    vertical-align: sub;
+    background-color: white;
+    color: black;
+    padding: 6px;
+    padding-top: 8px;
+    padding-bottom: 0;
+    border-radius: 6px;
+    border: 1px #0F2E3D solid;
+    width: 180px;
+  }
+
+
+  @media screen and (max-width: 768px) {
+    .distill-site-nav .algolia-autocomplete {
+      display: none;
+      visibility: hidden;
+    }
+    .distill-site-nav.responsive .algolia-autocomplete {
+      display: inline-block;
+      visibility: visible;
+    }
+    .distill-site-nav.responsive .algolia-autocomplete .aa-dropdown-menu {
+      margin-left: 0;
+      width: 400px;
+      max-height: 400px;
+    }
+  }
+
+  .algolia-autocomplete .aa-input, .algolia-autocomplete .aa-hint {
+    width: 90%;
+    outline: none;
+    border: none;
+  }
+
+  .algolia-autocomplete .aa-hint {
+    color: #999;
+  }
+  .algolia-autocomplete .aa-dropdown-menu {
+    width: 550px;
+    max-height: 70vh;
+    overflow-x: visible;
+    overflow-y: scroll;
+    padding: 5px;
+    margin-top: 3px;
+    margin-left: -150px;
+    background-color: #fff;
+    border-radius: 5px;
+    border: 1px solid #999;
+    border-top: none;
+  }
+
+  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion {
+    cursor: pointer;
+    padding: 5px 4px;
+    border-bottom: 1px solid #eee;
+  }
+
+  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion:last-of-type {
+    border-bottom: none;
+    margin-bottom: 2px;
+  }
+
+  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item {
+    overflow: hidden;
+    font-size: 0.8em;
+    line-height: 1.4em;
+  }
+
+  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item h3 {
+    font-size: 1rem;
+    margin-block-start: 0;
+    margin-block-end: 5px;
+  }
+
+  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item-description {
+    display: inline-block;
+    overflow: hidden;
+    height: 2.8em;
+    width: 80%;
+    margin-right: 4%;
+  }
+
+  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item-preview {
+    display: inline-block;
+    width: 15%;
+  }
+
+  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item-preview img {
+    height: 3em;
+    width: auto;
+    display: none;
+  }
+
+  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion .search-item-preview img[src] {
+    display: initial;
+  }
+
+  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion.aa-cursor {
+    background-color: #eee;
+  }
+  .algolia-autocomplete .aa-dropdown-menu .aa-suggestion em {
+    font-weight: bold;
+    font-style: normal;
+  }
+
+  </style>
+
+
+  <!--/radix_placeholder_navigation_in_header-->
+  <!--radix_placeholder_distill-->
+
+  <style type="text/css">
+
+  body {
+    background-color: white;
+  }
+
+  .pandoc-table {
+    width: 100%;
+  }
+
+  .pandoc-table>caption {
+    margin-bottom: 10px;
+  }
+
+  .pandoc-table th:not([align]) {
+    text-align: left;
+  }
+
+  .pagedtable-footer {
+    font-size: 15px;
+  }
+
+  d-byline .byline {
+    grid-template-columns: 2fr 2fr;
+  }
+
+  d-byline .byline h3 {
+    margin-block-start: 1.5em;
+  }
+
+  d-byline .byline .authors-affiliations h3 {
+    margin-block-start: 0.5em;
+  }
+
+  .authors-affiliations .orcid-id {
+    width: 16px;
+    height:16px;
+    margin-left: 4px;
+    margin-right: 4px;
+    vertical-align: middle;
+    padding-bottom: 2px;
+  }
+
+  d-title .dt-tags {
+    margin-top: 1em;
+    grid-column: text;
+  }
+
+  .dt-tags .dt-tag {
+    text-decoration: none;
+    display: inline-block;
+    color: rgba(0,0,0,0.6);
+    padding: 0em 0.4em;
+    margin-right: 0.5em;
+    margin-bottom: 0.4em;
+    font-size: 70%;
+    border: 1px solid rgba(0,0,0,0.2);
+    border-radius: 3px;
+    text-transform: uppercase;
+    font-weight: 500;
+  }
+
+  d-article table.gt_table td,
+  d-article table.gt_table th {
+    border-bottom: none;
+    font-size: 100%;
+  }
+
+  .html-widget {
+    margin-bottom: 2.0em;
+  }
+
+  .l-screen-inset {
+    padding-right: 16px;
+  }
+
+  .l-screen .caption {
+    margin-left: 10px;
+  }
+
+  .shaded {
+    background: rgb(247, 247, 247);
+    padding-top: 20px;
+    padding-bottom: 20px;
+    border-top: 1px solid rgba(0, 0, 0, 0.1);
+    border-bottom: 1px solid rgba(0, 0, 0, 0.1);
+  }
+
+  .shaded .html-widget {
+    margin-bottom: 0;
+    border: 1px solid rgba(0, 0, 0, 0.1);
+  }
+
+  .shaded .shaded-content {
+    background: white;
+  }
+
+  .text-output {
+    margin-top: 0;
+    line-height: 1.5em;
+  }
+
+  .hidden {
+    display: none !important;
+  }
+
+  hr.section-separator {
+    border: none;
+    border-top: 1px solid rgba(0, 0, 0, 0.1);
+    margin: 0px;
+  }
+
+
+  d-byline {
+    border-top: none;
+  }
+
+  d-article {
+    padding-top: 2.5rem;
+    padding-bottom: 30px;
+    border-top: none;
+  }
+
+  d-appendix {
+    padding-top: 30px;
+  }
+
+  d-article>p>img {
+    width: 100%;
+  }
+
+  d-article h2 {
+    margin: 1rem 0 1.5rem 0;
+  }
+
+  d-article h3 {
+    margin-top: 1.5rem;
+  }
+
+  d-article iframe {
+    border: 1px solid rgba(0, 0, 0, 0.1);
+    margin-bottom: 2.0em;
+    width: 100%;
+  }
+
+  /* Tweak code blocks */
+
+  d-article div.sourceCode code,
+  d-article pre code {
+    font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
+  }
+
+  d-article pre,
+  d-article div.sourceCode,
+  d-article div.sourceCode pre {
+    overflow: auto;
+  }
+
+  d-article div.sourceCode {
+    background-color: white;
+  }
+
+  d-article div.sourceCode pre {
+    padding-left: 10px;
+    font-size: 12px;
+    border-left: 2px solid rgba(0,0,0,0.1);
+  }
+
+  d-article pre {
+    font-size: 12px;
+    color: black;
+    background: none;
+    margin-top: 0;
+    text-align: left;
+    white-space: pre;
+    word-spacing: normal;
+    word-break: normal;
+    word-wrap: normal;
+    line-height: 1.5;
+
+    -moz-tab-size: 4;
+    -o-tab-size: 4;
+    tab-size: 4;
+
+    -webkit-hyphens: none;
+    -moz-hyphens: none;
+    -ms-hyphens: none;
+    hyphens: none;
+  }
+
+  d-article pre a {
+    border-bottom: none;
+  }
+
+  d-article pre a:hover {
+    border-bottom: none;
+    text-decoration: underline;
+  }
+
+  d-article details {
+    grid-column: text;
+    margin-bottom: 0.8em;
+  }
+
+  @media(min-width: 768px) {
+
+  d-article pre,
+  d-article div.sourceCode,
+  d-article div.sourceCode pre {
+    overflow: visible !important;
+  }
+
+  d-article div.sourceCode pre {
+    padding-left: 18px;
+    font-size: 14px;
+  }
+
+  /* tweak for Pandoc numbered line within distill */
+  d-article pre.numberSource code > span {
+      left: -2em;
+  }
+
+  d-article pre {
+    font-size: 14px;
+  }
+
+  }
+
+  figure img.external {
+    background: white;
+    border: 1px solid rgba(0, 0, 0, 0.1);
+    box-shadow: 0 1px 8px rgba(0, 0, 0, 0.1);
+    padding: 18px;
+    box-sizing: border-box;
+  }
+
+  /* CSS for d-contents */
+
+  .d-contents {
+    grid-column: text;
+    color: rgba(0,0,0,0.8);
+    font-size: 0.9em;
+    padding-bottom: 1em;
+    margin-bottom: 1em;
+    padding-bottom: 0.5em;
+    margin-bottom: 1em;
+    padding-left: 0.25em;
+    justify-self: start;
+  }
+
+  @media(min-width: 1000px) {
+    .d-contents.d-contents-float {
+      height: 0;
+      grid-column-start: 1;
+      grid-column-end: 4;
+      justify-self: center;
+      padding-right: 3em;
+      padding-left: 2em;
+    }
+  }
+
+  .d-contents nav h3 {
+    font-size: 18px;
+    margin-top: 0;
+    margin-bottom: 1em;
+  }
+
+  .d-contents li {
+    list-style-type: none
+  }
+
+  .d-contents nav > ul {
+    padding-left: 0;
+  }
+
+  .d-contents ul {
+    padding-left: 1em
+  }
+
+  .d-contents nav ul li {
+    margin-top: 0.6em;
+    margin-bottom: 0.2em;
+  }
+
+  .d-contents nav a {
+    font-size: 13px;
+    border-bottom: none;
+    text-decoration: none
+    color: rgba(0, 0, 0, 0.8);
+  }
+
+  .d-contents nav a:hover {
+    text-decoration: underline solid rgba(0, 0, 0, 0.6)
+  }
+
+  .d-contents nav > ul > li > a {
+    font-weight: 600;
+  }
+
+  .d-contents nav > ul > li > ul {
+    font-weight: inherit;
+  }
+
+  .d-contents nav > ul > li > ul > li {
+    margin-top: 0.2em;
+  }
+
+
+  .d-contents nav ul {
+    margin-top: 0;
+    margin-bottom: 0.25em;
+  }
+
+  .d-article-with-toc h2:nth-child(2) {
+    margin-top: 0;
+  }
+
+
+  /* Figure */
+
+  .figure {
+    position: relative;
+    margin-bottom: 2.5em;
+    margin-top: 1.5em;
+  }
+
+  .figure .caption {
+    color: rgba(0, 0, 0, 0.6);
+    font-size: 12px;
+    line-height: 1.5em;
+  }
+
+  .figure img.external {
+    background: white;
+    border: 1px solid rgba(0, 0, 0, 0.1);
+    box-shadow: 0 1px 8px rgba(0, 0, 0, 0.1);
+    padding: 18px;
+    box-sizing: border-box;
+  }
+
+  .figure .caption a {
+    color: rgba(0, 0, 0, 0.6);
+  }
+
+  .figure .caption b,
+  .figure .caption strong, {
+    font-weight: 600;
+    color: rgba(0, 0, 0, 1.0);
+  }
+
+  /* Citations */
+
+  d-article .citation {
+    color: inherit;
+    cursor: inherit;
+  }
+
+  div.hanging-indent{
+    margin-left: 1em; text-indent: -1em;
+  }
+
+  /* Citation hover box */
+
+  .tippy-box[data-theme~=light-border] {
+    background-color: rgba(250, 250, 250, 0.95);
+  }
+
+  .tippy-content > p {
+    margin-bottom: 0;
+    padding: 2px;
+  }
+
+
+  /* Tweak 1000px media break to show more text */
+
+  @media(min-width: 1000px) {
+    .base-grid,
+    distill-header,
+    d-title,
+    d-abstract,
+    d-article,
+    d-appendix,
+    distill-appendix,
+    d-byline,
+    d-footnote-list,
+    d-citation-list,
+    distill-footer {
+      grid-template-columns: [screen-start] 1fr [page-start kicker-start] 80px [middle-start] 50px [text-start kicker-end] 65px 65px 65px 65px 65px 65px 65px 65px [text-end gutter-start] 65px [middle-end] 65px [page-end gutter-end] 1fr [screen-end];
+      grid-column-gap: 16px;
+    }
+
+    .grid {
+      grid-column-gap: 16px;
+    }
+
+    d-article {
+      font-size: 1.06rem;
+      line-height: 1.7em;
+    }
+    figure .caption, .figure .caption, figure figcaption {
+      font-size: 13px;
+    }
+  }
+
+  @media(min-width: 1180px) {
+    .base-grid,
+    distill-header,
+    d-title,
+    d-abstract,
+    d-article,
+    d-appendix,
+    distill-appendix,
+    d-byline,
+    d-footnote-list,
+    d-citation-list,
+    distill-footer {
+      grid-template-columns: [screen-start] 1fr [page-start kicker-start] 60px [middle-start] 60px [text-start kicker-end] 60px 60px 60px 60px 60px 60px 60px 60px [text-end gutter-start] 60px [middle-end] 60px [page-end gutter-end] 1fr [screen-end];
+      grid-column-gap: 32px;
+    }
+
+    .grid {
+      grid-column-gap: 32px;
+    }
+  }
+
+
+  /* Get the citation styles for the appendix (not auto-injected on render since
+     we do our own rendering of the citation appendix) */
+
+  d-appendix .citation-appendix,
+  .d-appendix .citation-appendix {
+    font-size: 11px;
+    line-height: 15px;
+    border-left: 1px solid rgba(0, 0, 0, 0.1);
+    padding-left: 18px;
+    border: 1px solid rgba(0,0,0,0.1);
+    background: rgba(0, 0, 0, 0.02);
+    padding: 10px 18px;
+    border-radius: 3px;
+    color: rgba(150, 150, 150, 1);
+    overflow: hidden;
+    margin-top: -12px;
+    white-space: pre-wrap;
+    word-wrap: break-word;
+  }
+
+  /* Include appendix styles here so they can be overridden */
+
+  d-appendix {
+    contain: layout style;
+    font-size: 0.8em;
+    line-height: 1.7em;
+    margin-top: 60px;
+    margin-bottom: 0;
+    border-top: 1px solid rgba(0, 0, 0, 0.1);
+    color: rgba(0,0,0,0.5);
+    padding-top: 60px;
+    padding-bottom: 48px;
+  }
+
+  d-appendix h3 {
+    grid-column: page-start / text-start;
+    font-size: 15px;
+    font-weight: 500;
+    margin-top: 1em;
+    margin-bottom: 0;
+    color: rgba(0,0,0,0.65);
+  }
+
+  d-appendix h3 + * {
+    margin-top: 1em;
+  }
+
+  d-appendix ol {
+    padding: 0 0 0 15px;
+  }
+
+  @media (min-width: 768px) {
+    d-appendix ol {
+      padding: 0 0 0 30px;
+      margin-left: -30px;
+    }
+  }
+
+  d-appendix li {
+    margin-bottom: 1em;
+  }
+
+  d-appendix a {
+    color: rgba(0, 0, 0, 0.6);
+  }
+
+  d-appendix > * {
+    grid-column: text;
+  }
+
+  d-appendix > d-footnote-list,
+  d-appendix > d-citation-list,
+  d-appendix > distill-appendix {
+    grid-column: screen;
+  }
+
+  /* Include footnote styles here so they can be overridden */
+
+  d-footnote-list {
+    contain: layout style;
+  }
+
+  d-footnote-list > * {
+    grid-column: text;
+  }
+
+  d-footnote-list a.footnote-backlink {
+    color: rgba(0,0,0,0.3);
+    padding-left: 0.5em;
+  }
+
+
+
+  /* Anchor.js */
+
+  .anchorjs-link {
+    /*transition: all .25s linear; */
+    text-decoration: none;
+    border-bottom: none;
+  }
+  *:hover > .anchorjs-link {
+    margin-left: -1.125em !important;
+    text-decoration: none;
+    border-bottom: none;
+  }
+
+  /* Social footer */
+
+  .social_footer {
+    margin-top: 30px;
+    margin-bottom: 0;
+    color: rgba(0,0,0,0.67);
+  }
+
+  .disqus-comments {
+    margin-right: 30px;
+  }
+
+  .disqus-comment-count {
+    border-bottom: 1px solid rgba(0, 0, 0, 0.4);
+    cursor: pointer;
+  }
+
+  #disqus_thread {
+    margin-top: 30px;
+  }
+
+  .article-sharing a {
+    border-bottom: none;
+    margin-right: 8px;
+  }
+
+  .article-sharing a:hover {
+    border-bottom: none;
+  }
+
+  .sidebar-section.subscribe {
+    font-size: 12px;
+    line-height: 1.6em;
+  }
+
+  .subscribe p {
+    margin-bottom: 0.5em;
+  }
+
+
+  .article-footer .subscribe {
+    font-size: 15px;
+    margin-top: 45px;
+  }
+
+
+  .sidebar-section.custom {
+    font-size: 12px;
+    line-height: 1.6em;
+  }
+
+  .custom p {
+    margin-bottom: 0.5em;
+  }
+
+  /* Styles for listing layout (hide title) */
+  .layout-listing d-title, .layout-listing .d-title {
+    display: none;
+  }
+
+  /* Styles for posts lists (not auto-injected) */
+
+
+  .posts-with-sidebar {
+    padding-left: 45px;
+    padding-right: 45px;
+  }
+
+  .posts-list .description h2,
+  .posts-list .description p {
+    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen, Ubuntu, Cantarell, "Fira Sans", "Droid Sans", "Helvetica Neue", Arial, sans-serif;
+  }
+
+  .posts-list .description h2 {
+    font-weight: 700;
+    border-bottom: none;
+    padding-bottom: 0;
+  }
+
+  .posts-list h2.post-tag {
+    border-bottom: 1px solid rgba(0, 0, 0, 0.2);
+    padding-bottom: 12px;
+  }
+  .posts-list {
+    margin-top: 60px;
+    margin-bottom: 24px;
+  }
+
+  .posts-list .post-preview {
+    text-decoration: none;
+    overflow: hidden;
+    display: block;
+    border-bottom: 1px solid rgba(0, 0, 0, 0.1);
+    padding: 24px 0;
+  }
+
+  .post-preview-last {
+    border-bottom: none !important;
+  }
+
+  .posts-list .posts-list-caption {
+    grid-column: screen;
+    font-weight: 400;
+  }
+
+  .posts-list .post-preview h2 {
+    margin: 0 0 6px 0;
+    line-height: 1.2em;
+    font-style: normal;
+    font-size: 24px;
+  }
+
+  .posts-list .post-preview p {
+    margin: 0 0 12px 0;
+    line-height: 1.4em;
+    font-size: 16px;
+  }
+
+  .posts-list .post-preview .thumbnail {
+    box-sizing: border-box;
+    margin-bottom: 24px;
+    position: relative;
+    max-width: 500px;
+  }
+  .posts-list .post-preview img {
+    width: 100%;
+    display: block;
+  }
+
+  .posts-list .metadata {
+    font-size: 12px;
+    line-height: 1.4em;
+    margin-bottom: 18px;
+  }
+
+  .posts-list .metadata > * {
+    display: inline-block;
+  }
+
+  .posts-list .metadata .publishedDate {
+    margin-right: 2em;
+  }
+
+  .posts-list .metadata .dt-authors {
+    display: block;
+    margin-top: 0.3em;
+    margin-right: 2em;
+  }
+
+  .posts-list .dt-tags {
+    display: block;
+    line-height: 1em;
+  }
+
+  .posts-list .dt-tags .dt-tag {
+    display: inline-block;
+    color: rgba(0,0,0,0.6);
+    padding: 0.3em 0.4em;
+    margin-right: 0.2em;
+    margin-bottom: 0.4em;
+    font-size: 60%;
+    border: 1px solid rgba(0,0,0,0.2);
+    border-radius: 3px;
+    text-transform: uppercase;
+    font-weight: 500;
+  }
+
+  .posts-list img {
+    opacity: 1;
+  }
+
+  .posts-list img[data-src] {
+    opacity: 0;
+  }
+
+  .posts-more {
+    clear: both;
+  }
+
+
+  .posts-sidebar {
+    font-size: 16px;
+  }
+
+  .posts-sidebar h3 {
+    font-size: 16px;
+    margin-top: 0;
+    margin-bottom: 0.5em;
+    font-weight: 400;
+    text-transform: uppercase;
+  }
+
+  .sidebar-section {
+    margin-bottom: 30px;
+  }
+
+  .categories ul {
+    list-style-type: none;
+    margin: 0;
+    padding: 0;
+  }
+
+  .categories li {
+    color: rgba(0, 0, 0, 0.8);
+    margin-bottom: 0;
+  }
+
+  .categories li>a {
+    border-bottom: none;
+  }
+
+  .categories li>a:hover {
+    border-bottom: 1px solid rgba(0, 0, 0, 0.4);
+  }
+
+  .categories .active {
+    font-weight: 600;
+  }
+
+  .categories .category-count {
+    color: rgba(0, 0, 0, 0.4);
+  }
+
+
+  @media(min-width: 768px) {
+    .posts-list .post-preview h2 {
+      font-size: 26px;
+    }
+    .posts-list .post-preview .thumbnail {
+      float: right;
+      width: 30%;
+      margin-bottom: 0;
+    }
+    .posts-list .post-preview .description {
+      float: left;
+      width: 45%;
+    }
+    .posts-list .post-preview .metadata {
+      float: left;
+      width: 20%;
+      margin-top: 8px;
+    }
+    .posts-list .post-preview p {
+      margin: 0 0 12px 0;
+      line-height: 1.5em;
+      font-size: 16px;
+    }
+    .posts-with-sidebar .posts-list {
+      float: left;
+      width: 75%;
+    }
+    .posts-with-sidebar .posts-sidebar {
+      float: right;
+      width: 20%;
+      margin-top: 60px;
+      padding-top: 24px;
+      padding-bottom: 24px;
+    }
+  }
+
+
+  /* Improve display for browsers without grid (IE/Edge <= 15) */
+
+  .downlevel {
+    line-height: 1.6em;
+    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen, Ubuntu, Cantarell, "Fira Sans", "Droid Sans", "Helvetica Neue", Arial, sans-serif;
+    margin: 0;
+  }
+
+  .downlevel .d-title {
+    padding-top: 6rem;
+    padding-bottom: 1.5rem;
+  }
+
+  .downlevel .d-title h1 {
+    font-size: 50px;
+    font-weight: 700;
+    line-height: 1.1em;
+    margin: 0 0 0.5rem;
+  }
+
+  .downlevel .d-title p {
+    font-weight: 300;
+    font-size: 1.2rem;
+    line-height: 1.55em;
+    margin-top: 0;
+  }
+
+  .downlevel .d-byline {
+    padding-top: 0.8em;
+    padding-bottom: 0.8em;
+    font-size: 0.8rem;
+    line-height: 1.8em;
+  }
+
+  .downlevel .section-separator {
+    border: none;
+    border-top: 1px solid rgba(0, 0, 0, 0.1);
+  }
+
+  .downlevel .d-article {
+    font-size: 1.06rem;
+    line-height: 1.7em;
+    padding-top: 1rem;
+    padding-bottom: 2rem;
+  }
+
+
+  .downlevel .d-appendix {
+    padding-left: 0;
+    padding-right: 0;
+    max-width: none;
+    font-size: 0.8em;
+    line-height: 1.7em;
+    margin-bottom: 0;
+    color: rgba(0,0,0,0.5);
+    padding-top: 40px;
+    padding-bottom: 48px;
+  }
+
+  .downlevel .footnotes ol {
+    padding-left: 13px;
+  }
+
+  .downlevel .base-grid,
+  .downlevel .distill-header,
+  .downlevel .d-title,
+  .downlevel .d-abstract,
+  .downlevel .d-article,
+  .downlevel .d-appendix,
+  .downlevel .distill-appendix,
+  .downlevel .d-byline,
+  .downlevel .d-footnote-list,
+  .downlevel .d-citation-list,
+  .downlevel .distill-footer,
+  .downlevel .appendix-bottom,
+  .downlevel .posts-container {
+    padding-left: 40px;
+    padding-right: 40px;
+  }
+
+  @media(min-width: 768px) {
+    .downlevel .base-grid,
+    .downlevel .distill-header,
+    .downlevel .d-title,
+    .downlevel .d-abstract,
+    .downlevel .d-article,
+    .downlevel .d-appendix,
+    .downlevel .distill-appendix,
+    .downlevel .d-byline,
+    .downlevel .d-footnote-list,
+    .downlevel .d-citation-list,
+    .downlevel .distill-footer,
+    .downlevel .appendix-bottom,
+    .downlevel .posts-container {
+    padding-left: 150px;
+    padding-right: 150px;
+    max-width: 900px;
+  }
+  }
+
+  .downlevel pre code {
+    display: block;
+    border-left: 2px solid rgba(0, 0, 0, .1);
+    padding: 0 0 0 20px;
+    font-size: 14px;
+  }
+
+  .downlevel code, .downlevel pre {
+    color: black;
+    background: none;
+    font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
+    text-align: left;
+    white-space: pre;
+    word-spacing: normal;
+    word-break: normal;
+    word-wrap: normal;
+    line-height: 1.5;
+
+    -moz-tab-size: 4;
+    -o-tab-size: 4;
+    tab-size: 4;
+
+    -webkit-hyphens: none;
+    -moz-hyphens: none;
+    -ms-hyphens: none;
+    hyphens: none;
+  }
+
+  .downlevel .posts-list .post-preview {
+    color: inherit;
+  }
+
+
+
+  </style>
+
+  <script type="application/javascript">
+
+  function is_downlevel_browser() {
+    if (bowser.isUnsupportedBrowser({ msie: "12", msedge: "16"},
+                                   window.navigator.userAgent)) {
+      return true;
+    } else {
+      return window.load_distill_framework === undefined;
+    }
+  }
+
+  // show body when load is complete
+  function on_load_complete() {
+
+    // add anchors
+    if (window.anchors) {
+      window.anchors.options.placement = 'left';
+      window.anchors.add('d-article > h2, d-article > h3, d-article > h4, d-article > h5');
+    }
+
+
+    // set body to visible
+    document.body.style.visibility = 'visible';
+
+    // force redraw for leaflet widgets
+    if (window.HTMLWidgets) {
+      var maps = window.HTMLWidgets.findAll(".leaflet");
+      $.each(maps, function(i, el) {
+        var map = this.getMap();
+        map.invalidateSize();
+        map.eachLayer(function(layer) {
+          if (layer instanceof L.TileLayer)
+            layer.redraw();
+        });
+      });
+    }
+
+    // trigger 'shown' so htmlwidgets resize
+    $('d-article').trigger('shown');
+  }
+
+  function init_distill() {
+
+    init_common();
+
+    // create front matter
+    var front_matter = $('<d-front-matter></d-front-matter>');
+    $('#distill-front-matter').wrap(front_matter);
+
+    // create d-title
+    $('.d-title').changeElementType('d-title');
+
+    // separator
+    var separator = '<hr class="section-separator" style="clear: both"/>';
+    // prepend separator above appendix
+    $('.d-byline').before(separator);
+    $('.d-article').before(separator);
+
+    // create d-byline
+    var byline = $('<d-byline></d-byline>');
+    $('.d-byline').replaceWith(byline);
+
+    // create d-article
+    var article = $('<d-article></d-article>');
+    $('.d-article').wrap(article).children().unwrap();
+
+    // move posts container into article
+    $('.posts-container').appendTo($('d-article'));
+
+    // create d-appendix
+    $('.d-appendix').changeElementType('d-appendix');
+
+    // flag indicating that we have appendix items
+    var appendix = $('.appendix-bottom').children('h3').length > 0;
+
+    // replace footnotes with <d-footnote>
+    $('.footnote-ref').each(function(i, val) {
+      appendix = true;
+      var href = $(this).attr('href');
+      var id = href.replace('#', '');
+      var fn = $('#' + id);
+      var fn_p = $('#' + id + '>p');
+      fn_p.find('.footnote-back').remove();
+      var text = fn_p.html();
+      var dtfn = $('<d-footnote></d-footnote>');
+      dtfn.html(text);
+      $(this).replaceWith(dtfn);
+    });
+    // remove footnotes
+    $('.footnotes').remove();
+
+    // move refs into #references-listing
+    $('#references-listing').replaceWith($('#refs'));
+
+    $('h1.appendix, h2.appendix').each(function(i, val) {
+      $(this).changeElementType('h3');
+    });
+    $('h3.appendix').each(function(i, val) {
+      var id = $(this).attr('id');
+      $('.d-contents a[href="#' + id + '"]').parent().remove();
+      appendix = true;
+      $(this).nextUntil($('h1, h2, h3')).addBack().appendTo($('d-appendix'));
+    });
+
+    // show d-appendix if we have appendix content
+    $("d-appendix").css('display', appendix ? 'grid' : 'none');
+
+    // localize layout chunks to just output
+    $('.layout-chunk').each(function(i, val) {
+
+      // capture layout
+      var layout = $(this).attr('data-layout');
+
+      // apply layout to markdown level block elements
+      var elements = $(this).children().not('details, div.sourceCode, pre, script');
+      elements.each(function(i, el) {
+        var layout_div = $('<div class="' + layout + '"></div>');
+        if (layout_div.hasClass('shaded')) {
+          var shaded_content = $('<div class="shaded-content"></div>');
+          $(this).wrap(shaded_content);
+          $(this).parent().wrap(layout_div);
+        } else {
+          $(this).wrap(layout_div);
+        }
+      });
+
+
+      // unwrap the layout-chunk div
+      $(this).children().unwrap();
+    });
+
+    // remove code block used to force  highlighting css
+    $('.distill-force-highlighting-css').parent().remove();
+
+    // remove empty line numbers inserted by pandoc when using a
+    // custom syntax highlighting theme, except when numbering line
+    // in code chunk
+    $('pre:not(.numberLines) code.sourceCode a:empty').remove();
+
+    // load distill framework
+    load_distill_framework();
+
+    // wait for window.distillRunlevel == 4 to do post processing
+    function distill_post_process() {
+
+      if (!window.distillRunlevel || window.distillRunlevel < 4)
+        return;
+
+      // hide author/affiliations entirely if we have no authors
+      var front_matter = JSON.parse($("#distill-front-matter").html());
+      var have_authors = front_matter.authors && front_matter.authors.length > 0;
+      if (!have_authors)
+        $('d-byline').addClass('hidden');
+
+      // article with toc class
+      $('.d-contents').parent().addClass('d-article-with-toc');
+
+      // strip links that point to #
+      $('.authors-affiliations').find('a[href="#"]').removeAttr('href');
+
+      // add orcid ids
+      $('.authors-affiliations').find('.author').each(function(i, el) {
+        var orcid_id = front_matter.authors[i].orcidID;
+        var author_name = front_matter.authors[i].author
+        if (orcid_id) {
+          var a = $('<a></a>');
+          a.attr('href', 'https://orcid.org/' + orcid_id);
+          var img = $('<img></img>');
+          img.addClass('orcid-id');
+          img.attr('alt', author_name ? 'ORCID ID for ' + author_name : 'ORCID ID');
+          img.attr('src','data:image/png;base64,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');
+          a.append(img);
+          $(this).append(a);
+        }
+      });
+
+      // hide elements of author/affiliations grid that have no value
+      function hide_byline_column(caption) {
+        $('d-byline').find('h3:contains("' + caption + '")').parent().css('visibility', 'hidden');
+      }
+
+      // affiliations
+      var have_affiliations = false;
+      for (var i = 0; i<front_matter.authors.length; ++i) {
+        var author = front_matter.authors[i];
+        if (author.affiliation !== "&nbsp;") {
+          have_affiliations = true;
+          break;
+        }
+      }
+      if (!have_affiliations)
+        $('d-byline').find('h3:contains("Affiliations")').css('visibility', 'hidden');
+
+      // published date
+      if (!front_matter.publishedDate)
+        hide_byline_column("Published");
+
+      // document object identifier
+      var doi = $('d-byline').find('h3:contains("DOI")');
+      var doi_p = doi.next().empty();
+      if (!front_matter.doi) {
+        // if we have a citation and valid citationText then link to that
+        if ($('#citation').length > 0 && front_matter.citationText) {
+          doi.html('Citation');
+          $('<a href="#citation"></a>')
+            .text(front_matter.citationText)
+            .appendTo(doi_p);
+        } else {
+          hide_byline_column("DOI");
+        }
+      } else {
+        $('<a></a>')
+           .attr('href', "https://doi.org/" + front_matter.doi)
+           .html(front_matter.doi)
+           .appendTo(doi_p);
+      }
+
+       // change plural form of authors/affiliations
+      if (front_matter.authors.length === 1) {
+        var grid = $('.authors-affiliations');
+        grid.children('h3:contains("Authors")').text('Author');
+        grid.children('h3:contains("Affiliations")').text('Affiliation');
+      }
+
+      // remove d-appendix and d-footnote-list local styles
+      $('d-appendix > style:first-child').remove();
+      $('d-footnote-list > style:first-child').remove();
+
+      // move appendix-bottom entries to the bottom
+      $('.appendix-bottom').appendTo('d-appendix').children().unwrap();
+      $('.appendix-bottom').remove();
+
+      // hoverable references
+      $('span.citation[data-cites]').each(function() {
+        const citeChild = $(this).children()[0]
+        // Do not process if @xyz has been used without escaping and without bibliography activated
+        // https://github.com/rstudio/distill/issues/466
+        if (citeChild === undefined) return true
+
+        if (citeChild.nodeName == "D-FOOTNOTE") {
+          var fn = citeChild
+          $(this).html(fn.shadowRoot.querySelector("sup"))
+          $(this).id = fn.id
+          fn.remove()
+        }
+        var refs = $(this).attr('data-cites').split(" ");
+        var refHtml = refs.map(function(ref) {
+          // Could use CSS.escape too here, we insure backward compatibility in navigator
+          return "<p>" + $('div[id="ref-' + ref + '"]').html() + "</p>";
+        }).join("\n");
+        window.tippy(this, {
+          allowHTML: true,
+          content: refHtml,
+          maxWidth: 500,
+          interactive: true,
+          interactiveBorder: 10,
+          theme: 'light-border',
+          placement: 'bottom-start'
+        });
+      });
+
+      // fix footnotes in tables (#411)
+      // replacing broken distill.pub feature
+      $('table d-footnote').each(function() {
+        // we replace internal showAtNode methode which is triggered when hovering a footnote
+        this.hoverBox.showAtNode = function(node) {
+          // ported from https://github.com/distillpub/template/pull/105/files
+          calcOffset = function(elem) {
+              let x = elem.offsetLeft;
+              let y = elem.offsetTop;
+              // Traverse upwards until an `absolute` element is found or `elem`
+              // becomes null.
+              while (elem = elem.offsetParent && elem.style.position != 'absolute') {
+                  x += elem.offsetLeft;
+                  y += elem.offsetTop;
+              }
+
+              return { left: x, top: y };
+          }
+          // https://developer.mozilla.org/en-US/docs/Web/API/HTMLElement/offsetTop
+          const bbox = node.getBoundingClientRect();
+          const offset = calcOffset(node);
+          this.show([offset.left + bbox.width, offset.top + bbox.height]);
+        }
+      })
+
+      // clear polling timer
+      clearInterval(tid);
+
+      // show body now that everything is ready
+      on_load_complete();
+    }
+
+    var tid = setInterval(distill_post_process, 50);
+    distill_post_process();
+
+  }
+
+  function init_downlevel() {
+
+    init_common();
+
+     // insert hr after d-title
+    $('.d-title').after($('<hr class="section-separator"/>'));
+
+    // check if we have authors
+    var front_matter = JSON.parse($("#distill-front-matter").html());
+    var have_authors = front_matter.authors && front_matter.authors.length > 0;
+
+    // manage byline/border
+    if (!have_authors)
+      $('.d-byline').remove();
+    $('.d-byline').after($('<hr class="section-separator"/>'));
+    $('.d-byline a').remove();
+
+    // remove toc
+    $('.d-contents').remove();
+
+    // move appendix elements
+    $('h1.appendix, h2.appendix').each(function(i, val) {
+      $(this).changeElementType('h3');
+    });
+    $('h3.appendix').each(function(i, val) {
+      $(this).nextUntil($('h1, h2, h3')).addBack().appendTo($('.d-appendix'));
+    });
+
+
+    // inject headers into references and footnotes
+    var refs_header = $('<h3></h3>');
+    refs_header.text('References');
+    $('#refs').prepend(refs_header);
+
+    var footnotes_header = $('<h3></h3');
+    footnotes_header.text('Footnotes');
+    $('.footnotes').children('hr').first().replaceWith(footnotes_header);
+
+    // move appendix-bottom entries to the bottom
+    $('.appendix-bottom').appendTo('.d-appendix').children().unwrap();
+    $('.appendix-bottom').remove();
+
+    // remove appendix if it's empty
+    if ($('.d-appendix').children().length === 0)
+      $('.d-appendix').remove();
+
+    // prepend separator above appendix
+    $('.d-appendix').before($('<hr class="section-separator" style="clear: both"/>'));
+
+    // trim code
+    $('pre>code').each(function(i, val) {
+      $(this).html($.trim($(this).html()));
+    });
+
+    // move posts-container right before article
+    $('.posts-container').insertBefore($('.d-article'));
+
+    $('body').addClass('downlevel');
+
+    on_load_complete();
+  }
+
+
+  function init_common() {
+
+    // jquery plugin to change element types
+    (function($) {
+      $.fn.changeElementType = function(newType) {
+        var attrs = {};
+
+        $.each(this[0].attributes, function(idx, attr) {
+          attrs[attr.nodeName] = attr.nodeValue;
+        });
+
+        this.replaceWith(function() {
+          return $("<" + newType + "/>", attrs).append($(this).contents());
+        });
+      };
+    })(jQuery);
+
+    // prevent underline for linked images
+    $('a > img').parent().css({'border-bottom' : 'none'});
+
+    // mark non-body figures created by knitr chunks as 100% width
+    $('.layout-chunk').each(function(i, val) {
+      var figures = $(this).find('img, .html-widget');
+      // ignore leaflet img layers (#106)
+      figures = figures.filter(':not(img[class*="leaflet"])')
+      if ($(this).attr('data-layout') !== "l-body") {
+        figures.css('width', '100%');
+      } else {
+        figures.css('max-width', '100%');
+        figures.filter("[width]").each(function(i, val) {
+          var fig = $(this);
+          fig.css('width', fig.attr('width') + 'px');
+        });
+
+      }
+    });
+
+    // auto-append index.html to post-preview links in file: protocol
+    // and in rstudio ide preview
+    $('.post-preview').each(function(i, val) {
+      if (window.location.protocol === "file:")
+        $(this).attr('href', $(this).attr('href') + "index.html");
+    });
+
+    // get rid of index.html references in header
+    if (window.location.protocol !== "file:") {
+      $('.distill-site-header a[href]').each(function(i,val) {
+        $(this).attr('href', $(this).attr('href').replace(/^index[.]html/, "./"));
+      });
+    }
+
+    // add class to pandoc style tables
+    $('tr.header').parent('thead').parent('table').addClass('pandoc-table');
+    $('.kable-table').children('table').addClass('pandoc-table');
+
+    // add figcaption style to table captions
+    $('caption').parent('table').addClass("figcaption");
+
+    // initialize posts list
+    if (window.init_posts_list)
+      window.init_posts_list();
+
+    // implmement disqus comment link
+    $('.disqus-comment-count').click(function() {
+      window.headroom_prevent_pin = true;
+      $('#disqus_thread').toggleClass('hidden');
+      if (!$('#disqus_thread').hasClass('hidden')) {
+        var offset = $(this).offset();
+        $(window).resize();
+        $('html, body').animate({
+          scrollTop: offset.top - 35
+        });
+      }
+    });
+  }
+
+  document.addEventListener('DOMContentLoaded', function() {
+    if (is_downlevel_browser())
+      init_downlevel();
+    else
+      window.addEventListener('WebComponentsReady', init_distill);
+  });
+
+  </script>
+
+  <!--/radix_placeholder_distill-->
+  <script src="site_libs/header-attrs-2.27/header-attrs.js"></script>
+  <script src="site_libs/popper-2.6.0/popper.min.js"></script>
+  <link href="site_libs/tippy-6.2.7/tippy.css" rel="stylesheet" />
+  <link href="site_libs/tippy-6.2.7/tippy-light-border.css" rel="stylesheet" />
+  <script src="site_libs/tippy-6.2.7/tippy.umd.min.js"></script>
+  <script src="site_libs/anchor-4.2.2/anchor.min.js"></script>
+  <script src="site_libs/bowser-1.9.3/bowser.min.js"></script>
+  <script src="site_libs/webcomponents-2.0.0/webcomponents.js"></script>
+  <script src="site_libs/distill-2.2.21/template.v2.js"></script>
+  <!--radix_placeholder_site_in_header-->
+  <script type="text/javascript" cookie-consent="tracking" async src="https://www.googletagmanager.com/gtag/js?id=UA-178413324-1"></script>
+  <script type="text/javascript" cookie-consent="tracking">
+  window.dataLayer = window.dataLayer || [];
+  function gtag(){dataLayer.push(arguments);}
+  gtag('js', new Date());
+  gtag('config', 'UA-178413324-1');
+  </script>
+  <style type="text/css">
+  /* ---------- Global Styles ---------- */
+
+  @import url('https://fonts.googleapis.com/css?family=Atkinson+Hyperlegible&display=swap');
+  @import url('https://fonts.googleapis.com/css?family=Roboto+Mono&display=swap');
+  @import url('https://fonts.googleapis.com/css?family=Roboto+Slab&display=swap');
+  @import url('https://fonts.googleapis.com/css?family=Roboto&display=swap');
+  @import url('https://fonts.googleapis.com/css?family=Fira+Mono&display=swap');
+
+  html, body, p {
+    
+    font-family: 'Atkinson Hyperlegible';
+    font-weight: 400;
+    line-height: 1.7; 
+    font-size: 1em;
+    color: #333333;
+    font-style: normal;
+    
+  }
+
+  h2, h3 {
+    font-family: 'Roboto Slab'
+  }
+
+  d-article h4 {
+    font-size: 20px;
+    text-align: center;
+    margin-top: 0.5em;
+    padding: 5px 0px;
+    outline: 1px solid black;
+  }
+
+  d-article h5 {
+    font-size: 18px;
+    text-decoration: underline;
+    margin-bottom: 0.5em;
+  }
+
+  em {
+    margin-right: 3px;
+  }
+
+  div.opener {
+    text-align: justify;
+  }
+
+  /* Small caps */
+
+  .sc {
+    font-variant: small-caps;
+    letter-spacing: 0.1em;
+  }
+
+
+  /* ---------- Index Page Styles ---------- */
+
+
+  /* Name time */
+
+  div.nav-left.title {
+    font-family: 'Roboto Slab';
+  }
+
+
+  /* Search bar */
+
+  .angolia-autocomplete {
+    width: 300px;
+  }
+
+  .nav-search {
+      font-size: inherit;
+  }
+
+  /* Publication Date */
+
+  .publishedDate {
+    font-size: 1.1em;
+  }
+
+
+  /* Post Description */
+
+  .posts-list .description h2 {
+    font-family: 'Roboto Slab';
+  }
+
+  .description p {
+    font-style: italic;
+    padding-top: 5px;
+  }
+
+
+  /* Tags */
+
+  .posts-list .dt-tags {
+    margin-top: 10px;
+    margin-right: 10px;
+  }
+
+
+  .posts-list .dt-tags .dt-tag {
+    font-family: 'Roboto Slab';
+    font-weight: bold;
+    letter-spacing: 1px;
+    background-color: #565656;
+    color: white;
+  }
+
+  /* Top & Bot bars */
+
+  .distill-site-nav {
+    background-color: #262c2f;
+  }
+
+  .distill-site-footer p {
+    color: white;
+  }
+
+
+
+  /* Post published date medatada */
+  .posts-list .metadata .publishedDate{
+    font-family: 'Roboto Mono';
+  }
+
+
+  /* Post list caption */
+  .posts-list .posts-list-caption{
+    font-family: 'Fira Mono';
+    border-bottom: 5px solid #f3f3f3;
+    padding-bottom: 2rem;
+  }
+
+
+  /* Sidebar Categories */
+  .posts-sidebar {
+    font-family: 'Fira Mono';
+  }
+
+  .sidebar-section h3 {
+    font-size: 22px;
+    margin-bottom: 20px;
+  }
+
+
+  /* ---------- Article Styles ---------- */
+
+
+  /* Title */
+
+  d-title {
+    padding-bottom: 0;
+  }
+
+  d-title h1 {
+    font-family: 'Roboto Slab';
+    line-height: 1.3;
+  }
+
+  d-title p {
+    font-weight: 600;
+  }
+
+
+  /* General */
+
+  d-article > h2 {
+    margin: 2.5rem 0 1.5rem 0;
+    border-bottom: 2px solid black;
+  }
+
+  div.l-body + h2 {
+    margin-top: 0px;
+  }
+
+  d-article > h3 {
+    margin-top: 1em;
+    font-size: 28px;
+    padding-bottom: 10px;
+    border-bottom: 2px solid lightgrey;
+  }
+
+  d-article ol {
+    padding-bottom: 15px;
+  }
+
+  /* Aside */
+
+  aside {
+    margin-left: 20px;
+    width: 200px;
+    font-family: 'Roboto Slab';
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+<a href="posts/2024-09-22-fetch-files-web/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["tutorial"]}</script>
+<div class="metadata">
+<div class="publishedDate">Sept. 22, 2024</div>
+</div>
+<div class="thumbnail">
+<img src="posts/2024-09-22-fetch-files-web/github-dplyr-starwars.jpg"/>
+</div>
+<div class="description">
+<h2>Read files on the web into R</h2>
+<div class="dt-tags">
+<div class="dt-tag">tutorial</div>
+</div>
+<p>For the download-button-averse of us</p>
+</div>
+</a>
+<a href="posts/2023-06-11-row-relational-operations/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data wrangling","dplyr"]}</script>
+<div class="metadata">
+<div class="publishedDate">Sept. 22, 2024</div>
+</div>
+<div class="thumbnail">
+<img src="posts/2023-06-11-row-relational-operations/preview.png"/>
+</div>
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+<div class="dt-tags">
+<div class="dt-tag">data wrangling</div>
+<div class="dt-tag">dplyr</div>
+</div>
+<p>A love letter to dplyr::slice() and a gallery of usecases</p>
+</div>
+</a>
+<a href="posts/2024-07-21-enumerate-possible-options/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["design"]}</script>
+<div class="metadata">
+<div class="publishedDate">July 21, 2024</div>
+</div>
+<div class="thumbnail">
+<img src="posts/2024-07-21-enumerate-possible-options/preview.jpg"/>
+</div>
+<div class="description">
+<h2>Naming patterns for boolean enums</h2>
+<div class="dt-tags">
+<div class="dt-tag">design</div>
+</div>
+<p>Some thoughts on the principle of enumerating possible options, even for booleans</p>
+</div>
+</a>
+<a href="posts/2024-06-09-ave-for-the-average/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["dplyr"]}</script>
+<div class="metadata">
+<div class="publishedDate">June 23, 2024</div>
+</div>
+<div class="thumbnail">
+<img src="posts/2024-06-09-ave-for-the-average/preview.png"/>
+</div>
+<div class="description">
+<h2>`ave()` for the average {dplyr} user</h2>
+<div class="dt-tags">
+<div class="dt-tag">dplyr</div>
+</div>
+<p>tidyverse 🤝 base R</p>
+</div>
+</a>
+<a href="posts/2024-03-04-args-args-args-args/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["args","metaprogramming"]}</script>
+<div class="metadata">
+<div class="publishedDate">March 5, 2024</div>
+</div>
+<div class="thumbnail">
+<img src="posts/2024-03-04-args-args-args-args/preview.png"/>
+</div>
+<div class="description">
+<h2>args(args(args)(args))</h2>
+<div class="dt-tags">
+<div class="dt-tag">args</div>
+<div class="dt-tag">metaprogramming</div>
+</div>
+<p>The unexpected sequal to "R is a language optimized for meme-ing"</p>
+</div>
+</a>
+<a href="posts/2024-02-20-helloworld-print/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["metaprogramming"]}</script>
+<div class="metadata">
+<div class="publishedDate">Feb. 20, 2024</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2024-02-20-helloworld-print/preview.png"/>
+</div>
+<div class="description">
+<h2>HelloWorld("print")</h2>
+<div class="dt-tags">
+<div class="dt-tag">metaprogramming</div>
+</div>
+<p>R is a language optimized for meme-ing</p>
+</div>
+</a>
+<a href="posts/2023-12-31-2023-year-in-review/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["reflections"]}</script>
+<div class="metadata">
+<div class="publishedDate">Dec. 31, 2023</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2023-12-31-2023-year-in-review/preview.png"/>
+</div>
+<div class="description">
+<h2>2023 Year in Review</h2>
+<div class="dt-tags">
+<div class="dt-tag">reflections</div>
+</div>
+<p>Reflections and updates on what I've been up to in 2023</p>
+</div>
+</a>
+<a href="posts/2023-12-03-untidy-select/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data wrangling","dplyr","tidyselect"]}</script>
+<div class="metadata">
+<div class="publishedDate">Dec. 4, 2023</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2023-12-03-untidy-select/preview.png"/>
+</div>
+<div class="description">
+<h2>The many ways to (un)tidy-select</h2>
+<div class="dt-tags">
+<div class="dt-tag">data wrangling</div>
+<div class="dt-tag">dplyr</div>
+<div class="dt-tag">tidyselect</div>
+</div>
+<p>Deconstructing {tidyselect} and building it back up</p>
+</div>
+</a>
+<a href="posts/2023-07-09-x-y-problem/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["reflections"]}</script>
+<div class="metadata">
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+</div>
+<div class="thumbnail">
+<img data-src="posts/2023-07-09-x-y-problem/preview.png"/>
+</div>
+<div class="description">
+<h2>Fumbling my way through an XY problem</h2>
+<div class="dt-tags">
+<div class="dt-tag">reflections</div>
+</div>
+<p>Some lessons learned from a (personal) case study</p>
+</div>
+</a>
+<a href="posts/2022-11-13-dataframes-jl-and-accessories/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["julia","data wrangling","DataFrames.jl","dplyr","data.table"]}</script>
+<div class="metadata">
+<div class="publishedDate">Nov. 15, 2022</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2022-11-13-dataframes-jl-and-accessories/preview.jpg"/>
+</div>
+<div class="description">
+<h2>First impressions of DataFrames.jl and accessories</h2>
+<div class="dt-tags">
+<div class="dt-tag">julia</div>
+<div class="dt-tag">data wrangling</div>
+<div class="dt-tag">DataFrames.jl</div>
+<div class="dt-tag">dplyr</div>
+<div class="dt-tag">data.table</div>
+</div>
+<p>Perspectives from a {dplyr} and {data.table} useR</p>
+</div>
+</a>
+<a href="posts/2022-07-30-user2022/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["conference","ggtrace"]}</script>
+<div class="metadata">
+<div class="publishedDate">Aug. 1, 2022</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2022-07-30-user2022/preview.png"/>
+</div>
+<div class="description">
+<h2>Reflections on useR! 2022</h2>
+<div class="dt-tags">
+<div class="dt-tag">conference</div>
+<div class="dt-tag">ggtrace</div>
+</div>
+<p>Notes from attending and speaking at my first R conference</p>
+</div>
+</a>
+<a href="posts/2022-07-06-ggplot2-delayed-aes-2/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data visualization","ggplot2","tutorial"]}</script>
+<div class="metadata">
+<div class="publishedDate">July 6, 2022</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2022-07-06-ggplot2-delayed-aes-2/preview.png"/>
+</div>
+<div class="description">
+<h2>Demystifying delayed aesthetic evaluation: Part 2</h2>
+<div class="dt-tags">
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">ggplot2</div>
+<div class="dt-tag">tutorial</div>
+</div>
+<p>Exposing the `Stat` ggproto in functional programming terms</p>
+</div>
+</a>
+<a href="posts/2022-03-10-ggplot2-delayed-aes-1/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data visualization","ggplot2","ggplot internals","tutorial"]}</script>
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+<div class="publishedDate">March 17, 2022</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2022-03-10-ggplot2-delayed-aes-1/preview.png"/>
+</div>
+<div class="description">
+<h2>Demystifying delayed aesthetic evaluation: Part 1</h2>
+<div class="dt-tags">
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">ggplot2</div>
+<div class="dt-tag">ggplot internals</div>
+<div class="dt-tag">tutorial</div>
+</div>
+<p>Exploring the logic of `after_stat()` to peek inside ggplot internals</p>
+</div>
+</a>
+<a href="posts/2021-06-24-setting-up-and-debugging-custom-fonts/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data visualization","ggplot2","typography","tutorial"]}</script>
+<div class="metadata">
+<div class="publishedDate">June 24, 2021</div>
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+<div class="thumbnail">
+<img data-src="posts/2021-06-24-setting-up-and-debugging-custom-fonts/preview.png"/>
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+<h2>Setting up and debugging custom fonts</h2>
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+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">ggplot2</div>
+<div class="dt-tag">typography</div>
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+</div>
+<p>A practical introduction to all (new) things font in R</p>
+</div>
+</a>
+<a href="posts/2021-01-17-random-sampling-a-table-animation/" class="post-preview">
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+</div>
+<div class="thumbnail">
+<img data-src="posts/2021-01-17-random-sampling-a-table-animation/table_preview.png"/>
+</div>
+<div class="description">
+<h2>Random Sampling: A table animation</h2>
+<div class="dt-tags">
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">data wrangling</div>
+</div>
+<p>Plus a convenient way of rendering LaTeX expressions as images</p>
+</div>
+</a>
+<a href="posts/2020-12-13-collapse-repetitive-piping-with-reduce/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data wrangling","tutorial"]}</script>
+<div class="metadata">
+<div class="publishedDate">Dec. 13, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-12-13-collapse-repetitive-piping-with-reduce/reduce_ggplot.png"/>
+</div>
+<div class="description">
+<h2>Collapse repetitive piping with reduce()</h2>
+<div class="dt-tags">
+<div class="dt-tag">data wrangling</div>
+<div class="dt-tag">tutorial</div>
+</div>
+<p>Featuring accumulate()</p>
+</div>
+</a>
+<a href="posts/2020-11-08-plot-makeover-2/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["plot makeover","data visualization","ggplot2"]}</script>
+<div class="metadata">
+<div class="publishedDate">Nov. 8, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-11-08-plot-makeover-2/plot-makeover-2_files/figure-html5/final-1.png"/>
+</div>
+<div class="description">
+<h2>Plot Makeover #2</h2>
+<div class="dt-tags">
+<div class="dt-tag">plot makeover</div>
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">ggplot2</div>
+</div>
+<p>Making a dodged-stacked hybrid bar plot in {ggplot2}</p>
+</div>
+</a>
+<a href="posts/2020-11-03-tidytuesday-2020-week-45/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["ggplot2","data visualization","tidytuesday"]}</script>
+<div class="metadata">
+<div class="publishedDate">Nov. 3, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-11-03-tidytuesday-2020-week-45/preview.png"/>
+</div>
+<div class="description">
+<h2>TidyTuesday 2020 week 45</h2>
+<div class="dt-tags">
+<div class="dt-tag">ggplot2</div>
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">tidytuesday</div>
+</div>
+<p>Waffle chart of IKEA furnitures in stock</p>
+</div>
+</a>
+<a href="posts/2020-10-28-tidytuesday-2020-week-44/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["ggplot2","gganimate","spatial","data visualization","tidytuesday"]}</script>
+<div class="metadata">
+<div class="publishedDate">Oct. 28, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-10-28-tidytuesday-2020-week-44/preview.png"/>
+</div>
+<div class="description">
+<h2>TidyTuesday 2020 week 44</h2>
+<div class="dt-tags">
+<div class="dt-tag">ggplot2</div>
+<div class="dt-tag">gganimate</div>
+<div class="dt-tag">spatial</div>
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">tidytuesday</div>
+</div>
+<p>Patched animation of the location and cumulative capacity of wind turbines in Canada</p>
+</div>
+</a>
+<a href="posts/2020-10-22-analysis-of-everycolorbots-tweets/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data visualization","ggplot2","rtweet","colors"]}</script>
+<div class="metadata">
+<div class="publishedDate">Oct. 22, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-10-22-analysis-of-everycolorbots-tweets/preview.png"/>
+</div>
+<div class="description">
+<h2>Analysis of @everycolorbot's tweets</h2>
+<div class="dt-tags">
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">ggplot2</div>
+<div class="dt-tag">rtweet</div>
+<div class="dt-tag">colors</div>
+</div>
+<p>And why you should avoid neon colors</p>
+</div>
+</a>
+<a href="posts/2020-10-13-designing-guiding-aesthetics/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data visualization","ggplot2","tidytuesday"]}</script>
+<div class="metadata">
+<div class="publishedDate">Oct. 13, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-10-13-designing-guiding-aesthetics/preview.png"/>
+</div>
+<div class="description">
+<h2>Designing guiding aesthetics</h2>
+<div class="dt-tags">
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">ggplot2</div>
+<div class="dt-tag">tidytuesday</div>
+</div>
+<p>The fine line between creativity and noise</p>
+</div>
+</a>
+<a href="posts/2020-09-26-demystifying-stat-layers-ggplot2/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data visualization","ggplot2","tutorial"]}</script>
+<div class="metadata">
+<div class="publishedDate">Sept. 27, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-09-26-demystifying-stat-layers-ggplot2/preview.png"/>
+</div>
+<div class="description">
+<h2>Demystifying stat_ layers in {ggplot2}</h2>
+<div class="dt-tags">
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">ggplot2</div>
+<div class="dt-tag">tutorial</div>
+</div>
+<p>The motivation behind stat, the distinction between stat and geom, and a case study of stat_summary()</p>
+</div>
+</a>
+<a href="posts/2020-09-23-tidytuesday-2020-week-39/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["ggplot2","data visualization","tidytuesday"]}</script>
+<div class="metadata">
+<div class="publishedDate">Sept. 23, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-09-23-tidytuesday-2020-week-39/preview.png"/>
+</div>
+<div class="description">
+<h2>TidyTuesday 2020 week 39</h2>
+<div class="dt-tags">
+<div class="dt-tag">ggplot2</div>
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">tidytuesday</div>
+</div>
+<p>Stacked area plot of the heights of Himalayan peaks attempted over the last century</p>
+</div>
+</a>
+<a href="posts/2020-09-20-plot-makeover-1/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["plot makeover","data visualization","ggplot2"]}</script>
+<div class="metadata">
+<div class="publishedDate">Sept. 20, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-09-20-plot-makeover-1/plot-makeover-1_files/figure-html5/after_bar_plot-1.png"/>
+</div>
+<div class="description">
+<h2>Plot Makeover #1</h2>
+<div class="dt-tags">
+<div class="dt-tag">plot makeover</div>
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">ggplot2</div>
+</div>
+<p>Flattening a faceted grid for strictly horizontal comparisons</p>
+</div>
+</a>
+<a href="posts/2020-09-14-tidytuesday-2020-week-38/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["tables","data visualization","tidytuesday"]}</script>
+<div class="metadata">
+<div class="publishedDate">Sept. 14, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-09-14-tidytuesday-2020-week-38/preview.png"/>
+</div>
+<div class="description">
+<h2>TidyTuesday 2020 week 38</h2>
+<div class="dt-tags">
+<div class="dt-tag">tables</div>
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">tidytuesday</div>
+</div>
+<p>Visualizing two decades of primary and secondary education spending with {gt}</p>
+</div>
+</a>
+<a href="posts/2020-09-12-videos-in-reactable/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["tables","data visualization"]}</script>
+<div class="metadata">
+<div class="publishedDate">Sept. 12, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-09-12-videos-in-reactable/preview.png"/>
+</div>
+<div class="description">
+<h2>Embedding videos in {reactable} tables</h2>
+<div class="dt-tags">
+<div class="dt-tag">tables</div>
+<div class="dt-tag">data visualization</div>
+</div>
+<p>Pushing the limits of expandable row details</p>
+</div>
+</a>
+<a href="posts/2020-09-06-fonts-for-graphs/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data visualization","typography"]}</script>
+<div class="metadata">
+<div class="publishedDate">Sept. 6, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-09-06-fonts-for-graphs/preview.png"/>
+</div>
+<div class="description">
+<h2>Fonts for graphs</h2>
+<div class="dt-tags">
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">typography</div>
+</div>
+<p>A small collection of my favorite fonts for data visualization</p>
+</div>
+</a>
+<a href="posts/2020-08-17-tidytuesday-2020-week-33/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["tidytuesday","gganimate","ggplot2"]}</script>
+<div class="metadata">
+<div class="publishedDate">Aug. 17, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-08-17-tidytuesday-2020-week-33/preview.png"/>
+</div>
+<div class="description">
+<h2>TidyTuesday 2020 Week 33</h2>
+<div class="dt-tags">
+<div class="dt-tag">tidytuesday</div>
+<div class="dt-tag">gganimate</div>
+<div class="dt-tag">ggplot2</div>
+</div>
+<p>An animation of the main characters in Avatar</p>
+</div>
+</a>
+<a href="posts/2020-08-07-saving-a-line-of-piping/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data wrangling","dplyr","tutorial"]}</script>
+<div class="metadata">
+<div class="publishedDate">Aug. 7, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-08-07-saving-a-line-of-piping/preview.png"/>
+</div>
+<div class="description">
+<h2>Saving a line of piping</h2>
+<div class="dt-tags">
+<div class="dt-tag">data wrangling</div>
+<div class="dt-tag">dplyr</div>
+<div class="dt-tag">tutorial</div>
+</div>
+<p>Some notes on lesser known functions/functionalities that combine common chain of {dplyr} verbs.</p>
+</div>
+</a>
+<a href="posts/2020-08-04-tidytuesday-2020-week-32/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["tidytuesday","data visualization","ggplot2"]}</script>
+<div class="metadata">
+<div class="publishedDate">Aug. 4, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-08-04-tidytuesday-2020-week-32/preview.png"/>
+</div>
+<div class="description">
+<h2>TidyTuesday 2020 Week 32</h2>
+<div class="dt-tags">
+<div class="dt-tag">tidytuesday</div>
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">ggplot2</div>
+</div>
+<p>A dumbbell chart visualization of energy production trends among European countries</p>
+</div>
+</a>
+<a href="posts/2020-07-29-six-years-of-my-spotify-playlists/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["ggplot2","gganimate","spotifyr","data wrangling","data visualization"]}</script>
+<div class="metadata">
+<div class="publishedDate">July 29, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-07-29-six-years-of-my-spotify-playlists/preview.png"/>
+</div>
+<div class="description">
+<h2>Six years of my Spotify playlists</h2>
+<div class="dt-tags">
+<div class="dt-tag">ggplot2</div>
+<div class="dt-tag">gganimate</div>
+<div class="dt-tag">spotifyr</div>
+<div class="dt-tag">data wrangling</div>
+<div class="dt-tag">data visualization</div>
+</div>
+<p>An analysis of acoustic features with {spotifyr}</p>
+</div>
+</a>
+<a href="posts/2020-07-20-shiny-tips-1/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["shiny"]}</script>
+<div class="metadata">
+<div class="publishedDate">July 20, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-07-20-shiny-tips-1/preview.png"/>
+</div>
+<div class="description">
+<h2>Shiny tips - the first set</h2>
+<div class="dt-tags">
+<div class="dt-tag">shiny</div>
+</div>
+<p>%||%, imap() + {shinybusy}, and user inputs in modalDialog()</p>
+</div>
+</a>
+<a href="posts/2020-07-13-geom-paired-raincloud/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data visualization","ggplot2"]}</script>
+<div class="metadata">
+<div class="publishedDate">July 13, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-07-13-geom-paired-raincloud/preview.png"/>
+</div>
+<div class="description">
+<h2>geom_paired_raincloud()</h2>
+<div class="dt-tags">
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">ggplot2</div>
+</div>
+<p>A {ggplot2} geom for visualizing change in distribution between two conditions.</p>
+</div>
+</a>
+<a href="posts/2020-06-30-treemap-with-ggplot/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data visualization","treemap","ggplot2","tutorial"]}</script>
+<div class="metadata">
+<div class="publishedDate">June 30, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-06-30-treemap-with-ggplot/2020-06-30-treemap-with-ggplot_files/figure-html5/unnamed-chunk-12-1.png"/>
+</div>
+<div class="description">
+<h2>Plotting treemaps with {treemap} and {ggplot2}</h2>
+<div class="dt-tags">
+<div class="dt-tag">data visualization</div>
+<div class="dt-tag">treemap</div>
+<div class="dt-tag">ggplot2</div>
+<div class="dt-tag">tutorial</div>
+</div>
+<p>Using underlying plot data for maximum customization</p>
+</div>
+</a>
+<a href="posts/2020-06-25-indexing-tip-for-spacyr/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["data wrangling","NLP","spacyr"]}</script>
+<div class="metadata">
+<div class="publishedDate">June 25, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-06-25-indexing-tip-for-spacyr/preview.png"/>
+</div>
+<div class="description">
+<h2>Indexing tip for {spacyr}</h2>
+<div class="dt-tags">
+<div class="dt-tag">data wrangling</div>
+<div class="dt-tag">NLP</div>
+<div class="dt-tag">spacyr</div>
+</div>
+<p>Speeding up the analysis of dependency relations.</p>
+</div>
+</a>
+<a href="posts/2020-06-07-correlation-parameter-mem/" class="post-preview">
+<script class="post-metadata" type="text/json">{"categories":["statistics","mixed-effects models","tutorial"]}</script>
+<div class="metadata">
+<div class="publishedDate">June 7, 2020</div>
+</div>
+<div class="thumbnail">
+<img data-src="posts/2020-06-07-correlation-parameter-mem/preview.png"/>
+</div>
+<div class="description">
+<h2>The Correlation Parameter in Mixed Effects Models</h2>
+<div class="dt-tags">
+<div class="dt-tag">statistics</div>
+<div class="dt-tag">mixed-effects models</div>
+<div class="dt-tag">tutorial</div>
+</div>
+<p>Notes on the Corr term in {lme4} output</p>
+</div>
+</a>
+</div>
+<div class="posts-sidebar">
+<div class="sidebar-section categories">
+<h3>Categories</h3>
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+<a href="#">More articles &raquo;</a>
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+<div class="d-title">
+<h1>Blog Posts</h1>
+
+<!--radix_placeholder_categories-->
+<!--/radix_placeholder_categories-->
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+</div>
+
+
+<div class="d-article">
+<!--
+Scheduled blog posts:
+- rstudioconf reflections
+- across(scale()) vs. scale(across()) (NVM dplyr::pick())
+- principled aesthetic mappings
+- delayed aes eval part 3
+- slice() row-relational operations
+- constructing vectors with matrices
+- debugging with trace()
+- ggtrace: design and motivation
+- julia
+-->
+<div class="sourceCode" id="cb1"><pre class="sourceCode r distill-force-highlighting-css"><code class="sourceCode r"></code></pre></div>
+<!--radix_placeholder_article_footer-->
+<!--/radix_placeholder_article_footer-->
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+<div class="d-appendix">
+</div>
+
+
+<!--radix_placeholder_site_after_body-->
+<!--/radix_placeholder_site_after_body-->
+<!--radix_placeholder_appendices-->
+<div class="appendix-bottom"></div>
+<!--/radix_placeholder_appendices-->
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+<div class="distill-site-nav distill-site-footer">
+<p><span style="font-family: 'Open Sans'"> June Choe | Created with
+{<a href = "https://github.com/rstudio/distill" style = "color: #24addb">distill</a>}
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+</body>
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+</html>
diff --git a/docs/blog.xml b/docs/blog.xml
index c5ad6754..d0f3f727 100644
--- a/docs/blog.xml
+++ b/docs/blog.xml
@@ -23,6 +23,1846 @@
       <pubDate>Sun, 22 Sep 2024 00:00:00 +0000</pubDate>
       <media:content url="https://yjunechoe.github.io/posts/2024-09-22-fetch-files-web/github-dplyr-starwars.jpg" medium="image" type="image/jpeg"/>
     </item>
+    <item>
+      <title>Row relational operations with slice()</title>
+      <dc:creator>June Choe</dc:creator>
+      <link>https://yjunechoe.github.io/posts/2023-06-11-row-relational-operations</link>
+      <description>
+
+
+&lt;h2 id="intro"&gt;Intro&lt;/h2&gt;
+&lt;p&gt;In data wrangling, there are a handful of &lt;strong&gt;classes&lt;/strong&gt; of
+operations on data frames that we think of as theoretically well-defined
+and tackling distinct problems. To name a few, these include subsetting,
+joins, split-apply-combine, pairwise operations, nested-column
+workflows, and so on.&lt;/p&gt;
+&lt;p&gt;Against this rich backdrop, there’s one aspect of data wrangling that
+doesn’t receive as much attention: &lt;strong&gt;ordering of rows&lt;/strong&gt;.
+This isn’t necessarily surprising - we often think of row order as an
+auxiliary attribute of data frames since they don’t speak to the content
+of the data, &lt;em&gt;per se&lt;/em&gt;. I think we all share the intuition that
+two dataframe that differ only in row order are practically the same for
+most analysis purposes.&lt;/p&gt;
+&lt;p&gt;&lt;em&gt;Except when they aren’t.&lt;/em&gt;&lt;/p&gt;
+&lt;p&gt;In this blog post I want to talk about a few, somewhat esoteric cases
+of what I like to call &lt;strong&gt;row-relational operations&lt;/strong&gt;. My
+goal is to try to motivate row-relational operations as a full-blown
+class of data wrangling operation that includes not only row ordering,
+but also sampling, shuffling, repeating, interweaving, and so on (I’ll
+go over all of these later).&lt;/p&gt;
+&lt;p&gt;Without spoiling too much, I believe that &lt;code&gt;dplyr::slice()&lt;/code&gt;
+offers a powerful context for operations over row indices, even those
+that at first seem to lack a “tidy” solution. You may already know
+&lt;code&gt;slice()&lt;/code&gt; as an indexing function, but my hope is to convince
+you that it can do so much more.&lt;/p&gt;
+&lt;p&gt;Let’s start by first talking about some special properties of
+&lt;code&gt;dplyr::slice()&lt;/code&gt;, and then see how we can use it for various
+row-relational operations.&lt;/p&gt;
+&lt;h2 id="special-properties-of-dplyrslice"&gt;Special properties of
+&lt;code&gt;dplyr::slice()&lt;/code&gt;&lt;/h2&gt;
+&lt;h3 id="basic-usage"&gt;Basic usage&lt;/h3&gt;
+&lt;p&gt;For the following demonstration, I’ll use a small subset of the
+&lt;code&gt;dplyr::starwars&lt;/code&gt; dataset:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm &amp;lt;- dplyr::starwars[1:10, 1:3]
+starwars_sm&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 10 × 3
+     name               height  mass
+     &amp;lt;chr&amp;gt;               &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+   1 Luke Skywalker        172    77
+   2 C-3PO                 167    75
+   3 R2-D2                  96    32
+   4 Darth Vader           202   136
+   5 Leia Organa           150    49
+   6 Owen Lars             178   120
+   7 Beru Whitesun Lars    165    75
+   8 R5-D4                  97    32
+   9 Biggs Darklighter     183    84
+  10 Obi-Wan Kenobi        182    77&lt;/code&gt;&lt;/pre&gt;
+&lt;h4 id="row-selection"&gt;1) Row selection&lt;/h4&gt;
+&lt;p&gt;&lt;code&gt;slice()&lt;/code&gt; is a row indexing verb - if you pass it a vector
+of integers, it subsets data frame rows:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice(1:6) # First six rows&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 6 × 3
+    name           height  mass
+    &amp;lt;chr&amp;gt;           &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+  1 Luke Skywalker    172    77
+  2 C-3PO             167    75
+  3 R2-D2              96    32
+  4 Darth Vader       202   136
+  5 Leia Organa       150    49
+  6 Owen Lars         178   120&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Like other dplyr verbs with mutate-semantics, you can use &lt;a
+href="https://dplyr.tidyverse.org/reference/context.html"&gt;context-dependent
+expressions&lt;/a&gt; inside &lt;code&gt;slice()&lt;/code&gt;. For example, you can use
+&lt;code&gt;n()&lt;/code&gt; to grab the last row (or last couple of rows):&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice( n() ) # Last row&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 1 × 3
+    name           height  mass
+    &amp;lt;chr&amp;gt;           &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+  1 Obi-Wan Kenobi    182    77&lt;/code&gt;&lt;/pre&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice( n() - 2:0 ) # Last three rows&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 3 × 3
+    name              height  mass
+    &amp;lt;chr&amp;gt;              &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+  1 R5-D4                 97    32
+  2 Biggs Darklighter    183    84
+  3 Obi-Wan Kenobi       182    77&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Another context-dependent expression that comes in handy is
+&lt;code&gt;row_number()&lt;/code&gt;, which returns all row indices. Using it
+inside &lt;code&gt;slice()&lt;/code&gt; essentially performs an identity
+transformation:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;identical(
+  starwars_sm,
+  starwars_sm |&amp;gt; slice( row_number() )
+)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1] TRUE&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Lastly, similar to in &lt;code&gt;select()&lt;/code&gt;, you can use
+&lt;code&gt;-&lt;/code&gt; for negative indexing (to remove rows):&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;identical(
+  starwars_sm |&amp;gt; slice(1:3),      # First three rows
+  starwars_sm |&amp;gt; slice(-(4:n()))  # All rows except fourth row to last row
+)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1] TRUE&lt;/code&gt;&lt;/pre&gt;
+&lt;h4 id="dynamic-dots"&gt;2) Dynamic dots&lt;/h4&gt;
+&lt;p&gt;&lt;code&gt;slice()&lt;/code&gt; supports &lt;a
+href="https://rlang.r-lib.org/reference/dyn-dots.html"&gt;dynamic dots&lt;/a&gt;.
+If you pass row indices into multiple argument positions,
+&lt;code&gt;slice()&lt;/code&gt; will concatenate them for you:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;identical(
+  starwars_sm |&amp;gt; slice(1:6),
+  starwars_sm |&amp;gt; slice(1, 2:4, 5, 6)
+)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1] TRUE&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;If you have a &lt;code&gt;list()&lt;/code&gt; of row indices, you can use the &lt;a
+href="https://rlang.r-lib.org/reference/splice-operator.html"&gt;splice
+operator&lt;/a&gt; &lt;code&gt;!!!&lt;/code&gt; to spread them out:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice( !!!list(1, 2:4, 5, 6) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 6 × 3
+    name           height  mass
+    &amp;lt;chr&amp;gt;           &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+  1 Luke Skywalker    172    77
+  2 C-3PO             167    75
+  3 R2-D2              96    32
+  4 Darth Vader       202   136
+  5 Leia Organa       150    49
+  6 Owen Lars         178   120&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;The above call to &lt;code&gt;slice()&lt;/code&gt; evaluates to the following
+after splicing:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;rlang::expr( slice(!!!list(1, 2:4, 5, 6)) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  slice(1, 2:4, 5, 6)&lt;/code&gt;&lt;/pre&gt;
+&lt;h4 id="row-ordering"&gt;3) Row ordering&lt;/h4&gt;
+&lt;p&gt;&lt;code&gt;slice()&lt;/code&gt; respects the order in which you supplied the row
+indices:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice(3, 1, 2, 5)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 4 × 3
+    name           height  mass
+    &amp;lt;chr&amp;gt;           &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+  1 R2-D2              96    32
+  2 Luke Skywalker    172    77
+  3 C-3PO             167    75
+  4 Leia Organa       150    49&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;This means you can do stuff like random sampling with
+&lt;code&gt;sample()&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice( sample(n()) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 10 × 3
+     name               height  mass
+     &amp;lt;chr&amp;gt;               &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+   1 Obi-Wan Kenobi        182    77
+   2 Owen Lars             178   120
+   3 Leia Organa           150    49
+   4 Darth Vader           202   136
+   5 Luke Skywalker        172    77
+   6 R5-D4                  97    32
+   7 C-3PO                 167    75
+   8 Beru Whitesun Lars    165    75
+   9 Biggs Darklighter     183    84
+  10 R2-D2                  96    32&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;You can also shuffle a subset of rows (ex: just the first five):&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice( sample(5), 6:n() )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 10 × 3
+     name               height  mass
+     &amp;lt;chr&amp;gt;               &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+   1 C-3PO                 167    75
+   2 Leia Organa           150    49
+   3 R2-D2                  96    32
+   4 Darth Vader           202   136
+   5 Luke Skywalker        172    77
+   6 Owen Lars             178   120
+   7 Beru Whitesun Lars    165    75
+   8 R5-D4                  97    32
+   9 Biggs Darklighter     183    84
+  10 Obi-Wan Kenobi        182    77&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Or reorder all rows by their indices (ex: in reverse):&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice( rev(row_number()) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 10 × 3
+     name               height  mass
+     &amp;lt;chr&amp;gt;               &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+   1 Obi-Wan Kenobi        182    77
+   2 Biggs Darklighter     183    84
+   3 R5-D4                  97    32
+   4 Beru Whitesun Lars    165    75
+   5 Owen Lars             178   120
+   6 Leia Organa           150    49
+   7 Darth Vader           202   136
+   8 R2-D2                  96    32
+   9 C-3PO                 167    75
+  10 Luke Skywalker        172    77&lt;/code&gt;&lt;/pre&gt;
+&lt;h4 id="out-of-bounds-handling"&gt;4) Out-of-bounds handling&lt;/h4&gt;
+&lt;p&gt;If you pass a row index that’s out of bounds, &lt;code&gt;slice()&lt;/code&gt;
+returns a 0-row data frame:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice( n() + 1 ) # Select the row after the last row&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 0 × 3
+  # ℹ 3 variables: name &amp;lt;chr&amp;gt;, height &amp;lt;int&amp;gt;, mass &amp;lt;dbl&amp;gt;&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;When mixed with valid row indices, out-of-bounds indices are simply
+ignored (much 💜 for this behavior):&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice(
+    0,       # 0th row - ignored
+    1:3,     # first three rows
+    n() + 1  # 1 after last row - ignored
+  )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 3 × 3
+    name           height  mass
+    &amp;lt;chr&amp;gt;           &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+  1 Luke Skywalker    172    77
+  2 C-3PO             167    75
+  3 R2-D2              96    32&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;This lets you do funky stuff like select all even numbered rows by
+passing &lt;code&gt;slice()&lt;/code&gt; all row indices times 2:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice( row_number() * 2 ) # Add `- 1` at the end for *odd* rows!&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 5 × 3
+    name           height  mass
+    &amp;lt;chr&amp;gt;           &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+  1 C-3PO             167    75
+  2 Darth Vader       202   136
+  3 Owen Lars         178   120
+  4 R5-D4              97    32
+  5 Obi-Wan Kenobi    182    77&lt;/code&gt;&lt;/pre&gt;
+&lt;h3 id="re-imagining-slice-with-data-masking"&gt;Re-imagining
+&lt;code&gt;slice()&lt;/code&gt; with data-masking&lt;/h3&gt;
+&lt;p&gt;&lt;code&gt;slice()&lt;/code&gt; is already pretty neat as it is, but that’s just
+the tip of the iceberg.&lt;/p&gt;
+&lt;p&gt;The really cool, under-rated feature of &lt;code&gt;slice()&lt;/code&gt; is that
+it’s &lt;a
+href="https://dplyr.tidyverse.org/reference/dplyr_data_masking.html"&gt;&lt;strong&gt;data-masked&lt;/strong&gt;&lt;/a&gt;,
+meaning that you can reference column vectors as if they’re variables.
+Another way of describing this property of &lt;code&gt;slice()&lt;/code&gt; is to
+say that it has &lt;a
+href="https://rlang.r-lib.org/reference/topic-data-mask-programming.html"&gt;&lt;strong&gt;mutate-semantics&lt;/strong&gt;&lt;/a&gt;.&lt;/p&gt;
+&lt;p&gt;At a very basic level, this means that &lt;code&gt;slice()&lt;/code&gt; can
+straightforwardly replicate the behavior of some dplyr verbs like
+&lt;code&gt;arrange()&lt;/code&gt; and &lt;code&gt;filter()&lt;/code&gt;!&lt;/p&gt;
+&lt;h4 id="slice-as-arrange"&gt;&lt;code&gt;slice()&lt;/code&gt; as
+&lt;code&gt;arrange()&lt;/code&gt;&lt;/h4&gt;
+&lt;p&gt;From our &lt;code&gt;starwars_sm&lt;/code&gt; data, if we want to sort by
+&lt;code&gt;height&lt;/code&gt; we can use &lt;code&gt;arrange()&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  arrange(height)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 10 × 3
+     name               height  mass
+     &amp;lt;chr&amp;gt;               &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+   1 R2-D2                  96    32
+   2 R5-D4                  97    32
+   3 Leia Organa           150    49
+   4 Beru Whitesun Lars    165    75
+   5 C-3PO                 167    75
+   6 Luke Skywalker        172    77
+   7 Owen Lars             178   120
+   8 Obi-Wan Kenobi        182    77
+   9 Biggs Darklighter     183    84
+  10 Darth Vader           202   136&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;But we can also do this with &lt;code&gt;slice()&lt;/code&gt; to the same effect,
+using &lt;code&gt;order()&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice( order(height) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 10 × 3
+     name               height  mass
+     &amp;lt;chr&amp;gt;               &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+   1 R2-D2                  96    32
+   2 R5-D4                  97    32
+   3 Leia Organa           150    49
+   4 Beru Whitesun Lars    165    75
+   5 C-3PO                 167    75
+   6 Luke Skywalker        172    77
+   7 Owen Lars             178   120
+   8 Obi-Wan Kenobi        182    77
+   9 Biggs Darklighter     183    84
+  10 Darth Vader           202   136&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;This is conceptually equivalent to combining the following 2-step
+process:&lt;/p&gt;
+&lt;ol style="list-style-type: decimal"&gt;
+&lt;li&gt;&lt;pre class="r"&gt;&lt;code&gt;ordered_val_ind &amp;lt;- order(starwars_sm$height)
+ordered_val_ind&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;   [1]  3  8  5  7  2  1  6 10  9  4&lt;/code&gt;&lt;/pre&gt;&lt;/li&gt;
+&lt;li&gt;&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice( ordered_val_ind )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 10 × 3
+     name               height  mass
+     &amp;lt;chr&amp;gt;               &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+   1 R2-D2                  96    32
+   2 R5-D4                  97    32
+   3 Leia Organa           150    49
+   4 Beru Whitesun Lars    165    75
+   5 C-3PO                 167    75
+   6 Luke Skywalker        172    77
+   7 Owen Lars             178   120
+   8 Obi-Wan Kenobi        182    77
+   9 Biggs Darklighter     183    84
+  10 Darth Vader           202   136&lt;/code&gt;&lt;/pre&gt;&lt;/li&gt;
+&lt;/ol&gt;
+&lt;h4 id="slice-as-filter"&gt;&lt;code&gt;slice()&lt;/code&gt; as
+&lt;code&gt;filter()&lt;/code&gt;&lt;/h4&gt;
+&lt;p&gt;We can also use &lt;code&gt;slice()&lt;/code&gt; to &lt;code&gt;filter()&lt;/code&gt;, using
+&lt;code&gt;which()&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;identical(
+  starwars_sm |&amp;gt; filter( height &amp;gt; 150 ),
+  starwars_sm |&amp;gt; slice( which(height &amp;gt; 150) )
+)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1] TRUE&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Thus, we can think of &lt;code&gt;filter()&lt;/code&gt; and &lt;code&gt;slice()&lt;/code&gt;
+as two sides of the same coin:&lt;/p&gt;
+&lt;ul&gt;
+&lt;li&gt;&lt;p&gt;&lt;code&gt;filter()&lt;/code&gt; takes a logical vector that’s the same
+length as the number of rows in the data frame&lt;/p&gt;&lt;/li&gt;
+&lt;li&gt;&lt;p&gt;&lt;code&gt;slice()&lt;/code&gt; takes an integer vector that’s a (sub)set of
+a data frame’s row indices.&lt;/p&gt;&lt;/li&gt;
+&lt;/ul&gt;
+&lt;p&gt;To put it more concretely, this logical vector was being passed to
+the above &lt;code&gt;filter()&lt;/code&gt; call:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm$height &amp;gt; 150&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;   [1]  TRUE  TRUE FALSE  TRUE FALSE  TRUE  TRUE FALSE  TRUE  TRUE&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;While this integer vector was being passed to the above
+&lt;code&gt;slice()&lt;/code&gt; call, where &lt;code&gt;which()&lt;/code&gt; returns the
+position of &lt;code&gt;TRUE&lt;/code&gt; values, given a logical vector:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;which( starwars_sm$height &amp;gt; 150 )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1]  1  2  4  6  7  9 10&lt;/code&gt;&lt;/pre&gt;
+&lt;h3 id="special-properties-of-slice"&gt;Special properties of
+&lt;code&gt;slice()&lt;/code&gt;&lt;/h3&gt;
+&lt;p&gt;This re-imagined &lt;code&gt;slice()&lt;/code&gt; that heavily exploits
+data-masking gives us two interesting properties:&lt;/p&gt;
+&lt;ol style="list-style-type: decimal"&gt;
+&lt;li&gt;&lt;p&gt;We can work with &lt;strong&gt;sets&lt;/strong&gt; of row indices that need
+not to be the same length as the data frame
+(vs. &lt;code&gt;filter()&lt;/code&gt;).&lt;/p&gt;&lt;/li&gt;
+&lt;li&gt;&lt;p&gt;We can work with row indices as &lt;strong&gt;integers&lt;/strong&gt;, which
+are legible to arithmetic operations (ex: &lt;code&gt;+&lt;/code&gt; and
+&lt;code&gt;*&lt;/code&gt;)&lt;/p&gt;&lt;/li&gt;
+&lt;/ol&gt;
+&lt;p&gt;To grok the significance of working with rows as &lt;strong&gt;integer
+sets&lt;/strong&gt;, let’s work through some examples where
+&lt;code&gt;slice()&lt;/code&gt; comes in very handy.&lt;/p&gt;
+&lt;h2 id="a-gallery-of-row-operations-with-slice"&gt;A gallery of row
+operations with &lt;code&gt;slice()&lt;/code&gt;&lt;/h2&gt;
+&lt;h3 id="repeat-rows-in-place"&gt;Repeat rows (in place)&lt;/h3&gt;
+&lt;p&gt;In &lt;code&gt;{tidyr}&lt;/code&gt;, there’s a function called
+&lt;code&gt;uncount()&lt;/code&gt; which does the opposite of
+&lt;code&gt;dplyr::count()&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;library(tidyr)
+# Example from `tidyr::uncount()` docs
+uncount_df &amp;lt;- tibble(x = c(&amp;quot;a&amp;quot;, &amp;quot;b&amp;quot;), n = c(1, 2))
+uncount_df&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 2 × 2
+    x         n
+    &amp;lt;chr&amp;gt; &amp;lt;dbl&amp;gt;
+  1 a         1
+  2 b         2&lt;/code&gt;&lt;/pre&gt;
+&lt;pre class="r"&gt;&lt;code&gt;uncount_df |&amp;gt; 
+  uncount(n)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 3 × 1
+    x    
+    &amp;lt;chr&amp;gt;
+  1 a    
+  2 b    
+  3 b&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;We can mimic this behavior with &lt;code&gt;slice()&lt;/code&gt;, using
+&lt;code&gt;rep(times = ...)&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;rep(1:nrow(uncount_df), times = uncount_df$n)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1] 1 2 2&lt;/code&gt;&lt;/pre&gt;
+&lt;pre class="r"&gt;&lt;code&gt;uncount_df |&amp;gt; 
+  slice( rep(row_number(), times = n) ) |&amp;gt; 
+  select( -n )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 3 × 1
+    x    
+    &amp;lt;chr&amp;gt;
+  1 a    
+  2 b    
+  3 b&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;What if instead of a whole column storing that information, we only
+have information about row position?&lt;/p&gt;
+&lt;p&gt;Let’s say we want to duplicate the rows of &lt;code&gt;starwars_sm&lt;/code&gt;
+at the &lt;code&gt;repeat_at&lt;/code&gt; positions:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;repeat_at &amp;lt;- sample(5, 2)
+repeat_at&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1] 4 5&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;In &lt;code&gt;slice()&lt;/code&gt;, you’d just select all rows plus those
+additional rows, then sort the integer row indices:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice( sort(c(row_number(), repeat_at)) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 12 × 3
+     name               height  mass
+     &amp;lt;chr&amp;gt;               &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+   1 Luke Skywalker        172    77
+   2 C-3PO                 167    75
+   3 R2-D2                  96    32
+   4 Darth Vader           202   136
+   5 Darth Vader           202   136
+   6 Leia Organa           150    49
+   7 Leia Organa           150    49
+   8 Owen Lars             178   120
+   9 Beru Whitesun Lars    165    75
+  10 R5-D4                  97    32
+  11 Biggs Darklighter     183    84
+  12 Obi-Wan Kenobi        182    77&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;What if we also separately have information about how much to repeat
+those rows by?&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;repeat_by &amp;lt;- c(3, 4)&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;You can apply the same &lt;code&gt;rep()&lt;/code&gt; method for just the subset
+of rows to repeat:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  slice( sort(c(row_number(), rep(repeat_at, times = repeat_by - 1))) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 15 × 3
+     name               height  mass
+     &amp;lt;chr&amp;gt;               &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+   1 Luke Skywalker        172    77
+   2 C-3PO                 167    75
+   3 R2-D2                  96    32
+   4 Darth Vader           202   136
+   5 Darth Vader           202   136
+   6 Darth Vader           202   136
+   7 Leia Organa           150    49
+   8 Leia Organa           150    49
+   9 Leia Organa           150    49
+  10 Leia Organa           150    49
+  11 Owen Lars             178   120
+  12 Beru Whitesun Lars    165    75
+  13 R5-D4                  97    32
+  14 Biggs Darklighter     183    84
+  15 Obi-Wan Kenobi        182    77&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Circling back to &lt;code&gt;uncount()&lt;/code&gt;, you could also initialize a
+vector of &lt;code&gt;1s&lt;/code&gt; and &lt;code&gt;replace()&lt;/code&gt; where the rows
+should be repeated:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars_sm |&amp;gt; 
+  uncount( replace(rep(1, n()), repeat_at, repeat_by) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 15 × 3
+     name               height  mass
+     &amp;lt;chr&amp;gt;               &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+   1 Luke Skywalker        172    77
+   2 C-3PO                 167    75
+   3 R2-D2                  96    32
+   4 Darth Vader           202   136
+   5 Darth Vader           202   136
+   6 Darth Vader           202   136
+   7 Leia Organa           150    49
+   8 Leia Organa           150    49
+   9 Leia Organa           150    49
+  10 Leia Organa           150    49
+  11 Owen Lars             178   120
+  12 Beru Whitesun Lars    165    75
+  13 R5-D4                  97    32
+  14 Biggs Darklighter     183    84
+  15 Obi-Wan Kenobi        182    77&lt;/code&gt;&lt;/pre&gt;
+&lt;h3 id="subset-a-selection-of-rows-the-following-row"&gt;Subset a selection
+of rows + the following row&lt;/h3&gt;
+&lt;p&gt;Row order can sometimes encode a meaningful continuous measure, like
+time.&lt;/p&gt;
+&lt;p&gt;Take for example this subset of the &lt;code&gt;flights&lt;/code&gt; dataset in
+&lt;code&gt;{nycflights13}&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;flights_df &amp;lt;- nycflights13::flights |&amp;gt; 
+  filter(month == 3, day == 3, origin == &amp;quot;JFK&amp;quot;) |&amp;gt; 
+  select(dep_time, flight, carrier) |&amp;gt; 
+  slice(1:100) |&amp;gt; 
+  arrange(dep_time)
+flights_df&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 100 × 3
+     dep_time flight carrier
+        &amp;lt;int&amp;gt;  &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;  
+   1      535   1141 AA     
+   2      551   5716 EV     
+   3      555    145 B6     
+   4      556    208 B6     
+   5      556     79 B6     
+   6      601    501 B6     
+   7      604    725 B6     
+   8      606    135 B6     
+   9      606    600 UA     
+  10      607    829 US     
+  # ℹ 90 more rows&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Here, the rows are ordered by &lt;code&gt;dep_time&lt;/code&gt;, such that given
+a row, the next row is a data point for the next flight that departed
+from the airport.&lt;/p&gt;
+&lt;p&gt;And let’s say we’re interested in flights that took off immediately
+after American Airlines (&lt;code&gt;"AA"&lt;/code&gt;) flights. Given what we just
+noted about the ordering of rows in the data frame, we can do this in
+&lt;code&gt;slice()&lt;/code&gt; by adding &lt;code&gt;1&lt;/code&gt; to the row index of AA
+flights:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;flights_df |&amp;gt; 
+  slice( which(carrier == &amp;quot;AA&amp;quot;) + 1 )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 14 × 3
+     dep_time flight carrier
+        &amp;lt;int&amp;gt;  &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;  
+   1      551   5716 EV     
+   2      627    905 B6     
+   3      652    117 B6     
+   4      714    825 AA     
+   5      717    987 B6     
+   6      724     11 VX     
+   7      742    183 DL     
+   8      802    655 AA     
+   9      805   2143 DL     
+  10      847     59 B6     
+  11      858    647 AA     
+  12      859    120 DL     
+  13     1031    179 AA     
+  14     1036    641 B6&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;What if we also want to keep observations for the preceding AA
+flights as well? We can just stick &lt;code&gt;which(carrier == "AA")&lt;/code&gt;
+inside &lt;code&gt;slice()&lt;/code&gt; too:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;flights_df |&amp;gt; 
+  slice(
+    which(carrier == &amp;quot;AA&amp;quot;),
+    which(carrier == &amp;quot;AA&amp;quot;) + 1
+  )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 28 × 3
+     dep_time flight carrier
+        &amp;lt;int&amp;gt;  &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;  
+   1      535   1141 AA     
+   2      626    413 AA     
+   3      652   1815 AA     
+   4      711    443 AA     
+   5      714    825 AA     
+   6      724     33 AA     
+   7      739     59 AA     
+   8      802   1838 AA     
+   9      802    655 AA     
+  10      843   1357 AA     
+  # ℹ 18 more rows&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;But now the rows are now ordered such that all the AA flights come
+before the other flights! How can we preserve the original order of
+increasing &lt;code&gt;dep_time&lt;/code&gt;?&lt;/p&gt;
+&lt;p&gt;We &lt;em&gt;could&lt;/em&gt; reconstruct the initial row order by piping the
+result into &lt;code&gt;arrange(dep_time)&lt;/code&gt; again, but the simplest
+solution would be to concatenate the set of row indices and
+&lt;code&gt;sort()&lt;/code&gt; them, since the output of &lt;code&gt;which()&lt;/code&gt; is
+already integer!&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;flights_df |&amp;gt; 
+  slice(
+    sort(c(
+      which(carrier == &amp;quot;AA&amp;quot;),
+      which(carrier == &amp;quot;AA&amp;quot;) + 1
+    ))
+  )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 28 × 3
+     dep_time flight carrier
+        &amp;lt;int&amp;gt;  &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;  
+   1      535   1141 AA     
+   2      551   5716 EV     
+   3      626    413 AA     
+   4      627    905 B6     
+   5      652   1815 AA     
+   6      652    117 B6     
+   7      711    443 AA     
+   8      714    825 AA     
+   9      714    825 AA     
+  10      717    987 B6     
+  # ℹ 18 more rows&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Notice how the 8th and 9th rows are repeated here - that’s because 2
+AA flights departed in a row (ha!). We can use &lt;code&gt;unique()&lt;/code&gt; to
+remove duplicate rows in the same call to &lt;code&gt;slice()&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;flights_df |&amp;gt; 
+  slice(
+    unique(sort(c(
+      which(carrier == &amp;quot;AA&amp;quot;),
+      which(carrier == &amp;quot;AA&amp;quot;) + 1
+    )))
+  )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 24 × 3
+     dep_time flight carrier
+        &amp;lt;int&amp;gt;  &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;  
+   1      535   1141 AA     
+   2      551   5716 EV     
+   3      626    413 AA     
+   4      627    905 B6     
+   5      652   1815 AA     
+   6      652    117 B6     
+   7      711    443 AA     
+   8      714    825 AA     
+   9      717    987 B6     
+  10      724     33 AA     
+  # ℹ 14 more rows&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Importantly, we can do all of this inside &lt;code&gt;slice()&lt;/code&gt;
+because we’re working with &lt;strong&gt;integer sets&lt;/strong&gt;. The
+&lt;strong&gt;integer&lt;/strong&gt; part allows us to do things like
+&lt;code&gt;+ 1&lt;/code&gt; and &lt;code&gt;sort()&lt;/code&gt;, while the &lt;strong&gt;set&lt;/strong&gt;
+part allows us to combine with &lt;code&gt;c()&lt;/code&gt; and remove duplicates
+with &lt;code&gt;unique()&lt;/code&gt;.&lt;/p&gt;
+&lt;h3 id="subset-a-selection-of-rows-multiple-following-rows"&gt;Subset a
+selection of rows + multiple following rows&lt;/h3&gt;
+&lt;p&gt;In this example, let’s problematize our approach with the repeated
+&lt;code&gt;which()&lt;/code&gt; calls in our previous solution.&lt;/p&gt;
+&lt;p&gt;Imagine another scenario where we want to filter for all AA flights
+and &lt;em&gt;three&lt;/em&gt; subsequent flights for each.&lt;/p&gt;
+&lt;p&gt;Do we need to write the solution out like this? That’s a lot of
+repetition!&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;flights_df |&amp;gt; 
+  slice(
+    which(carrier == &amp;quot;AA&amp;quot;),
+    which(carrier == &amp;quot;AA&amp;quot;) + 1,
+    which(carrier == &amp;quot;AA&amp;quot;) + 2,
+    which(carrier == &amp;quot;AA&amp;quot;) + 3
+  )&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;You might think we can get away with &lt;code&gt;+ 0:3&lt;/code&gt;, but it
+doesn’t work as we’d like. The &lt;code&gt;+&lt;/code&gt; just forces
+&lt;code&gt;0:3&lt;/code&gt; to be (partially) recycled to the same length as
+&lt;code&gt;carrier&lt;/code&gt; for element-wise addition:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;which(flights_df$carrier == &amp;quot;AA&amp;quot;) + 0:3&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  Warning in which(flights_df$carrier == &amp;quot;AA&amp;quot;) + 0:3: longer object length is not
+  a multiple of shorter object length&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;   [1]  1 14 20 27 25 28 34 40 38 62 66 68 91 93&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;If only we can get the &lt;strong&gt;outer&lt;/strong&gt; sum of the two arrays,
+&lt;code&gt;0:3&lt;/code&gt; and &lt;code&gt;which(carrier == "AA")&lt;/code&gt; … Oh wait, we
+can - that’s what &lt;code&gt;outer()&lt;/code&gt; does!&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;outer(0:3, which(flights_df$carrier == &amp;quot;AA&amp;quot;), `+`)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
+  [1,]    1   13   18   24   25   27   32   37   38    61    64    65    91    92
+  [2,]    2   14   19   25   26   28   33   38   39    62    65    66    92    93
+  [3,]    3   15   20   26   27   29   34   39   40    63    66    67    93    94
+  [4,]    4   16   21   27   28   30   35   40   41    64    67    68    94    95&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;This is essentially the repeated &lt;code&gt;which()&lt;/code&gt; vectors stacked
+on top of each other, but as a matrix:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;print( which(flights_df$carrier == &amp;quot;AA&amp;quot;)     )
+print( which(flights_df$carrier == &amp;quot;AA&amp;quot;) + 1 )
+print( which(flights_df$carrier == &amp;quot;AA&amp;quot;) + 2 )
+print( which(flights_df$carrier == &amp;quot;AA&amp;quot;) + 3 )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;   [1]  1 13 18 24 25 27 32 37 38 61 64 65 91 92
+   [1]  2 14 19 25 26 28 33 38 39 62 65 66 92 93
+   [1]  3 15 20 26 27 29 34 39 40 63 66 67 93 94
+   [1]  4 16 21 27 28 30 35 40 41 64 67 68 94 95&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;The fact that &lt;code&gt;outer()&lt;/code&gt; returns all the relevant row
+indices inside a single matrix is nice because we can collect the
+indices column-by-column, preserving row order. Matrices, like data
+frames, are &lt;strong&gt;column-major&lt;/strong&gt;, so coercing a matrix to a
+vector collapses it column-wise:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;as.integer( outer(0:3, which(flights_df$carrier == &amp;quot;AA&amp;quot;), `+`) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;   [1]  1  2  3  4 13 14 15 16 18 19 20 21 24 25 26 27 25 26 27 28 27 28 29 30 32
+  [26] 33 34 35 37 38 39 40 38 39 40 41 61 62 63 64 64 65 66 67 65 66 67 68 91 92
+  [51] 93 94 92 93 94 95&lt;/code&gt;&lt;/pre&gt;
+&lt;details&gt;
+&lt;summary&gt;
+Other ways to coerce matrix to vector
+&lt;/summary&gt;
+&lt;p&gt;There are two other options for coercing a matrix to vector -
+&lt;code&gt;c()&lt;/code&gt; and &lt;code&gt;as.vector()&lt;/code&gt;. I like to stick with
+&lt;code&gt;as.integer()&lt;/code&gt; because that enforces integer type (which
+makes sense for row indices), and &lt;code&gt;c()&lt;/code&gt; can be nice because
+it’s less to type (although it’s &lt;a
+href="https://youtu.be/izFssYRsLZs?t=1143"&gt;off-label usage&lt;/a&gt;):&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;# Not run, but equivalent to `as.integer()` method
+as.vector( outer(0:3, which(flights_df$carrier == &amp;quot;AA&amp;quot;), `+`) )
+c( outer(0:3, which(flights_df$carrier == &amp;quot;AA&amp;quot;), `+`) )&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Somewhat relatedly - and this only works inside the tidy-eval context
+of &lt;code&gt;slice()&lt;/code&gt; - you can get a similar effect of “collapsing” a
+matrix using the &lt;a
+href="https://rlang.r-lib.org/reference/topic-inject.html#splicing-with-"&gt;splice
+operator&lt;/a&gt; &lt;code&gt;!!!&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;seq_matrix &amp;lt;- matrix(1:9, byrow = TRUE, nrow = 3)
+as.integer(seq_matrix)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1] 1 4 7 2 5 8 3 6 9&lt;/code&gt;&lt;/pre&gt;
+&lt;pre class="r"&gt;&lt;code&gt;identical(
+  mtcars |&amp;gt; slice( as.vector(seq_matrix) ),
+  mtcars |&amp;gt; slice( !!!seq_matrix )
+)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1] TRUE&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Here, the &lt;code&gt;!!!seq_matrix&lt;/code&gt; was slotting each individual
+“cell” as argument to &lt;code&gt;slice()&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;rlang::expr( slice(!!!seq_matrix) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  slice(1L, 4L, 7L, 2L, 5L, 8L, 3L, 6L, 9L)&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;A big difference in behavior between &lt;code&gt;as.integer()&lt;/code&gt;
+vs. &lt;code&gt;!!!&lt;/code&gt; is that the latter works for &lt;strong&gt;lists&lt;/strong&gt;
+of indices too, by slotting each element of the list as an argument to
+&lt;code&gt;slice()&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;seq_list &amp;lt;- list(c(1, 4, 7, 2), c(5, 8, 3, 6, 9))
+rlang::expr( slice( !!!seq_list ) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  slice(c(1, 4, 7, 2), c(5, 8, 3, 6, 9))&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;However, as you may already know, &lt;code&gt;as.integer()&lt;/code&gt; cannot
+flatten lists:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;as.integer(seq_list)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  Error in eval(expr, envir, enclos): &amp;#39;list&amp;#39; object cannot be coerced to type &amp;#39;integer&amp;#39;&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Note that &lt;code&gt;as.vector()&lt;/code&gt; and &lt;code&gt;c()&lt;/code&gt; leaves lists
+&lt;em&gt;as is&lt;/em&gt;, which is another reason to prefer
+&lt;code&gt;as.integer()&lt;/code&gt; for type-checking:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;identical(seq_list, as.vector(seq_list))
+identical(seq_list, c(seq_list))&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1] TRUE
+  [1] TRUE&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Finally, back in our &lt;code&gt;!!!seq_matrix&lt;/code&gt; example, we could
+have applied &lt;code&gt;asplit(MARGIN = 2)&lt;/code&gt; to chunk the splicing by
+&lt;em&gt;matrix column&lt;/em&gt;, although the overall effect would be the
+same:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;rlang::expr(slice( !!!seq_matrix            ))&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  slice(1L, 4L, 7L, 2L, 5L, 8L, 3L, 6L, 9L)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre class="r"&gt;&lt;code&gt;rlang::expr(slice( !!!asplit(seq_matrix, 2) ))&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  slice(c(1L, 4L, 7L), c(2L, 5L, 8L), c(3L, 6L, 9L))&lt;/code&gt;&lt;/pre&gt;
+&lt;/details&gt;
+&lt;p&gt;This lets us ask questions like: Which AA flights departed within 3
+flights of another AA flight?&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;flights_df |&amp;gt; 
+  slice( as.integer( outer(0:3, which(carrier == &amp;quot;AA&amp;quot;), `+`) ) ) |&amp;gt; 
+  filter( carrier == &amp;quot;AA&amp;quot;, duplicated(flight) ) |&amp;gt; 
+  distinct(flight, carrier)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 6 × 2
+    flight carrier
+     &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;  
+  1    825 AA     
+  2     33 AA     
+  3    655 AA     
+  4      1 AA     
+  5    647 AA     
+  6    179 AA&lt;/code&gt;&lt;/pre&gt;
+&lt;details&gt;
+&lt;summary&gt;
+Slicing all the way down: Case 1
+&lt;/summary&gt;
+&lt;p&gt;With the addition of the &lt;code&gt;.by&lt;/code&gt; argument to
+&lt;code&gt;slice()&lt;/code&gt; in &lt;a
+href="https://www.tidyverse.org/blog/2023/02/dplyr-1-1-0-per-operation-grouping/"&gt;dplyr
+v1.10&lt;/a&gt;, we can re-write the above code as three calls to
+&lt;code&gt;slice()&lt;/code&gt; (+ a call to &lt;code&gt;select()&lt;/code&gt;):&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;flights_df |&amp;gt; 
+  slice( as.integer( outer(0:3, which(carrier == &amp;quot;AA&amp;quot;), `+`) ) ) |&amp;gt; 
+  slice( which(carrier == &amp;quot;AA&amp;quot; &amp;amp; duplicated(flight)) ) |&amp;gt;  # filter()
+  slice( 1, .by = c(flight, carrier) ) |&amp;gt;                  # distinct()
+  select(flight, carrier)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 6 × 2
+    flight carrier
+     &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;  
+  1    825 AA     
+  2     33 AA     
+  3    655 AA     
+  4      1 AA     
+  5    647 AA     
+  6    179 AA&lt;/code&gt;&lt;/pre&gt;
+&lt;/details&gt;
+&lt;p&gt;The next example will demonstrate another, perhaps more practical
+usecase for &lt;code&gt;outer()&lt;/code&gt; in &lt;code&gt;slice()&lt;/code&gt;.&lt;/p&gt;
+&lt;h3 id="filter-and-encode-neighboring-rows"&gt;Filter (and encode)
+neighboring rows&lt;/h3&gt;
+&lt;p&gt;Let’s use a subset of the &lt;code&gt;{gapminder}&lt;/code&gt; data set for this
+one. Here, we have data for each European country’s GDP-per-capita by
+year, between 1992 to 2007:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;gapminder_df &amp;lt;- gapminder::gapminder |&amp;gt; 
+  left_join(gapminder::country_codes, by = &amp;quot;country&amp;quot;) |&amp;gt;  # `multiple = &amp;quot;all&amp;quot;`
+  filter(year &amp;gt;= 1992, continent == &amp;quot;Europe&amp;quot;) |&amp;gt; 
+  select(country, country_code = iso_alpha, year, gdpPercap)
+gapminder_df&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 120 × 4
+     country country_code  year gdpPercap
+     &amp;lt;chr&amp;gt;   &amp;lt;chr&amp;gt;        &amp;lt;int&amp;gt;     &amp;lt;dbl&amp;gt;
+   1 Albania ALB           1992     2497.
+   2 Albania ALB           1997     3193.
+   3 Albania ALB           2002     4604.
+   4 Albania ALB           2007     5937.
+   5 Austria AUT           1992    27042.
+   6 Austria AUT           1997    29096.
+   7 Austria AUT           2002    32418.
+   8 Austria AUT           2007    36126.
+   9 Belgium BEL           1992    25576.
+  10 Belgium BEL           1997    27561.
+  # ℹ 110 more rows&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;This time, let’s see the desired output (plot) first and build our
+way up. The goal is to plot the GDP growth of Germany over the years,
+&lt;em&gt;and&lt;/em&gt; its yearly &lt;strong&gt;GDP neighbors&lt;/strong&gt; side-by-side:&lt;/p&gt;
+&lt;p&gt;&lt;img src="file86a47c2865f8_files/figure-html/final-gapminder-plot-1.png" width="672" /&gt;&lt;/p&gt;
+&lt;p&gt;First, let’s think about what a “GDP neighbor” means in
+row-relational terms. If you arranged the data by GDP, the GDP neighbors
+would be the rows that come immediately before and after the rows for
+Germany. You need to recalculate neighbors every year though, so this
+&lt;code&gt;arrange()&lt;/code&gt; + &lt;code&gt;slice()&lt;/code&gt; combo should happen
+by-year.&lt;/p&gt;
+&lt;p&gt;With that in mind, let’s set up a &lt;code&gt;year&lt;/code&gt; grouping and
+arrange by &lt;code&gt;gdpPercap&lt;/code&gt; within &lt;code&gt;year&lt;/code&gt;:&lt;a
+href="#fn1" class="footnote-ref" id="fnref1"&gt;&lt;sup&gt;1&lt;/sup&gt;&lt;/a&gt;&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;gapminder_df |&amp;gt; 
+  group_by(year) |&amp;gt; 
+  arrange(gdpPercap, .by_group = TRUE)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 120 × 4
+  # Groups:   year [4]
+     country                country_code  year gdpPercap
+     &amp;lt;chr&amp;gt;                  &amp;lt;chr&amp;gt;        &amp;lt;int&amp;gt;     &amp;lt;dbl&amp;gt;
+   1 Albania                ALB           1992     2497.
+   2 Bosnia and Herzegovina BIH           1992     2547.
+   3 Turkey                 TUR           1992     5678.
+   4 Bulgaria               BGR           1992     6303.
+   5 Romania                ROU           1992     6598.
+   6 Montenegro             MNE           1992     7003.
+   7 Poland                 POL           1992     7739.
+   8 Croatia                HRV           1992     8448.
+   9 Serbia                 SRB           1992     9325.
+  10 Slovak Republic        SVK           1992     9498.
+  # ℹ 110 more rows&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Now within each year, we want to grab the row for Germany
+&lt;em&gt;and&lt;/em&gt; its neighboring rows. We can do this by taking the
+&lt;code&gt;outer()&lt;/code&gt; sum of &lt;code&gt;-1:1&lt;/code&gt; and the row indices for
+Germany:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;gapminder_df |&amp;gt; 
+  group_by(year) |&amp;gt; 
+  arrange(gdpPercap, .by_group = TRUE) |&amp;gt; 
+  slice( as.integer(outer( -1:1, which(country == &amp;quot;Germany&amp;quot;), `+` )) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 12 × 4
+  # Groups:   year [4]
+     country        country_code  year gdpPercap
+     &amp;lt;chr&amp;gt;          &amp;lt;chr&amp;gt;        &amp;lt;int&amp;gt;     &amp;lt;dbl&amp;gt;
+   1 Denmark        DNK           1992    26407.
+   2 Germany        DEU           1992    26505.
+   3 Netherlands    NLD           1992    26791.
+   4 Belgium        BEL           1997    27561.
+   5 Germany        DEU           1997    27789.
+   6 Iceland        ISL           1997    28061.
+   7 United Kingdom GBR           2002    29479.
+   8 Germany        DEU           2002    30036.
+   9 Belgium        BEL           2002    30486.
+  10 France         FRA           2007    30470.
+  11 Germany        DEU           2007    32170.
+  12 United Kingdom GBR           2007    33203.&lt;/code&gt;&lt;/pre&gt;
+&lt;details&gt;
+&lt;summary&gt;
+Slicing all the way down: Case 2
+&lt;/summary&gt;
+&lt;p&gt;The new &lt;code&gt;.by&lt;/code&gt; argument in &lt;code&gt;slice()&lt;/code&gt; comes in
+handy again here, allowing us to collapse the &lt;code&gt;group_by()&lt;/code&gt; +
+&lt;code&gt;arrange()&lt;/code&gt; combo into one &lt;code&gt;slice()&lt;/code&gt; call:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;gapminder_df |&amp;gt; 
+  slice( order(gdpPercap), .by = year) |&amp;gt; 
+  slice( as.integer(outer( -1:1, which(country == &amp;quot;Germany&amp;quot;), `+` )) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 12 × 4
+     country        country_code  year gdpPercap
+     &amp;lt;chr&amp;gt;          &amp;lt;chr&amp;gt;        &amp;lt;int&amp;gt;     &amp;lt;dbl&amp;gt;
+   1 Denmark        DNK           1992    26407.
+   2 Germany        DEU           1992    26505.
+   3 Netherlands    NLD           1992    26791.
+   4 Belgium        BEL           1997    27561.
+   5 Germany        DEU           1997    27789.
+   6 Iceland        ISL           1997    28061.
+   7 United Kingdom GBR           2002    29479.
+   8 Germany        DEU           2002    30036.
+   9 Belgium        BEL           2002    30486.
+  10 France         FRA           2007    30470.
+  11 Germany        DEU           2007    32170.
+  12 United Kingdom GBR           2007    33203.&lt;/code&gt;&lt;/pre&gt;
+For our purposes here we want actually the grouping to
+&lt;strong&gt;persist&lt;/strong&gt; for the following &lt;code&gt;mutate()&lt;/code&gt; call,
+but there may be other cases where you’d want to use
+&lt;code&gt;slice(.by = )&lt;/code&gt; for temporary grouping.
+&lt;/details&gt;
+&lt;p&gt;Now we’re already starting to see the shape of the data that we want!
+The last step is to encode the relationship of each row to Germany -
+does a row represent Germany itself, or a country that’s one GDP ranking
+below or above Germany?&lt;/p&gt;
+&lt;p&gt;Continuing with our grouped context, we make a new column
+&lt;code&gt;grp&lt;/code&gt; that assigns a factor value
+&lt;code&gt;"lo"&lt;/code&gt;-&lt;code&gt;"is"&lt;/code&gt;-&lt;code&gt;"hi"&lt;/code&gt; (for “lower” than
+Germany, “is” Germany and “higher” than Germany) to each country trio by
+year. Notice the use of &lt;code&gt;fct_inorder()&lt;/code&gt; below - this ensures
+that the factor levels are in the order of their occurrence (necessary
+for the correct ordering of bars in &lt;code&gt;geom_col()&lt;/code&gt; later):&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;gapminder_df |&amp;gt; 
+  group_by(year) |&amp;gt; 
+  arrange(gdpPercap) |&amp;gt; 
+  slice( as.integer(outer( -1:1, which(country == &amp;quot;Germany&amp;quot;), `+` )) ) |&amp;gt; 
+  mutate(grp = forcats::fct_inorder(c(&amp;quot;lo&amp;quot;, &amp;quot;is&amp;quot;, &amp;quot;hi&amp;quot;)))&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 12 × 5
+  # Groups:   year [4]
+     country        country_code  year gdpPercap grp  
+     &amp;lt;chr&amp;gt;          &amp;lt;chr&amp;gt;        &amp;lt;int&amp;gt;     &amp;lt;dbl&amp;gt; &amp;lt;fct&amp;gt;
+   1 Denmark        DNK           1992    26407. lo   
+   2 Germany        DEU           1992    26505. is   
+   3 Netherlands    NLD           1992    26791. hi   
+   4 Belgium        BEL           1997    27561. lo   
+   5 Germany        DEU           1997    27789. is   
+   6 Iceland        ISL           1997    28061. hi   
+   7 United Kingdom GBR           2002    29479. lo   
+   8 Germany        DEU           2002    30036. is   
+   9 Belgium        BEL           2002    30486. hi   
+  10 France         FRA           2007    30470. lo   
+  11 Germany        DEU           2007    32170. is   
+  12 United Kingdom GBR           2007    33203. hi&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;We now have everything that’s necessary to make our desired plot, so
+we &lt;code&gt;ungroup()&lt;/code&gt;, write some &lt;code&gt;{ggplot2}&lt;/code&gt; code, and
+voila!&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;gapminder_df |&amp;gt; 
+  group_by(year) |&amp;gt; 
+  arrange(gdpPercap) |&amp;gt; 
+  slice( as.integer(outer( -1:1, which(country == &amp;quot;Germany&amp;quot;), `+` )) ) |&amp;gt; 
+  mutate(grp = forcats::fct_inorder(c(&amp;quot;lo&amp;quot;, &amp;quot;is&amp;quot;, &amp;quot;hi&amp;quot;))) |&amp;gt; 
+  # Ungroup and make ggplot
+  ungroup() |&amp;gt; 
+  ggplot(aes(as.factor(year), gdpPercap, group = grp)) +
+  geom_col(aes(fill = grp == &amp;quot;is&amp;quot;), position = position_dodge()) +
+  geom_text(
+    aes(label = country_code),
+    vjust = 1.3,
+    position = position_dodge(width = .9)
+  ) +
+  scale_fill_manual(
+    values = c(&amp;quot;grey75&amp;quot;, &amp;quot;steelblue&amp;quot;),
+    guide = guide_none()
+  ) +
+  theme_classic() +
+  labs(x = &amp;quot;Year&amp;quot;, y = &amp;quot;GDP per capita&amp;quot;)&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;&lt;img src="file86a47c2865f8_files/figure-html/final-gapminder-plot-1.png" width="672" /&gt;&lt;/p&gt;
+&lt;details&gt;
+&lt;summary&gt;
+Solving the harder version of the problem
+&lt;/summary&gt;
+&lt;p&gt;The solution presented above relies on a fragile assumption that
+Germany will always have a higher &lt;em&gt;and&lt;/em&gt; lower ranking GDP
+neighbor every year. But nothing about the problem description
+guarantees this, so how can we re-write our code to be more robust?&lt;/p&gt;
+&lt;p&gt;First, let’s simulate a data where Germany is the lowest ranking
+country in 2002 and the highest ranking in 2007. In other words, Germany
+only has one GDP neighbor in those years:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;gapminder_harder_df &amp;lt;- gapminder_df |&amp;gt; 
+  slice( order(gdpPercap), .by = year) |&amp;gt; 
+  slice( as.integer(outer( -1:1, which(country == &amp;quot;Germany&amp;quot;), `+` )) ) |&amp;gt; 
+  slice( -7, -12 )
+gapminder_harder_df&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 10 × 4
+     country     country_code  year gdpPercap
+     &amp;lt;chr&amp;gt;       &amp;lt;chr&amp;gt;        &amp;lt;int&amp;gt;     &amp;lt;dbl&amp;gt;
+   1 Denmark     DNK           1992    26407.
+   2 Germany     DEU           1992    26505.
+   3 Netherlands NLD           1992    26791.
+   4 Belgium     BEL           1997    27561.
+   5 Germany     DEU           1997    27789.
+   6 Iceland     ISL           1997    28061.
+   7 Germany     DEU           2002    30036.
+   8 Belgium     BEL           2002    30486.
+   9 France      FRA           2007    30470.
+  10 Germany     DEU           2007    32170.&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Given this data, we cannot assign the full, length-3 lo-is-hi factor
+by group, because the groups for year 2002 and 2007 only have 2
+observations:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;gapminder_harder_df |&amp;gt; 
+  group_by(year) |&amp;gt; 
+  mutate(grp = forcats::fct_inorder(c(&amp;quot;lo&amp;quot;, &amp;quot;is&amp;quot;, &amp;quot;hi&amp;quot;)))&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  Error in `mutate()`:
+  ℹ In argument: `grp = forcats::fct_inorder(c(&amp;quot;lo&amp;quot;, &amp;quot;is&amp;quot;, &amp;quot;hi&amp;quot;))`.
+  ℹ In group 3: `year = 2002`.
+  Caused by error:
+  ! `grp` must be size 2 or 1, not 3.&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;The trick here is to turn each group of rows into an integer sequence
+where Germany is “anchored” to 2, and then use that vector to subset the
+lo-is-hi factor:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;gapminder_harder_df |&amp;gt; 
+  group_by(year) |&amp;gt; 
+  mutate(
+    Germany_anchored_to_2 = row_number() - which(country == &amp;quot;Germany&amp;quot;) + 2,
+    grp = forcats::fct_inorder(c(&amp;quot;lo&amp;quot;, &amp;quot;is&amp;quot;, &amp;quot;hi&amp;quot;))[Germany_anchored_to_2]
+  )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 10 × 6
+  # Groups:   year [4]
+     country     country_code  year gdpPercap Germany_anchored_to_2 grp  
+     &amp;lt;chr&amp;gt;       &amp;lt;chr&amp;gt;        &amp;lt;int&amp;gt;     &amp;lt;dbl&amp;gt;                 &amp;lt;dbl&amp;gt; &amp;lt;fct&amp;gt;
+   1 Denmark     DNK           1992    26407.                     1 lo   
+   2 Germany     DEU           1992    26505.                     2 is   
+   3 Netherlands NLD           1992    26791.                     3 hi   
+   4 Belgium     BEL           1997    27561.                     1 lo   
+   5 Germany     DEU           1997    27789.                     2 is   
+   6 Iceland     ISL           1997    28061.                     3 hi   
+   7 Germany     DEU           2002    30036.                     2 is   
+   8 Belgium     BEL           2002    30486.                     3 hi   
+   9 France      FRA           2007    30470.                     1 lo   
+  10 Germany     DEU           2007    32170.                     2 is&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;We find that the lessons of working with row indices from
+&lt;code&gt;slice()&lt;/code&gt; translated to solving this complex
+&lt;code&gt;mutate()&lt;/code&gt; problem - neat!&lt;/p&gt;
+&lt;/details&gt;
+&lt;h3 id="aside-kronecker-as-as.vectorouter"&gt;Aside:
+&lt;code&gt;kronecker()&lt;/code&gt; as &lt;code&gt;as.vector(outer())&lt;/code&gt;&lt;/h3&gt;
+&lt;p&gt;Following from the &lt;code&gt;slice()&lt;/code&gt; + &lt;code&gt;outer()&lt;/code&gt;
+strategy demoed above, imagine if we wanted to filter for
+&lt;code&gt;"Luke Skywalker"&lt;/code&gt; and 4 other characters that are neighbors
+in the &lt;code&gt;height&lt;/code&gt; and &lt;code&gt;mass&lt;/code&gt; values.&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;dplyr::starwars[, 1:3]&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 87 × 3
+     name               height  mass
+     &amp;lt;chr&amp;gt;               &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+   1 Luke Skywalker        172    77
+   2 C-3PO                 167    75
+   3 R2-D2                  96    32
+   4 Darth Vader           202   136
+   5 Leia Organa           150    49
+   6 Owen Lars             178   120
+   7 Beru Whitesun Lars    165    75
+   8 R5-D4                  97    32
+   9 Biggs Darklighter     183    84
+  10 Obi-Wan Kenobi        182    77
+  # ℹ 77 more rows&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;In row-relational terms, “filtering neighboring values” just means
+“filtering rows after arranging by the values we care about”. We can
+express this using &lt;code&gt;slice()&lt;/code&gt; and &lt;code&gt;outer()&lt;/code&gt; as:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars %&amp;gt;% 
+  select(name, mass, height) %&amp;gt;% 
+  arrange(mass, height) %&amp;gt;% 
+  slice( as.vector(outer(-2:2, which(name == &amp;quot;Luke Skywalker&amp;quot;), `+`)) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 5 × 3
+    name            mass height
+    &amp;lt;chr&amp;gt;          &amp;lt;dbl&amp;gt;  &amp;lt;int&amp;gt;
+  1 Palpatine       75      170
+  2 Wedge Antilles  77      170
+  3 Luke Skywalker  77      172
+  4 Obi-Wan Kenobi  77      182
+  5 Boba Fett       78.2    183&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;I raised this example on an unrelated thread on the &lt;a
+href="https://fosstodon.org/@DSLC"&gt;R4DS/DSLC slack&lt;/a&gt;, where Anthony
+Durrant pointed me to &lt;code&gt;kronecker()&lt;/code&gt; as a version of
+&lt;code&gt;outer()&lt;/code&gt; that unlist before returning the output.&lt;/p&gt;
+&lt;p&gt;So in examples involving &lt;code&gt;outer()&lt;/code&gt; to generate row indices
+in &lt;code&gt;slice()&lt;/code&gt;, we can also use &lt;code&gt;kronecker()&lt;/code&gt;
+instead to save a call to a flattening function like
+&lt;code&gt;as.vector()&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;starwars %&amp;gt;% 
+  select(name, mass, height) %&amp;gt;% 
+  arrange(mass, height) %&amp;gt;% 
+  slice( kronecker(-2:2, which(name == &amp;quot;Luke Skywalker&amp;quot;), `+`) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 5 × 3
+    name            mass height
+    &amp;lt;chr&amp;gt;          &amp;lt;dbl&amp;gt;  &amp;lt;int&amp;gt;
+  1 Palpatine       75      170
+  2 Wedge Antilles  77      170
+  3 Luke Skywalker  77      172
+  4 Obi-Wan Kenobi  77      182
+  5 Boba Fett       78.2    183&lt;/code&gt;&lt;/pre&gt;
+&lt;h3 id="windowed-minmaxmedian-etc."&gt;Windowed min/max/median (etc.)&lt;/h3&gt;
+&lt;p&gt;Let’s say we have this small time series data, and we want to
+calculate a &lt;strong&gt;lagged 3-window moving minimum&lt;/strong&gt; for the
+&lt;code&gt;val&lt;/code&gt; column:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;ts_df &amp;lt;- tibble(
+  time = 1:6,
+  val = sample(1:6 * 10)
+)
+ts_df&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 6 × 2
+     time   val
+    &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+  1     1    50
+  2     2    40
+  3     3    60
+  4     4    30
+  5     5    20
+  6     6    10&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;If you’re new to window functions, think of them as a special kind of
+&lt;code&gt;group_by()&lt;/code&gt; + &lt;code&gt;summarize()&lt;/code&gt; where groups are
+chunks of observations along a (typically unique) continuous measure
+like time, and observations can be shared between groups.&lt;/p&gt;
+&lt;p&gt;There are several packages implementing moving/sliding/rolling window
+functions. My current favorite is &lt;code&gt;{r2c}&lt;/code&gt; (see a &lt;a
+href="https://github.com/brodieG/r2c#fast-group-and-rolling-statistics"&gt;review
+of other implementations therein&lt;/a&gt;), but I also like
+&lt;code&gt;{slider}&lt;/code&gt; for an implementation that follows familiar &lt;a
+href="https://design.tidyverse.org/"&gt;“tidy” design principles&lt;/a&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;library(slider)
+ts_df |&amp;gt; 
+  mutate(moving_min = slide_min(val, before = 2L, complete = TRUE))&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 6 × 3
+     time   val moving_min
+    &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;      &amp;lt;dbl&amp;gt;
+  1     1    50         NA
+  2     2    40         NA
+  3     3    60         40
+  4     4    30         30
+  5     5    20         20
+  6     6    10         10&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Moving window is a general class of operations that encompass any
+arbitrary summary statistic - so not just min but other reducing
+functions like mean, standard deviation, etc. But what makes moving
+&lt;strong&gt;min&lt;/strong&gt; (along with max, median, etc.) a particularly
+interesting case for our current discussion is that the value comes from
+&lt;strong&gt;an existing observation&lt;/strong&gt; in the data. And if our time
+series is tidy, every observation makes up a row. See where I’m going
+with this?&lt;/p&gt;
+&lt;p&gt;Using &lt;code&gt;outer()&lt;/code&gt; again, we can take the outer sum of all
+row indices of &lt;code&gt;ts_df&lt;/code&gt; and &lt;code&gt;-2:0&lt;/code&gt;. This gives us a
+matrix where each column represents a lagged size-3 moving window:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;windows_3lag &amp;lt;- outer(-2:0, 1:nrow(ts_df), &amp;quot;+&amp;quot;)
+windows_3lag&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;       [,1] [,2] [,3] [,4] [,5] [,6]
+  [1,]   -1    0    1    2    3    4
+  [2,]    0    1    2    3    4    5
+  [3,]    1    2    3    4    5    6&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;The “lagged size-3” property of this moving window means that the
+first two windows are incomplete (consisting of less than 3
+observations). We want to treat those as invalid, so we can drop the
+first two columns from our matrix:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;windows_3lag[,-(1:2)]&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;       [,1] [,2] [,3] [,4]
+  [1,]    1    2    3    4
+  [2,]    2    3    4    5
+  [3,]    3    4    5    6&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;For each remaining column, we want to grab the values of
+&lt;code&gt;val&lt;/code&gt; at the corresponding row indices and find which row has
+the minimum &lt;code&gt;val&lt;/code&gt;. In terms of code, we use
+&lt;code&gt;apply()&lt;/code&gt; with &lt;code&gt;MARGIN = 2L&lt;/code&gt; to column-wise apply
+a function where we use &lt;code&gt;which.min()&lt;/code&gt; to find the location of
+the minimum &lt;code&gt;val&lt;/code&gt; and convert it back to row index via
+subsetting:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;windows_3lag[, -(1:2)] |&amp;gt; 
+  apply(MARGIN = 2L, \(i) i[which.min(ts_df$val[i])])&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1] 2 4 5 6&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Now let’s stick this inside &lt;code&gt;slice()&lt;/code&gt;, exploiting the fact
+that it’s &lt;em&gt;data-masked&lt;/em&gt; (&lt;code&gt;ts_df$val&lt;/code&gt; can just be
+&lt;code&gt;val&lt;/code&gt;) and exposes &lt;em&gt;context-dependent expressions&lt;/em&gt;
+(&lt;code&gt;1:nrow(ts_df)&lt;/code&gt; can just be &lt;code&gt;row_number()&lt;/code&gt;):&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;moving_mins &amp;lt;- ts_df |&amp;gt; 
+  slice(
+    outer(-2:0, row_number(), &amp;quot;+&amp;quot;)[,-(1:2)] |&amp;gt; 
+      apply(MARGIN = 2L, \(i) i[which.min(val[i])])
+  )
+moving_mins&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 4 × 2
+     time   val
+    &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;
+  1     2    40
+  2     4    30
+  3     5    20
+  4     6    10&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;From here, we can grab the &lt;code&gt;val&lt;/code&gt; column and pad it with
+&lt;code&gt;NA&lt;/code&gt; to add our desired &lt;code&gt;window_min&lt;/code&gt; column to the
+original data frame:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;ts_df |&amp;gt; 
+  mutate(moving_min = c(NA, NA, moving_mins$val))&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 6 × 3
+     time   val moving_min
+    &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;      &amp;lt;dbl&amp;gt;
+  1     1    50         NA
+  2     2    40         NA
+  3     3    60         40
+  4     4    30         30
+  5     5    20         20
+  6     6    10         10&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;At this point you might think that this is a very round-about way of
+solving the same problem. But actually I think that it’s a faster route
+to solving a slightly more complicated problem - augmenting each
+observation of a data frame with information about &lt;strong&gt;comparison
+observations&lt;/strong&gt;.&lt;/p&gt;
+&lt;p&gt;For example, our &lt;code&gt;slice()&lt;/code&gt;-based solution sets us up
+nicely for also bringing along information about the time at which the
+&lt;code&gt;moving_min&lt;/code&gt; occurred. After some &lt;code&gt;rename()&lt;/code&gt;-ing
+and adding the original time information back in, we get back a
+relational data structure where &lt;code&gt;time&lt;/code&gt; is a
+&lt;strong&gt;key&lt;/strong&gt; shared with &lt;code&gt;ts_df&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;moving_mins2 &amp;lt;- moving_mins |&amp;gt; 
+  rename(moving_min_val = val, moving_min_time = time) |&amp;gt; 
+  mutate(time = ts_df$time[-(1:2)], .before = 1L)
+moving_mins2&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 4 × 3
+     time moving_min_time moving_min_val
+    &amp;lt;int&amp;gt;           &amp;lt;int&amp;gt;          &amp;lt;dbl&amp;gt;
+  1     3               2             40
+  2     4               4             30
+  3     5               5             20
+  4     6               6             10&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;We can then left-join this to the original data to augment it with
+information about both the value of the 3-window minimum and the time
+that the minimum occurred:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;left_join(ts_df, moving_mins2, by = &amp;quot;time&amp;quot;)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 6 × 4
+     time   val moving_min_time moving_min_val
+    &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;           &amp;lt;int&amp;gt;          &amp;lt;dbl&amp;gt;
+  1     1    50              NA             NA
+  2     2    40              NA             NA
+  3     3    60               2             40
+  4     4    30               4             30
+  5     5    20               5             20
+  6     6    10               6             10&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;This is particularly useful if rows contain other useful information
+for comparison and you have memory to spare:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;ts_wide_df &amp;lt;- ts_df |&amp;gt; 
+  mutate(
+    col1 = rnorm(6),
+    col2 = rnorm(6)
+  )
+ts_wide_df&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 6 × 4
+     time   val    col1     col2
+    &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;   &amp;lt;dbl&amp;gt;    &amp;lt;dbl&amp;gt;
+  1     1    50  0.0183  0.00501
+  2     2    40  0.705  -0.0376 
+  3     3    60 -0.647   0.724  
+  4     4    30  0.868  -0.497  
+  5     5    20  0.376   0.0114 
+  6     6    10  0.310   0.00986&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;The below code augments each observation in the original
+&lt;code&gt;ts_wide_df&lt;/code&gt; data with information about the corresponding
+3-window moving min (columns prefixed with &lt;code&gt;"min3val_"&lt;/code&gt;)&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;moving_mins_wide &amp;lt;- ts_wide_df |&amp;gt; 
+  slice(
+    outer(-2:0, row_number(), &amp;quot;+&amp;quot;)[,-(1:2)] |&amp;gt; 
+      apply(MARGIN = 2L, \(i) i[which.min(val[i])])
+  ) |&amp;gt; 
+  rename_with(~ paste0(&amp;quot;min3val_&amp;quot;, .x)) |&amp;gt; 
+  mutate(time = ts_wide_df$time[-(1:2)])
+left_join(ts_wide_df, moving_mins_wide, by = &amp;quot;time&amp;quot;)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 6 × 8
+     time   val    col1     col2 min3val_time min3val_val min3val_col1
+    &amp;lt;int&amp;gt; &amp;lt;dbl&amp;gt;   &amp;lt;dbl&amp;gt;    &amp;lt;dbl&amp;gt;        &amp;lt;int&amp;gt;       &amp;lt;dbl&amp;gt;        &amp;lt;dbl&amp;gt;
+  1     1    50  0.0183  0.00501           NA          NA       NA    
+  2     2    40  0.705  -0.0376            NA          NA       NA    
+  3     3    60 -0.647   0.724              2          40        0.705
+  4     4    30  0.868  -0.497              4          30        0.868
+  5     5    20  0.376   0.0114             5          20        0.376
+  6     6    10  0.310   0.00986            6          10        0.310
+  # ℹ 1 more variable: min3val_col2 &amp;lt;dbl&amp;gt;&lt;/code&gt;&lt;/pre&gt;
+&lt;!-- ### Dependency relations between rows --&gt;
+&lt;!-- In tidy representations of nested, hierarchical data, the parent-child relationship between rows are often encoded in a column that reference other rows in the data. --&gt;
+&lt;!-- Let's take the case of dependency parsing in NLP (using [spaCy](https://spacy.io/)) for example. Given a sentence like "June likes cute cats", the dependency relationship between tokens can be represented like so: --&gt;
+&lt;!-- &lt;details&gt; --&gt;
+&lt;!-- &lt;summary&gt;Code to produce the figure&lt;/summary&gt; --&gt;
+&lt;!-- ```{r displacy, eval = FALSE} --&gt;
+&lt;!-- library(reticulate) --&gt;
+&lt;!-- spacy &lt;- import("spacy") --&gt;
+&lt;!-- nlp &lt;- spacy$load("en_core_web_sm") --&gt;
+&lt;!-- py_parsed &lt;- nlp("June likes cute cats") --&gt;
+&lt;!-- displacy_render &lt;- function(x) { --&gt;
+&lt;!--   spacy$displacy$render(x) |&gt;  --&gt;
+&lt;!--     htmltools::HTML() |&gt; --&gt;
+&lt;!--     htmltools::html_print() --&gt;
+&lt;!-- } --&gt;
+&lt;!-- displacy_render(py_parsed) --&gt;
+&lt;!-- ``` --&gt;
+&lt;!-- &lt;/details&gt; --&gt;
+&lt;!-- ```{r displacy, message = FALSE} --&gt;
+&lt;!-- ``` --&gt;
+&lt;!-- There's a lot going on here, but I want to draw attention to the fact that there's an arrow going from `"likes"` to `"cats"` and from `"cats"` to `"cute"`. In NLP terms, we say that in this sentence, the head of "cute" is "cats", and the head of "cats" is "likes". --&gt;
+&lt;!-- To demonstrate this using **spacy** in *python*, we can parse the sentence and store the parsed object in `py_parsed`: --&gt;
+&lt;!-- ```{r, eval = FALSE} --&gt;
+&lt;!-- library(reticulate) --&gt;
+&lt;!-- spacy &lt;- import("spacy") --&gt;
+&lt;!-- nlp &lt;- spacy$load("en_core_web_sm") --&gt;
+&lt;!-- py_parsed &lt;- nlp("June likes cute cats") --&gt;
+&lt;!-- ``` --&gt;
+&lt;!-- Using python's 0-indexing, we extract the token object corresponding to "cats". From there, we can see the dependency relationship where the head of "cute" is "cats" and the head of "cats" is "likes": --&gt;
+&lt;!-- ```{r} --&gt;
+&lt;!-- py_parsed[2] --&gt;
+&lt;!-- py_parsed[2]$head --&gt;
+&lt;!-- py_parsed[2]$head$head --&gt;
+&lt;!-- ``` --&gt;
+&lt;!-- We see that this dependency relationship between "cute"-"cats"-"likes" is expressed concisely in object-oriented programming (you just follow the `head` property of tokens). This gets a bit trickier to work with in tidy data form. --&gt;
+&lt;!-- Using the `{spacyr}` package, we can generate a dataframe equivalent of `py_parsed` which stores the dependency relationship in the `head_token_id` column: --&gt;
+&lt;!-- ```{r, message = FALSE} --&gt;
+&lt;!-- library(spacyr) --&gt;
+&lt;!-- sentence &lt;- "June likes cute cats" --&gt;
+&lt;!-- parsed &lt;- spacy_parse(sentence, dependency = TRUE, entity = FALSE)[,-c(1:2)] --&gt;
+&lt;!-- parsed --&gt;
+&lt;!-- ``` --&gt;
+&lt;!-- To get from "cute" to "cats" and "likes" by following the arrows, we can use `slice()`: --&gt;
+&lt;!-- ```{r} --&gt;
+&lt;!-- # Child token --&gt;
+&lt;!-- parsed |&gt;  --&gt;
+&lt;!--   slice(3) --&gt;
+&lt;!-- # Parent head --&gt;
+&lt;!-- parsed |&gt;  --&gt;
+&lt;!--   slice( head_token_id[3] ) --&gt;
+&lt;!-- # Grandparent head --&gt;
+&lt;!-- parsed |&gt;  --&gt;
+&lt;!--   slice( head_token_id[token_id == head_token_id[3]] ) --&gt;
+&lt;!-- ``` --&gt;
+&lt;!-- &lt;details&gt; --&gt;
+&lt;!-- &lt;summary&gt;The recursive generalization&lt;/summary&gt; --&gt;
+&lt;!-- ```{r} --&gt;
+&lt;!-- # Special case for init --&gt;
+&lt;!-- parsed |&gt;  --&gt;
+&lt;!--   slice( 3 ) --&gt;
+&lt;!-- # Recursive call to `head_token_id[token_id == PREV]` --&gt;
+&lt;!-- parsed |&gt;  --&gt;
+&lt;!--   slice( head_token_id[token_id == 3] ) --&gt;
+&lt;!-- parsed |&gt;  --&gt;
+&lt;!--   slice( head_token_id[token_id == head_token_id[token_id == 3]] ) --&gt;
+&lt;!-- ``` --&gt;
+&lt;!-- &lt;/details&gt; --&gt;
+&lt;!-- Now let's say that we have a paragraph of sentences describing what June likes and doesn't likes. --&gt;
+&lt;!-- ```{r} --&gt;
+&lt;!-- paragraph &lt;- "June likes cute cats. June hates angry cats. June likes small dogs." --&gt;
+&lt;!-- parsed_paragraph &lt;- spacy_parse(paragraph, dependency = TRUE, entity = FALSE) --&gt;
+&lt;!-- parsed_paragraph &lt;- parsed_paragraph |&gt;  --&gt;
+&lt;!--   filter(pos != "PUNCT") --&gt;
+&lt;!-- parsed_paragraph --&gt;
+&lt;!-- ``` --&gt;
+&lt;!-- And let's say that our research question is: what kinds of cats does June like? In other words we want to end up with a set of `ADJ`s where the head token is `cats` and the head token of that is `likes`. In `parsed_paragraph`, there's only one token (row) meeting this criteria: --&gt;
+&lt;!-- ```{r} --&gt;
+&lt;!-- parsed_paragraph[3,] --&gt;
+&lt;!-- ``` --&gt;
+&lt;!-- In our solution we use a helper function `get_head_tokens()`, which recursively searches for token head using `slice()`. This blog post is already getting too long so I'll just dump the code for now and maybe I'll come back to add more explanations later... --&gt;
+&lt;!-- ```{r} --&gt;
+&lt;!-- get_head_tokens &lt;- function(df, child, n) { --&gt;
+&lt;!--   child &lt;- rlang::eval_tidy(enquo(child), data = df) --&gt;
+&lt;!--   purrr::accumulate( --&gt;
+&lt;!--     .x = seq_len(n), --&gt;
+&lt;!--     .f = ~ slice(df, head_token_id[token_id == .x$token_id]), --&gt;
+&lt;!--     .init = slice(df, child) --&gt;
+&lt;!--   ) |&gt;  --&gt;
+&lt;!--     slice(-1) |&gt;  --&gt;
+&lt;!--     pull(token) --&gt;
+&lt;!-- } --&gt;
+&lt;!-- parsed_paragraph |&gt;  --&gt;
+&lt;!--   filter(sentence_id == 1) |&gt;  --&gt;
+&lt;!--   get_head_tokens(child = which(pos == "ADJ"), n = 2) --&gt;
+&lt;!-- ``` --&gt;
+&lt;!-- Applying `get_head_tokens()` for each sentence gets us the solution: --&gt;
+&lt;!-- ```{r} --&gt;
+&lt;!-- parsed_paragraph |&gt;  --&gt;
+&lt;!--   group_by(sentence_id) |&gt;  --&gt;
+&lt;!--   filter( --&gt;
+&lt;!--     pos == "ADJ", --&gt;
+&lt;!--     identical( --&gt;
+&lt;!--       c("cats", "likes"), --&gt;
+&lt;!--       get_head_tokens(pick(everything()), which(pos == "ADJ"), 2) --&gt;
+&lt;!--     ) --&gt;
+&lt;!--   ) |&gt;  --&gt;
+&lt;!--   ungroup() --&gt;
+&lt;!-- ``` --&gt;
+&lt;h3 id="evenly-distributed-row-shuffling-of-balanced-categories"&gt;Evenly
+distributed row shuffling of balanced categories&lt;/h3&gt;
+&lt;p&gt;Sometimes the ordering of rows in a data frame can be meaningful for
+an external application.&lt;/p&gt;
+&lt;p&gt;For example, many experiment-building platforms for psychology
+research require researchers to specify the running order of trials in
+an experiment via a csv, where each row represents a trial and each
+column represents information about the trial.&lt;/p&gt;
+&lt;p&gt;So an experiment testing the classic &lt;a
+href="https://www.psytoolkit.org/lessons/stroop.html"&gt;Stroop effect&lt;/a&gt;
+may have the following template:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;mismatch_trials &amp;lt;- tibble(
+  item_id = 1:5,
+  trial = &amp;quot;mismatch&amp;quot;,
+  word = c(&amp;quot;red&amp;quot;, &amp;quot;green&amp;quot;, &amp;quot;purple&amp;quot;, &amp;quot;brown&amp;quot;, &amp;quot;blue&amp;quot;),
+  color = c(&amp;quot;brown&amp;quot;, &amp;quot;red&amp;quot;, &amp;quot;green&amp;quot;, &amp;quot;blue&amp;quot;, &amp;quot;purple&amp;quot;)
+)
+mismatch_trials&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 5 × 4
+    item_id trial    word   color 
+      &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;    &amp;lt;chr&amp;gt;  &amp;lt;chr&amp;gt; 
+  1       1 mismatch red    brown 
+  2       2 mismatch green  red   
+  3       3 mismatch purple green 
+  4       4 mismatch brown  blue  
+  5       5 mismatch blue   purple&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;We probably also want to mix in some &lt;em&gt;control&lt;/em&gt; trials where
+the word and color do match:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;match_trials &amp;lt;- mismatch_trials |&amp;gt; 
+  mutate(trial = &amp;quot;match&amp;quot;, color = word)
+match_trials&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 5 × 4
+    item_id trial word   color 
+      &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt; &amp;lt;chr&amp;gt;  &amp;lt;chr&amp;gt; 
+  1       1 match red    red   
+  2       2 match green  green 
+  3       3 match purple purple
+  4       4 match brown  brown 
+  5       5 match blue   blue&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Now that we have all materials for our experiment, we next want the
+running order to interleave the match and mismatch trials.&lt;/p&gt;
+&lt;p&gt;We first add them together into a longer data frame:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;stroop_trials &amp;lt;- bind_rows(mismatch_trials, match_trials)
+stroop_trials&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 10 × 4
+     item_id trial    word   color 
+       &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;    &amp;lt;chr&amp;gt;  &amp;lt;chr&amp;gt; 
+   1       1 mismatch red    brown 
+   2       2 mismatch green  red   
+   3       3 mismatch purple green 
+   4       4 mismatch brown  blue  
+   5       5 mismatch blue   purple
+   6       1 match    red    red   
+   7       2 match    green  green 
+   8       3 match    purple purple
+   9       4 match    brown  brown 
+  10       5 match    blue   blue&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;And from here we can exploit the fact that all mismatch items come
+before match items, and that they share the same length of 5:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;stroop_trials |&amp;gt; 
+  slice( as.integer(outer(c(0, 5), 1:5, &amp;quot;+&amp;quot;)) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 10 × 4
+     item_id trial    word   color 
+       &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;    &amp;lt;chr&amp;gt;  &amp;lt;chr&amp;gt; 
+   1       1 mismatch red    brown 
+   2       1 match    red    red   
+   3       2 mismatch green  red   
+   4       2 match    green  green 
+   5       3 mismatch purple green 
+   6       3 match    purple purple
+   7       4 mismatch brown  blue  
+   8       4 match    brown  brown 
+   9       5 mismatch blue   purple
+  10       5 match    blue   blue&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;This relies on a strong assumptions about the row order in the
+original data, though. So a safer alternative is to represent the row
+indices for &lt;code&gt;"match"&lt;/code&gt; and &lt;code&gt;"mismatch"&lt;/code&gt; trials as
+rows of a matrix, and then collapse column-wise.&lt;/p&gt;
+&lt;p&gt;Let’s try this outside of &lt;code&gt;slice()&lt;/code&gt; first. We start with a
+call to &lt;code&gt;sapply()&lt;/code&gt; to construct a matrix where the columns
+contain row indices for each unique category of &lt;code&gt;trial&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;sapply(unique(stroop_trials$trial), \(x) which(stroop_trials$trial == x))&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;       mismatch match
+  [1,]        1     6
+  [2,]        2     7
+  [3,]        3     8
+  [4,]        4     9
+  [5,]        5    10&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Then we transpose the matrix with &lt;code&gt;t()&lt;/code&gt;, which rotates
+it:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;t( sapply(unique(stroop_trials$trial), \(x) which(stroop_trials$trial == x)) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;           [,1] [,2] [,3] [,4] [,5]
+  mismatch    1    2    3    4    5
+  match       6    7    8    9   10&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Now lets stick that inside slice, remembering to collapse the
+transposed matrix into vector:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;interleaved_stroop_trials &amp;lt;- stroop_trials |&amp;gt; 
+  slice( as.integer(t(sapply(unique(trial), \(x) which(trial == x)))) )
+interleaved_stroop_trials&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 10 × 4
+     item_id trial    word   color 
+       &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;    &amp;lt;chr&amp;gt;  &amp;lt;chr&amp;gt; 
+   1       1 mismatch red    brown 
+   2       1 match    red    red   
+   3       2 mismatch green  red   
+   4       2 match    green  green 
+   5       3 mismatch purple green 
+   6       3 match    purple purple
+   7       4 mismatch brown  blue  
+   8       4 match    brown  brown 
+   9       5 mismatch blue   purple
+  10       5 match    blue   blue&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;At the moment, we have both “red” word trails showing up together,
+and then the “green”s, the “purple”s, and so on. If we wanted to
+introduce some randomness to the presentation order within each type of
+trial, we can wrap the row indices in &lt;code&gt;sample()&lt;/code&gt; to shuffle
+them first:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;shuffled_stroop_trials &amp;lt;- stroop_trials |&amp;gt; 
+  slice( as.integer(t(sapply(unique(trial), \(x) sample(which(trial == x))))) )
+shuffled_stroop_trials&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 10 × 4
+     item_id trial    word   color 
+       &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;    &amp;lt;chr&amp;gt;  &amp;lt;chr&amp;gt; 
+   1       1 mismatch red    brown 
+   2       5 match    blue   blue  
+   3       2 mismatch green  red   
+   4       4 match    brown  brown 
+   5       3 mismatch purple green 
+   6       1 match    red    red   
+   7       4 mismatch brown  blue  
+   8       3 match    purple purple
+   9       5 mismatch blue   purple
+  10       2 match    green  green&lt;/code&gt;&lt;/pre&gt;
+&lt;!-- applies to monotonically increasing continuous sequences too --&gt;
+&lt;h3 id="inserting-a-new-row-at-specific-intervals"&gt;Inserting a new row
+at specific intervals&lt;/h3&gt;
+&lt;p&gt;Continuing with our Stroop experiment template example, let’s say we
+want to give participants a break every two trials.&lt;/p&gt;
+&lt;p&gt;In a matrix representation, this means constructing this 2-row matrix
+of row indices:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;matrix(1:nrow(shuffled_stroop_trials), nrow = 2)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;       [,1] [,2] [,3] [,4] [,5]
+  [1,]    1    3    5    7    9
+  [2,]    2    4    6    8   10&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;And adding a row of that represent a separator/break, before
+collapsing column-wise:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;matrix(1:nrow(shuffled_stroop_trials), nrow = 2) |&amp;gt; 
+  rbind(11)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;       [,1] [,2] [,3] [,4] [,5]
+  [1,]    1    3    5    7    9
+  [2,]    2    4    6    8   10
+  [3,]   11   11   11   11   11&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Using slice, this means adding a row to the data representing a break
+trial first, and then adding a row to the row index matrix representing
+that row:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;stroop_with_breaks &amp;lt;- shuffled_stroop_trials |&amp;gt; 
+  add_row(trial = &amp;quot;BREAK&amp;quot;) |&amp;gt; 
+  slice(
+    matrix(row_number()[-n()], nrow = 2) |&amp;gt; 
+      rbind(n()) |&amp;gt; 
+      as.integer()
+  )
+stroop_with_breaks&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 15 × 4
+     item_id trial    word   color 
+       &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;    &amp;lt;chr&amp;gt;  &amp;lt;chr&amp;gt; 
+   1       1 mismatch red    brown 
+   2       5 match    blue   blue  
+   3      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+   4       2 mismatch green  red   
+   5       4 match    brown  brown 
+   6      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+   7       3 mismatch purple green 
+   8       1 match    red    red   
+   9      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+  10       4 mismatch brown  blue  
+  11       3 match    purple purple
+  12      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+  13       5 mismatch blue   purple
+  14       2 match    green  green 
+  15      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;If we don’t want a break after the last trial, we can use negative
+indexing with &lt;code&gt;slice(-n())&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;stroop_with_breaks |&amp;gt; 
+  slice(-n())&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 14 × 4
+     item_id trial    word   color 
+       &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;    &amp;lt;chr&amp;gt;  &amp;lt;chr&amp;gt; 
+   1       1 mismatch red    brown 
+   2       5 match    blue   blue  
+   3      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+   4       2 mismatch green  red   
+   5       4 match    brown  brown 
+   6      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+   7       3 mismatch purple green 
+   8       1 match    red    red   
+   9      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+  10       4 mismatch brown  blue  
+  11       3 match    purple purple
+  12      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+  13       5 mismatch blue   purple
+  14       2 match    green  green&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;What about after 3 trials, where the number of trials (10) is not
+divisibly by 3? Can we still use a matrix?&lt;/p&gt;
+&lt;p&gt;Yes, you’d just need to explicitly fill in the “blanks”!&lt;/p&gt;
+&lt;p&gt;Conceptually, we want a matrix like this, where extra “cells” are
+padded with 0s (recall that 0s are ignored in &lt;code&gt;slice()&lt;/code&gt;):&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;matrix(c(1:10, rep(0, 3 - 10 %% 3)), nrow = 3)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;       [,1] [,2] [,3] [,4]
+  [1,]    1    4    7   10
+  [2,]    2    5    8    0
+  [3,]    3    6    9    0&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;And this is how that could be implemented inside
+&lt;code&gt;slice()&lt;/code&gt;, minding the fact that adding the break trial
+increases original row count by 1:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;shuffled_stroop_trials |&amp;gt; 
+  add_row(trial = &amp;quot;BREAK&amp;quot;) |&amp;gt; 
+  slice(
+    c(seq_len(n()-1), rep(0, 3 - (n()-1) %% 3)) |&amp;gt; 
+      matrix(nrow = 3) |&amp;gt; 
+      rbind(n()) |&amp;gt; 
+      as.integer()
+  ) |&amp;gt; 
+  slice(-n())&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 13 × 4
+     item_id trial    word   color 
+       &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;    &amp;lt;chr&amp;gt;  &amp;lt;chr&amp;gt; 
+   1       1 mismatch red    brown 
+   2       5 match    blue   blue  
+   3       2 mismatch green  red   
+   4      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+   5       4 match    brown  brown 
+   6       3 mismatch purple green 
+   7       1 match    red    red   
+   8      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+   9       4 mismatch brown  blue  
+  10       3 match    purple purple
+  11       5 mismatch blue   purple
+  12      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+  13       2 match    green  green&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;How about inserting a break trial after every &lt;code&gt;"purple"&lt;/code&gt;
+word trials?&lt;/p&gt;
+&lt;p&gt;Conceptually, we want a matrix that binds these two vectors as rows
+before collapsing:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;print( 1:nrow(shuffled_stroop_trials) )
+print(
+  replace(rep(0, nrow(shuffled_stroop_trials)),
+          which(shuffled_stroop_trials$word == &amp;quot;purple&amp;quot;), 11)
+)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;   [1]  1  2  3  4  5  6  7  8  9 10
+   [1]  0  0  0  0 11  0  0 11  0  0&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;And this is how you could do that inside &lt;code&gt;slice()&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;shuffled_stroop_trials |&amp;gt; 
+  add_row(trial = &amp;quot;BREAK&amp;quot;) |&amp;gt; 
+  slice(
+    c(seq_len(n()-1), replace(rep(0, n()-1), which(word == &amp;quot;purple&amp;quot;), n())) |&amp;gt;
+      matrix(nrow = 2, byrow = TRUE) |&amp;gt; 
+      as.integer()
+  )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 12 × 4
+     item_id trial    word   color 
+       &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;    &amp;lt;chr&amp;gt;  &amp;lt;chr&amp;gt; 
+   1       1 mismatch red    brown 
+   2       5 match    blue   blue  
+   3       2 mismatch green  red   
+   4       4 match    brown  brown 
+   5       3 mismatch purple green 
+   6      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+   7       1 match    red    red   
+   8       4 mismatch brown  blue  
+   9       3 match    purple purple
+  10      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+  11       5 mismatch blue   purple
+  12       2 match    green  green&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;You might protest that this is a pretty convoluted approach to a
+seemingly simple problem of inserting rows, and you’d be right!&lt;a
+href="#fn2" class="footnote-ref" id="fnref2"&gt;&lt;sup&gt;2&lt;/sup&gt;&lt;/a&gt; Not only
+is the code difficult to read, you can only insert the same single row
+over and over.&lt;/p&gt;
+&lt;p&gt;It turns out that these cases of row insertion actually fall under
+the broader class of interweaving &lt;strong&gt;unequal categories&lt;/strong&gt; -
+let’s see this next.&lt;/p&gt;
+&lt;h3 id="evenly-distributed-row-shuffling-of-unequal-categories"&gt;Evenly
+distributed row shuffling of unequal categories&lt;/h3&gt;
+&lt;p&gt;Let’s return to our solution for the initial “break every 2 trials”
+problem:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;shuffled_stroop_trials |&amp;gt; 
+  add_row(trial = &amp;quot;BREAK&amp;quot;) |&amp;gt; 
+  slice(
+    matrix(row_number()[-n()], nrow = 2) |&amp;gt; 
+      rbind(n()) |&amp;gt; 
+      as.integer()
+  ) |&amp;gt; 
+  slice(-n())&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 14 × 4
+     item_id trial    word   color 
+       &amp;lt;int&amp;gt; &amp;lt;chr&amp;gt;    &amp;lt;chr&amp;gt;  &amp;lt;chr&amp;gt; 
+   1       1 mismatch red    brown 
+   2       5 match    blue   blue  
+   3      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+   4       2 mismatch green  red   
+   5       4 match    brown  brown 
+   6      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+   7       3 mismatch purple green 
+   8       1 match    red    red   
+   9      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+  10       4 mismatch brown  blue  
+  11       3 match    purple purple
+  12      NA BREAK    &amp;lt;NA&amp;gt;   &amp;lt;NA&amp;gt;  
+  13       5 mismatch blue   purple
+  14       2 match    green  green&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Here, we were working with a matrix that looks like this, where
+&lt;code&gt;11&lt;/code&gt; represents the new row we added representing a break
+trial:&lt;/p&gt;
+&lt;pre&gt;&lt;code&gt;       [,1] [,2] [,3] [,4] [,5]
+  [1,]    1    3    5    7    9
+  [2,]    2    4    6    8   10
+  [3,]   11   11   11   11   11&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;And recall that to insert every &lt;em&gt;3&lt;/em&gt; rows, we needed to pad
+with &lt;code&gt;0&lt;/code&gt; first to satisfy the matrix’s rectangle
+constraint:&lt;/p&gt;
+&lt;pre&gt;&lt;code&gt;       [,1] [,2] [,3] [,4]
+  [1,]    1    4    7   10
+  [2,]    2    5    8    0
+  [3,]    3    6    9    0
+  [4,]   11   11   11   11&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;But a better way of thinking about this is to have one matrix row
+representing all row indices, and then add a &lt;strong&gt;sparse row&lt;/strong&gt;
+that represent breaks:&lt;/p&gt;
+&lt;ul&gt;
+&lt;li&gt;&lt;p&gt;Break after every 2 trials:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;matrix(c(1:10, rep_len(c(0, 11), 10)), nrow = 2, byrow = TRUE)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
+  [1,]    1    2    3    4    5    6    7    8    9    10
+  [2,]    0   11    0   11    0   11    0   11    0    11&lt;/code&gt;&lt;/pre&gt;&lt;/li&gt;
+&lt;li&gt;&lt;p&gt;Break after every 3 trials:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;matrix(c(1:10, rep_len(c(0, 0, 11), 10)), nrow = 2, byrow = TRUE)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
+  [1,]    1    2    3    4    5    6    7    8    9    10
+  [2,]    0    0   11    0    0   11    0    0   11     0&lt;/code&gt;&lt;/pre&gt;&lt;/li&gt;
+&lt;li&gt;&lt;p&gt;Break after every 4 trials:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;matrix(c(1:10, rep_len(c(0, 0, 0, 11), 10)), nrow = 2, byrow = TRUE)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
+  [1,]    1    2    3    4    5    6    7    8    9    10
+  [2,]    0    0    0   11    0    0    0   11    0     0&lt;/code&gt;&lt;/pre&gt;&lt;/li&gt;
+&lt;/ul&gt;
+&lt;p&gt;And it turns out that this method generalizes to balanced shuffling
+across categories that are not equal in size!&lt;/p&gt;
+&lt;p&gt;Let’s start with a really basic example - here we have three kinds of
+fruits with varying counts:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;fruits &amp;lt;- c(&amp;quot;🍎&amp;quot;, &amp;quot;🍋&amp;quot;, &amp;quot;🍇&amp;quot;)[c(2,1,3,3,2,3,1,2,2,1,2,2,3,3,3)]
+fruits &amp;lt;- factor(fruits, levels = c(&amp;quot;🍇&amp;quot;, &amp;quot;🍋&amp;quot;, &amp;quot;🍎&amp;quot;))
+table(fruits)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  fruits
+  🍇 🍋 🍎 
+   6  6  3&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Their current order looks like this:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;cat(levels(fruits)[fruits])&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  🍋 🍎 🍇 🍇 🍋 🍇 🍎 🍋 🍋 🍎 🍋 🍋 🍇 🍇 🍇&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;But I want them to be ordered such that individuals of the same fruit
+kind are maximally apart from one another. This effectively re-orders
+the fruits to be distributed “evenly”:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;cat(levels(fruits)[fruits[c(3,1,2,4,5,0,6,8,10,13,9,0,14,11,7,15,12,0)]])&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  🍇 🍋 🍎 🍇 🍋 🍇 🍋 🍎 🍇 🍋 🍇 🍋 🍎 🍇 🍋&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;With our “build row-wise, collapse col-wise” approach, this takes the
+following steps:&lt;/p&gt;
+&lt;ol style="list-style-type: decimal"&gt;
+&lt;li&gt;&lt;p&gt;Find the most frequent category - that N-max becomes the number
+of columns in the matrix of row indices.&lt;/p&gt;
+&lt;p&gt;In this case it’s grapes and lemons, of which there are 6 each:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;grape_rows &amp;lt;- which(fruits == &amp;quot;🍇&amp;quot;)
+setNames(grape_rows, rep(&amp;quot;🍇&amp;quot;, 6))&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  🍇 🍇 🍇 🍇 🍇 🍇 
+   3  4  6 13 14 15&lt;/code&gt;&lt;/pre&gt;
+&lt;pre class="r"&gt;&lt;code&gt;lemon_rows &amp;lt;- which(fruits == &amp;quot;🍋&amp;quot;)
+setNames(lemon_rows, rep(&amp;quot;🍋&amp;quot;, 6))&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  🍋 🍋 🍋 🍋 🍋 🍋 
+   1  5  8  9 11 12&lt;/code&gt;&lt;/pre&gt;&lt;/li&gt;
+&lt;li&gt;&lt;p&gt;Normalize (“stretch”) all vectors to have the same length as
+N.&lt;/p&gt;
+&lt;p&gt;In this case we need to stretch the apples vector, which is currently
+only length-3:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;apple_rows &amp;lt;- which(fruits == &amp;quot;🍎&amp;quot;)
+apple_rows&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1]  2  7 10&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;The desired “sparse” representation is something like this, where
+each instance of apple is equidistant, with 0s in between:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;apple_rows_sparse &amp;lt;- c(2, 0, 7, 0, 10, 0)
+setNames(apple_rows_sparse, c(&amp;quot;🍎&amp;quot;, &amp;quot;&amp;quot;, &amp;quot;🍎&amp;quot;, &amp;quot;&amp;quot;, &amp;quot;🍎&amp;quot;, &amp;quot;&amp;quot;))&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  🍎    🍎    🍎    
+   2  0  7  0 10  0&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;There are many ways to get at this, but one trick involves creating
+an evenly spaced float sequence from 1 to N-apple over N-max steps:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;seq(1, 3, length.out = 6)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1] 1.0 1.4 1.8 2.2 2.6 3.0&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;From there, we round the numbers:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;round(seq(1, 3, length.out = 6))&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1] 1 1 2 2 3 3&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Then mark the first occurance of each number using
+&lt;code&gt;!duplicated()&lt;/code&gt;:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;!duplicated(round(seq(1, 3, length.out = 6)))&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1]  TRUE FALSE  TRUE FALSE  TRUE FALSE&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;And lastly, we initialize a vector of 0s and &lt;code&gt;replace()&lt;/code&gt;
+the &lt;code&gt;TRUE&lt;/code&gt;s with apple indices:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;replace(
+  rep(0, 6),
+  !duplicated(round(seq(1, 3, length.out = 6))),
+  which(fruits == &amp;quot;🍎&amp;quot;)
+)&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  [1]  2  0  7  0 10  0&lt;/code&gt;&lt;/pre&gt;&lt;/li&gt;
+&lt;li&gt;&lt;p&gt;Stack up the category vectors by row and collapse
+column-wise:&lt;/p&gt;
+&lt;p&gt;Manually, we would build the full matrix row-by-row like this:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;fruits_matrix &amp;lt;- matrix(
+  c(grape_rows, lemon_rows, apple_rows_sparse),
+  nrow = 3, byrow = TRUE
+)
+rownames(fruits_matrix) &amp;lt;- c(&amp;quot;🍇&amp;quot;, &amp;quot;🍋&amp;quot;, &amp;quot;🍎&amp;quot;)
+fruits_matrix&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;     [,1] [,2] [,3] [,4] [,5] [,6]
+  🍇    3    4    6   13   14   15
+  🍋    1    5    8    9   11   12
+  🍎    2    0    7    0   10    0&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;And dynamically we can use &lt;code&gt;sapply()&lt;/code&gt; to fill the matrix
+column-by-column, and then &lt;code&gt;t()&lt;/code&gt;-ing the output:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;fruits_distributed &amp;lt;- sapply(levels(fruits), \(x) {
+  n_max &amp;lt;- max(table(fruits))
+  ind &amp;lt;- which(fruits == x)
+  nums &amp;lt;- seq(1, length(ind), length.out = n_max)
+  replace(rep(0, n_max), !duplicated(round(nums)), ind)
+}) |&amp;gt; 
+  t()
+fruits_distributed&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;     [,1] [,2] [,3] [,4] [,5] [,6]
+  🍇    3    4    6   13   14   15
+  🍋    1    5    8    9   11   12
+  🍎    2    0    7    0   10    0&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Finally, we collapse the vector and we see that it indeed distributed
+the fruits evenly!&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;fruits[as.integer(fruits_distributed)]&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;   [1] 🍇 🍋 🍎 🍇 🍋 🍇 🍋 🍎 🍇 🍋 🍇 🍋 🍎 🍇 🍋
+  Levels: 🍇 🍋 🍎&lt;/code&gt;&lt;/pre&gt;&lt;/li&gt;
+&lt;/ol&gt;
+&lt;p&gt;We can go even further and wrap the dynamic,
+&lt;code&gt;sapply()&lt;/code&gt;-based solution into a function for use within
+&lt;code&gt;slice()&lt;/code&gt;. Here, I also added an optional argument for
+shuffling within categories:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;rshuffle &amp;lt;- function(x, shuffle_within = FALSE) {
+  categories &amp;lt;- as.factor(x)
+  n_max &amp;lt;- max(table(categories))
+  sapply(levels(categories), \(lvl) {
+    ind &amp;lt;- which(categories == lvl)
+    if (shuffle_within) ind &amp;lt;- sample(ind)
+    nums &amp;lt;- seq(1, length(ind), length.out = n_max)
+    replace(rep(0, n_max), !duplicated(round(nums)), ind)
+  }) |&amp;gt; 
+    t() |&amp;gt; 
+    as.integer()
+}&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;Returning back to our Stroop experiment template example, imagine we
+also had two filler trials, where no word is shown and just the color
+flashes on the screen:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;stroop_fillers &amp;lt;- tibble(
+  item_id = 1:2,
+  trial = &amp;quot;filler&amp;quot;,
+  word = NA,
+  color = c(&amp;quot;red&amp;quot;, &amp;quot;blue&amp;quot;)
+)
+stroop_with_fillers &amp;lt;- bind_rows(stroop_fillers, stroop_trials) |&amp;gt; 
+  mutate(trial = factor(trial, c(&amp;quot;match&amp;quot;, &amp;quot;mismatch&amp;quot;, &amp;quot;filler&amp;quot;)))
+stroop_with_fillers&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 12 × 4
+     item_id trial    word   color 
+       &amp;lt;int&amp;gt; &amp;lt;fct&amp;gt;    &amp;lt;chr&amp;gt;  &amp;lt;chr&amp;gt; 
+   1       1 filler   &amp;lt;NA&amp;gt;   red   
+   2       2 filler   &amp;lt;NA&amp;gt;   blue  
+   3       1 mismatch red    brown 
+   4       2 mismatch green  red   
+   5       3 mismatch purple green 
+   6       4 mismatch brown  blue  
+   7       5 mismatch blue   purple
+   8       1 match    red    red   
+   9       2 match    green  green 
+  10       3 match    purple purple
+  11       4 match    brown  brown 
+  12       5 match    blue   blue&lt;/code&gt;&lt;/pre&gt;
+&lt;p&gt;We can evenly shuffle between the unequal trial types with our new
+&lt;code&gt;rshuffle()&lt;/code&gt; function:&lt;/p&gt;
+&lt;pre class="r"&gt;&lt;code&gt;stroop_with_fillers |&amp;gt; 
+  slice( rshuffle(trial, shuffle_within = TRUE) )&lt;/code&gt;&lt;/pre&gt;
+&lt;pre&gt;&lt;code&gt;  # A tibble: 12 × 4
+     item_id trial    word   color 
+       &amp;lt;int&amp;gt; &amp;lt;fct&amp;gt;    &amp;lt;chr&amp;gt;  &amp;lt;chr&amp;gt; 
+   1       2 match    green  green 
+   2       2 mismatch green  red   
+   3       1 filler   &amp;lt;NA&amp;gt;   red   
+   4       1 match    red    red   
+   5       4 mismatch brown  blue  
+   6       3 match    purple purple
+   7       3 mismatch purple green 
+   8       2 filler   &amp;lt;NA&amp;gt;   blue  
+   9       4 match    brown  brown 
+  10       5 mismatch blue   purple
+  11       5 match    blue   blue  
+  12       1 mismatch red    brown&lt;/code&gt;&lt;/pre&gt;
+&lt;h2 id="conclusion"&gt;Conclusion&lt;/h2&gt;
+&lt;p&gt;When I started drafting this blog post, I thought I’d come with a
+principled taxonomy of row-relational operations. Ha. This was a lot
+trickier to think through than I thought.&lt;/p&gt;
+&lt;p&gt;But I hope that this gallery of esoteric use-cases for
+&lt;code&gt;slice()&lt;/code&gt; inspires you to use it more, and to think about
+“tidy” solutions to seemingly “untidy” problems.&lt;/p&gt;
+&lt;pre class="r distill-force-highlighting-css"&gt;&lt;code&gt;&lt;/code&gt;&lt;/pre&gt;
+&lt;div class="footnotes footnotes-end-of-document"&gt;
+&lt;hr /&gt;
+&lt;ol&gt;
+&lt;li id="fn1"&gt;&lt;p&gt;The &lt;code&gt;.by_group = TRUE&lt;/code&gt; is not strictly
+necessary here, but it’s good for visually inspecting the within-group
+ordering.&lt;a href="#fnref1" class="footnote-back"&gt;↩︎&lt;/a&gt;&lt;/p&gt;&lt;/li&gt;
+&lt;li id="fn2"&gt;&lt;p&gt;Although row insertion is a generally tricky problem for
+column-major data frame structures, which is partly why dplyr’s &lt;a
+href="https://dplyr.tidyverse.org/reference/rows.html"&gt;row manipulation
+verbs&lt;/a&gt; have stayed experimental for quite some time.&lt;a href="#fnref2"
+class="footnote-back"&gt;↩︎&lt;/a&gt;&lt;/p&gt;&lt;/li&gt;
+&lt;/ol&gt;
+&lt;/div&gt;</description>
+      <distill:md5>5f086a5db2d8a7a771b81537a421b2fb</distill:md5>
+      <category>data wrangling</category>
+      <category>dplyr</category>
+      <guid>https://yjunechoe.github.io/posts/2023-06-11-row-relational-operations</guid>
+      <pubDate>Sun, 22 Sep 2024 00:00:00 +0000</pubDate>
+      <media:content url="https://yjunechoe.github.io/posts/2023-06-11-row-relational-operations/preview.png" medium="image" type="image/png" width="1800" height="1080"/>
+    </item>
     <item>
       <title>Naming patterns for boolean enums</title>
       <dc:creator>June Choe</dc:creator>
@@ -96,17 +1936,6 @@
       <pubDate>Mon, 10 Jul 2023 00:00:00 +0000</pubDate>
       <media:content url="https://yjunechoe.github.io/posts/2023-07-09-x-y-problem/preview.png" medium="image" type="image/png" width="238" height="205"/>
     </item>
-    <item>
-      <title>Row relational operations with slice()</title>
-      <dc:creator>June Choe</dc:creator>
-      <link>https://yjunechoe.github.io/posts/2023-06-11-row-relational-operations</link>
-      <description>A love letter to dplyr::slice() and a gallery of usecases</description>
-      <category>data wrangling</category>
-      <category>dplyr</category>
-      <guid>https://yjunechoe.github.io/posts/2023-06-11-row-relational-operations</guid>
-      <pubDate>Sun, 11 Jun 2023 00:00:00 +0000</pubDate>
-      <media:content url="https://yjunechoe.github.io/posts/2023-06-11-row-relational-operations/preview.png" medium="image" type="image/png" width="1800" height="1080"/>
-    </item>
     <item>
       <title>First impressions of DataFrames.jl and accessories</title>
       <dc:creator>June Choe</dc:creator>
diff --git a/docs/posts/2023-06-11-row-relational-operations/index.html b/docs/posts/2023-06-11-row-relational-operations/index.html
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 <div class="d-title">
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@@ -2691,7 +2692,7 @@ <h1>Row relational operations with slice()</h1>
 <div class="d-byline">
   June Choe  (University of Pennsylvania Linguistics)<a href="https://live-sas-www-ling.pantheon.sas.upenn.edu/" class="uri">https://live-sas-www-ling.pantheon.sas.upenn.edu/</a>
   
-<br/>2023-06-11
+<br/>2024-09-22
 </div>
 
 <div class="d-article">
@@ -2712,6 +2713,7 @@ <h3>Contents</h3>
 <li><a href="#subset-a-selection-of-rows-the-following-row" id="toc-subset-a-selection-of-rows-the-following-row">Subset a selection of rows + the following row</a></li>
 <li><a href="#subset-a-selection-of-rows-multiple-following-rows" id="toc-subset-a-selection-of-rows-multiple-following-rows">Subset a selection of rows + multiple following rows</a></li>
 <li><a href="#filter-and-encode-neighboring-rows" id="toc-filter-and-encode-neighboring-rows">Filter (and encode) neighboring rows</a></li>
+<li><a href="#aside-kronecker-as-as.vectorouter" id="toc-aside-kronecker-as-as.vectorouter">Aside: <code>kronecker()</code> as <code>as.vector(outer())</code></a></li>
 <li><a href="#windowed-minmaxmedian-etc." id="toc-windowed-minmaxmedian-etc.">Windowed min/max/median (etc.)</a></li>
 <li><a href="#evenly-distributed-row-shuffling-of-balanced-categories" id="toc-evenly-distributed-row-shuffling-of-balanced-categories">Evenly distributed row shuffling of balanced categories</a></li>
 <li><a href="#inserting-a-new-row-at-specific-intervals" id="toc-inserting-a-new-row-at-specific-intervals">Inserting a new row at specific intervals</a></li>
@@ -2745,7 +2747,7 @@ <h3 id="basic-usage">Basic usage</h3>
    4 Darth Vader           202   136
    5 Leia Organa           150    49
    6 Owen Lars             178   120
-   7 Beru Whitesun lars    165    75
+   7 Beru Whitesun Lars    165    75
    8 R5-D4                  97    32
    9 Biggs Darklighter     183    84
   10 Obi-Wan Kenobi        182    77</code></pre>
@@ -2873,7 +2875,7 @@ <h4 id="row-ordering">3) Row ordering</h4>
    5 Luke Skywalker        172    77
    6 R5-D4                  97    32
    7 C-3PO                 167    75
-   8 Beru Whitesun lars    165    75
+   8 Beru Whitesun Lars    165    75
    9 Biggs Darklighter     183    84
   10 R2-D2                  96    32</code></pre>
 </div>
@@ -2892,7 +2894,7 @@ <h4 id="row-ordering">3) Row ordering</h4>
    4 Darth Vader           202   136
    5 Luke Skywalker        172    77
    6 Owen Lars             178   120
-   7 Beru Whitesun lars    165    75
+   7 Beru Whitesun Lars    165    75
    8 R5-D4                  97    32
    9 Biggs Darklighter     183    84
   10 Obi-Wan Kenobi        182    77</code></pre>
@@ -2909,7 +2911,7 @@ <h4 id="row-ordering">3) Row ordering</h4>
    1 Obi-Wan Kenobi        182    77
    2 Biggs Darklighter     183    84
    3 R5-D4                  97    32
-   4 Beru Whitesun lars    165    75
+   4 Beru Whitesun Lars    165    75
    5 Owen Lars             178   120
    6 Leia Organa           150    49
    7 Darth Vader           202   136
@@ -2976,7 +2978,7 @@ <h4 id="slice-as-arrange"><code>slice()</code> as <code>arrange()</code></h4>
    1 R2-D2                  96    32
    2 R5-D4                  97    32
    3 Leia Organa           150    49
-   4 Beru Whitesun lars    165    75
+   4 Beru Whitesun Lars    165    75
    5 C-3PO                 167    75
    6 Luke Skywalker        172    77
    7 Owen Lars             178   120
@@ -2996,7 +2998,7 @@ <h4 id="slice-as-arrange"><code>slice()</code> as <code>arrange()</code></h4>
    1 R2-D2                  96    32
    2 R5-D4                  97    32
    3 Leia Organa           150    49
-   4 Beru Whitesun lars    165    75
+   4 Beru Whitesun Lars    165    75
    5 C-3PO                 167    75
    6 Luke Skywalker        172    77
    7 Owen Lars             178   120
@@ -3024,7 +3026,7 @@ <h4 id="slice-as-arrange"><code>slice()</code> as <code>arrange()</code></h4>
    1 R2-D2                  96    32
    2 R5-D4                  97    32
    3 Leia Organa           150    49
-   4 Beru Whitesun lars    165    75
+   4 Beru Whitesun Lars    165    75
    5 C-3PO                 167    75
    6 Luke Skywalker        172    77
    7 Owen Lars             178   120
@@ -3140,7 +3142,7 @@ <h3 id="repeat-rows-in-place">Repeat rows (in place)</h3>
    6 Leia Organa           150    49
    7 Leia Organa           150    49
    8 Owen Lars             178   120
-   9 Beru Whitesun lars    165    75
+   9 Beru Whitesun Lars    165    75
   10 R5-D4                  97    32
   11 Biggs Darklighter     183    84
   12 Obi-Wan Kenobi        182    77</code></pre>
@@ -3171,7 +3173,7 @@ <h3 id="repeat-rows-in-place">Repeat rows (in place)</h3>
    9 Leia Organa           150    49
   10 Leia Organa           150    49
   11 Owen Lars             178   120
-  12 Beru Whitesun lars    165    75
+  12 Beru Whitesun Lars    165    75
   13 R5-D4                  97    32
   14 Biggs Darklighter     183    84
   15 Obi-Wan Kenobi        182    77</code></pre>
@@ -3196,7 +3198,7 @@ <h3 id="repeat-rows-in-place">Repeat rows (in place)</h3>
    9 Leia Organa           150    49
   10 Leia Organa           150    49
   11 Owen Lars             178   120
-  12 Beru Whitesun lars    165    75
+  12 Beru Whitesun Lars    165    75
   13 R5-D4                  97    32
   14 Biggs Darklighter     183    84
   15 Obi-Wan Kenobi        182    77</code></pre>
@@ -3729,6 +3731,62 @@ <h3 id="filter-and-encode-neighboring-rows">Filter (and encode) neighboring rows
 </div>
 <p>We find that the lessons of working with row indices from <code>slice()</code> translated to solving this complex <code>mutate()</code> problem - neat!</p>
 </details>
+<h3 id="aside-kronecker-as-as.vectorouter">Aside: <code>kronecker()</code> as <code>as.vector(outer())</code></h3>
+<p>Following from the <code>slice()</code> + <code>outer()</code> strategy demoed above, imagine if we wanted to filter for <code>"Luke Skywalker"</code> and 4 other characters that are neighbors in the <code>height</code> and <code>mass</code> values.</p>
+<div class="layout-chunk" data-layout="l-body">
+<div class="sourceCode">
+<pre class="sourceCode r"><code class="sourceCode r"><span><span class='fu'>dplyr</span><span class='fu'>::</span><span class='va'><a href='https://dplyr.tidyverse.org/reference/starwars.html'>starwars</a></span><span class='op'>[</span>, <span class='fl'>1</span><span class='op'>:</span><span class='fl'>3</span><span class='op'>]</span></span></code></pre>
+</div>
+<pre><code>  # A tibble: 87 × 3
+     name               height  mass
+     &lt;chr&gt;               &lt;int&gt; &lt;dbl&gt;
+   1 Luke Skywalker        172    77
+   2 C-3PO                 167    75
+   3 R2-D2                  96    32
+   4 Darth Vader           202   136
+   5 Leia Organa           150    49
+   6 Owen Lars             178   120
+   7 Beru Whitesun Lars    165    75
+   8 R5-D4                  97    32
+   9 Biggs Darklighter     183    84
+  10 Obi-Wan Kenobi        182    77
+  # ℹ 77 more rows</code></pre>
+</div>
+<p>In row-relational terms, “filtering neighboring values” just means “filtering rows after arranging by the values we care about”. We can express this using <code>slice()</code> and <code>outer()</code> as:</p>
+<div class="layout-chunk" data-layout="l-body">
+<div class="sourceCode">
+<pre class="sourceCode r"><code class="sourceCode r"><span><span class='va'>starwars</span> <span class='op'><a href='https://magrittr.tidyverse.org/reference/pipe.html'>%&gt;%</a></span> </span>
+<span>  <span class='fu'><a href='https://dplyr.tidyverse.org/reference/select.html'>select</a></span><span class='op'>(</span><span class='va'>name</span>, <span class='va'>mass</span>, <span class='va'>height</span><span class='op'>)</span> <span class='op'><a href='https://magrittr.tidyverse.org/reference/pipe.html'>%&gt;%</a></span> </span>
+<span>  <span class='fu'><a href='https://dplyr.tidyverse.org/reference/arrange.html'>arrange</a></span><span class='op'>(</span><span class='va'>mass</span>, <span class='va'>height</span><span class='op'>)</span> <span class='op'><a href='https://magrittr.tidyverse.org/reference/pipe.html'>%&gt;%</a></span> </span>
+<span>  <span class='fu'><a href='https://dplyr.tidyverse.org/reference/slice.html'>slice</a></span><span class='op'>(</span> <span class='fu'><a href='https://rdrr.io/r/base/vector.html'>as.vector</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/outer.html'>outer</a></span><span class='op'>(</span><span class='op'>-</span><span class='fl'>2</span><span class='op'>:</span><span class='fl'>2</span>, <span class='fu'><a href='https://rdrr.io/r/base/which.html'>which</a></span><span class='op'>(</span><span class='va'>name</span> <span class='op'>==</span> <span class='st'>"Luke Skywalker"</span><span class='op'>)</span>, <span class='va'>`+`</span><span class='op'>)</span><span class='op'>)</span> <span class='op'>)</span></span></code></pre>
+</div>
+<pre><code>  # A tibble: 5 × 3
+    name            mass height
+    &lt;chr&gt;          &lt;dbl&gt;  &lt;int&gt;
+  1 Palpatine       75      170
+  2 Wedge Antilles  77      170
+  3 Luke Skywalker  77      172
+  4 Obi-Wan Kenobi  77      182
+  5 Boba Fett       78.2    183</code></pre>
+</div>
+<p>I raised this example on an unrelated thread on the <a href="https://fosstodon.org/@DSLC">R4DS/DSLC slack</a>, where Anthony Durrant pointed me to <code>kronecker()</code> as a version of <code>outer()</code> that unlist before returning the output.</p>
+<p>So in examples involving <code>outer()</code> to generate row indices in <code>slice()</code>, we can also use <code>kronecker()</code> instead to save a call to a flattening function like <code>as.vector()</code>:</p>
+<div class="layout-chunk" data-layout="l-body">
+<div class="sourceCode">
+<pre class="sourceCode r"><code class="sourceCode r"><span><span class='va'>starwars</span> <span class='op'><a href='https://magrittr.tidyverse.org/reference/pipe.html'>%&gt;%</a></span> </span>
+<span>  <span class='fu'><a href='https://dplyr.tidyverse.org/reference/select.html'>select</a></span><span class='op'>(</span><span class='va'>name</span>, <span class='va'>mass</span>, <span class='va'>height</span><span class='op'>)</span> <span class='op'><a href='https://magrittr.tidyverse.org/reference/pipe.html'>%&gt;%</a></span> </span>
+<span>  <span class='fu'><a href='https://dplyr.tidyverse.org/reference/arrange.html'>arrange</a></span><span class='op'>(</span><span class='va'>mass</span>, <span class='va'>height</span><span class='op'>)</span> <span class='op'><a href='https://magrittr.tidyverse.org/reference/pipe.html'>%&gt;%</a></span> </span>
+<span>  <span class='fu'><a href='https://dplyr.tidyverse.org/reference/slice.html'>slice</a></span><span class='op'>(</span> <span class='fu'><a href='https://rdrr.io/r/base/kronecker.html'>kronecker</a></span><span class='op'>(</span><span class='op'>-</span><span class='fl'>2</span><span class='op'>:</span><span class='fl'>2</span>, <span class='fu'><a href='https://rdrr.io/r/base/which.html'>which</a></span><span class='op'>(</span><span class='va'>name</span> <span class='op'>==</span> <span class='st'>"Luke Skywalker"</span><span class='op'>)</span>, <span class='va'>`+`</span><span class='op'>)</span> <span class='op'>)</span></span></code></pre>
+</div>
+<pre><code>  # A tibble: 5 × 3
+    name            mass height
+    &lt;chr&gt;          &lt;dbl&gt;  &lt;int&gt;
+  1 Palpatine       75      170
+  2 Wedge Antilles  77      170
+  3 Luke Skywalker  77      172
+  4 Obi-Wan Kenobi  77      182
+  5 Boba Fett       78.2    183</code></pre>
+</div>
 <h3 id="windowed-minmaxmedian-etc.">Windowed min/max/median (etc.)</h3>
 <p>Let’s say we have this small time series data, and we want to calculate a <strong>lagged 3-window moving minimum</strong> for the <code>val</code> column:</p>
 <div class="layout-chunk" data-layout="l-body">
@@ -4605,7 +4663,7 @@ <h3 id="evenly-distributed-row-shuffling-of-unequal-categories">Evenly distribut
 <h2 id="conclusion">Conclusion</h2>
 <p>When I started drafting this blog post, I thought I’d come with a principled taxonomy of row-relational operations. Ha. This was a lot trickier to think through than I thought.</p>
 <p>But I hope that this gallery of esoteric use-cases for <code>slice()</code> inspires you to use it more, and to think about “tidy” solutions to seemingly “untidy” problems.</p>
-<div class="sourceCode" id="cb109"><pre class="sourceCode r distill-force-highlighting-css"><code class="sourceCode r"></code></pre></div>
+<div class="sourceCode" id="cb112"><pre class="sourceCode r distill-force-highlighting-css"><code class="sourceCode r"></code></pre></div>
 <section id="footnotes" class="footnotes footnotes-end-of-document" role="doc-endnotes">
 <hr />
 <ol>
diff --git a/docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/figure-html5/final-gapminder-plot-1.png b/docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/figure-html5/final-gapminder-plot-1.png
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diff --git a/docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/header-attrs-2.21/header-attrs.js b/docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/header-attrs-2.21/header-attrs.js
new file mode 100644
index 00000000..dd57d92e
--- /dev/null
+++ b/docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/header-attrs-2.21/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
diff --git a/docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.2.6/panelset.css b/docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.2.6/panelset.css
new file mode 100644
index 00000000..6665f55c
--- /dev/null
+++ b/docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.2.6/panelset.css
@@ -0,0 +1,227 @@
+/* prefixed by https://autoprefixer.github.io (PostCSS: v7.0.23, autoprefixer: v9.7.3) */
+
+.panelset {
+  width: 100%;
+  position: relative;
+  --panel-tabs-border-bottom: #ddd;
+  --panel-tabs-sideways-max-width: 25%;
+  --panel-tab-foreground: currentColor;
+  --panel-tab-background: unset;
+  --panel-tab-active-foreground: currentColor;
+  --panel-tab-active-background: unset;
+  --panel-tab-hover-foreground: currentColor;
+  --panel-tab-hover-background: unset;
+  --panel-tab-active-border-color: currentColor;
+  --panel-tab-hover-border-color: currentColor;
+  --panel-tab-inactive-opacity: 0.5;
+  --panel-tab-font-family: inherit;
+}
+
+.panelset * {
+  box-sizing: border-box;
+}
+
+.panelset .panel-tabs {
+  display: -webkit-box;
+  display: flex;
+  flex-wrap: wrap;
+  -webkit-box-orient: horizontal;
+  -webkit-box-direction: normal;
+          flex-direction: row;
+  -webkit-box-pack: start;
+          justify-content: start;
+  -webkit-box-align: center;
+          align-items: center;
+  overflow-y: visible;
+  overflow-x: auto;
+  -webkit-overflow-scrolling: touch;
+  padding: 0 0 2px 0;
+  box-shadow: inset 0 -2px 0px var(--panel-tabs-border-bottom);
+}
+
+.panelset .panel-tabs * {
+  -webkit-transition: opacity 0.5s ease;
+  transition: opacity 0.5s ease;
+}
+
+.panelset .panel-tabs .panel-tab {
+  min-height: 50px;
+  display: -webkit-box;
+  display: flex;
+  -webkit-box-pack: center;
+          justify-content: center;
+  -webkit-box-align: center;
+          align-items: center;
+  padding: 0.5em 1em;
+  font-family: var(--panel-tab-font-family);
+  opacity: var(--panel-tab-inactive-opacity);
+  border-top: 2px solid transparent;
+  border-bottom: 2px solid transparent;
+  margin-bottom: -2px;
+  color: var(--panel-tab-foreground);
+  background-color: var(--panel-tab-background);
+  list-style: none;
+  z-index: 5;
+}
+
+.panelset .panel-tabs .panel-tab > a {
+  color: currentColor;
+  text-decoration: none;
+  border: none;
+  width: 100%;
+  height: 100%;
+}
+
+.panelset .panel-tabs .panel-tab > a:focus {
+  outline: none;
+  text-decoration: none;
+  border: none;
+}
+
+.panelset .panel-tabs .panel-tab > a:hover {
+  text-decoration: none;
+  border: none;
+}
+
+.panelset .panel-tabs .panel-tab:hover {
+  border-bottom-color: var(--panel-tab-hover-border-color);
+  color: var(--panel-tab-hover-foreground);
+  background-color: var(--panel-tab-hover-background);
+  opacity: 1;
+  cursor: pointer;
+  z-index: 10;
+}
+
+.panelset .panel-tabs .panel-tab:focus {
+  outline: none;
+  color: var(--panel-tab-hover-foreground);
+  border-bottom-color: var(--panel-tab-hover-border-color);
+  background-color: var(--panel-tab-hover-background);
+}
+
+.panelset .panel-tabs .panel-tab.panel-tab-active {
+  border-top-color: var(--panel-tab-active-border-color);
+  color: var(--panel-tab-active-foreground);
+  background-color: var(--panel-tab-active-background);
+  opacity: 1;
+}
+
+.panelset .panel {
+  display: none;
+}
+
+.panelset .panel-active {
+  display: block;
+}
+
+/* ---- Sideways Panelset ---- */
+
+@media (min-width: 480px) {
+  .panelset.sideways {
+    display: flex;
+    flex-direction: row;
+  }
+
+  .panelset.sideways .panel-tabs {
+    box-shadow: none;
+    flex-direction: column;
+    align-items: start;
+    margin: 0;
+    margin-right: 1em;
+    border-right: 2px solid var(--panel-tabs-border-bottom);
+    max-width: var(--panel-tabs-sideways-max-width);
+  }
+
+  .panelset.sideways .panel {
+    max-width: calc(100% - var(--panel-tabs-sideways-max-width) - 1em);
+  }
+
+  .panelset.sideways .panel-tabs .panel-tab {
+    border-top: unset;
+    border-bottom: unset;
+    padding-left: 0;
+  }
+
+  .panelset.sideways.right {
+    flex-direction: row-reverse;
+    justify-content: space-between;
+  }
+
+  .panelset.sideways.right {
+  	text-align: inherit;
+  }
+
+  .panelset.sideways.right .panel-tabs {
+    align-items: end;
+    margin-right: 0;
+    margin-left: 1em;
+    border-right: unset;
+    border-left: 2px solid var(--panel-tabs-border-bottom);
+  }
+
+  .panelset.sideways.right .panel-tabs .panel-tab {
+    padding-left: 1em;
+    width: 100%;
+  }
+
+  .panelset.sideways.right .panel-tabs .panel-tab a {
+    text-align: right;
+  }
+}
+
+/*
+  This next part repeats the same CSS inside the @media query above but with
+  remarkjs-specific classes to ensure that sideways panelsets are always used.
+  In the future, we could use @container queries instead once they're availble.
+*/
+
+.remark-container .panelset.sideways {
+  display: flex;
+  flex-direction: row;
+}
+
+.remark-container .panelset.sideways .panel-tabs {
+  box-shadow: none;
+  flex-direction: column;
+  align-items: start;
+  margin: 0;
+  margin-right: 1em;
+  border-right: 2px solid var(--panel-tabs-border-bottom);
+  max-width: var(--panel-tabs-sideways-max-width);
+}
+
+.remark-container .panelset.sideways .panel {
+  max-width: calc(100% - var(--panel-tabs-sideways-max-width) - 1em);
+}
+
+.remark-container .panelset.sideways .panel-tabs .panel-tab {
+  border-top: unset;
+  border-bottom: unset;
+  padding-left: 0;
+}
+
+.remark-container .panelset.sideways.right {
+  flex-direction: row-reverse;
+  justify-content: space-between;
+}
+
+.remark-container .panelset.sideways.right {
+	text-align: inherit;
+}
+
+.remark-container .panelset.sideways.right .panel-tabs {
+  align-items: end;
+  margin-right: 0;
+  margin-left: 1em;
+  border-right: unset;
+  border-left: 2px solid var(--panel-tabs-border-bottom);
+}
+
+.remark-container .panelset.sideways.right .panel-tabs .panel-tab {
+  padding-left: 1em;
+  width: 100%;
+}
+
+.remark-container .panelset.sideways.right .panel-tabs .panel-tab a {
+  text-align: right;
+}
diff --git a/docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.2.6/panelset.js b/docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.2.6/panelset.js
new file mode 100644
index 00000000..730d54d6
--- /dev/null
+++ b/docs/posts/2023-06-11-row-relational-operations/row-relational-operations_files/panelset-0.2.6/panelset.js
@@ -0,0 +1,325 @@
+/* global slideshow */
+(function () {
+  const ready = function (fn) {
+    /* MIT License Copyright (c) 2016 Nuclei */
+    /* https://github.com/nuclei/readyjs */
+    const completed = () => {
+      document.removeEventListener('DOMContentLoaded', completed)
+      window.removeEventListener('load', completed)
+      fn()
+    }
+    if (document.readyState !== 'loading') {
+      setTimeout(fn)
+    } else {
+      document.addEventListener('DOMContentLoaded', completed)
+      window.addEventListener('load', completed)
+    }
+  }
+
+  ready(function () {
+    [...document.querySelectorAll('.panel-name')]
+      .map(el => el.textContent.trim())
+
+    const panelIds = {}
+
+    const uniquePanelId = (name) => {
+      name = encodeURIComponent(name.toLowerCase().replace(/[\s]/g, '-'))
+      if (Object.keys(panelIds).includes(name)) {
+        name += ++panelIds[name]
+      } else {
+        panelIds[name] = 1
+      }
+      return name
+    }
+
+    const identifyPanelName = (item) => {
+      let name = 'Panel'
+
+      // If the item doesn't have a parent element, then we've already processed
+      // it, probably because we're in an Rmd, and it's been removed from the DOM
+      if (!item.parentElement) {
+        return
+      }
+
+      // In R Markdown when header-attrs.js is present, we may have found a
+      // section header but the class attributes won't be duplicated on the <hX> tag
+      if (
+        (item.tagName === 'SECTION' || item.classList.contains('section')) &&
+        /^H[1-6]/.test(item.children[0].tagName)
+      ) {
+        name = item.children[0].textContent
+        item.classList.remove('panel-name')
+        item.removeChild(item.children[0])
+        return name
+      }
+
+      const nameDiv = item.querySelector('.panel-name')
+      if (!nameDiv) return name
+
+      // In remarkjs the .panel-name span might be in a paragraph tag
+      // and if the <p> is empty, we'll remove it
+      if (
+        nameDiv.tagName === 'SPAN' &&
+        nameDiv.parentNode.tagName === 'P' &&
+        nameDiv.textContent === nameDiv.parentNode.textContent
+      ) {
+        name = nameDiv.textContent
+        item.removeChild(nameDiv.parentNode)
+        return name
+      }
+
+      // If none of the above, remove the nameDiv and return the name
+      name = nameDiv.textContent
+      nameDiv.parentNode.removeChild(nameDiv)
+      return name
+    }
+
+    const processPanelItem = (item) => {
+      const name = identifyPanelName(item)
+      if (!name) {
+        return null
+      }
+      return { name, content: item.children, id: uniquePanelId(name) }
+    }
+
+    const getCurrentPanelFromUrl = (panelset) => {
+      const params = new URLSearchParams(window.location.search)
+      return params.get(panelset)
+    }
+
+    const reflowPanelSet = (panels, idx) => {
+      const res = document.createElement('div')
+      res.className = 'panelset'
+      res.id = 'panelset' + (idx > 0 ? idx : '')
+      const panelSelected = getCurrentPanelFromUrl(res.id)
+
+      // create header row
+      const headerRow = document.createElement('ul')
+      headerRow.className = 'panel-tabs'
+      headerRow.setAttribute('role', 'tablist')
+      panels
+        .map((p, idx) => {
+          const panelHeaderItem = document.createElement('li')
+          panelHeaderItem.className = 'panel-tab'
+          panelHeaderItem.setAttribute('role', 'tab')
+          const thisPanelIsActive = panelSelected ? panelSelected === p.id : idx === 0
+          if (thisPanelIsActive) {
+            panelHeaderItem.classList.add('panel-tab-active')
+            panelHeaderItem.setAttribute('aria-selected', true)
+          }
+          panelHeaderItem.tabIndex = 0
+          panelHeaderItem.id = res.id + '_' + p.id // #panelsetid_panelid
+
+          const panelHeaderLink = document.createElement('a')
+          panelHeaderLink.href = '?' + res.id + '=' + p.id + '#' + panelHeaderItem.id
+          panelHeaderLink.setAttribute('onclick', 'return false;')
+          panelHeaderLink.tabIndex = -1 // list item is tabable, not link
+          panelHeaderLink.innerHTML = p.name
+          panelHeaderLink.setAttribute('aria-controls', p.id)
+
+          panelHeaderItem.appendChild(panelHeaderLink)
+          return panelHeaderItem
+        })
+        .forEach(el => headerRow.appendChild(el))
+
+      res.appendChild(headerRow)
+
+      panels
+        .map((p, idx) => {
+          const panelContent = document.createElement('section')
+          panelContent.className = 'panel'
+          panelContent.setAttribute('role', 'tabpanel')
+          const thisPanelIsActive = panelSelected ? panelSelected === p.id : idx === 0
+          panelContent.classList.toggle('panel-active', thisPanelIsActive)
+          panelContent.id = p.id
+          panelContent.setAttribute('aria-labelledby', p.id)
+          Array.from(p.content).forEach(el => panelContent.appendChild(el))
+          return panelContent
+        })
+        .forEach(el => res.appendChild(el))
+
+      return res
+    }
+
+    /*
+     * Update selected panel for panelset or delete panelset from query string
+     *
+     * @param panelset Panelset ID to update in the search params
+     * @param panel Panel ID of selected panel in panelset, or null to delete from search params
+     * @param params Current params object, or params from window.location.search
+     */
+    function updateSearchParams (panelset, panel, params = new URLSearchParams(window.location.search)) {
+      if (panel) {
+        params.set(panelset, panel)
+      } else {
+        params.delete(panelset)
+      }
+      return params
+    }
+
+    /*
+     * Update the URL to match params
+     */
+    const updateUrl = (params) => {
+      if (typeof params === 'undefined') return
+      params = params.toString() ? ('?' + params.toString()) : ''
+      const { pathname, hash } = window.location
+      const uri = pathname + params + hash
+      window.history.replaceState(uri, '', uri)
+    }
+
+    const togglePanel = (clicked) => {
+      if (clicked.nodeName.toUpperCase() === 'A') {
+        clicked = clicked.parentElement
+      }
+      if (!clicked.classList.contains('panel-tab')) return
+      if (clicked.classList.contains('panel-tab-active')) return
+
+      const tabs = clicked.parentNode
+        .querySelectorAll('.panel-tab')
+      const panels = clicked.parentNode.parentNode
+        .querySelectorAll('.panel')
+      const panelTabClicked = clicked.children[0].getAttribute('aria-controls')
+      const panelClicked = clicked.parentNode.parentNode.id
+
+      Array.from(tabs)
+        .forEach(t => {
+          t.classList.remove('panel-tab-active')
+          t.removeAttribute('aria-selected')
+        })
+      Array.from(panels)
+        .forEach(p => {
+          const active = p.id === panelTabClicked
+          p.classList.toggle('panel-active', active)
+          // make inactive panels inaccessible by keyboard navigation
+          if (active) {
+            p.removeAttribute('tabIndex')
+            p.removeAttribute('aria-hidden')
+          } else {
+            p.setAttribute('tabIndex', -1)
+            p.setAttribute('aria-hidden', true)
+          }
+        })
+
+      clicked.classList.add('panel-tab-active')
+      clicked.setAttribute('aria-selected', true)
+
+      // emit window resize event to trick html widgets into fitting to the panel width
+      window.dispatchEvent(new Event('resize'))
+
+      // update query string
+      const params = updateSearchParams(panelClicked, panelTabClicked)
+      updateUrl(params)
+    }
+
+    const initPanelSet = (panelset, idx) => {
+      let panels = Array.from(panelset.querySelectorAll('.panel'))
+      if (!panels.length && panelset.matches('.section[class*="level"]')) {
+        // we're in tabset-alike R Markdown
+        const panelsetLevel = [...panelset.classList]
+          .filter(s => s.match(/^level/))[0]
+          .replace('level', '')
+
+        // move children that aren't inside a section up above the panelset
+        Array.from(panelset.children).forEach(function (el) {
+          if (el.matches('div.section[class*="level"]')) return
+          panelset.parentElement.insertBefore(el, panelset)
+        })
+
+        // panels are all .sections with .level<panelsetLevel + 1>
+        const panelLevel = +panelsetLevel + 1
+        panels = Array.from(panelset.querySelectorAll(`.section.level${panelLevel}`))
+      }
+
+      if (!panels.length) return
+
+      const contents = panels.map(processPanelItem).filter(o => o !== null)
+      const newPanelSet = reflowPanelSet(contents, idx)
+      newPanelSet.classList = panelset.classList
+      panelset.parentNode.insertBefore(newPanelSet, panelset)
+      panelset.parentNode.removeChild(panelset)
+
+      // click and touch events
+      const panelTabs = newPanelSet.querySelector('.panel-tabs');
+      ['click', 'touchend'].forEach(eventType => {
+        panelTabs.addEventListener(eventType, function (ev) {
+          togglePanel(ev.target)
+          ev.stopPropagation()
+        })
+      })
+      panelTabs.addEventListener('touchmove', function (ev) {
+        ev.preventDefault()
+      })
+
+      // key events
+      newPanelSet
+        .querySelector('.panel-tabs')
+        .addEventListener('keydown', (ev) => {
+          const self = ev.currentTarget.querySelector('.panel-tab-active')
+          if (ev.code === 'Space' || ev.code === 'Enter') {
+            togglePanel(ev.target)
+            ev.stopPropagation()
+          } else if (ev.code === 'ArrowLeft' && self.previousSibling) {
+            togglePanel(self.previousSibling)
+            self.previousSibling.focus()
+            ev.stopPropagation()
+          } else if (ev.code === 'ArrowRight' && self.nextSibling) {
+            togglePanel(self.nextSibling)
+            self.nextSibling.focus()
+            ev.stopPropagation()
+          }
+        })
+
+      return panels
+    }
+
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+          updateUrl(params)
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diff --git a/docs/posts/posts.json b/docs/posts/posts.json
index cdeebe72..4a0e9b2f 100644
--- a/docs/posts/posts.json
+++ b/docs/posts/posts.json
@@ -18,6 +18,28 @@
     "last_modified": "2024-09-22T18:49:08-04:00",
     "input_file": {}
   },
+  {
+    "path": "posts/2023-06-11-row-relational-operations/",
+    "title": "Row relational operations with slice()",
+    "description": "A love letter to dplyr::slice() and a gallery of usecases",
+    "author": [
+      {
+        "name": "June Choe",
+        "url": {}
+      }
+    ],
+    "date": "2024-09-22",
+    "categories": [
+      "data wrangling",
+      "dplyr"
+    ],
+    "contents": "\r\n\r\nContents\r\nIntro\r\nSpecial properties of dplyr::slice()\r\nBasic usage\r\nRe-imagining slice() with data-masking\r\nSpecial properties of slice()\r\n\r\nA gallery of row operations with slice()\r\nRepeat rows (in place)\r\nSubset a selection of rows + the following row\r\nSubset a selection of rows + multiple following rows\r\nFilter (and encode) neighboring rows\r\nAside: kronecker() as as.vector(outer())\r\nWindowed min/max/median (etc.)\r\nEvenly distributed row shuffling of balanced categories\r\nInserting a new row at specific intervals\r\nEvenly distributed row shuffling of unequal categories\r\n\r\nConclusion\r\n\r\nIntro\r\nIn data wrangling, there are a handful of classes of operations on data frames that we think of as theoretically well-defined and tackling distinct problems. To name a few, these include subsetting, joins, split-apply-combine, pairwise operations, nested-column workflows, and so on.\r\nAgainst this rich backdrop, there’s one aspect of data wrangling that doesn’t receive as much attention: ordering of rows. This isn’t necessarily surprising - we often think of row order as an auxiliary attribute of data frames since they don’t speak to the content of the data, per se. I think we all share the intuition that two dataframe that differ only in row order are practically the same for most analysis purposes.\r\nExcept when they aren’t.\r\nIn this blog post I want to talk about a few, somewhat esoteric cases of what I like to call row-relational operations. My goal is to try to motivate row-relational operations as a full-blown class of data wrangling operation that includes not only row ordering, but also sampling, shuffling, repeating, interweaving, and so on (I’ll go over all of these later).\r\nWithout spoiling too much, I believe that dplyr::slice() offers a powerful context for operations over row indices, even those that at first seem to lack a “tidy” solution. You may already know slice() as an indexing function, but my hope is to convince you that it can do so much more.\r\nLet’s start by first talking about some special properties of dplyr::slice(), and then see how we can use it for various row-relational operations.\r\nSpecial properties of dplyr::slice()\r\nBasic usage\r\nFor the following demonstration, I’ll use a small subset of the dplyr::starwars dataset:\r\n\r\n\r\nstarwars_sm <- dplyr::starwars[1:10, 1:3]\r\nstarwars_sm\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 Luke Skywalker        172    77\r\n   2 C-3PO                 167    75\r\n   3 R2-D2                  96    32\r\n   4 Darth Vader           202   136\r\n   5 Leia Organa           150    49\r\n   6 Owen Lars             178   120\r\n   7 Beru Whitesun Lars    165    75\r\n   8 R5-D4                  97    32\r\n   9 Biggs Darklighter     183    84\r\n  10 Obi-Wan Kenobi        182    77\r\n\r\n1) Row selection\r\nslice() is a row indexing verb - if you pass it a vector of integers, it subsets data frame rows:\r\n\r\n\r\nstarwars_sm |> \r\n  slice(1:6) # First six rows\r\n\r\n  # A tibble: 6 × 3\r\n    name           height  mass\r\n    <chr>           <int> <dbl>\r\n  1 Luke Skywalker    172    77\r\n  2 C-3PO             167    75\r\n  3 R2-D2              96    32\r\n  4 Darth Vader       202   136\r\n  5 Leia Organa       150    49\r\n  6 Owen Lars         178   120\r\n\r\nLike other dplyr verbs with mutate-semantics, you can use context-dependent expressions inside slice(). For example, you can use n() to grab the last row (or last couple of rows):\r\n\r\n\r\nstarwars_sm |> \r\n  slice( n() ) # Last row\r\n\r\n  # A tibble: 1 × 3\r\n    name           height  mass\r\n    <chr>           <int> <dbl>\r\n  1 Obi-Wan Kenobi    182    77\r\n\r\nstarwars_sm |> \r\n  slice( n() - 2:0 ) # Last three rows\r\n\r\n  # A tibble: 3 × 3\r\n    name              height  mass\r\n    <chr>              <int> <dbl>\r\n  1 R5-D4                 97    32\r\n  2 Biggs Darklighter    183    84\r\n  3 Obi-Wan Kenobi       182    77\r\n\r\nAnother context-dependent expression that comes in handy is row_number(), which returns all row indices. Using it inside slice() essentially performs an identity transformation:\r\n\r\n\r\nidentical(\r\n  starwars_sm,\r\n  starwars_sm |> slice( row_number() )\r\n)\r\n\r\n  [1] TRUE\r\n\r\nLastly, similar to in select(), you can use - for negative indexing (to remove rows):\r\n\r\n\r\nidentical(\r\n  starwars_sm |> slice(1:3),      # First three rows\r\n  starwars_sm |> slice(-(4:n()))  # All rows except fourth row to last row\r\n)\r\n\r\n  [1] TRUE\r\n\r\n2) Dynamic dots\r\nslice() supports dynamic dots. If you pass row indices into multiple argument positions, slice() will concatenate them for you:\r\n\r\n\r\nidentical(\r\n  starwars_sm |> slice(1:6),\r\n  starwars_sm |> slice(1, 2:4, 5, 6)\r\n)\r\n\r\n  [1] TRUE\r\n\r\nIf you have a list() of row indices, you can use the splice operator !!! to spread them out:\r\n\r\n\r\nstarwars_sm |> \r\n  slice( !!!list(1, 2:4, 5, 6) )\r\n\r\n  # A tibble: 6 × 3\r\n    name           height  mass\r\n    <chr>           <int> <dbl>\r\n  1 Luke Skywalker    172    77\r\n  2 C-3PO             167    75\r\n  3 R2-D2              96    32\r\n  4 Darth Vader       202   136\r\n  5 Leia Organa       150    49\r\n  6 Owen Lars         178   120\r\n\r\nThe above call to slice() evaluates to the following after splicing:\r\n\r\n\r\nrlang::expr( slice(!!!list(1, 2:4, 5, 6)) )\r\n\r\n  slice(1, 2:4, 5, 6)\r\n\r\n3) Row ordering\r\nslice() respects the order in which you supplied the row indices:\r\n\r\n\r\nstarwars_sm |> \r\n  slice(3, 1, 2, 5)\r\n\r\n  # A tibble: 4 × 3\r\n    name           height  mass\r\n    <chr>           <int> <dbl>\r\n  1 R2-D2              96    32\r\n  2 Luke Skywalker    172    77\r\n  3 C-3PO             167    75\r\n  4 Leia Organa       150    49\r\n\r\nThis means you can do stuff like random sampling with sample():\r\n\r\n\r\nstarwars_sm |> \r\n  slice( sample(n()) )\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 Obi-Wan Kenobi        182    77\r\n   2 Owen Lars             178   120\r\n   3 Leia Organa           150    49\r\n   4 Darth Vader           202   136\r\n   5 Luke Skywalker        172    77\r\n   6 R5-D4                  97    32\r\n   7 C-3PO                 167    75\r\n   8 Beru Whitesun Lars    165    75\r\n   9 Biggs Darklighter     183    84\r\n  10 R2-D2                  96    32\r\n\r\nYou can also shuffle a subset of rows (ex: just the first five):\r\n\r\n\r\nstarwars_sm |> \r\n  slice( sample(5), 6:n() )\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 C-3PO                 167    75\r\n   2 Leia Organa           150    49\r\n   3 R2-D2                  96    32\r\n   4 Darth Vader           202   136\r\n   5 Luke Skywalker        172    77\r\n   6 Owen Lars             178   120\r\n   7 Beru Whitesun Lars    165    75\r\n   8 R5-D4                  97    32\r\n   9 Biggs Darklighter     183    84\r\n  10 Obi-Wan Kenobi        182    77\r\n\r\nOr reorder all rows by their indices (ex: in reverse):\r\n\r\n\r\nstarwars_sm |> \r\n  slice( rev(row_number()) )\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 Obi-Wan Kenobi        182    77\r\n   2 Biggs Darklighter     183    84\r\n   3 R5-D4                  97    32\r\n   4 Beru Whitesun Lars    165    75\r\n   5 Owen Lars             178   120\r\n   6 Leia Organa           150    49\r\n   7 Darth Vader           202   136\r\n   8 R2-D2                  96    32\r\n   9 C-3PO                 167    75\r\n  10 Luke Skywalker        172    77\r\n\r\n4) Out-of-bounds handling\r\nIf you pass a row index that’s out of bounds, slice() returns a 0-row data frame:\r\n\r\n\r\nstarwars_sm |> \r\n  slice( n() + 1 ) # Select the row after the last row\r\n\r\n  # A tibble: 0 × 3\r\n  # ℹ 3 variables: name <chr>, height <int>, mass <dbl>\r\n\r\nWhen mixed with valid row indices, out-of-bounds indices are simply ignored (much 💜 for this behavior):\r\n\r\n\r\nstarwars_sm |> \r\n  slice(\r\n    0,       # 0th row - ignored\r\n    1:3,     # first three rows\r\n    n() + 1  # 1 after last row - ignored\r\n  )\r\n\r\n  # A tibble: 3 × 3\r\n    name           height  mass\r\n    <chr>           <int> <dbl>\r\n  1 Luke Skywalker    172    77\r\n  2 C-3PO             167    75\r\n  3 R2-D2              96    32\r\n\r\nThis lets you do funky stuff like select all even numbered rows by passing slice() all row indices times 2:\r\n\r\n\r\nstarwars_sm |> \r\n  slice( row_number() * 2 ) # Add `- 1` at the end for *odd* rows!\r\n\r\n  # A tibble: 5 × 3\r\n    name           height  mass\r\n    <chr>           <int> <dbl>\r\n  1 C-3PO             167    75\r\n  2 Darth Vader       202   136\r\n  3 Owen Lars         178   120\r\n  4 R5-D4              97    32\r\n  5 Obi-Wan Kenobi    182    77\r\n\r\nRe-imagining slice() with data-masking\r\nslice() is already pretty neat as it is, but that’s just the tip of the iceberg.\r\nThe really cool, under-rated feature of slice() is that it’s data-masked, meaning that you can reference column vectors as if they’re variables. Another way of describing this property of slice() is to say that it has mutate-semantics.\r\nAt a very basic level, this means that slice() can straightforwardly replicate the behavior of some dplyr verbs like arrange() and filter()!\r\nslice() as arrange()\r\nFrom our starwars_sm data, if we want to sort by height we can use arrange():\r\n\r\n\r\nstarwars_sm |> \r\n  arrange(height)\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 R2-D2                  96    32\r\n   2 R5-D4                  97    32\r\n   3 Leia Organa           150    49\r\n   4 Beru Whitesun Lars    165    75\r\n   5 C-3PO                 167    75\r\n   6 Luke Skywalker        172    77\r\n   7 Owen Lars             178   120\r\n   8 Obi-Wan Kenobi        182    77\r\n   9 Biggs Darklighter     183    84\r\n  10 Darth Vader           202   136\r\n\r\nBut we can also do this with slice() to the same effect, using order():\r\n\r\n\r\nstarwars_sm |> \r\n  slice( order(height) )\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 R2-D2                  96    32\r\n   2 R5-D4                  97    32\r\n   3 Leia Organa           150    49\r\n   4 Beru Whitesun Lars    165    75\r\n   5 C-3PO                 167    75\r\n   6 Luke Skywalker        172    77\r\n   7 Owen Lars             178   120\r\n   8 Obi-Wan Kenobi        182    77\r\n   9 Biggs Darklighter     183    84\r\n  10 Darth Vader           202   136\r\n\r\nThis is conceptually equivalent to combining the following 2-step process:\r\n\r\n\r\nordered_val_ind <- order(starwars_sm$height)\r\n  ordered_val_ind\r\n\r\n   [1]  3  8  5  7  2  1  6 10  9  4\r\n\r\n\r\n\r\nstarwars_sm |> \r\n    slice( ordered_val_ind )\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 R2-D2                  96    32\r\n   2 R5-D4                  97    32\r\n   3 Leia Organa           150    49\r\n   4 Beru Whitesun Lars    165    75\r\n   5 C-3PO                 167    75\r\n   6 Luke Skywalker        172    77\r\n   7 Owen Lars             178   120\r\n   8 Obi-Wan Kenobi        182    77\r\n   9 Biggs Darklighter     183    84\r\n  10 Darth Vader           202   136\r\n\r\nslice() as filter()\r\nWe can also use slice() to filter(), using which():\r\n\r\n\r\nidentical(\r\n  starwars_sm |> filter( height > 150 ),\r\n  starwars_sm |> slice( which(height > 150) )\r\n)\r\n\r\n  [1] TRUE\r\n\r\nThus, we can think of filter() and slice() as two sides of the same coin:\r\nfilter() takes a logical vector that’s the same length as the number of rows in the data frame\r\nslice() takes an integer vector that’s a (sub)set of a data frame’s row indices.\r\nTo put it more concretely, this logical vector was being passed to the above filter() call:\r\n\r\n\r\nstarwars_sm$height > 150\r\n\r\n   [1]  TRUE  TRUE FALSE  TRUE FALSE  TRUE  TRUE FALSE  TRUE  TRUE\r\n\r\nWhile this integer vector was being passed to the above slice() call, where which() returns the position of TRUE values, given a logical vector:\r\n\r\n\r\nwhich( starwars_sm$height > 150 )\r\n\r\n  [1]  1  2  4  6  7  9 10\r\n\r\nSpecial properties of slice()\r\nThis re-imagined slice() that heavily exploits data-masking gives us two interesting properties:\r\nWe can work with sets of row indices that need not to be the same length as the data frame (vs. filter()).\r\nWe can work with row indices as integers, which are legible to arithmetic operations (ex: + and *)\r\nTo grok the significance of working with rows as integer sets, let’s work through some examples where slice() comes in very handy.\r\nA gallery of row operations with slice()\r\nRepeat rows (in place)\r\nIn {tidyr}, there’s a function called uncount() which does the opposite of dplyr::count():\r\n\r\n\r\nlibrary(tidyr)\r\n# Example from `tidyr::uncount()` docs\r\nuncount_df <- tibble(x = c(\"a\", \"b\"), n = c(1, 2))\r\nuncount_df\r\n\r\n  # A tibble: 2 × 2\r\n    x         n\r\n    <chr> <dbl>\r\n  1 a         1\r\n  2 b         2\r\n\r\nuncount_df |> \r\n  uncount(n)\r\n\r\n  # A tibble: 3 × 1\r\n    x    \r\n    <chr>\r\n  1 a    \r\n  2 b    \r\n  3 b\r\n\r\nWe can mimic this behavior with slice(), using rep(times = ...):\r\n\r\n\r\nrep(1:nrow(uncount_df), times = uncount_df$n)\r\n\r\n  [1] 1 2 2\r\n\r\nuncount_df |> \r\n  slice( rep(row_number(), times = n) ) |> \r\n  select( -n )\r\n\r\n  # A tibble: 3 × 1\r\n    x    \r\n    <chr>\r\n  1 a    \r\n  2 b    \r\n  3 b\r\n\r\nWhat if instead of a whole column storing that information, we only have information about row position?\r\nLet’s say we want to duplicate the rows of starwars_sm at the repeat_at positions:\r\n\r\n\r\nrepeat_at <- sample(5, 2)\r\nrepeat_at\r\n\r\n  [1] 4 5\r\n\r\nIn slice(), you’d just select all rows plus those additional rows, then sort the integer row indices:\r\n\r\n\r\nstarwars_sm |> \r\n  slice( sort(c(row_number(), repeat_at)) )\r\n\r\n  # A tibble: 12 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 Luke Skywalker        172    77\r\n   2 C-3PO                 167    75\r\n   3 R2-D2                  96    32\r\n   4 Darth Vader           202   136\r\n   5 Darth Vader           202   136\r\n   6 Leia Organa           150    49\r\n   7 Leia Organa           150    49\r\n   8 Owen Lars             178   120\r\n   9 Beru Whitesun Lars    165    75\r\n  10 R5-D4                  97    32\r\n  11 Biggs Darklighter     183    84\r\n  12 Obi-Wan Kenobi        182    77\r\n\r\nWhat if we also separately have information about how much to repeat those rows by?\r\n\r\n\r\nrepeat_by <- c(3, 4)\r\n\r\n\r\nYou can apply the same rep() method for just the subset of rows to repeat:\r\n\r\n\r\nstarwars_sm |> \r\n  slice( sort(c(row_number(), rep(repeat_at, times = repeat_by - 1))) )\r\n\r\n  # A tibble: 15 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 Luke Skywalker        172    77\r\n   2 C-3PO                 167    75\r\n   3 R2-D2                  96    32\r\n   4 Darth Vader           202   136\r\n   5 Darth Vader           202   136\r\n   6 Darth Vader           202   136\r\n   7 Leia Organa           150    49\r\n   8 Leia Organa           150    49\r\n   9 Leia Organa           150    49\r\n  10 Leia Organa           150    49\r\n  11 Owen Lars             178   120\r\n  12 Beru Whitesun Lars    165    75\r\n  13 R5-D4                  97    32\r\n  14 Biggs Darklighter     183    84\r\n  15 Obi-Wan Kenobi        182    77\r\n\r\nCircling back to uncount(), you could also initialize a vector of 1s and replace() where the rows should be repeated:\r\n\r\n\r\nstarwars_sm |> \r\n  uncount( replace(rep(1, n()), repeat_at, repeat_by) )\r\n\r\n  # A tibble: 15 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 Luke Skywalker        172    77\r\n   2 C-3PO                 167    75\r\n   3 R2-D2                  96    32\r\n   4 Darth Vader           202   136\r\n   5 Darth Vader           202   136\r\n   6 Darth Vader           202   136\r\n   7 Leia Organa           150    49\r\n   8 Leia Organa           150    49\r\n   9 Leia Organa           150    49\r\n  10 Leia Organa           150    49\r\n  11 Owen Lars             178   120\r\n  12 Beru Whitesun Lars    165    75\r\n  13 R5-D4                  97    32\r\n  14 Biggs Darklighter     183    84\r\n  15 Obi-Wan Kenobi        182    77\r\n\r\nSubset a selection of rows + the following row\r\nRow order can sometimes encode a meaningful continuous measure, like time.\r\nTake for example this subset of the flights dataset in {nycflights13}:\r\n\r\n\r\nflights_df <- nycflights13::flights |> \r\n  filter(month == 3, day == 3, origin == \"JFK\") |> \r\n  select(dep_time, flight, carrier) |> \r\n  slice(1:100) |> \r\n  arrange(dep_time)\r\nflights_df\r\n\r\n  # A tibble: 100 × 3\r\n     dep_time flight carrier\r\n        <int>  <int> <chr>  \r\n   1      535   1141 AA     \r\n   2      551   5716 EV     \r\n   3      555    145 B6     \r\n   4      556    208 B6     \r\n   5      556     79 B6     \r\n   6      601    501 B6     \r\n   7      604    725 B6     \r\n   8      606    135 B6     \r\n   9      606    600 UA     \r\n  10      607    829 US     \r\n  # ℹ 90 more rows\r\n\r\nHere, the rows are ordered by dep_time, such that given a row, the next row is a data point for the next flight that departed from the airport.\r\nAnd let’s say we’re interested in flights that took off immediately after American Airlines (\"AA\") flights. Given what we just noted about the ordering of rows in the data frame, we can do this in slice() by adding 1 to the row index of AA flights:\r\n\r\n\r\nflights_df |> \r\n  slice( which(carrier == \"AA\") + 1 )\r\n\r\n  # A tibble: 14 × 3\r\n     dep_time flight carrier\r\n        <int>  <int> <chr>  \r\n   1      551   5716 EV     \r\n   2      627    905 B6     \r\n   3      652    117 B6     \r\n   4      714    825 AA     \r\n   5      717    987 B6     \r\n   6      724     11 VX     \r\n   7      742    183 DL     \r\n   8      802    655 AA     \r\n   9      805   2143 DL     \r\n  10      847     59 B6     \r\n  11      858    647 AA     \r\n  12      859    120 DL     \r\n  13     1031    179 AA     \r\n  14     1036    641 B6\r\n\r\nWhat if we also want to keep observations for the preceding AA flights as well? We can just stick which(carrier == \"AA\") inside slice() too:\r\n\r\n\r\nflights_df |> \r\n  slice(\r\n    which(carrier == \"AA\"),\r\n    which(carrier == \"AA\") + 1\r\n  )\r\n\r\n  # A tibble: 28 × 3\r\n     dep_time flight carrier\r\n        <int>  <int> <chr>  \r\n   1      535   1141 AA     \r\n   2      626    413 AA     \r\n   3      652   1815 AA     \r\n   4      711    443 AA     \r\n   5      714    825 AA     \r\n   6      724     33 AA     \r\n   7      739     59 AA     \r\n   8      802   1838 AA     \r\n   9      802    655 AA     \r\n  10      843   1357 AA     \r\n  # ℹ 18 more rows\r\n\r\nBut now the rows are now ordered such that all the AA flights come before the other flights! How can we preserve the original order of increasing dep_time?\r\nWe could reconstruct the initial row order by piping the result into arrange(dep_time) again, but the simplest solution would be to concatenate the set of row indices and sort() them, since the output of which() is already integer!\r\n\r\n\r\nflights_df |> \r\n  slice(\r\n    sort(c(\r\n      which(carrier == \"AA\"),\r\n      which(carrier == \"AA\") + 1\r\n    ))\r\n  )\r\n\r\n  # A tibble: 28 × 3\r\n     dep_time flight carrier\r\n        <int>  <int> <chr>  \r\n   1      535   1141 AA     \r\n   2      551   5716 EV     \r\n   3      626    413 AA     \r\n   4      627    905 B6     \r\n   5      652   1815 AA     \r\n   6      652    117 B6     \r\n   7      711    443 AA     \r\n   8      714    825 AA     \r\n   9      714    825 AA     \r\n  10      717    987 B6     \r\n  # ℹ 18 more rows\r\n\r\nNotice how the 8th and 9th rows are repeated here - that’s because 2 AA flights departed in a row (ha!). We can use unique() to remove duplicate rows in the same call to slice():\r\n\r\n\r\nflights_df |> \r\n  slice(\r\n    unique(sort(c(\r\n      which(carrier == \"AA\"),\r\n      which(carrier == \"AA\") + 1\r\n    )))\r\n  )\r\n\r\n  # A tibble: 24 × 3\r\n     dep_time flight carrier\r\n        <int>  <int> <chr>  \r\n   1      535   1141 AA     \r\n   2      551   5716 EV     \r\n   3      626    413 AA     \r\n   4      627    905 B6     \r\n   5      652   1815 AA     \r\n   6      652    117 B6     \r\n   7      711    443 AA     \r\n   8      714    825 AA     \r\n   9      717    987 B6     \r\n  10      724     33 AA     \r\n  # ℹ 14 more rows\r\n\r\nImportantly, we can do all of this inside slice() because we’re working with integer sets. The integer part allows us to do things like + 1 and sort(), while the set part allows us to combine with c() and remove duplicates with unique().\r\nSubset a selection of rows + multiple following rows\r\nIn this example, let’s problematize our approach with the repeated which() calls in our previous solution.\r\nImagine another scenario where we want to filter for all AA flights and three subsequent flights for each.\r\nDo we need to write the solution out like this? That’s a lot of repetition!\r\n\r\n\r\nflights_df |> \r\n  slice(\r\n    which(carrier == \"AA\"),\r\n    which(carrier == \"AA\") + 1,\r\n    which(carrier == \"AA\") + 2,\r\n    which(carrier == \"AA\") + 3\r\n  )\r\n\r\n\r\nYou might think we can get away with + 0:3, but it doesn’t work as we’d like. The + just forces 0:3 to be (partially) recycled to the same length as carrier for element-wise addition:\r\n\r\n\r\nwhich(flights_df$carrier == \"AA\") + 0:3\r\n\r\n  Warning in which(flights_df$carrier == \"AA\") + 0:3: longer object length is not\r\n  a multiple of shorter object length\r\n   [1]  1 14 20 27 25 28 34 40 38 62 66 68 91 93\r\n\r\nIf only we can get the outer sum of the two arrays, 0:3 and which(carrier == \"AA\") … Oh wait, we can - that’s what outer() does!\r\n\r\n\r\nouter(0:3, which(flights_df$carrier == \"AA\"), `+`)\r\n\r\n       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\r\n  [1,]    1   13   18   24   25   27   32   37   38    61    64    65    91    92\r\n  [2,]    2   14   19   25   26   28   33   38   39    62    65    66    92    93\r\n  [3,]    3   15   20   26   27   29   34   39   40    63    66    67    93    94\r\n  [4,]    4   16   21   27   28   30   35   40   41    64    67    68    94    95\r\n\r\nThis is essentially the repeated which() vectors stacked on top of each other, but as a matrix:\r\n\r\n\r\nprint( which(flights_df$carrier == \"AA\")     )\r\nprint( which(flights_df$carrier == \"AA\") + 1 )\r\nprint( which(flights_df$carrier == \"AA\") + 2 )\r\nprint( which(flights_df$carrier == \"AA\") + 3 )\r\n\r\n   [1]  1 13 18 24 25 27 32 37 38 61 64 65 91 92\r\n   [1]  2 14 19 25 26 28 33 38 39 62 65 66 92 93\r\n   [1]  3 15 20 26 27 29 34 39 40 63 66 67 93 94\r\n   [1]  4 16 21 27 28 30 35 40 41 64 67 68 94 95\r\n\r\nThe fact that outer() returns all the relevant row indices inside a single matrix is nice because we can collect the indices column-by-column, preserving row order. Matrices, like data frames, are column-major, so coercing a matrix to a vector collapses it column-wise:\r\n\r\n\r\nas.integer( outer(0:3, which(flights_df$carrier == \"AA\"), `+`) )\r\n\r\n   [1]  1  2  3  4 13 14 15 16 18 19 20 21 24 25 26 27 25 26 27 28 27 28 29 30 32\r\n  [26] 33 34 35 37 38 39 40 38 39 40 41 61 62 63 64 64 65 66 67 65 66 67 68 91 92\r\n  [51] 93 94 92 93 94 95\r\n\r\n\r\nOther ways to coerce matrix to vector\r\nThere are two other options for coercing a matrix to vector - c() and as.vector(). I like to stick with as.integer() because that enforces integer type (which makes sense for row indices), and c() can be nice because it’s less to type (although it’s off-label usage):\r\n\r\n\r\n# Not run, but equivalent to `as.integer()` method\r\nas.vector( outer(0:3, which(flights_df$carrier == \"AA\"), `+`) )\r\nc( outer(0:3, which(flights_df$carrier == \"AA\"), `+`) )\r\n\r\n\r\nSomewhat relatedly - and this only works inside the tidy-eval context of slice() - you can get a similar effect of “collapsing” a matrix using the splice operator !!!:\r\n\r\n\r\nseq_matrix <- matrix(1:9, byrow = TRUE, nrow = 3)\r\nas.integer(seq_matrix)\r\n\r\n  [1] 1 4 7 2 5 8 3 6 9\r\n\r\nidentical(\r\n  mtcars |> slice( as.vector(seq_matrix) ),\r\n  mtcars |> slice( !!!seq_matrix )\r\n)\r\n\r\n  [1] TRUE\r\n\r\nHere, the !!!seq_matrix was slotting each individual “cell” as argument to slice():\r\n\r\n\r\nrlang::expr( slice(!!!seq_matrix) )\r\n\r\n  slice(1L, 4L, 7L, 2L, 5L, 8L, 3L, 6L, 9L)\r\n\r\nA big difference in behavior between as.integer() vs. !!! is that the latter works for lists of indices too, by slotting each element of the list as an argument to slice():\r\n\r\n\r\nseq_list <- list(c(1, 4, 7, 2), c(5, 8, 3, 6, 9))\r\nrlang::expr( slice( !!!seq_list ) )\r\n\r\n  slice(c(1, 4, 7, 2), c(5, 8, 3, 6, 9))\r\n\r\nHowever, as you may already know, as.integer() cannot flatten lists:\r\n\r\n\r\nas.integer(seq_list)\r\n\r\n  Error in eval(expr, envir, enclos): 'list' object cannot be coerced to type 'integer'\r\n\r\nNote that as.vector() and c() leaves lists as is, which is another reason to prefer as.integer() for type-checking:\r\n\r\n\r\nidentical(seq_list, as.vector(seq_list))\r\nidentical(seq_list, c(seq_list))\r\n\r\n  [1] TRUE\r\n  [1] TRUE\r\n\r\nFinally, back in our !!!seq_matrix example, we could have applied asplit(MARGIN = 2) to chunk the splicing by matrix column, although the overall effect would be the same:\r\n\r\n\r\nrlang::expr(slice( !!!seq_matrix            ))\r\n\r\n  slice(1L, 4L, 7L, 2L, 5L, 8L, 3L, 6L, 9L)\r\n\r\nrlang::expr(slice( !!!asplit(seq_matrix, 2) ))\r\n\r\n  slice(c(1L, 4L, 7L), c(2L, 5L, 8L), c(3L, 6L, 9L))\r\n\r\nThis lets us ask questions like: Which AA flights departed within 3 flights of another AA flight?\r\n\r\n\r\nflights_df |> \r\n  slice( as.integer( outer(0:3, which(carrier == \"AA\"), `+`) ) ) |> \r\n  filter( carrier == \"AA\", duplicated(flight) ) |> \r\n  distinct(flight, carrier)\r\n\r\n  # A tibble: 6 × 2\r\n    flight carrier\r\n     <int> <chr>  \r\n  1    825 AA     \r\n  2     33 AA     \r\n  3    655 AA     \r\n  4      1 AA     \r\n  5    647 AA     \r\n  6    179 AA\r\n\r\n\r\nSlicing all the way down: Case 1\r\nWith the addition of the .by argument to slice() in dplyr v1.10, we can re-write the above code as three calls to slice() (+ a call to select()):\r\n\r\n\r\nflights_df |> \r\n  slice( as.integer( outer(0:3, which(carrier == \"AA\"), `+`) ) ) |> \r\n  slice( which(carrier == \"AA\" & duplicated(flight)) ) |>  # filter()\r\n  slice( 1, .by = c(flight, carrier) ) |>                  # distinct()\r\n  select(flight, carrier)\r\n\r\n  # A tibble: 6 × 2\r\n    flight carrier\r\n     <int> <chr>  \r\n  1    825 AA     \r\n  2     33 AA     \r\n  3    655 AA     \r\n  4      1 AA     \r\n  5    647 AA     \r\n  6    179 AA\r\n\r\nThe next example will demonstrate another, perhaps more practical usecase for outer() in slice().\r\nFilter (and encode) neighboring rows\r\nLet’s use a subset of the {gapminder} data set for this one. Here, we have data for each European country’s GDP-per-capita by year, between 1992 to 2007:\r\n\r\n\r\ngapminder_df <- gapminder::gapminder |> \r\n  left_join(gapminder::country_codes, by = \"country\") |>  # `multiple = \"all\"`\r\n  filter(year >= 1992, continent == \"Europe\") |> \r\n  select(country, country_code = iso_alpha, year, gdpPercap)\r\ngapminder_df\r\n\r\n  # A tibble: 120 × 4\r\n     country country_code  year gdpPercap\r\n     <chr>   <chr>        <int>     <dbl>\r\n   1 Albania ALB           1992     2497.\r\n   2 Albania ALB           1997     3193.\r\n   3 Albania ALB           2002     4604.\r\n   4 Albania ALB           2007     5937.\r\n   5 Austria AUT           1992    27042.\r\n   6 Austria AUT           1997    29096.\r\n   7 Austria AUT           2002    32418.\r\n   8 Austria AUT           2007    36126.\r\n   9 Belgium BEL           1992    25576.\r\n  10 Belgium BEL           1997    27561.\r\n  # ℹ 110 more rows\r\n\r\nThis time, let’s see the desired output (plot) first and build our way up. The goal is to plot the GDP growth of Germany over the years, and its yearly GDP neighbors side-by-side:\r\n\r\n\r\n\r\nFirst, let’s think about what a “GDP neighbor” means in row-relational terms. If you arranged the data by GDP, the GDP neighbors would be the rows that come immediately before and after the rows for Germany. You need to recalculate neighbors every year though, so this arrange() + slice() combo should happen by-year.\r\nWith that in mind, let’s set up a year grouping and arrange by gdpPercap within year:1\r\n\r\n\r\ngapminder_df |> \r\n  group_by(year) |> \r\n  arrange(gdpPercap, .by_group = TRUE)\r\n\r\n  # A tibble: 120 × 4\r\n  # Groups:   year [4]\r\n     country                country_code  year gdpPercap\r\n     <chr>                  <chr>        <int>     <dbl>\r\n   1 Albania                ALB           1992     2497.\r\n   2 Bosnia and Herzegovina BIH           1992     2547.\r\n   3 Turkey                 TUR           1992     5678.\r\n   4 Bulgaria               BGR           1992     6303.\r\n   5 Romania                ROU           1992     6598.\r\n   6 Montenegro             MNE           1992     7003.\r\n   7 Poland                 POL           1992     7739.\r\n   8 Croatia                HRV           1992     8448.\r\n   9 Serbia                 SRB           1992     9325.\r\n  10 Slovak Republic        SVK           1992     9498.\r\n  # ℹ 110 more rows\r\n\r\nNow within each year, we want to grab the row for Germany and its neighboring rows. We can do this by taking the outer() sum of -1:1 and the row indices for Germany:\r\n\r\n\r\ngapminder_df |> \r\n  group_by(year) |> \r\n  arrange(gdpPercap, .by_group = TRUE) |> \r\n  slice( as.integer(outer( -1:1, which(country == \"Germany\"), `+` )) )\r\n\r\n  # A tibble: 12 × 4\r\n  # Groups:   year [4]\r\n     country        country_code  year gdpPercap\r\n     <chr>          <chr>        <int>     <dbl>\r\n   1 Denmark        DNK           1992    26407.\r\n   2 Germany        DEU           1992    26505.\r\n   3 Netherlands    NLD           1992    26791.\r\n   4 Belgium        BEL           1997    27561.\r\n   5 Germany        DEU           1997    27789.\r\n   6 Iceland        ISL           1997    28061.\r\n   7 United Kingdom GBR           2002    29479.\r\n   8 Germany        DEU           2002    30036.\r\n   9 Belgium        BEL           2002    30486.\r\n  10 France         FRA           2007    30470.\r\n  11 Germany        DEU           2007    32170.\r\n  12 United Kingdom GBR           2007    33203.\r\n\r\n\r\nSlicing all the way down: Case 2\r\nThe new .by argument in slice() comes in handy again here, allowing us to collapse the group_by() + arrange() combo into one slice() call:\r\n\r\n\r\ngapminder_df |> \r\n  slice( order(gdpPercap), .by = year) |> \r\n  slice( as.integer(outer( -1:1, which(country == \"Germany\"), `+` )) )\r\n\r\n  # A tibble: 12 × 4\r\n     country        country_code  year gdpPercap\r\n     <chr>          <chr>        <int>     <dbl>\r\n   1 Denmark        DNK           1992    26407.\r\n   2 Germany        DEU           1992    26505.\r\n   3 Netherlands    NLD           1992    26791.\r\n   4 Belgium        BEL           1997    27561.\r\n   5 Germany        DEU           1997    27789.\r\n   6 Iceland        ISL           1997    28061.\r\n   7 United Kingdom GBR           2002    29479.\r\n   8 Germany        DEU           2002    30036.\r\n   9 Belgium        BEL           2002    30486.\r\n  10 France         FRA           2007    30470.\r\n  11 Germany        DEU           2007    32170.\r\n  12 United Kingdom GBR           2007    33203.\r\n\r\nFor our purposes here we want actually the grouping to persist for the following mutate() call, but there may be other cases where you’d want to use slice(.by = ) for temporary grouping.\r\nNow we’re already starting to see the shape of the data that we want! The last step is to encode the relationship of each row to Germany - does a row represent Germany itself, or a country that’s one GDP ranking below or above Germany?\r\nContinuing with our grouped context, we make a new column grp that assigns a factor value \"lo\"-\"is\"-\"hi\" (for “lower” than Germany, “is” Germany and “higher” than Germany) to each country trio by year. Notice the use of fct_inorder() below - this ensures that the factor levels are in the order of their occurrence (necessary for the correct ordering of bars in geom_col() later):\r\n\r\n\r\ngapminder_df |> \r\n  group_by(year) |> \r\n  arrange(gdpPercap) |> \r\n  slice( as.integer(outer( -1:1, which(country == \"Germany\"), `+` )) ) |> \r\n  mutate(grp = forcats::fct_inorder(c(\"lo\", \"is\", \"hi\")))\r\n\r\n  # A tibble: 12 × 5\r\n  # Groups:   year [4]\r\n     country        country_code  year gdpPercap grp  \r\n     <chr>          <chr>        <int>     <dbl> <fct>\r\n   1 Denmark        DNK           1992    26407. lo   \r\n   2 Germany        DEU           1992    26505. is   \r\n   3 Netherlands    NLD           1992    26791. hi   \r\n   4 Belgium        BEL           1997    27561. lo   \r\n   5 Germany        DEU           1997    27789. is   \r\n   6 Iceland        ISL           1997    28061. hi   \r\n   7 United Kingdom GBR           2002    29479. lo   \r\n   8 Germany        DEU           2002    30036. is   \r\n   9 Belgium        BEL           2002    30486. hi   \r\n  10 France         FRA           2007    30470. lo   \r\n  11 Germany        DEU           2007    32170. is   \r\n  12 United Kingdom GBR           2007    33203. hi\r\n\r\nWe now have everything that’s necessary to make our desired plot, so we ungroup(), write some {ggplot2} code, and voila!\r\n\r\n\r\ngapminder_df |> \r\n  group_by(year) |> \r\n  arrange(gdpPercap) |> \r\n  slice( as.integer(outer( -1:1, which(country == \"Germany\"), `+` )) ) |> \r\n  mutate(grp = forcats::fct_inorder(c(\"lo\", \"is\", \"hi\"))) |> \r\n  # Ungroup and make ggplot\r\n  ungroup() |> \r\n  ggplot(aes(as.factor(year), gdpPercap, group = grp)) +\r\n  geom_col(aes(fill = grp == \"is\"), position = position_dodge()) +\r\n  geom_text(\r\n    aes(label = country_code),\r\n    vjust = 1.3,\r\n    position = position_dodge(width = .9)\r\n  ) +\r\n  scale_fill_manual(\r\n    values = c(\"grey75\", \"steelblue\"),\r\n    guide = guide_none()\r\n  ) +\r\n  theme_classic() +\r\n  labs(x = \"Year\", y = \"GDP per capita\")\r\n\r\n\r\n\r\n\r\nSolving the harder version of the problem\r\nThe solution presented above relies on a fragile assumption that Germany will always have a higher and lower ranking GDP neighbor every year. But nothing about the problem description guarantees this, so how can we re-write our code to be more robust?\r\nFirst, let’s simulate a data where Germany is the lowest ranking country in 2002 and the highest ranking in 2007. In other words, Germany only has one GDP neighbor in those years:\r\n\r\n\r\ngapminder_harder_df <- gapminder_df |> \r\n  slice( order(gdpPercap), .by = year) |> \r\n  slice( as.integer(outer( -1:1, which(country == \"Germany\"), `+` )) ) |> \r\n  slice( -7, -12 )\r\ngapminder_harder_df\r\n\r\n  # A tibble: 10 × 4\r\n     country     country_code  year gdpPercap\r\n     <chr>       <chr>        <int>     <dbl>\r\n   1 Denmark     DNK           1992    26407.\r\n   2 Germany     DEU           1992    26505.\r\n   3 Netherlands NLD           1992    26791.\r\n   4 Belgium     BEL           1997    27561.\r\n   5 Germany     DEU           1997    27789.\r\n   6 Iceland     ISL           1997    28061.\r\n   7 Germany     DEU           2002    30036.\r\n   8 Belgium     BEL           2002    30486.\r\n   9 France      FRA           2007    30470.\r\n  10 Germany     DEU           2007    32170.\r\n\r\nGiven this data, we cannot assign the full, length-3 lo-is-hi factor by group, because the groups for year 2002 and 2007 only have 2 observations:\r\n\r\n\r\ngapminder_harder_df |> \r\n  group_by(year) |> \r\n  mutate(grp = forcats::fct_inorder(c(\"lo\", \"is\", \"hi\")))\r\n\r\n  Error in `mutate()`:\r\n  ℹ In argument: `grp = forcats::fct_inorder(c(\"lo\", \"is\", \"hi\"))`.\r\n  ℹ In group 3: `year = 2002`.\r\n  Caused by error:\r\n  ! `grp` must be size 2 or 1, not 3.\r\n\r\nThe trick here is to turn each group of rows into an integer sequence where Germany is “anchored” to 2, and then use that vector to subset the lo-is-hi factor:\r\n\r\n\r\ngapminder_harder_df |> \r\n  group_by(year) |> \r\n  mutate(\r\n    Germany_anchored_to_2 = row_number() - which(country == \"Germany\") + 2,\r\n    grp = forcats::fct_inorder(c(\"lo\", \"is\", \"hi\"))[Germany_anchored_to_2]\r\n  )\r\n\r\n  # A tibble: 10 × 6\r\n  # Groups:   year [4]\r\n     country     country_code  year gdpPercap Germany_anchored_to_2 grp  \r\n     <chr>       <chr>        <int>     <dbl>                 <dbl> <fct>\r\n   1 Denmark     DNK           1992    26407.                     1 lo   \r\n   2 Germany     DEU           1992    26505.                     2 is   \r\n   3 Netherlands NLD           1992    26791.                     3 hi   \r\n   4 Belgium     BEL           1997    27561.                     1 lo   \r\n   5 Germany     DEU           1997    27789.                     2 is   \r\n   6 Iceland     ISL           1997    28061.                     3 hi   \r\n   7 Germany     DEU           2002    30036.                     2 is   \r\n   8 Belgium     BEL           2002    30486.                     3 hi   \r\n   9 France      FRA           2007    30470.                     1 lo   \r\n  10 Germany     DEU           2007    32170.                     2 is\r\n\r\nWe find that the lessons of working with row indices from slice() translated to solving this complex mutate() problem - neat!\r\nAside: kronecker() as as.vector(outer())\r\nFollowing from the slice() + outer() strategy demoed above, imagine if we wanted to filter for \"Luke Skywalker\" and 4 other characters that are neighbors in the height and mass values.\r\n\r\n\r\ndplyr::starwars[, 1:3]\r\n\r\n  # A tibble: 87 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 Luke Skywalker        172    77\r\n   2 C-3PO                 167    75\r\n   3 R2-D2                  96    32\r\n   4 Darth Vader           202   136\r\n   5 Leia Organa           150    49\r\n   6 Owen Lars             178   120\r\n   7 Beru Whitesun Lars    165    75\r\n   8 R5-D4                  97    32\r\n   9 Biggs Darklighter     183    84\r\n  10 Obi-Wan Kenobi        182    77\r\n  # ℹ 77 more rows\r\n\r\nIn row-relational terms, “filtering neighboring values” just means “filtering rows after arranging by the values we care about”. We can express this using slice() and outer() as:\r\n\r\n\r\nstarwars %>% \r\n  select(name, mass, height) %>% \r\n  arrange(mass, height) %>% \r\n  slice( as.vector(outer(-2:2, which(name == \"Luke Skywalker\"), `+`)) )\r\n\r\n  # A tibble: 5 × 3\r\n    name            mass height\r\n    <chr>          <dbl>  <int>\r\n  1 Palpatine       75      170\r\n  2 Wedge Antilles  77      170\r\n  3 Luke Skywalker  77      172\r\n  4 Obi-Wan Kenobi  77      182\r\n  5 Boba Fett       78.2    183\r\n\r\nI raised this example on an unrelated thread on the R4DS/DSLC slack, where Anthony Durrant pointed me to kronecker() as a version of outer() that unlist before returning the output.\r\nSo in examples involving outer() to generate row indices in slice(), we can also use kronecker() instead to save a call to a flattening function like as.vector():\r\n\r\n\r\nstarwars %>% \r\n  select(name, mass, height) %>% \r\n  arrange(mass, height) %>% \r\n  slice( kronecker(-2:2, which(name == \"Luke Skywalker\"), `+`) )\r\n\r\n  # A tibble: 5 × 3\r\n    name            mass height\r\n    <chr>          <dbl>  <int>\r\n  1 Palpatine       75      170\r\n  2 Wedge Antilles  77      170\r\n  3 Luke Skywalker  77      172\r\n  4 Obi-Wan Kenobi  77      182\r\n  5 Boba Fett       78.2    183\r\n\r\nWindowed min/max/median (etc.)\r\nLet’s say we have this small time series data, and we want to calculate a lagged 3-window moving minimum for the val column:\r\n\r\n\r\nts_df <- tibble(\r\n  time = 1:6,\r\n  val = sample(1:6 * 10)\r\n)\r\nts_df\r\n\r\n  # A tibble: 6 × 2\r\n     time   val\r\n    <int> <dbl>\r\n  1     1    50\r\n  2     2    40\r\n  3     3    60\r\n  4     4    30\r\n  5     5    20\r\n  6     6    10\r\n\r\nIf you’re new to window functions, think of them as a special kind of group_by() + summarize() where groups are chunks of observations along a (typically unique) continuous measure like time, and observations can be shared between groups.\r\nThere are several packages implementing moving/sliding/rolling window functions. My current favorite is {r2c} (see a review of other implementations therein), but I also like {slider} for an implementation that follows familiar “tidy” design principles:\r\n\r\n\r\nlibrary(slider)\r\nts_df |> \r\n  mutate(moving_min = slide_min(val, before = 2L, complete = TRUE))\r\n\r\n  # A tibble: 6 × 3\r\n     time   val moving_min\r\n    <int> <dbl>      <dbl>\r\n  1     1    50         NA\r\n  2     2    40         NA\r\n  3     3    60         40\r\n  4     4    30         30\r\n  5     5    20         20\r\n  6     6    10         10\r\n\r\nMoving window is a general class of operations that encompass any arbitrary summary statistic - so not just min but other reducing functions like mean, standard deviation, etc. But what makes moving min (along with max, median, etc.) a particularly interesting case for our current discussion is that the value comes from an existing observation in the data. And if our time series is tidy, every observation makes up a row. See where I’m going with this?\r\nUsing outer() again, we can take the outer sum of all row indices of ts_df and -2:0. This gives us a matrix where each column represents a lagged size-3 moving window:\r\n\r\n\r\nwindows_3lag <- outer(-2:0, 1:nrow(ts_df), \"+\")\r\nwindows_3lag\r\n\r\n       [,1] [,2] [,3] [,4] [,5] [,6]\r\n  [1,]   -1    0    1    2    3    4\r\n  [2,]    0    1    2    3    4    5\r\n  [3,]    1    2    3    4    5    6\r\n\r\nThe “lagged size-3” property of this moving window means that the first two windows are incomplete (consisting of less than 3 observations). We want to treat those as invalid, so we can drop the first two columns from our matrix:\r\n\r\n\r\nwindows_3lag[,-(1:2)]\r\n\r\n       [,1] [,2] [,3] [,4]\r\n  [1,]    1    2    3    4\r\n  [2,]    2    3    4    5\r\n  [3,]    3    4    5    6\r\n\r\nFor each remaining column, we want to grab the values of val at the corresponding row indices and find which row has the minimum val. In terms of code, we use apply() with MARGIN = 2L to column-wise apply a function where we use which.min() to find the location of the minimum val and convert it back to row index via subsetting:\r\n\r\n\r\nwindows_3lag[, -(1:2)] |> \r\n  apply(MARGIN = 2L, \\(i) i[which.min(ts_df$val[i])])\r\n\r\n  [1] 2 4 5 6\r\n\r\nNow let’s stick this inside slice(), exploiting the fact that it’s data-masked (ts_df$val can just be val) and exposes context-dependent expressions (1:nrow(ts_df) can just be row_number()):\r\n\r\n\r\nmoving_mins <- ts_df |> \r\n  slice(\r\n    outer(-2:0, row_number(), \"+\")[,-(1:2)] |> \r\n      apply(MARGIN = 2L, \\(i) i[which.min(val[i])])\r\n  )\r\nmoving_mins\r\n\r\n  # A tibble: 4 × 2\r\n     time   val\r\n    <int> <dbl>\r\n  1     2    40\r\n  2     4    30\r\n  3     5    20\r\n  4     6    10\r\n\r\nFrom here, we can grab the val column and pad it with NA to add our desired window_min column to the original data frame:\r\n\r\n\r\nts_df |> \r\n  mutate(moving_min = c(NA, NA, moving_mins$val))\r\n\r\n  # A tibble: 6 × 3\r\n     time   val moving_min\r\n    <int> <dbl>      <dbl>\r\n  1     1    50         NA\r\n  2     2    40         NA\r\n  3     3    60         40\r\n  4     4    30         30\r\n  5     5    20         20\r\n  6     6    10         10\r\n\r\nAt this point you might think that this is a very round-about way of solving the same problem. But actually I think that it’s a faster route to solving a slightly more complicated problem - augmenting each observation of a data frame with information about comparison observations.\r\nFor example, our slice()-based solution sets us up nicely for also bringing along information about the time at which the moving_min occurred. After some rename()-ing and adding the original time information back in, we get back a relational data structure where time is a key shared with ts_df:\r\n\r\n\r\nmoving_mins2 <- moving_mins |> \r\n  rename(moving_min_val = val, moving_min_time = time) |> \r\n  mutate(time = ts_df$time[-(1:2)], .before = 1L)\r\nmoving_mins2\r\n\r\n  # A tibble: 4 × 3\r\n     time moving_min_time moving_min_val\r\n    <int>           <int>          <dbl>\r\n  1     3               2             40\r\n  2     4               4             30\r\n  3     5               5             20\r\n  4     6               6             10\r\n\r\nWe can then left-join this to the original data to augment it with information about both the value of the 3-window minimum and the time that the minimum occurred:\r\n\r\n\r\nleft_join(ts_df, moving_mins2, by = \"time\")\r\n\r\n  # A tibble: 6 × 4\r\n     time   val moving_min_time moving_min_val\r\n    <int> <dbl>           <int>          <dbl>\r\n  1     1    50              NA             NA\r\n  2     2    40              NA             NA\r\n  3     3    60               2             40\r\n  4     4    30               4             30\r\n  5     5    20               5             20\r\n  6     6    10               6             10\r\n\r\nThis is particularly useful if rows contain other useful information for comparison and you have memory to spare:\r\n\r\n\r\nts_wide_df <- ts_df |> \r\n  mutate(\r\n    col1 = rnorm(6),\r\n    col2 = rnorm(6)\r\n  )\r\nts_wide_df\r\n\r\n  # A tibble: 6 × 4\r\n     time   val    col1     col2\r\n    <int> <dbl>   <dbl>    <dbl>\r\n  1     1    50  0.0183  0.00501\r\n  2     2    40  0.705  -0.0376 \r\n  3     3    60 -0.647   0.724  \r\n  4     4    30  0.868  -0.497  \r\n  5     5    20  0.376   0.0114 \r\n  6     6    10  0.310   0.00986\r\n\r\nThe below code augments each observation in the original ts_wide_df data with information about the corresponding 3-window moving min (columns prefixed with \"min3val_\")\r\n\r\n\r\nmoving_mins_wide <- ts_wide_df |> \r\n  slice(\r\n    outer(-2:0, row_number(), \"+\")[,-(1:2)] |> \r\n      apply(MARGIN = 2L, \\(i) i[which.min(val[i])])\r\n  ) |> \r\n  rename_with(~ paste0(\"min3val_\", .x)) |> \r\n  mutate(time = ts_wide_df$time[-(1:2)])\r\nleft_join(ts_wide_df, moving_mins_wide, by = \"time\")\r\n\r\n  # A tibble: 6 × 8\r\n     time   val    col1     col2 min3val_time min3val_val min3val_col1\r\n    <int> <dbl>   <dbl>    <dbl>        <int>       <dbl>        <dbl>\r\n  1     1    50  0.0183  0.00501           NA          NA       NA    \r\n  2     2    40  0.705  -0.0376            NA          NA       NA    \r\n  3     3    60 -0.647   0.724              2          40        0.705\r\n  4     4    30  0.868  -0.497              4          30        0.868\r\n  5     5    20  0.376   0.0114             5          20        0.376\r\n  6     6    10  0.310   0.00986            6          10        0.310\r\n  # ℹ 1 more variable: min3val_col2 <dbl>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\nEvenly distributed row shuffling of balanced categories\r\nSometimes the ordering of rows in a data frame can be meaningful for an external application.\r\nFor example, many experiment-building platforms for psychology research require researchers to specify the running order of trials in an experiment via a csv, where each row represents a trial and each column represents information about the trial.\r\nSo an experiment testing the classic Stroop effect may have the following template:\r\n\r\n\r\nmismatch_trials <- tibble(\r\n  item_id = 1:5,\r\n  trial = \"mismatch\",\r\n  word = c(\"red\", \"green\", \"purple\", \"brown\", \"blue\"),\r\n  color = c(\"brown\", \"red\", \"green\", \"blue\", \"purple\")\r\n)\r\nmismatch_trials\r\n\r\n  # A tibble: 5 × 4\r\n    item_id trial    word   color \r\n      <int> <chr>    <chr>  <chr> \r\n  1       1 mismatch red    brown \r\n  2       2 mismatch green  red   \r\n  3       3 mismatch purple green \r\n  4       4 mismatch brown  blue  \r\n  5       5 mismatch blue   purple\r\n\r\nWe probably also want to mix in some control trials where the word and color do match:\r\n\r\n\r\nmatch_trials <- mismatch_trials |> \r\n  mutate(trial = \"match\", color = word)\r\nmatch_trials\r\n\r\n  # A tibble: 5 × 4\r\n    item_id trial word   color \r\n      <int> <chr> <chr>  <chr> \r\n  1       1 match red    red   \r\n  2       2 match green  green \r\n  3       3 match purple purple\r\n  4       4 match brown  brown \r\n  5       5 match blue   blue\r\n\r\nNow that we have all materials for our experiment, we next want the running order to interleave the match and mismatch trials.\r\nWe first add them together into a longer data frame:\r\n\r\n\r\nstroop_trials <- bind_rows(mismatch_trials, match_trials)\r\nstroop_trials\r\n\r\n  # A tibble: 10 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       2 mismatch green  red   \r\n   3       3 mismatch purple green \r\n   4       4 mismatch brown  blue  \r\n   5       5 mismatch blue   purple\r\n   6       1 match    red    red   \r\n   7       2 match    green  green \r\n   8       3 match    purple purple\r\n   9       4 match    brown  brown \r\n  10       5 match    blue   blue\r\n\r\nAnd from here we can exploit the fact that all mismatch items come before match items, and that they share the same length of 5:\r\n\r\n\r\nstroop_trials |> \r\n  slice( as.integer(outer(c(0, 5), 1:5, \"+\")) )\r\n\r\n  # A tibble: 10 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       1 match    red    red   \r\n   3       2 mismatch green  red   \r\n   4       2 match    green  green \r\n   5       3 mismatch purple green \r\n   6       3 match    purple purple\r\n   7       4 mismatch brown  blue  \r\n   8       4 match    brown  brown \r\n   9       5 mismatch blue   purple\r\n  10       5 match    blue   blue\r\n\r\nThis relies on a strong assumptions about the row order in the original data, though. So a safer alternative is to represent the row indices for \"match\" and \"mismatch\" trials as rows of a matrix, and then collapse column-wise.\r\nLet’s try this outside of slice() first. We start with a call to sapply() to construct a matrix where the columns contain row indices for each unique category of trial:\r\n\r\n\r\nsapply(unique(stroop_trials$trial), \\(x) which(stroop_trials$trial == x))\r\n\r\n       mismatch match\r\n  [1,]        1     6\r\n  [2,]        2     7\r\n  [3,]        3     8\r\n  [4,]        4     9\r\n  [5,]        5    10\r\n\r\nThen we transpose the matrix with t(), which rotates it:\r\n\r\n\r\nt( sapply(unique(stroop_trials$trial), \\(x) which(stroop_trials$trial == x)) )\r\n\r\n           [,1] [,2] [,3] [,4] [,5]\r\n  mismatch    1    2    3    4    5\r\n  match       6    7    8    9   10\r\n\r\nNow lets stick that inside slice, remembering to collapse the transposed matrix into vector:\r\n\r\n\r\ninterleaved_stroop_trials <- stroop_trials |> \r\n  slice( as.integer(t(sapply(unique(trial), \\(x) which(trial == x)))) )\r\ninterleaved_stroop_trials\r\n\r\n  # A tibble: 10 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       1 match    red    red   \r\n   3       2 mismatch green  red   \r\n   4       2 match    green  green \r\n   5       3 mismatch purple green \r\n   6       3 match    purple purple\r\n   7       4 mismatch brown  blue  \r\n   8       4 match    brown  brown \r\n   9       5 mismatch blue   purple\r\n  10       5 match    blue   blue\r\n\r\nAt the moment, we have both “red” word trails showing up together, and then the “green”s, the “purple”s, and so on. If we wanted to introduce some randomness to the presentation order within each type of trial, we can wrap the row indices in sample() to shuffle them first:\r\n\r\n\r\nshuffled_stroop_trials <- stroop_trials |> \r\n  slice( as.integer(t(sapply(unique(trial), \\(x) sample(which(trial == x))))) )\r\nshuffled_stroop_trials\r\n\r\n  # A tibble: 10 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       5 match    blue   blue  \r\n   3       2 mismatch green  red   \r\n   4       4 match    brown  brown \r\n   5       3 mismatch purple green \r\n   6       1 match    red    red   \r\n   7       4 mismatch brown  blue  \r\n   8       3 match    purple purple\r\n   9       5 mismatch blue   purple\r\n  10       2 match    green  green\r\n\r\n\r\nInserting a new row at specific intervals\r\nContinuing with our Stroop experiment template example, let’s say we want to give participants a break every two trials.\r\nIn a matrix representation, this means constructing this 2-row matrix of row indices:\r\n\r\n\r\nmatrix(1:nrow(shuffled_stroop_trials), nrow = 2)\r\n\r\n       [,1] [,2] [,3] [,4] [,5]\r\n  [1,]    1    3    5    7    9\r\n  [2,]    2    4    6    8   10\r\n\r\nAnd adding a row of that represent a separator/break, before collapsing column-wise:\r\n\r\n\r\nmatrix(1:nrow(shuffled_stroop_trials), nrow = 2) |> \r\n  rbind(11)\r\n\r\n       [,1] [,2] [,3] [,4] [,5]\r\n  [1,]    1    3    5    7    9\r\n  [2,]    2    4    6    8   10\r\n  [3,]   11   11   11   11   11\r\n\r\nUsing slice, this means adding a row to the data representing a break trial first, and then adding a row to the row index matrix representing that row:\r\n\r\n\r\nstroop_with_breaks <- shuffled_stroop_trials |> \r\n  add_row(trial = \"BREAK\") |> \r\n  slice(\r\n    matrix(row_number()[-n()], nrow = 2) |> \r\n      rbind(n()) |> \r\n      as.integer()\r\n  )\r\nstroop_with_breaks\r\n\r\n  # A tibble: 15 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       5 match    blue   blue  \r\n   3      NA BREAK    <NA>   <NA>  \r\n   4       2 mismatch green  red   \r\n   5       4 match    brown  brown \r\n   6      NA BREAK    <NA>   <NA>  \r\n   7       3 mismatch purple green \r\n   8       1 match    red    red   \r\n   9      NA BREAK    <NA>   <NA>  \r\n  10       4 mismatch brown  blue  \r\n  11       3 match    purple purple\r\n  12      NA BREAK    <NA>   <NA>  \r\n  13       5 mismatch blue   purple\r\n  14       2 match    green  green \r\n  15      NA BREAK    <NA>   <NA>\r\n\r\nIf we don’t want a break after the last trial, we can use negative indexing with slice(-n()):\r\n\r\n\r\nstroop_with_breaks |> \r\n  slice(-n())\r\n\r\n  # A tibble: 14 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       5 match    blue   blue  \r\n   3      NA BREAK    <NA>   <NA>  \r\n   4       2 mismatch green  red   \r\n   5       4 match    brown  brown \r\n   6      NA BREAK    <NA>   <NA>  \r\n   7       3 mismatch purple green \r\n   8       1 match    red    red   \r\n   9      NA BREAK    <NA>   <NA>  \r\n  10       4 mismatch brown  blue  \r\n  11       3 match    purple purple\r\n  12      NA BREAK    <NA>   <NA>  \r\n  13       5 mismatch blue   purple\r\n  14       2 match    green  green\r\n\r\nWhat about after 3 trials, where the number of trials (10) is not divisibly by 3? Can we still use a matrix?\r\nYes, you’d just need to explicitly fill in the “blanks”!\r\nConceptually, we want a matrix like this, where extra “cells” are padded with 0s (recall that 0s are ignored in slice()):\r\n\r\n\r\nmatrix(c(1:10, rep(0, 3 - 10 %% 3)), nrow = 3)\r\n\r\n       [,1] [,2] [,3] [,4]\r\n  [1,]    1    4    7   10\r\n  [2,]    2    5    8    0\r\n  [3,]    3    6    9    0\r\n\r\nAnd this is how that could be implemented inside slice(), minding the fact that adding the break trial increases original row count by 1:\r\n\r\n\r\nshuffled_stroop_trials |> \r\n  add_row(trial = \"BREAK\") |> \r\n  slice(\r\n    c(seq_len(n()-1), rep(0, 3 - (n()-1) %% 3)) |> \r\n      matrix(nrow = 3) |> \r\n      rbind(n()) |> \r\n      as.integer()\r\n  ) |> \r\n  slice(-n())\r\n\r\n  # A tibble: 13 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       5 match    blue   blue  \r\n   3       2 mismatch green  red   \r\n   4      NA BREAK    <NA>   <NA>  \r\n   5       4 match    brown  brown \r\n   6       3 mismatch purple green \r\n   7       1 match    red    red   \r\n   8      NA BREAK    <NA>   <NA>  \r\n   9       4 mismatch brown  blue  \r\n  10       3 match    purple purple\r\n  11       5 mismatch blue   purple\r\n  12      NA BREAK    <NA>   <NA>  \r\n  13       2 match    green  green\r\n\r\nHow about inserting a break trial after every \"purple\" word trials?\r\nConceptually, we want a matrix that binds these two vectors as rows before collapsing:\r\n\r\n\r\nprint( 1:nrow(shuffled_stroop_trials) )\r\nprint(\r\n  replace(rep(0, nrow(shuffled_stroop_trials)),\r\n          which(shuffled_stroop_trials$word == \"purple\"), 11)\r\n)\r\n\r\n   [1]  1  2  3  4  5  6  7  8  9 10\r\n   [1]  0  0  0  0 11  0  0 11  0  0\r\n\r\nAnd this is how you could do that inside slice():\r\n\r\n\r\nshuffled_stroop_trials |> \r\n  add_row(trial = \"BREAK\") |> \r\n  slice(\r\n    c(seq_len(n()-1), replace(rep(0, n()-1), which(word == \"purple\"), n())) |>\r\n      matrix(nrow = 2, byrow = TRUE) |> \r\n      as.integer()\r\n  )\r\n\r\n  # A tibble: 12 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       5 match    blue   blue  \r\n   3       2 mismatch green  red   \r\n   4       4 match    brown  brown \r\n   5       3 mismatch purple green \r\n   6      NA BREAK    <NA>   <NA>  \r\n   7       1 match    red    red   \r\n   8       4 mismatch brown  blue  \r\n   9       3 match    purple purple\r\n  10      NA BREAK    <NA>   <NA>  \r\n  11       5 mismatch blue   purple\r\n  12       2 match    green  green\r\n\r\nYou might protest that this is a pretty convoluted approach to a seemingly simple problem of inserting rows, and you’d be right!2 Not only is the code difficult to read, you can only insert the same single row over and over.\r\nIt turns out that these cases of row insertion actually fall under the broader class of interweaving unequal categories - let’s see this next.\r\nEvenly distributed row shuffling of unequal categories\r\nLet’s return to our solution for the initial “break every 2 trials” problem:\r\n\r\n\r\nshuffled_stroop_trials |> \r\n  add_row(trial = \"BREAK\") |> \r\n  slice(\r\n    matrix(row_number()[-n()], nrow = 2) |> \r\n      rbind(n()) |> \r\n      as.integer()\r\n  ) |> \r\n  slice(-n())\r\n\r\n  # A tibble: 14 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       5 match    blue   blue  \r\n   3      NA BREAK    <NA>   <NA>  \r\n   4       2 mismatch green  red   \r\n   5       4 match    brown  brown \r\n   6      NA BREAK    <NA>   <NA>  \r\n   7       3 mismatch purple green \r\n   8       1 match    red    red   \r\n   9      NA BREAK    <NA>   <NA>  \r\n  10       4 mismatch brown  blue  \r\n  11       3 match    purple purple\r\n  12      NA BREAK    <NA>   <NA>  \r\n  13       5 mismatch blue   purple\r\n  14       2 match    green  green\r\n\r\nHere, we were working with a matrix that looks like this, where 11 represents the new row we added representing a break trial:\r\n\r\n       [,1] [,2] [,3] [,4] [,5]\r\n  [1,]    1    3    5    7    9\r\n  [2,]    2    4    6    8   10\r\n  [3,]   11   11   11   11   11\r\n\r\nAnd recall that to insert every 3 rows, we needed to pad with 0 first to satisfy the matrix’s rectangle constraint:\r\n\r\n       [,1] [,2] [,3] [,4]\r\n  [1,]    1    4    7   10\r\n  [2,]    2    5    8    0\r\n  [3,]    3    6    9    0\r\n  [4,]   11   11   11   11\r\n\r\nBut a better way of thinking about this is to have one matrix row representing all row indices, and then add a sparse row that represent breaks:\r\nBreak after every 2 trials:\r\n\r\n\r\nmatrix(c(1:10, rep_len(c(0, 11), 10)), nrow = 2, byrow = TRUE)\r\n\r\n       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]\r\n  [1,]    1    2    3    4    5    6    7    8    9    10\r\n  [2,]    0   11    0   11    0   11    0   11    0    11\r\n\r\nBreak after every 3 trials:\r\n\r\n\r\nmatrix(c(1:10, rep_len(c(0, 0, 11), 10)), nrow = 2, byrow = TRUE)\r\n\r\n       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]\r\n  [1,]    1    2    3    4    5    6    7    8    9    10\r\n  [2,]    0    0   11    0    0   11    0    0   11     0\r\n\r\nBreak after every 4 trials:\r\n\r\n\r\nmatrix(c(1:10, rep_len(c(0, 0, 0, 11), 10)), nrow = 2, byrow = TRUE)\r\n\r\n       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]\r\n  [1,]    1    2    3    4    5    6    7    8    9    10\r\n  [2,]    0    0    0   11    0    0    0   11    0     0\r\n\r\nAnd it turns out that this method generalizes to balanced shuffling across categories that are not equal in size!\r\nLet’s start with a really basic example - here we have three kinds of fruits with varying counts:\r\n\r\n\r\nfruits <- c(\"🍎\", \"🍋\", \"🍇\")[c(2,1,3,3,2,3,1,2,2,1,2,2,3,3,3)]\r\nfruits <- factor(fruits, levels = c(\"🍇\", \"🍋\", \"🍎\"))\r\ntable(fruits)\r\n\r\n  fruits\r\n  🍇 🍋 🍎 \r\n   6  6  3\r\n\r\nTheir current order looks like this:\r\n\r\n\r\ncat(levels(fruits)[fruits])\r\n\r\n  🍋 🍎 🍇 🍇 🍋 🍇 🍎 🍋 🍋 🍎 🍋 🍋 🍇 🍇 🍇\r\n\r\nBut I want them to be ordered such that individuals of the same fruit kind are maximally apart from one another. This effectively re-orders the fruits to be distributed “evenly”:\r\n\r\n\r\ncat(levels(fruits)[fruits[c(3,1,2,4,5,0,6,8,10,13,9,0,14,11,7,15,12,0)]])\r\n\r\n  🍇 🍋 🍎 🍇 🍋 🍇 🍋 🍎 🍇 🍋 🍇 🍋 🍎 🍇 🍋\r\n\r\nWith our “build row-wise, collapse col-wise” approach, this takes the following steps:\r\nFind the most frequent category - that N-max becomes the number of columns in the matrix of row indices.\r\nIn this case it’s grapes and lemons, of which there are 6 each:\r\n\r\n\r\ngrape_rows <- which(fruits == \"🍇\")\r\n setNames(grape_rows, rep(\"🍇\", 6))\r\n\r\n  🍇 🍇 🍇 🍇 🍇 🍇 \r\n   3  4  6 13 14 15\r\n\r\n\r\n\r\nlemon_rows <- which(fruits == \"🍋\")\r\n setNames(lemon_rows, rep(\"🍋\", 6))\r\n\r\n  🍋 🍋 🍋 🍋 🍋 🍋 \r\n   1  5  8  9 11 12\r\n\r\nNormalize (“stretch”) all vectors to have the same length as N.\r\nIn this case we need to stretch the apples vector, which is currently only length-3:\r\n\r\n\r\napple_rows <- which(fruits == \"🍎\")\r\n apple_rows\r\n\r\n  [1]  2  7 10\r\n\r\nThe desired “sparse” representation is something like this, where each instance of apple is equidistant, with 0s in between:\r\n\r\n\r\napple_rows_sparse <- c(2, 0, 7, 0, 10, 0)\r\n setNames(apple_rows_sparse, c(\"🍎\", \"\", \"🍎\", \"\", \"🍎\", \"\"))\r\n\r\n  🍎    🍎    🍎    \r\n   2  0  7  0 10  0\r\n\r\nThere are many ways to get at this, but one trick involves creating an evenly spaced float sequence from 1 to N-apple over N-max steps:\r\n\r\n\r\nseq(1, 3, length.out = 6)\r\n\r\n  [1] 1.0 1.4 1.8 2.2 2.6 3.0\r\n\r\nFrom there, we round the numbers:\r\n\r\n\r\nround(seq(1, 3, length.out = 6))\r\n\r\n  [1] 1 1 2 2 3 3\r\n\r\nThen mark the first occurance of each number using !duplicated():\r\n\r\n\r\n!duplicated(round(seq(1, 3, length.out = 6)))\r\n\r\n  [1]  TRUE FALSE  TRUE FALSE  TRUE FALSE\r\n\r\nAnd lastly, we initialize a vector of 0s and replace() the TRUEs with apple indices:\r\n\r\n\r\nreplace(\r\n   rep(0, 6),\r\n   !duplicated(round(seq(1, 3, length.out = 6))),\r\n   which(fruits == \"🍎\")\r\n )\r\n\r\n  [1]  2  0  7  0 10  0\r\n\r\nStack up the category vectors by row and collapse column-wise:\r\nManually, we would build the full matrix row-by-row like this:\r\n\r\n\r\nfruits_matrix <- matrix(\r\n   c(grape_rows, lemon_rows, apple_rows_sparse),\r\n   nrow = 3, byrow = TRUE\r\n )\r\n rownames(fruits_matrix) <- c(\"🍇\", \"🍋\", \"🍎\")\r\n fruits_matrix\r\n\r\n     [,1] [,2] [,3] [,4] [,5] [,6]\r\n  🍇    3    4    6   13   14   15\r\n  🍋    1    5    8    9   11   12\r\n  🍎    2    0    7    0   10    0\r\n\r\nAnd dynamically we can use sapply() to fill the matrix column-by-column, and then t()-ing the output:\r\n\r\n\r\nfruits_distributed <- sapply(levels(fruits), \\(x) {\r\n   n_max <- max(table(fruits))\r\n   ind <- which(fruits == x)\r\n   nums <- seq(1, length(ind), length.out = n_max)\r\n   replace(rep(0, n_max), !duplicated(round(nums)), ind)\r\n }) |> \r\n   t()\r\n fruits_distributed\r\n\r\n     [,1] [,2] [,3] [,4] [,5] [,6]\r\n  🍇    3    4    6   13   14   15\r\n  🍋    1    5    8    9   11   12\r\n  🍎    2    0    7    0   10    0\r\n\r\nFinally, we collapse the vector and we see that it indeed distributed the fruits evenly!\r\n\r\n\r\nfruits[as.integer(fruits_distributed)]\r\n\r\n   [1] 🍇 🍋 🍎 🍇 🍋 🍇 🍋 🍎 🍇 🍋 🍇 🍋 🍎 🍇 🍋\r\n  Levels: 🍇 🍋 🍎\r\n\r\nWe can go even further and wrap the dynamic, sapply()-based solution into a function for use within slice(). Here, I also added an optional argument for shuffling within categories:\r\n\r\n\r\nrshuffle <- function(x, shuffle_within = FALSE) {\r\n  categories <- as.factor(x)\r\n  n_max <- max(table(categories))\r\n  sapply(levels(categories), \\(lvl) {\r\n    ind <- which(categories == lvl)\r\n    if (shuffle_within) ind <- sample(ind)\r\n    nums <- seq(1, length(ind), length.out = n_max)\r\n    replace(rep(0, n_max), !duplicated(round(nums)), ind)\r\n  }) |> \r\n    t() |> \r\n    as.integer()\r\n}\r\n\r\n\r\nReturning back to our Stroop experiment template example, imagine we also had two filler trials, where no word is shown and just the color flashes on the screen:\r\n\r\n\r\nstroop_fillers <- tibble(\r\n  item_id = 1:2,\r\n  trial = \"filler\",\r\n  word = NA,\r\n  color = c(\"red\", \"blue\")\r\n)\r\nstroop_with_fillers <- bind_rows(stroop_fillers, stroop_trials) |> \r\n  mutate(trial = factor(trial, c(\"match\", \"mismatch\", \"filler\")))\r\nstroop_with_fillers\r\n\r\n  # A tibble: 12 × 4\r\n     item_id trial    word   color \r\n       <int> <fct>    <chr>  <chr> \r\n   1       1 filler   <NA>   red   \r\n   2       2 filler   <NA>   blue  \r\n   3       1 mismatch red    brown \r\n   4       2 mismatch green  red   \r\n   5       3 mismatch purple green \r\n   6       4 mismatch brown  blue  \r\n   7       5 mismatch blue   purple\r\n   8       1 match    red    red   \r\n   9       2 match    green  green \r\n  10       3 match    purple purple\r\n  11       4 match    brown  brown \r\n  12       5 match    blue   blue\r\n\r\nWe can evenly shuffle between the unequal trial types with our new rshuffle() function:\r\n\r\n\r\nstroop_with_fillers |> \r\n  slice( rshuffle(trial, shuffle_within = TRUE) )\r\n\r\n  # A tibble: 12 × 4\r\n     item_id trial    word   color \r\n       <int> <fct>    <chr>  <chr> \r\n   1       2 match    green  green \r\n   2       2 mismatch green  red   \r\n   3       1 filler   <NA>   red   \r\n   4       1 match    red    red   \r\n   5       4 mismatch brown  blue  \r\n   6       3 match    purple purple\r\n   7       3 mismatch purple green \r\n   8       2 filler   <NA>   blue  \r\n   9       4 match    brown  brown \r\n  10       5 mismatch blue   purple\r\n  11       5 match    blue   blue  \r\n  12       1 mismatch red    brown\r\n\r\nConclusion\r\nWhen I started drafting this blog post, I thought I’d come with a principled taxonomy of row-relational operations. Ha. This was a lot trickier to think through than I thought.\r\nBut I hope that this gallery of esoteric use-cases for slice() inspires you to use it more, and to think about “tidy” solutions to seemingly “untidy” problems.\r\n\r\nThe .by_group = TRUE is not strictly necessary here, but it’s good for visually inspecting the within-group ordering.↩︎\r\nAlthough row insertion is a generally tricky problem for column-major data frame structures, which is partly why dplyr’s row manipulation verbs have stayed experimental for quite some time.↩︎\r\n",
+    "preview": "posts/2023-06-11-row-relational-operations/preview.png",
+    "last_modified": "2024-09-22T19:50:35-04:00",
+    "input_file": "row-relational-operations.knit.md",
+    "preview_width": 1800,
+    "preview_height": 1080
+  },
   {
     "path": "posts/2024-07-21-enumerate-possible-options/",
     "title": "Naming patterns for boolean enums",
@@ -166,28 +188,6 @@
     "preview_width": 238,
     "preview_height": 205
   },
-  {
-    "path": "posts/2023-06-11-row-relational-operations/",
-    "title": "Row relational operations with slice()",
-    "description": "A love letter to dplyr::slice() and a gallery of usecases",
-    "author": [
-      {
-        "name": "June Choe",
-        "url": {}
-      }
-    ],
-    "date": "2023-06-11",
-    "categories": [
-      "data wrangling",
-      "dplyr"
-    ],
-    "contents": "\r\n\r\nContents\r\nIntro\r\nSpecial properties of dplyr::slice()\r\nBasic usage\r\nRe-imagining slice() with data-masking\r\nSpecial properties of slice()\r\n\r\nA gallery of row operations with slice()\r\nRepeat rows (in place)\r\nSubset a selection of rows + the following row\r\nSubset a selection of rows + multiple following rows\r\nFilter (and encode) neighboring rows\r\nWindowed min/max/median (etc.)\r\nEvenly distributed row shuffling of balanced categories\r\nInserting a new row at specific intervals\r\nEvenly distributed row shuffling of unequal categories\r\n\r\nConclusion\r\n\r\nIntro\r\nIn data wrangling, there are a handful of classes of operations on data frames that we think of as theoretically well-defined and tackling distinct problems. To name a few, these include subsetting, joins, split-apply-combine, pairwise operations, nested-column workflows, and so on.\r\nAgainst this rich backdrop, there’s one aspect of data wrangling that doesn’t receive as much attention: ordering of rows. This isn’t necessarily surprising - we often think of row order as an auxiliary attribute of data frames since they don’t speak to the content of the data, per se. I think we all share the intuition that two dataframe that differ only in row order are practically the same for most analysis purposes.\r\nExcept when they aren’t.\r\nIn this blog post I want to talk about a few, somewhat esoteric cases of what I like to call row-relational operations. My goal is to try to motivate row-relational operations as a full-blown class of data wrangling operation that includes not only row ordering, but also sampling, shuffling, repeating, interweaving, and so on (I’ll go over all of these later).\r\nWithout spoiling too much, I believe that dplyr::slice() offers a powerful context for operations over row indices, even those that at first seem to lack a “tidy” solution. You may already know slice() as an indexing function, but my hope is to convince you that it can do so much more.\r\nLet’s start by first talking about some special properties of dplyr::slice(), and then see how we can use it for various row-relational operations.\r\nSpecial properties of dplyr::slice()\r\nBasic usage\r\nFor the following demonstration, I’ll use a small subset of the dplyr::starwars dataset:\r\n\r\n\r\nstarwars_sm <- dplyr::starwars[1:10, 1:3]\r\nstarwars_sm\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 Luke Skywalker        172    77\r\n   2 C-3PO                 167    75\r\n   3 R2-D2                  96    32\r\n   4 Darth Vader           202   136\r\n   5 Leia Organa           150    49\r\n   6 Owen Lars             178   120\r\n   7 Beru Whitesun lars    165    75\r\n   8 R5-D4                  97    32\r\n   9 Biggs Darklighter     183    84\r\n  10 Obi-Wan Kenobi        182    77\r\n\r\n1) Row selection\r\nslice() is a row indexing verb - if you pass it a vector of integers, it subsets data frame rows:\r\n\r\n\r\nstarwars_sm |> \r\n  slice(1:6) # First six rows\r\n\r\n  # A tibble: 6 × 3\r\n    name           height  mass\r\n    <chr>           <int> <dbl>\r\n  1 Luke Skywalker    172    77\r\n  2 C-3PO             167    75\r\n  3 R2-D2              96    32\r\n  4 Darth Vader       202   136\r\n  5 Leia Organa       150    49\r\n  6 Owen Lars         178   120\r\n\r\nLike other dplyr verbs with mutate-semantics, you can use context-dependent expressions inside slice(). For example, you can use n() to grab the last row (or last couple of rows):\r\n\r\n\r\nstarwars_sm |> \r\n  slice( n() ) # Last row\r\n\r\n  # A tibble: 1 × 3\r\n    name           height  mass\r\n    <chr>           <int> <dbl>\r\n  1 Obi-Wan Kenobi    182    77\r\n\r\nstarwars_sm |> \r\n  slice( n() - 2:0 ) # Last three rows\r\n\r\n  # A tibble: 3 × 3\r\n    name              height  mass\r\n    <chr>              <int> <dbl>\r\n  1 R5-D4                 97    32\r\n  2 Biggs Darklighter    183    84\r\n  3 Obi-Wan Kenobi       182    77\r\n\r\nAnother context-dependent expression that comes in handy is row_number(), which returns all row indices. Using it inside slice() essentially performs an identity transformation:\r\n\r\n\r\nidentical(\r\n  starwars_sm,\r\n  starwars_sm |> slice( row_number() )\r\n)\r\n\r\n  [1] TRUE\r\n\r\nLastly, similar to in select(), you can use - for negative indexing (to remove rows):\r\n\r\n\r\nidentical(\r\n  starwars_sm |> slice(1:3),      # First three rows\r\n  starwars_sm |> slice(-(4:n()))  # All rows except fourth row to last row\r\n)\r\n\r\n  [1] TRUE\r\n\r\n2) Dynamic dots\r\nslice() supports dynamic dots. If you pass row indices into multiple argument positions, slice() will concatenate them for you:\r\n\r\n\r\nidentical(\r\n  starwars_sm |> slice(1:6),\r\n  starwars_sm |> slice(1, 2:4, 5, 6)\r\n)\r\n\r\n  [1] TRUE\r\n\r\nIf you have a list() of row indices, you can use the splice operator !!! to spread them out:\r\n\r\n\r\nstarwars_sm |> \r\n  slice( !!!list(1, 2:4, 5, 6) )\r\n\r\n  # A tibble: 6 × 3\r\n    name           height  mass\r\n    <chr>           <int> <dbl>\r\n  1 Luke Skywalker    172    77\r\n  2 C-3PO             167    75\r\n  3 R2-D2              96    32\r\n  4 Darth Vader       202   136\r\n  5 Leia Organa       150    49\r\n  6 Owen Lars         178   120\r\n\r\nThe above call to slice() evaluates to the following after splicing:\r\n\r\n\r\nrlang::expr( slice(!!!list(1, 2:4, 5, 6)) )\r\n\r\n  slice(1, 2:4, 5, 6)\r\n\r\n3) Row ordering\r\nslice() respects the order in which you supplied the row indices:\r\n\r\n\r\nstarwars_sm |> \r\n  slice(3, 1, 2, 5)\r\n\r\n  # A tibble: 4 × 3\r\n    name           height  mass\r\n    <chr>           <int> <dbl>\r\n  1 R2-D2              96    32\r\n  2 Luke Skywalker    172    77\r\n  3 C-3PO             167    75\r\n  4 Leia Organa       150    49\r\n\r\nThis means you can do stuff like random sampling with sample():\r\n\r\n\r\nstarwars_sm |> \r\n  slice( sample(n()) )\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 Obi-Wan Kenobi        182    77\r\n   2 Owen Lars             178   120\r\n   3 Leia Organa           150    49\r\n   4 Darth Vader           202   136\r\n   5 Luke Skywalker        172    77\r\n   6 R5-D4                  97    32\r\n   7 C-3PO                 167    75\r\n   8 Beru Whitesun lars    165    75\r\n   9 Biggs Darklighter     183    84\r\n  10 R2-D2                  96    32\r\n\r\nYou can also shuffle a subset of rows (ex: just the first five):\r\n\r\n\r\nstarwars_sm |> \r\n  slice( sample(5), 6:n() )\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 C-3PO                 167    75\r\n   2 Leia Organa           150    49\r\n   3 R2-D2                  96    32\r\n   4 Darth Vader           202   136\r\n   5 Luke Skywalker        172    77\r\n   6 Owen Lars             178   120\r\n   7 Beru Whitesun lars    165    75\r\n   8 R5-D4                  97    32\r\n   9 Biggs Darklighter     183    84\r\n  10 Obi-Wan Kenobi        182    77\r\n\r\nOr reorder all rows by their indices (ex: in reverse):\r\n\r\n\r\nstarwars_sm |> \r\n  slice( rev(row_number()) )\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 Obi-Wan Kenobi        182    77\r\n   2 Biggs Darklighter     183    84\r\n   3 R5-D4                  97    32\r\n   4 Beru Whitesun lars    165    75\r\n   5 Owen Lars             178   120\r\n   6 Leia Organa           150    49\r\n   7 Darth Vader           202   136\r\n   8 R2-D2                  96    32\r\n   9 C-3PO                 167    75\r\n  10 Luke Skywalker        172    77\r\n\r\n4) Out-of-bounds handling\r\nIf you pass a row index that’s out of bounds, slice() returns a 0-row data frame:\r\n\r\n\r\nstarwars_sm |> \r\n  slice( n() + 1 ) # Select the row after the last row\r\n\r\n  # A tibble: 0 × 3\r\n  # ℹ 3 variables: name <chr>, height <int>, mass <dbl>\r\n\r\nWhen mixed with valid row indices, out-of-bounds indices are simply ignored (much 💜 for this behavior):\r\n\r\n\r\nstarwars_sm |> \r\n  slice(\r\n    0,       # 0th row - ignored\r\n    1:3,     # first three rows\r\n    n() + 1  # 1 after last row - ignored\r\n  )\r\n\r\n  # A tibble: 3 × 3\r\n    name           height  mass\r\n    <chr>           <int> <dbl>\r\n  1 Luke Skywalker    172    77\r\n  2 C-3PO             167    75\r\n  3 R2-D2              96    32\r\n\r\nThis lets you do funky stuff like select all even numbered rows by passing slice() all row indices times 2:\r\n\r\n\r\nstarwars_sm |> \r\n  slice( row_number() * 2 ) # Add `- 1` at the end for *odd* rows!\r\n\r\n  # A tibble: 5 × 3\r\n    name           height  mass\r\n    <chr>           <int> <dbl>\r\n  1 C-3PO             167    75\r\n  2 Darth Vader       202   136\r\n  3 Owen Lars         178   120\r\n  4 R5-D4              97    32\r\n  5 Obi-Wan Kenobi    182    77\r\n\r\nRe-imagining slice() with data-masking\r\nslice() is already pretty neat as it is, but that’s just the tip of the iceberg.\r\nThe really cool, under-rated feature of slice() is that it’s data-masked, meaning that you can reference column vectors as if they’re variables. Another way of describing this property of slice() is to say that it has mutate-semantics.\r\nAt a very basic level, this means that slice() can straightforwardly replicate the behavior of some dplyr verbs like arrange() and filter()!\r\nslice() as arrange()\r\nFrom our starwars_sm data, if we want to sort by height we can use arrange():\r\n\r\n\r\nstarwars_sm |> \r\n  arrange(height)\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 R2-D2                  96    32\r\n   2 R5-D4                  97    32\r\n   3 Leia Organa           150    49\r\n   4 Beru Whitesun lars    165    75\r\n   5 C-3PO                 167    75\r\n   6 Luke Skywalker        172    77\r\n   7 Owen Lars             178   120\r\n   8 Obi-Wan Kenobi        182    77\r\n   9 Biggs Darklighter     183    84\r\n  10 Darth Vader           202   136\r\n\r\nBut we can also do this with slice() to the same effect, using order():\r\n\r\n\r\nstarwars_sm |> \r\n  slice( order(height) )\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 R2-D2                  96    32\r\n   2 R5-D4                  97    32\r\n   3 Leia Organa           150    49\r\n   4 Beru Whitesun lars    165    75\r\n   5 C-3PO                 167    75\r\n   6 Luke Skywalker        172    77\r\n   7 Owen Lars             178   120\r\n   8 Obi-Wan Kenobi        182    77\r\n   9 Biggs Darklighter     183    84\r\n  10 Darth Vader           202   136\r\n\r\nThis is conceptually equivalent to combining the following 2-step process:\r\n\r\n\r\nordered_val_ind <- order(starwars_sm$height)\r\n  ordered_val_ind\r\n\r\n   [1]  3  8  5  7  2  1  6 10  9  4\r\n\r\n\r\n\r\nstarwars_sm |> \r\n    slice( ordered_val_ind )\r\n\r\n  # A tibble: 10 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 R2-D2                  96    32\r\n   2 R5-D4                  97    32\r\n   3 Leia Organa           150    49\r\n   4 Beru Whitesun lars    165    75\r\n   5 C-3PO                 167    75\r\n   6 Luke Skywalker        172    77\r\n   7 Owen Lars             178   120\r\n   8 Obi-Wan Kenobi        182    77\r\n   9 Biggs Darklighter     183    84\r\n  10 Darth Vader           202   136\r\n\r\nslice() as filter()\r\nWe can also use slice() to filter(), using which():\r\n\r\n\r\nidentical(\r\n  starwars_sm |> filter( height > 150 ),\r\n  starwars_sm |> slice( which(height > 150) )\r\n)\r\n\r\n  [1] TRUE\r\n\r\nThus, we can think of filter() and slice() as two sides of the same coin:\r\nfilter() takes a logical vector that’s the same length as the number of rows in the data frame\r\nslice() takes an integer vector that’s a (sub)set of a data frame’s row indices.\r\nTo put it more concretely, this logical vector was being passed to the above filter() call:\r\n\r\n\r\nstarwars_sm$height > 150\r\n\r\n   [1]  TRUE  TRUE FALSE  TRUE FALSE  TRUE  TRUE FALSE  TRUE  TRUE\r\n\r\nWhile this integer vector was being passed to the above slice() call, where which() returns the position of TRUE values, given a logical vector:\r\n\r\n\r\nwhich( starwars_sm$height > 150 )\r\n\r\n  [1]  1  2  4  6  7  9 10\r\n\r\nSpecial properties of slice()\r\nThis re-imagined slice() that heavily exploits data-masking gives us two interesting properties:\r\nWe can work with sets of row indices that need not to be the same length as the data frame (vs. filter()).\r\nWe can work with row indices as integers, which are legible to arithmetic operations (ex: + and *)\r\nTo grok the significance of working with rows as integer sets, let’s work through some examples where slice() comes in very handy.\r\nA gallery of row operations with slice()\r\nRepeat rows (in place)\r\nIn {tidyr}, there’s a function called uncount() which does the opposite of dplyr::count():\r\n\r\n\r\nlibrary(tidyr)\r\n# Example from `tidyr::uncount()` docs\r\nuncount_df <- tibble(x = c(\"a\", \"b\"), n = c(1, 2))\r\nuncount_df\r\n\r\n  # A tibble: 2 × 2\r\n    x         n\r\n    <chr> <dbl>\r\n  1 a         1\r\n  2 b         2\r\n\r\nuncount_df |> \r\n  uncount(n)\r\n\r\n  # A tibble: 3 × 1\r\n    x    \r\n    <chr>\r\n  1 a    \r\n  2 b    \r\n  3 b\r\n\r\nWe can mimic this behavior with slice(), using rep(times = ...):\r\n\r\n\r\nrep(1:nrow(uncount_df), times = uncount_df$n)\r\n\r\n  [1] 1 2 2\r\n\r\nuncount_df |> \r\n  slice( rep(row_number(), times = n) ) |> \r\n  select( -n )\r\n\r\n  # A tibble: 3 × 1\r\n    x    \r\n    <chr>\r\n  1 a    \r\n  2 b    \r\n  3 b\r\n\r\nWhat if instead of a whole column storing that information, we only have information about row position?\r\nLet’s say we want to duplicate the rows of starwars_sm at the repeat_at positions:\r\n\r\n\r\nrepeat_at <- sample(5, 2)\r\nrepeat_at\r\n\r\n  [1] 4 5\r\n\r\nIn slice(), you’d just select all rows plus those additional rows, then sort the integer row indices:\r\n\r\n\r\nstarwars_sm |> \r\n  slice( sort(c(row_number(), repeat_at)) )\r\n\r\n  # A tibble: 12 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 Luke Skywalker        172    77\r\n   2 C-3PO                 167    75\r\n   3 R2-D2                  96    32\r\n   4 Darth Vader           202   136\r\n   5 Darth Vader           202   136\r\n   6 Leia Organa           150    49\r\n   7 Leia Organa           150    49\r\n   8 Owen Lars             178   120\r\n   9 Beru Whitesun lars    165    75\r\n  10 R5-D4                  97    32\r\n  11 Biggs Darklighter     183    84\r\n  12 Obi-Wan Kenobi        182    77\r\n\r\nWhat if we also separately have information about how much to repeat those rows by?\r\n\r\n\r\nrepeat_by <- c(3, 4)\r\n\r\n\r\nYou can apply the same rep() method for just the subset of rows to repeat:\r\n\r\n\r\nstarwars_sm |> \r\n  slice( sort(c(row_number(), rep(repeat_at, times = repeat_by - 1))) )\r\n\r\n  # A tibble: 15 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 Luke Skywalker        172    77\r\n   2 C-3PO                 167    75\r\n   3 R2-D2                  96    32\r\n   4 Darth Vader           202   136\r\n   5 Darth Vader           202   136\r\n   6 Darth Vader           202   136\r\n   7 Leia Organa           150    49\r\n   8 Leia Organa           150    49\r\n   9 Leia Organa           150    49\r\n  10 Leia Organa           150    49\r\n  11 Owen Lars             178   120\r\n  12 Beru Whitesun lars    165    75\r\n  13 R5-D4                  97    32\r\n  14 Biggs Darklighter     183    84\r\n  15 Obi-Wan Kenobi        182    77\r\n\r\nCircling back to uncount(), you could also initialize a vector of 1s and replace() where the rows should be repeated:\r\n\r\n\r\nstarwars_sm |> \r\n  uncount( replace(rep(1, n()), repeat_at, repeat_by) )\r\n\r\n  # A tibble: 15 × 3\r\n     name               height  mass\r\n     <chr>               <int> <dbl>\r\n   1 Luke Skywalker        172    77\r\n   2 C-3PO                 167    75\r\n   3 R2-D2                  96    32\r\n   4 Darth Vader           202   136\r\n   5 Darth Vader           202   136\r\n   6 Darth Vader           202   136\r\n   7 Leia Organa           150    49\r\n   8 Leia Organa           150    49\r\n   9 Leia Organa           150    49\r\n  10 Leia Organa           150    49\r\n  11 Owen Lars             178   120\r\n  12 Beru Whitesun lars    165    75\r\n  13 R5-D4                  97    32\r\n  14 Biggs Darklighter     183    84\r\n  15 Obi-Wan Kenobi        182    77\r\n\r\nSubset a selection of rows + the following row\r\nRow order can sometimes encode a meaningful continuous measure, like time.\r\nTake for example this subset of the flights dataset in {nycflights13}:\r\n\r\n\r\nflights_df <- nycflights13::flights |> \r\n  filter(month == 3, day == 3, origin == \"JFK\") |> \r\n  select(dep_time, flight, carrier) |> \r\n  slice(1:100) |> \r\n  arrange(dep_time)\r\nflights_df\r\n\r\n  # A tibble: 100 × 3\r\n     dep_time flight carrier\r\n        <int>  <int> <chr>  \r\n   1      535   1141 AA     \r\n   2      551   5716 EV     \r\n   3      555    145 B6     \r\n   4      556    208 B6     \r\n   5      556     79 B6     \r\n   6      601    501 B6     \r\n   7      604    725 B6     \r\n   8      606    135 B6     \r\n   9      606    600 UA     \r\n  10      607    829 US     \r\n  # ℹ 90 more rows\r\n\r\nHere, the rows are ordered by dep_time, such that given a row, the next row is a data point for the next flight that departed from the airport.\r\nAnd let’s say we’re interested in flights that took off immediately after American Airlines (\"AA\") flights. Given what we just noted about the ordering of rows in the data frame, we can do this in slice() by adding 1 to the row index of AA flights:\r\n\r\n\r\nflights_df |> \r\n  slice( which(carrier == \"AA\") + 1 )\r\n\r\n  # A tibble: 14 × 3\r\n     dep_time flight carrier\r\n        <int>  <int> <chr>  \r\n   1      551   5716 EV     \r\n   2      627    905 B6     \r\n   3      652    117 B6     \r\n   4      714    825 AA     \r\n   5      717    987 B6     \r\n   6      724     11 VX     \r\n   7      742    183 DL     \r\n   8      802    655 AA     \r\n   9      805   2143 DL     \r\n  10      847     59 B6     \r\n  11      858    647 AA     \r\n  12      859    120 DL     \r\n  13     1031    179 AA     \r\n  14     1036    641 B6\r\n\r\nWhat if we also want to keep observations for the preceding AA flights as well? We can just stick which(carrier == \"AA\") inside slice() too:\r\n\r\n\r\nflights_df |> \r\n  slice(\r\n    which(carrier == \"AA\"),\r\n    which(carrier == \"AA\") + 1\r\n  )\r\n\r\n  # A tibble: 28 × 3\r\n     dep_time flight carrier\r\n        <int>  <int> <chr>  \r\n   1      535   1141 AA     \r\n   2      626    413 AA     \r\n   3      652   1815 AA     \r\n   4      711    443 AA     \r\n   5      714    825 AA     \r\n   6      724     33 AA     \r\n   7      739     59 AA     \r\n   8      802   1838 AA     \r\n   9      802    655 AA     \r\n  10      843   1357 AA     \r\n  # ℹ 18 more rows\r\n\r\nBut now the rows are now ordered such that all the AA flights come before the other flights! How can we preserve the original order of increasing dep_time?\r\nWe could reconstruct the initial row order by piping the result into arrange(dep_time) again, but the simplest solution would be to concatenate the set of row indices and sort() them, since the output of which() is already integer!\r\n\r\n\r\nflights_df |> \r\n  slice(\r\n    sort(c(\r\n      which(carrier == \"AA\"),\r\n      which(carrier == \"AA\") + 1\r\n    ))\r\n  )\r\n\r\n  # A tibble: 28 × 3\r\n     dep_time flight carrier\r\n        <int>  <int> <chr>  \r\n   1      535   1141 AA     \r\n   2      551   5716 EV     \r\n   3      626    413 AA     \r\n   4      627    905 B6     \r\n   5      652   1815 AA     \r\n   6      652    117 B6     \r\n   7      711    443 AA     \r\n   8      714    825 AA     \r\n   9      714    825 AA     \r\n  10      717    987 B6     \r\n  # ℹ 18 more rows\r\n\r\nNotice how the 8th and 9th rows are repeated here - that’s because 2 AA flights departed in a row (ha!). We can use unique() to remove duplicate rows in the same call to slice():\r\n\r\n\r\nflights_df |> \r\n  slice(\r\n    unique(sort(c(\r\n      which(carrier == \"AA\"),\r\n      which(carrier == \"AA\") + 1\r\n    )))\r\n  )\r\n\r\n  # A tibble: 24 × 3\r\n     dep_time flight carrier\r\n        <int>  <int> <chr>  \r\n   1      535   1141 AA     \r\n   2      551   5716 EV     \r\n   3      626    413 AA     \r\n   4      627    905 B6     \r\n   5      652   1815 AA     \r\n   6      652    117 B6     \r\n   7      711    443 AA     \r\n   8      714    825 AA     \r\n   9      717    987 B6     \r\n  10      724     33 AA     \r\n  # ℹ 14 more rows\r\n\r\nImportantly, we can do all of this inside slice() because we’re working with integer sets. The integer part allows us to do things like + 1 and sort(), while the set part allows us to combine with c() and remove duplicates with unique().\r\nSubset a selection of rows + multiple following rows\r\nIn this example, let’s problematize our approach with the repeated which() calls in our previous solution.\r\nImagine another scenario where we want to filter for all AA flights and three subsequent flights for each.\r\nDo we need to write the solution out like this? That’s a lot of repetition!\r\n\r\n\r\nflights_df |> \r\n  slice(\r\n    which(carrier == \"AA\"),\r\n    which(carrier == \"AA\") + 1,\r\n    which(carrier == \"AA\") + 2,\r\n    which(carrier == \"AA\") + 3\r\n  )\r\n\r\n\r\nYou might think we can get away with + 0:3, but it doesn’t work as we’d like. The + just forces 0:3 to be (partially) recycled to the same length as carrier for element-wise addition:\r\n\r\n\r\nwhich(flights_df$carrier == \"AA\") + 0:3\r\n\r\n  Warning in which(flights_df$carrier == \"AA\") + 0:3: longer object length is not\r\n  a multiple of shorter object length\r\n   [1]  1 14 20 27 25 28 34 40 38 62 66 68 91 93\r\n\r\nIf only we can get the outer sum of the two arrays, 0:3 and which(carrier == \"AA\") … Oh wait, we can - that’s what outer() does!\r\n\r\n\r\nouter(0:3, which(flights_df$carrier == \"AA\"), `+`)\r\n\r\n       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]\r\n  [1,]    1   13   18   24   25   27   32   37   38    61    64    65    91    92\r\n  [2,]    2   14   19   25   26   28   33   38   39    62    65    66    92    93\r\n  [3,]    3   15   20   26   27   29   34   39   40    63    66    67    93    94\r\n  [4,]    4   16   21   27   28   30   35   40   41    64    67    68    94    95\r\n\r\nThis is essentially the repeated which() vectors stacked on top of each other, but as a matrix:\r\n\r\n\r\nprint( which(flights_df$carrier == \"AA\")     )\r\nprint( which(flights_df$carrier == \"AA\") + 1 )\r\nprint( which(flights_df$carrier == \"AA\") + 2 )\r\nprint( which(flights_df$carrier == \"AA\") + 3 )\r\n\r\n   [1]  1 13 18 24 25 27 32 37 38 61 64 65 91 92\r\n   [1]  2 14 19 25 26 28 33 38 39 62 65 66 92 93\r\n   [1]  3 15 20 26 27 29 34 39 40 63 66 67 93 94\r\n   [1]  4 16 21 27 28 30 35 40 41 64 67 68 94 95\r\n\r\nThe fact that outer() returns all the relevant row indices inside a single matrix is nice because we can collect the indices column-by-column, preserving row order. Matrices, like data frames, are column-major, so coercing a matrix to a vector collapses it column-wise:\r\n\r\n\r\nas.integer( outer(0:3, which(flights_df$carrier == \"AA\"), `+`) )\r\n\r\n   [1]  1  2  3  4 13 14 15 16 18 19 20 21 24 25 26 27 25 26 27 28 27 28 29 30 32\r\n  [26] 33 34 35 37 38 39 40 38 39 40 41 61 62 63 64 64 65 66 67 65 66 67 68 91 92\r\n  [51] 93 94 92 93 94 95\r\n\r\n\r\nOther ways to coerce matrix to vector\r\nThere are two other options for coercing a matrix to vector - c() and as.vector(). I like to stick with as.integer() because that enforces integer type (which makes sense for row indices), and c() can be nice because it’s less to type (although it’s off-label usage):\r\n\r\n\r\n# Not run, but equivalent to `as.integer()` method\r\nas.vector( outer(0:3, which(flights_df$carrier == \"AA\"), `+`) )\r\nc( outer(0:3, which(flights_df$carrier == \"AA\"), `+`) )\r\n\r\n\r\nSomewhat relatedly - and this only works inside the tidy-eval context of slice() - you can get a similar effect of “collapsing” a matrix using the splice operator !!!:\r\n\r\n\r\nseq_matrix <- matrix(1:9, byrow = TRUE, nrow = 3)\r\nas.integer(seq_matrix)\r\n\r\n  [1] 1 4 7 2 5 8 3 6 9\r\n\r\nidentical(\r\n  mtcars |> slice( as.vector(seq_matrix) ),\r\n  mtcars |> slice( !!!seq_matrix )\r\n)\r\n\r\n  [1] TRUE\r\n\r\nHere, the !!!seq_matrix was slotting each individual “cell” as argument to slice():\r\n\r\n\r\nrlang::expr( slice(!!!seq_matrix) )\r\n\r\n  slice(1L, 4L, 7L, 2L, 5L, 8L, 3L, 6L, 9L)\r\n\r\nA big difference in behavior between as.integer() vs. !!! is that the latter works for lists of indices too, by slotting each element of the list as an argument to slice():\r\n\r\n\r\nseq_list <- list(c(1, 4, 7, 2), c(5, 8, 3, 6, 9))\r\nrlang::expr( slice( !!!seq_list ) )\r\n\r\n  slice(c(1, 4, 7, 2), c(5, 8, 3, 6, 9))\r\n\r\nHowever, as you may already know, as.integer() cannot flatten lists:\r\n\r\n\r\nas.integer(seq_list)\r\n\r\n  Error in eval(expr, envir, enclos): 'list' object cannot be coerced to type 'integer'\r\n\r\nNote that as.vector() and c() leaves lists as is, which is another reason to prefer as.integer() for type-checking:\r\n\r\n\r\nidentical(seq_list, as.vector(seq_list))\r\nidentical(seq_list, c(seq_list))\r\n\r\n  [1] TRUE\r\n  [1] TRUE\r\n\r\nFinally, back in our !!!seq_matrix example, we could have applied asplit(MARGIN = 2) to chunk the splicing by matrix column, although the overall effect would be the same:\r\n\r\n\r\nrlang::expr(slice( !!!seq_matrix            ))\r\n\r\n  slice(1L, 4L, 7L, 2L, 5L, 8L, 3L, 6L, 9L)\r\n\r\nrlang::expr(slice( !!!asplit(seq_matrix, 2) ))\r\n\r\n  slice(c(1L, 4L, 7L), c(2L, 5L, 8L), c(3L, 6L, 9L))\r\n\r\nThis lets us ask questions like: Which AA flights departed within 3 flights of another AA flight?\r\n\r\n\r\nflights_df |> \r\n  slice( as.integer( outer(0:3, which(carrier == \"AA\"), `+`) ) ) |> \r\n  filter( carrier == \"AA\", duplicated(flight) ) |> \r\n  distinct(flight, carrier)\r\n\r\n  # A tibble: 6 × 2\r\n    flight carrier\r\n     <int> <chr>  \r\n  1    825 AA     \r\n  2     33 AA     \r\n  3    655 AA     \r\n  4      1 AA     \r\n  5    647 AA     \r\n  6    179 AA\r\n\r\n\r\nSlicing all the way down: Case 1\r\nWith the addition of the .by argument to slice() in dplyr v1.10, we can re-write the above code as three calls to slice() (+ a call to select()):\r\n\r\n\r\nflights_df |> \r\n  slice( as.integer( outer(0:3, which(carrier == \"AA\"), `+`) ) ) |> \r\n  slice( which(carrier == \"AA\" & duplicated(flight)) ) |>  # filter()\r\n  slice( 1, .by = c(flight, carrier) ) |>                  # distinct()\r\n  select(flight, carrier)\r\n\r\n  # A tibble: 6 × 2\r\n    flight carrier\r\n     <int> <chr>  \r\n  1    825 AA     \r\n  2     33 AA     \r\n  3    655 AA     \r\n  4      1 AA     \r\n  5    647 AA     \r\n  6    179 AA\r\n\r\nThe next example will demonstrate another, perhaps more practical usecase for outer() in slice().\r\nFilter (and encode) neighboring rows\r\nLet’s use a subset of the {gapminder} data set for this one. Here, we have data for each European country’s GDP-per-capita by year, between 1992 to 2007:\r\n\r\n\r\ngapminder_df <- gapminder::gapminder |> \r\n  left_join(gapminder::country_codes, by = \"country\") |>  # `multiple = \"all\"`\r\n  filter(year >= 1992, continent == \"Europe\") |> \r\n  select(country, country_code = iso_alpha, year, gdpPercap)\r\ngapminder_df\r\n\r\n  # A tibble: 120 × 4\r\n     country country_code  year gdpPercap\r\n     <chr>   <chr>        <int>     <dbl>\r\n   1 Albania ALB           1992     2497.\r\n   2 Albania ALB           1997     3193.\r\n   3 Albania ALB           2002     4604.\r\n   4 Albania ALB           2007     5937.\r\n   5 Austria AUT           1992    27042.\r\n   6 Austria AUT           1997    29096.\r\n   7 Austria AUT           2002    32418.\r\n   8 Austria AUT           2007    36126.\r\n   9 Belgium BEL           1992    25576.\r\n  10 Belgium BEL           1997    27561.\r\n  # ℹ 110 more rows\r\n\r\nThis time, let’s see the desired output (plot) first and build our way up. The goal is to plot the GDP growth of Germany over the years, and its yearly GDP neighbors side-by-side:\r\n\r\n\r\n\r\nFirst, let’s think about what a “GDP neighbor” means in row-relational terms. If you arranged the data by GDP, the GDP neighbors would be the rows that come immediately before and after the rows for Germany. You need to recalculate neighbors every year though, so this arrange() + slice() combo should happen by-year.\r\nWith that in mind, let’s set up a year grouping and arrange by gdpPercap within year:1\r\n\r\n\r\ngapminder_df |> \r\n  group_by(year) |> \r\n  arrange(gdpPercap, .by_group = TRUE)\r\n\r\n  # A tibble: 120 × 4\r\n  # Groups:   year [4]\r\n     country                country_code  year gdpPercap\r\n     <chr>                  <chr>        <int>     <dbl>\r\n   1 Albania                ALB           1992     2497.\r\n   2 Bosnia and Herzegovina BIH           1992     2547.\r\n   3 Turkey                 TUR           1992     5678.\r\n   4 Bulgaria               BGR           1992     6303.\r\n   5 Romania                ROU           1992     6598.\r\n   6 Montenegro             MNE           1992     7003.\r\n   7 Poland                 POL           1992     7739.\r\n   8 Croatia                HRV           1992     8448.\r\n   9 Serbia                 SRB           1992     9325.\r\n  10 Slovak Republic        SVK           1992     9498.\r\n  # ℹ 110 more rows\r\n\r\nNow within each year, we want to grab the row for Germany and its neighboring rows. We can do this by taking the outer() sum of -1:1 and the row indices for Germany:\r\n\r\n\r\ngapminder_df |> \r\n  group_by(year) |> \r\n  arrange(gdpPercap, .by_group = TRUE) |> \r\n  slice( as.integer(outer( -1:1, which(country == \"Germany\"), `+` )) )\r\n\r\n  # A tibble: 12 × 4\r\n  # Groups:   year [4]\r\n     country        country_code  year gdpPercap\r\n     <chr>          <chr>        <int>     <dbl>\r\n   1 Denmark        DNK           1992    26407.\r\n   2 Germany        DEU           1992    26505.\r\n   3 Netherlands    NLD           1992    26791.\r\n   4 Belgium        BEL           1997    27561.\r\n   5 Germany        DEU           1997    27789.\r\n   6 Iceland        ISL           1997    28061.\r\n   7 United Kingdom GBR           2002    29479.\r\n   8 Germany        DEU           2002    30036.\r\n   9 Belgium        BEL           2002    30486.\r\n  10 France         FRA           2007    30470.\r\n  11 Germany        DEU           2007    32170.\r\n  12 United Kingdom GBR           2007    33203.\r\n\r\n\r\nSlicing all the way down: Case 2\r\nThe new .by argument in slice() comes in handy again here, allowing us to collapse the group_by() + arrange() combo into one slice() call:\r\n\r\n\r\ngapminder_df |> \r\n  slice( order(gdpPercap), .by = year) |> \r\n  slice( as.integer(outer( -1:1, which(country == \"Germany\"), `+` )) )\r\n\r\n  # A tibble: 12 × 4\r\n     country        country_code  year gdpPercap\r\n     <chr>          <chr>        <int>     <dbl>\r\n   1 Denmark        DNK           1992    26407.\r\n   2 Germany        DEU           1992    26505.\r\n   3 Netherlands    NLD           1992    26791.\r\n   4 Belgium        BEL           1997    27561.\r\n   5 Germany        DEU           1997    27789.\r\n   6 Iceland        ISL           1997    28061.\r\n   7 United Kingdom GBR           2002    29479.\r\n   8 Germany        DEU           2002    30036.\r\n   9 Belgium        BEL           2002    30486.\r\n  10 France         FRA           2007    30470.\r\n  11 Germany        DEU           2007    32170.\r\n  12 United Kingdom GBR           2007    33203.\r\n\r\nFor our purposes here we want actually the grouping to persist for the following mutate() call, but there may be other cases where you’d want to use slice(.by = ) for temporary grouping.\r\nNow we’re already starting to see the shape of the data that we want! The last step is to encode the relationship of each row to Germany - does a row represent Germany itself, or a country that’s one GDP ranking below or above Germany?\r\nContinuing with our grouped context, we make a new column grp that assigns a factor value \"lo\"-\"is\"-\"hi\" (for “lower” than Germany, “is” Germany and “higher” than Germany) to each country trio by year. Notice the use of fct_inorder() below - this ensures that the factor levels are in the order of their occurrence (necessary for the correct ordering of bars in geom_col() later):\r\n\r\n\r\ngapminder_df |> \r\n  group_by(year) |> \r\n  arrange(gdpPercap) |> \r\n  slice( as.integer(outer( -1:1, which(country == \"Germany\"), `+` )) ) |> \r\n  mutate(grp = forcats::fct_inorder(c(\"lo\", \"is\", \"hi\")))\r\n\r\n  # A tibble: 12 × 5\r\n  # Groups:   year [4]\r\n     country        country_code  year gdpPercap grp  \r\n     <chr>          <chr>        <int>     <dbl> <fct>\r\n   1 Denmark        DNK           1992    26407. lo   \r\n   2 Germany        DEU           1992    26505. is   \r\n   3 Netherlands    NLD           1992    26791. hi   \r\n   4 Belgium        BEL           1997    27561. lo   \r\n   5 Germany        DEU           1997    27789. is   \r\n   6 Iceland        ISL           1997    28061. hi   \r\n   7 United Kingdom GBR           2002    29479. lo   \r\n   8 Germany        DEU           2002    30036. is   \r\n   9 Belgium        BEL           2002    30486. hi   \r\n  10 France         FRA           2007    30470. lo   \r\n  11 Germany        DEU           2007    32170. is   \r\n  12 United Kingdom GBR           2007    33203. hi\r\n\r\nWe now have everything that’s necessary to make our desired plot, so we ungroup(), write some {ggplot2} code, and voila!\r\n\r\n\r\ngapminder_df |> \r\n  group_by(year) |> \r\n  arrange(gdpPercap) |> \r\n  slice( as.integer(outer( -1:1, which(country == \"Germany\"), `+` )) ) |> \r\n  mutate(grp = forcats::fct_inorder(c(\"lo\", \"is\", \"hi\"))) |> \r\n  # Ungroup and make ggplot\r\n  ungroup() |> \r\n  ggplot(aes(as.factor(year), gdpPercap, group = grp)) +\r\n  geom_col(aes(fill = grp == \"is\"), position = position_dodge()) +\r\n  geom_text(\r\n    aes(label = country_code),\r\n    vjust = 1.3,\r\n    position = position_dodge(width = .9)\r\n  ) +\r\n  scale_fill_manual(\r\n    values = c(\"grey75\", \"steelblue\"),\r\n    guide = guide_none()\r\n  ) +\r\n  theme_classic() +\r\n  labs(x = \"Year\", y = \"GDP per capita\")\r\n\r\n\r\n\r\n\r\nSolving the harder version of the problem\r\nThe solution presented above relies on a fragile assumption that Germany will always have a higher and lower ranking GDP neighbor every year. But nothing about the problem description guarantees this, so how can we re-write our code to be more robust?\r\nFirst, let’s simulate a data where Germany is the lowest ranking country in 2002 and the highest ranking in 2007. In other words, Germany only has one GDP neighbor in those years:\r\n\r\n\r\ngapminder_harder_df <- gapminder_df |> \r\n  slice( order(gdpPercap), .by = year) |> \r\n  slice( as.integer(outer( -1:1, which(country == \"Germany\"), `+` )) ) |> \r\n  slice( -7, -12 )\r\ngapminder_harder_df\r\n\r\n  # A tibble: 10 × 4\r\n     country     country_code  year gdpPercap\r\n     <chr>       <chr>        <int>     <dbl>\r\n   1 Denmark     DNK           1992    26407.\r\n   2 Germany     DEU           1992    26505.\r\n   3 Netherlands NLD           1992    26791.\r\n   4 Belgium     BEL           1997    27561.\r\n   5 Germany     DEU           1997    27789.\r\n   6 Iceland     ISL           1997    28061.\r\n   7 Germany     DEU           2002    30036.\r\n   8 Belgium     BEL           2002    30486.\r\n   9 France      FRA           2007    30470.\r\n  10 Germany     DEU           2007    32170.\r\n\r\nGiven this data, we cannot assign the full, length-3 lo-is-hi factor by group, because the groups for year 2002 and 2007 only have 2 observations:\r\n\r\n\r\ngapminder_harder_df |> \r\n  group_by(year) |> \r\n  mutate(grp = forcats::fct_inorder(c(\"lo\", \"is\", \"hi\")))\r\n\r\n  Error in `mutate()`:\r\n  ℹ In argument: `grp = forcats::fct_inorder(c(\"lo\", \"is\", \"hi\"))`.\r\n  ℹ In group 3: `year = 2002`.\r\n  Caused by error:\r\n  ! `grp` must be size 2 or 1, not 3.\r\n\r\nThe trick here is to turn each group of rows into an integer sequence where Germany is “anchored” to 2, and then use that vector to subset the lo-is-hi factor:\r\n\r\n\r\ngapminder_harder_df |> \r\n  group_by(year) |> \r\n  mutate(\r\n    Germany_anchored_to_2 = row_number() - which(country == \"Germany\") + 2,\r\n    grp = forcats::fct_inorder(c(\"lo\", \"is\", \"hi\"))[Germany_anchored_to_2]\r\n  )\r\n\r\n  # A tibble: 10 × 6\r\n  # Groups:   year [4]\r\n     country     country_code  year gdpPercap Germany_anchored_to_2 grp  \r\n     <chr>       <chr>        <int>     <dbl>                 <dbl> <fct>\r\n   1 Denmark     DNK           1992    26407.                     1 lo   \r\n   2 Germany     DEU           1992    26505.                     2 is   \r\n   3 Netherlands NLD           1992    26791.                     3 hi   \r\n   4 Belgium     BEL           1997    27561.                     1 lo   \r\n   5 Germany     DEU           1997    27789.                     2 is   \r\n   6 Iceland     ISL           1997    28061.                     3 hi   \r\n   7 Germany     DEU           2002    30036.                     2 is   \r\n   8 Belgium     BEL           2002    30486.                     3 hi   \r\n   9 France      FRA           2007    30470.                     1 lo   \r\n  10 Germany     DEU           2007    32170.                     2 is\r\n\r\nWe find that the lessons of working with row indices from slice() translated to solving this complex mutate() problem - neat!\r\nWindowed min/max/median (etc.)\r\nLet’s say we have this small time series data, and we want to calculate a lagged 3-window moving minimum for the val column:\r\n\r\n\r\nts_df <- tibble(\r\n  time = 1:6,\r\n  val = sample(1:6 * 10)\r\n)\r\nts_df\r\n\r\n  # A tibble: 6 × 2\r\n     time   val\r\n    <int> <dbl>\r\n  1     1    50\r\n  2     2    40\r\n  3     3    60\r\n  4     4    30\r\n  5     5    20\r\n  6     6    10\r\n\r\nIf you’re new to window functions, think of them as a special kind of group_by() + summarize() where groups are chunks of observations along a (typically unique) continuous measure like time, and observations can be shared between groups.\r\nThere are several packages implementing moving/sliding/rolling window functions. My current favorite is {r2c} (see a review of other implementations therein), but I also like {slider} for an implementation that follows familiar “tidy” design principles:\r\n\r\n\r\nlibrary(slider)\r\nts_df |> \r\n  mutate(moving_min = slide_min(val, before = 2L, complete = TRUE))\r\n\r\n  # A tibble: 6 × 3\r\n     time   val moving_min\r\n    <int> <dbl>      <dbl>\r\n  1     1    50         NA\r\n  2     2    40         NA\r\n  3     3    60         40\r\n  4     4    30         30\r\n  5     5    20         20\r\n  6     6    10         10\r\n\r\nMoving window is a general class of operations that encompass any arbitrary summary statistic - so not just min but other reducing functions like mean, standard deviation, etc. But what makes moving min (along with max, median, etc.) a particularly interesting case for our current discussion is that the value comes from an existing observation in the data. And if our time series is tidy, every observation makes up a row. See where I’m going with this?\r\nUsing outer() again, we can take the outer sum of all row indices of ts_df and -2:0. This gives us a matrix where each column represents a lagged size-3 moving window:\r\n\r\n\r\nwindows_3lag <- outer(-2:0, 1:nrow(ts_df), \"+\")\r\nwindows_3lag\r\n\r\n       [,1] [,2] [,3] [,4] [,5] [,6]\r\n  [1,]   -1    0    1    2    3    4\r\n  [2,]    0    1    2    3    4    5\r\n  [3,]    1    2    3    4    5    6\r\n\r\nThe “lagged size-3” property of this moving window means that the first two windows are incomplete (consisting of less than 3 observations). We want to treat those as invalid, so we can drop the first two columns from our matrix:\r\n\r\n\r\nwindows_3lag[,-(1:2)]\r\n\r\n       [,1] [,2] [,3] [,4]\r\n  [1,]    1    2    3    4\r\n  [2,]    2    3    4    5\r\n  [3,]    3    4    5    6\r\n\r\nFor each remaining column, we want to grab the values of val at the corresponding row indices and find which row has the minimum val. In terms of code, we use apply() with MARGIN = 2L to column-wise apply a function where we use which.min() to find the location of the minimum val and convert it back to row index via subsetting:\r\n\r\n\r\nwindows_3lag[, -(1:2)] |> \r\n  apply(MARGIN = 2L, \\(i) i[which.min(ts_df$val[i])])\r\n\r\n  [1] 2 4 5 6\r\n\r\nNow let’s stick this inside slice(), exploiting the fact that it’s data-masked (ts_df$val can just be val) and exposes context-dependent expressions (1:nrow(ts_df) can just be row_number()):\r\n\r\n\r\nmoving_mins <- ts_df |> \r\n  slice(\r\n    outer(-2:0, row_number(), \"+\")[,-(1:2)] |> \r\n      apply(MARGIN = 2L, \\(i) i[which.min(val[i])])\r\n  )\r\nmoving_mins\r\n\r\n  # A tibble: 4 × 2\r\n     time   val\r\n    <int> <dbl>\r\n  1     2    40\r\n  2     4    30\r\n  3     5    20\r\n  4     6    10\r\n\r\nFrom here, we can grab the val column and pad it with NA to add our desired window_min column to the original data frame:\r\n\r\n\r\nts_df |> \r\n  mutate(moving_min = c(NA, NA, moving_mins$val))\r\n\r\n  # A tibble: 6 × 3\r\n     time   val moving_min\r\n    <int> <dbl>      <dbl>\r\n  1     1    50         NA\r\n  2     2    40         NA\r\n  3     3    60         40\r\n  4     4    30         30\r\n  5     5    20         20\r\n  6     6    10         10\r\n\r\nAt this point you might think that this is a very round-about way of solving the same problem. But actually I think that it’s a faster route to solving a slightly more complicated problem - augmenting each observation of a data frame with information about comparison observations.\r\nFor example, our slice()-based solution sets us up nicely for also bringing along information about the time at which the moving_min occurred. After some rename()-ing and adding the original time information back in, we get back a relational data structure where time is a key shared with ts_df:\r\n\r\n\r\nmoving_mins2 <- moving_mins |> \r\n  rename(moving_min_val = val, moving_min_time = time) |> \r\n  mutate(time = ts_df$time[-(1:2)], .before = 1L)\r\nmoving_mins2\r\n\r\n  # A tibble: 4 × 3\r\n     time moving_min_time moving_min_val\r\n    <int>           <int>          <dbl>\r\n  1     3               2             40\r\n  2     4               4             30\r\n  3     5               5             20\r\n  4     6               6             10\r\n\r\nWe can then left-join this to the original data to augment it with information about both the value of the 3-window minimum and the time that the minimum occurred:\r\n\r\n\r\nleft_join(ts_df, moving_mins2, by = \"time\")\r\n\r\n  # A tibble: 6 × 4\r\n     time   val moving_min_time moving_min_val\r\n    <int> <dbl>           <int>          <dbl>\r\n  1     1    50              NA             NA\r\n  2     2    40              NA             NA\r\n  3     3    60               2             40\r\n  4     4    30               4             30\r\n  5     5    20               5             20\r\n  6     6    10               6             10\r\n\r\nThis is particularly useful if rows contain other useful information for comparison and you have memory to spare:\r\n\r\n\r\nts_wide_df <- ts_df |> \r\n  mutate(\r\n    col1 = rnorm(6),\r\n    col2 = rnorm(6)\r\n  )\r\nts_wide_df\r\n\r\n  # A tibble: 6 × 4\r\n     time   val    col1     col2\r\n    <int> <dbl>   <dbl>    <dbl>\r\n  1     1    50  0.0183  0.00501\r\n  2     2    40  0.705  -0.0376 \r\n  3     3    60 -0.647   0.724  \r\n  4     4    30  0.868  -0.497  \r\n  5     5    20  0.376   0.0114 \r\n  6     6    10  0.310   0.00986\r\n\r\nThe below code augments each observation in the original ts_wide_df data with information about the corresponding 3-window moving min (columns prefixed with \"min3val_\")\r\n\r\n\r\nmoving_mins_wide <- ts_wide_df |> \r\n  slice(\r\n    outer(-2:0, row_number(), \"+\")[,-(1:2)] |> \r\n      apply(MARGIN = 2L, \\(i) i[which.min(val[i])])\r\n  ) |> \r\n  rename_with(~ paste0(\"min3val_\", .x)) |> \r\n  mutate(time = ts_wide_df$time[-(1:2)])\r\nleft_join(ts_wide_df, moving_mins_wide, by = \"time\")\r\n\r\n  # A tibble: 6 × 8\r\n     time   val    col1     col2 min3val_time min3val_val min3val_col1\r\n    <int> <dbl>   <dbl>    <dbl>        <int>       <dbl>        <dbl>\r\n  1     1    50  0.0183  0.00501           NA          NA       NA    \r\n  2     2    40  0.705  -0.0376            NA          NA       NA    \r\n  3     3    60 -0.647   0.724              2          40        0.705\r\n  4     4    30  0.868  -0.497              4          30        0.868\r\n  5     5    20  0.376   0.0114             5          20        0.376\r\n  6     6    10  0.310   0.00986            6          10        0.310\r\n  # ℹ 1 more variable: min3val_col2 <dbl>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\nEvenly distributed row shuffling of balanced categories\r\nSometimes the ordering of rows in a data frame can be meaningful for an external application.\r\nFor example, many experiment-building platforms for psychology research require researchers to specify the running order of trials in an experiment via a csv, where each row represents a trial and each column represents information about the trial.\r\nSo an experiment testing the classic Stroop effect may have the following template:\r\n\r\n\r\nmismatch_trials <- tibble(\r\n  item_id = 1:5,\r\n  trial = \"mismatch\",\r\n  word = c(\"red\", \"green\", \"purple\", \"brown\", \"blue\"),\r\n  color = c(\"brown\", \"red\", \"green\", \"blue\", \"purple\")\r\n)\r\nmismatch_trials\r\n\r\n  # A tibble: 5 × 4\r\n    item_id trial    word   color \r\n      <int> <chr>    <chr>  <chr> \r\n  1       1 mismatch red    brown \r\n  2       2 mismatch green  red   \r\n  3       3 mismatch purple green \r\n  4       4 mismatch brown  blue  \r\n  5       5 mismatch blue   purple\r\n\r\nWe probably also want to mix in some control trials where the word and color do match:\r\n\r\n\r\nmatch_trials <- mismatch_trials |> \r\n  mutate(trial = \"match\", color = word)\r\nmatch_trials\r\n\r\n  # A tibble: 5 × 4\r\n    item_id trial word   color \r\n      <int> <chr> <chr>  <chr> \r\n  1       1 match red    red   \r\n  2       2 match green  green \r\n  3       3 match purple purple\r\n  4       4 match brown  brown \r\n  5       5 match blue   blue\r\n\r\nNow that we have all materials for our experiment, we next want the running order to interleave the match and mismatch trials.\r\nWe first add them together into a longer data frame:\r\n\r\n\r\nstroop_trials <- bind_rows(mismatch_trials, match_trials)\r\nstroop_trials\r\n\r\n  # A tibble: 10 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       2 mismatch green  red   \r\n   3       3 mismatch purple green \r\n   4       4 mismatch brown  blue  \r\n   5       5 mismatch blue   purple\r\n   6       1 match    red    red   \r\n   7       2 match    green  green \r\n   8       3 match    purple purple\r\n   9       4 match    brown  brown \r\n  10       5 match    blue   blue\r\n\r\nAnd from here we can exploit the fact that all mismatch items come before match items, and that they share the same length of 5:\r\n\r\n\r\nstroop_trials |> \r\n  slice( as.integer(outer(c(0, 5), 1:5, \"+\")) )\r\n\r\n  # A tibble: 10 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       1 match    red    red   \r\n   3       2 mismatch green  red   \r\n   4       2 match    green  green \r\n   5       3 mismatch purple green \r\n   6       3 match    purple purple\r\n   7       4 mismatch brown  blue  \r\n   8       4 match    brown  brown \r\n   9       5 mismatch blue   purple\r\n  10       5 match    blue   blue\r\n\r\nThis relies on a strong assumptions about the row order in the original data, though. So a safer alternative is to represent the row indices for \"match\" and \"mismatch\" trials as rows of a matrix, and then collapse column-wise.\r\nLet’s try this outside of slice() first. We start with a call to sapply() to construct a matrix where the columns contain row indices for each unique category of trial:\r\n\r\n\r\nsapply(unique(stroop_trials$trial), \\(x) which(stroop_trials$trial == x))\r\n\r\n       mismatch match\r\n  [1,]        1     6\r\n  [2,]        2     7\r\n  [3,]        3     8\r\n  [4,]        4     9\r\n  [5,]        5    10\r\n\r\nThen we transpose the matrix with t(), which rotates it:\r\n\r\n\r\nt( sapply(unique(stroop_trials$trial), \\(x) which(stroop_trials$trial == x)) )\r\n\r\n           [,1] [,2] [,3] [,4] [,5]\r\n  mismatch    1    2    3    4    5\r\n  match       6    7    8    9   10\r\n\r\nNow lets stick that inside slice, remembering to collapse the transposed matrix into vector:\r\n\r\n\r\ninterleaved_stroop_trials <- stroop_trials |> \r\n  slice( as.integer(t(sapply(unique(trial), \\(x) which(trial == x)))) )\r\ninterleaved_stroop_trials\r\n\r\n  # A tibble: 10 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       1 match    red    red   \r\n   3       2 mismatch green  red   \r\n   4       2 match    green  green \r\n   5       3 mismatch purple green \r\n   6       3 match    purple purple\r\n   7       4 mismatch brown  blue  \r\n   8       4 match    brown  brown \r\n   9       5 mismatch blue   purple\r\n  10       5 match    blue   blue\r\n\r\nAt the moment, we have both “red” word trails showing up together, and then the “green”s, the “purple”s, and so on. If we wanted to introduce some randomness to the presentation order within each type of trial, we can wrap the row indices in sample() to shuffle them first:\r\n\r\n\r\nshuffled_stroop_trials <- stroop_trials |> \r\n  slice( as.integer(t(sapply(unique(trial), \\(x) sample(which(trial == x))))) )\r\nshuffled_stroop_trials\r\n\r\n  # A tibble: 10 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       5 match    blue   blue  \r\n   3       2 mismatch green  red   \r\n   4       4 match    brown  brown \r\n   5       3 mismatch purple green \r\n   6       1 match    red    red   \r\n   7       4 mismatch brown  blue  \r\n   8       3 match    purple purple\r\n   9       5 mismatch blue   purple\r\n  10       2 match    green  green\r\n\r\n\r\nInserting a new row at specific intervals\r\nContinuing with our Stroop experiment template example, let’s say we want to give participants a break every two trials.\r\nIn a matrix representation, this means constructing this 2-row matrix of row indices:\r\n\r\n\r\nmatrix(1:nrow(shuffled_stroop_trials), nrow = 2)\r\n\r\n       [,1] [,2] [,3] [,4] [,5]\r\n  [1,]    1    3    5    7    9\r\n  [2,]    2    4    6    8   10\r\n\r\nAnd adding a row of that represent a separator/break, before collapsing column-wise:\r\n\r\n\r\nmatrix(1:nrow(shuffled_stroop_trials), nrow = 2) |> \r\n  rbind(11)\r\n\r\n       [,1] [,2] [,3] [,4] [,5]\r\n  [1,]    1    3    5    7    9\r\n  [2,]    2    4    6    8   10\r\n  [3,]   11   11   11   11   11\r\n\r\nUsing slice, this means adding a row to the data representing a break trial first, and then adding a row to the row index matrix representing that row:\r\n\r\n\r\nstroop_with_breaks <- shuffled_stroop_trials |> \r\n  add_row(trial = \"BREAK\") |> \r\n  slice(\r\n    matrix(row_number()[-n()], nrow = 2) |> \r\n      rbind(n()) |> \r\n      as.integer()\r\n  )\r\nstroop_with_breaks\r\n\r\n  # A tibble: 15 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       5 match    blue   blue  \r\n   3      NA BREAK    <NA>   <NA>  \r\n   4       2 mismatch green  red   \r\n   5       4 match    brown  brown \r\n   6      NA BREAK    <NA>   <NA>  \r\n   7       3 mismatch purple green \r\n   8       1 match    red    red   \r\n   9      NA BREAK    <NA>   <NA>  \r\n  10       4 mismatch brown  blue  \r\n  11       3 match    purple purple\r\n  12      NA BREAK    <NA>   <NA>  \r\n  13       5 mismatch blue   purple\r\n  14       2 match    green  green \r\n  15      NA BREAK    <NA>   <NA>\r\n\r\nIf we don’t want a break after the last trial, we can use negative indexing with slice(-n()):\r\n\r\n\r\nstroop_with_breaks |> \r\n  slice(-n())\r\n\r\n  # A tibble: 14 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       5 match    blue   blue  \r\n   3      NA BREAK    <NA>   <NA>  \r\n   4       2 mismatch green  red   \r\n   5       4 match    brown  brown \r\n   6      NA BREAK    <NA>   <NA>  \r\n   7       3 mismatch purple green \r\n   8       1 match    red    red   \r\n   9      NA BREAK    <NA>   <NA>  \r\n  10       4 mismatch brown  blue  \r\n  11       3 match    purple purple\r\n  12      NA BREAK    <NA>   <NA>  \r\n  13       5 mismatch blue   purple\r\n  14       2 match    green  green\r\n\r\nWhat about after 3 trials, where the number of trials (10) is not divisibly by 3? Can we still use a matrix?\r\nYes, you’d just need to explicitly fill in the “blanks”!\r\nConceptually, we want a matrix like this, where extra “cells” are padded with 0s (recall that 0s are ignored in slice()):\r\n\r\n\r\nmatrix(c(1:10, rep(0, 3 - 10 %% 3)), nrow = 3)\r\n\r\n       [,1] [,2] [,3] [,4]\r\n  [1,]    1    4    7   10\r\n  [2,]    2    5    8    0\r\n  [3,]    3    6    9    0\r\n\r\nAnd this is how that could be implemented inside slice(), minding the fact that adding the break trial increases original row count by 1:\r\n\r\n\r\nshuffled_stroop_trials |> \r\n  add_row(trial = \"BREAK\") |> \r\n  slice(\r\n    c(seq_len(n()-1), rep(0, 3 - (n()-1) %% 3)) |> \r\n      matrix(nrow = 3) |> \r\n      rbind(n()) |> \r\n      as.integer()\r\n  ) |> \r\n  slice(-n())\r\n\r\n  # A tibble: 13 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       5 match    blue   blue  \r\n   3       2 mismatch green  red   \r\n   4      NA BREAK    <NA>   <NA>  \r\n   5       4 match    brown  brown \r\n   6       3 mismatch purple green \r\n   7       1 match    red    red   \r\n   8      NA BREAK    <NA>   <NA>  \r\n   9       4 mismatch brown  blue  \r\n  10       3 match    purple purple\r\n  11       5 mismatch blue   purple\r\n  12      NA BREAK    <NA>   <NA>  \r\n  13       2 match    green  green\r\n\r\nHow about inserting a break trial after every \"purple\" word trials?\r\nConceptually, we want a matrix that binds these two vectors as rows before collapsing:\r\n\r\n\r\nprint( 1:nrow(shuffled_stroop_trials) )\r\nprint(\r\n  replace(rep(0, nrow(shuffled_stroop_trials)),\r\n          which(shuffled_stroop_trials$word == \"purple\"), 11)\r\n)\r\n\r\n   [1]  1  2  3  4  5  6  7  8  9 10\r\n   [1]  0  0  0  0 11  0  0 11  0  0\r\n\r\nAnd this is how you could do that inside slice():\r\n\r\n\r\nshuffled_stroop_trials |> \r\n  add_row(trial = \"BREAK\") |> \r\n  slice(\r\n    c(seq_len(n()-1), replace(rep(0, n()-1), which(word == \"purple\"), n())) |>\r\n      matrix(nrow = 2, byrow = TRUE) |> \r\n      as.integer()\r\n  )\r\n\r\n  # A tibble: 12 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       5 match    blue   blue  \r\n   3       2 mismatch green  red   \r\n   4       4 match    brown  brown \r\n   5       3 mismatch purple green \r\n   6      NA BREAK    <NA>   <NA>  \r\n   7       1 match    red    red   \r\n   8       4 mismatch brown  blue  \r\n   9       3 match    purple purple\r\n  10      NA BREAK    <NA>   <NA>  \r\n  11       5 mismatch blue   purple\r\n  12       2 match    green  green\r\n\r\nYou might protest that this is a pretty convoluted approach to a seemingly simple problem of inserting rows, and you’d be right!2 Not only is the code difficult to read, you can only insert the same single row over and over.\r\nIt turns out that these cases of row insertion actually fall under the broader class of interweaving unequal categories - let’s see this next.\r\nEvenly distributed row shuffling of unequal categories\r\nLet’s return to our solution for the initial “break every 2 trials” problem:\r\n\r\n\r\nshuffled_stroop_trials |> \r\n  add_row(trial = \"BREAK\") |> \r\n  slice(\r\n    matrix(row_number()[-n()], nrow = 2) |> \r\n      rbind(n()) |> \r\n      as.integer()\r\n  ) |> \r\n  slice(-n())\r\n\r\n  # A tibble: 14 × 4\r\n     item_id trial    word   color \r\n       <int> <chr>    <chr>  <chr> \r\n   1       1 mismatch red    brown \r\n   2       5 match    blue   blue  \r\n   3      NA BREAK    <NA>   <NA>  \r\n   4       2 mismatch green  red   \r\n   5       4 match    brown  brown \r\n   6      NA BREAK    <NA>   <NA>  \r\n   7       3 mismatch purple green \r\n   8       1 match    red    red   \r\n   9      NA BREAK    <NA>   <NA>  \r\n  10       4 mismatch brown  blue  \r\n  11       3 match    purple purple\r\n  12      NA BREAK    <NA>   <NA>  \r\n  13       5 mismatch blue   purple\r\n  14       2 match    green  green\r\n\r\nHere, we were working with a matrix that looks like this, where 11 represents the new row we added representing a break trial:\r\n\r\n       [,1] [,2] [,3] [,4] [,5]\r\n  [1,]    1    3    5    7    9\r\n  [2,]    2    4    6    8   10\r\n  [3,]   11   11   11   11   11\r\n\r\nAnd recall that to insert every 3 rows, we needed to pad with 0 first to satisfy the matrix’s rectangle constraint:\r\n\r\n       [,1] [,2] [,3] [,4]\r\n  [1,]    1    4    7   10\r\n  [2,]    2    5    8    0\r\n  [3,]    3    6    9    0\r\n  [4,]   11   11   11   11\r\n\r\nBut a better way of thinking about this is to have one matrix row representing all row indices, and then add a sparse row that represent breaks:\r\nBreak after every 2 trials:\r\n\r\n\r\nmatrix(c(1:10, rep_len(c(0, 11), 10)), nrow = 2, byrow = TRUE)\r\n\r\n       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]\r\n  [1,]    1    2    3    4    5    6    7    8    9    10\r\n  [2,]    0   11    0   11    0   11    0   11    0    11\r\n\r\nBreak after every 3 trials:\r\n\r\n\r\nmatrix(c(1:10, rep_len(c(0, 0, 11), 10)), nrow = 2, byrow = TRUE)\r\n\r\n       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]\r\n  [1,]    1    2    3    4    5    6    7    8    9    10\r\n  [2,]    0    0   11    0    0   11    0    0   11     0\r\n\r\nBreak after every 4 trials:\r\n\r\n\r\nmatrix(c(1:10, rep_len(c(0, 0, 0, 11), 10)), nrow = 2, byrow = TRUE)\r\n\r\n       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]\r\n  [1,]    1    2    3    4    5    6    7    8    9    10\r\n  [2,]    0    0    0   11    0    0    0   11    0     0\r\n\r\nAnd it turns out that this method generalizes to balanced shuffling across categories that are not equal in size!\r\nLet’s start with a really basic example - here we have three kinds of fruits with varying counts:\r\n\r\n\r\nfruits <- c(\"🍎\", \"🍋\", \"🍇\")[c(2,1,3,3,2,3,1,2,2,1,2,2,3,3,3)]\r\nfruits <- factor(fruits, levels = c(\"🍇\", \"🍋\", \"🍎\"))\r\ntable(fruits)\r\n\r\n  fruits\r\n  🍇 🍋 🍎 \r\n   6  6  3\r\n\r\nTheir current order looks like this:\r\n\r\n\r\ncat(levels(fruits)[fruits])\r\n\r\n  🍋 🍎 🍇 🍇 🍋 🍇 🍎 🍋 🍋 🍎 🍋 🍋 🍇 🍇 🍇\r\n\r\nBut I want them to be ordered such that individuals of the same fruit kind are maximally apart from one another. This effectively re-orders the fruits to be distributed “evenly”:\r\n\r\n\r\ncat(levels(fruits)[fruits[c(3,1,2,4,5,0,6,8,10,13,9,0,14,11,7,15,12,0)]])\r\n\r\n  🍇 🍋 🍎 🍇 🍋 🍇 🍋 🍎 🍇 🍋 🍇 🍋 🍎 🍇 🍋\r\n\r\nWith our “build row-wise, collapse col-wise” approach, this takes the following steps:\r\nFind the most frequent category - that N-max becomes the number of columns in the matrix of row indices.\r\nIn this case it’s grapes and lemons, of which there are 6 each:\r\n\r\n\r\ngrape_rows <- which(fruits == \"🍇\")\r\n setNames(grape_rows, rep(\"🍇\", 6))\r\n\r\n  🍇 🍇 🍇 🍇 🍇 🍇 \r\n   3  4  6 13 14 15\r\n\r\n\r\n\r\nlemon_rows <- which(fruits == \"🍋\")\r\n setNames(lemon_rows, rep(\"🍋\", 6))\r\n\r\n  🍋 🍋 🍋 🍋 🍋 🍋 \r\n   1  5  8  9 11 12\r\n\r\nNormalize (“stretch”) all vectors to have the same length as N.\r\nIn this case we need to stretch the apples vector, which is currently only length-3:\r\n\r\n\r\napple_rows <- which(fruits == \"🍎\")\r\n apple_rows\r\n\r\n  [1]  2  7 10\r\n\r\nThe desired “sparse” representation is something like this, where each instance of apple is equidistant, with 0s in between:\r\n\r\n\r\napple_rows_sparse <- c(2, 0, 7, 0, 10, 0)\r\n setNames(apple_rows_sparse, c(\"🍎\", \"\", \"🍎\", \"\", \"🍎\", \"\"))\r\n\r\n  🍎    🍎    🍎    \r\n   2  0  7  0 10  0\r\n\r\nThere are many ways to get at this, but one trick involves creating an evenly spaced float sequence from 1 to N-apple over N-max steps:\r\n\r\n\r\nseq(1, 3, length.out = 6)\r\n\r\n  [1] 1.0 1.4 1.8 2.2 2.6 3.0\r\n\r\nFrom there, we round the numbers:\r\n\r\n\r\nround(seq(1, 3, length.out = 6))\r\n\r\n  [1] 1 1 2 2 3 3\r\n\r\nThen mark the first occurance of each number using !duplicated():\r\n\r\n\r\n!duplicated(round(seq(1, 3, length.out = 6)))\r\n\r\n  [1]  TRUE FALSE  TRUE FALSE  TRUE FALSE\r\n\r\nAnd lastly, we initialize a vector of 0s and replace() the TRUEs with apple indices:\r\n\r\n\r\nreplace(\r\n   rep(0, 6),\r\n   !duplicated(round(seq(1, 3, length.out = 6))),\r\n   which(fruits == \"🍎\")\r\n )\r\n\r\n  [1]  2  0  7  0 10  0\r\n\r\nStack up the category vectors by row and collapse column-wise:\r\nManually, we would build the full matrix row-by-row like this:\r\n\r\n\r\nfruits_matrix <- matrix(\r\n   c(grape_rows, lemon_rows, apple_rows_sparse),\r\n   nrow = 3, byrow = TRUE\r\n )\r\n rownames(fruits_matrix) <- c(\"🍇\", \"🍋\", \"🍎\")\r\n fruits_matrix\r\n\r\n     [,1] [,2] [,3] [,4] [,5] [,6]\r\n  🍇    3    4    6   13   14   15\r\n  🍋    1    5    8    9   11   12\r\n  🍎    2    0    7    0   10    0\r\n\r\nAnd dynamically we can use sapply() to fill the matrix column-by-column, and then t()-ing the output:\r\n\r\n\r\nfruits_distributed <- sapply(levels(fruits), \\(x) {\r\n   n_max <- max(table(fruits))\r\n   ind <- which(fruits == x)\r\n   nums <- seq(1, length(ind), length.out = n_max)\r\n   replace(rep(0, n_max), !duplicated(round(nums)), ind)\r\n }) |> \r\n   t()\r\n fruits_distributed\r\n\r\n     [,1] [,2] [,3] [,4] [,5] [,6]\r\n  🍇    3    4    6   13   14   15\r\n  🍋    1    5    8    9   11   12\r\n  🍎    2    0    7    0   10    0\r\n\r\nFinally, we collapse the vector and we see that it indeed distributed the fruits evenly!\r\n\r\n\r\nfruits[as.integer(fruits_distributed)]\r\n\r\n   [1] 🍇 🍋 🍎 🍇 🍋 🍇 🍋 🍎 🍇 🍋 🍇 🍋 🍎 🍇 🍋\r\n  Levels: 🍇 🍋 🍎\r\n\r\nWe can go even further and wrap the dynamic, sapply()-based solution into a function for use within slice(). Here, I also added an optional argument for shuffling within categories:\r\n\r\n\r\nrshuffle <- function(x, shuffle_within = FALSE) {\r\n  categories <- as.factor(x)\r\n  n_max <- max(table(categories))\r\n  sapply(levels(categories), \\(lvl) {\r\n    ind <- which(categories == lvl)\r\n    if (shuffle_within) ind <- sample(ind)\r\n    nums <- seq(1, length(ind), length.out = n_max)\r\n    replace(rep(0, n_max), !duplicated(round(nums)), ind)\r\n  }) |> \r\n    t() |> \r\n    as.integer()\r\n}\r\n\r\n\r\nReturning back to our Stroop experiment template example, imagine we also had two filler trials, where no word is shown and just the color flashes on the screen:\r\n\r\n\r\nstroop_fillers <- tibble(\r\n  item_id = 1:2,\r\n  trial = \"filler\",\r\n  word = NA,\r\n  color = c(\"red\", \"blue\")\r\n)\r\nstroop_with_fillers <- bind_rows(stroop_fillers, stroop_trials) |> \r\n  mutate(trial = factor(trial, c(\"match\", \"mismatch\", \"filler\")))\r\nstroop_with_fillers\r\n\r\n  # A tibble: 12 × 4\r\n     item_id trial    word   color \r\n       <int> <fct>    <chr>  <chr> \r\n   1       1 filler   <NA>   red   \r\n   2       2 filler   <NA>   blue  \r\n   3       1 mismatch red    brown \r\n   4       2 mismatch green  red   \r\n   5       3 mismatch purple green \r\n   6       4 mismatch brown  blue  \r\n   7       5 mismatch blue   purple\r\n   8       1 match    red    red   \r\n   9       2 match    green  green \r\n  10       3 match    purple purple\r\n  11       4 match    brown  brown \r\n  12       5 match    blue   blue\r\n\r\nWe can evenly shuffle between the unequal trial types with our new rshuffle() function:\r\n\r\n\r\nstroop_with_fillers |> \r\n  slice( rshuffle(trial, shuffle_within = TRUE) )\r\n\r\n  # A tibble: 12 × 4\r\n     item_id trial    word   color \r\n       <int> <fct>    <chr>  <chr> \r\n   1       2 match    green  green \r\n   2       2 mismatch green  red   \r\n   3       1 filler   <NA>   red   \r\n   4       1 match    red    red   \r\n   5       4 mismatch brown  blue  \r\n   6       3 match    purple purple\r\n   7       3 mismatch purple green \r\n   8       2 filler   <NA>   blue  \r\n   9       4 match    brown  brown \r\n  10       5 mismatch blue   purple\r\n  11       5 match    blue   blue  \r\n  12       1 mismatch red    brown\r\n\r\nConclusion\r\nWhen I started drafting this blog post, I thought I’d come with a principled taxonomy of row-relational operations. Ha. This was a lot trickier to think through than I thought.\r\nBut I hope that this gallery of esoteric use-cases for slice() inspires you to use it more, and to think about “tidy” solutions to seemingly “untidy” problems.\r\n\r\nThe .by_group = TRUE is not strictly necessary here, but it’s good for visually inspecting the within-group ordering.↩︎\r\nAlthough row insertion is a generally tricky problem for column-major data frame structures, which is partly why dplyr’s row manipulation verbs have stayed experimental for quite some time.↩︎\r\n",
-    "preview": "posts/2023-06-11-row-relational-operations/preview.png",
-    "last_modified": "2023-06-11T00:51:42-04:00",
-    "input_file": {},
-    "preview_width": 1800,
-    "preview_height": 1080
-  },
   {
     "path": "posts/2022-11-13-dataframes-jl-and-accessories/",
     "title": "First impressions of DataFrames.jl and accessories",
diff --git a/docs/site_libs/panelset-0.3.0/panelset.css b/docs/site_libs/panelset-0.3.0/panelset.css
new file mode 100644
index 00000000..b1d32552
--- /dev/null
+++ b/docs/site_libs/panelset-0.3.0/panelset.css
@@ -0,0 +1,291 @@
+/*
+* Prefixed by https://autoprefixer.github.io
+* PostCSS: v8.4.14,
+* Autoprefixer: v10.4.7
+* Browsers: >0.3%,last 2 versions,not dead
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diff --git a/docs/site_libs/panelset-0.3.0/panelset.js b/docs/site_libs/panelset-0.3.0/panelset.js
new file mode 100644
index 00000000..31b8c294
--- /dev/null
+++ b/docs/site_libs/panelset-0.3.0/panelset.js
@@ -0,0 +1,826 @@
+/* Panelset
+ * Tab panels for web projects created from markdown with Quarto and R Markdown.
+ *
+ * https://pkg.garrickadenbuie.com/xaringanExtra/#/panelset
+ *
+ * Copyright (c) 2019-2024 Garrick Aden-Buie
+ *
+ * This software is released under the MIT License.
+ * https://opensource.org/licenses/MIT
+ */
+
+/* VERSION: 0.3.0 */
+
+/* global slideshow */
+;(function () {
+  const ready = function (fn) {
+    /* MIT License Copyright (c) 2016 Nuclei */
+    /* https://github.com/nuclei/readyjs */
+    const completed = () => {
+      document.removeEventListener('DOMContentLoaded', completed)
+      window.removeEventListener('load', completed)
+      fn()
+    }
+    if (document.readyState !== 'loading') {
+      setTimeout(fn)
+    } else {
+      document.addEventListener('DOMContentLoaded', completed)
+      window.addEventListener('load', completed)
+    }
+  }
+
+  ready(function () {
+    ;[...document.querySelectorAll('.panel-name')].map(el =>
+      el.textContent.trim()
+    )
+
+    function inRevealjs () {
+      return typeof window.Reveal !== 'undefined'
+    }
+
+    function inRemarkjs () {
+      return typeof window.remark !== 'undefined'
+    }
+
+    function inRemarkSlide (el) {
+      return inRemarkjs() && el.closest('.remark-slide')
+    }
+
+    const panelIds = {}
+    let panelsetIdx = 0
+    const panelsetIds = []
+
+    /**
+     * Generates a unique panelset ID.
+     * @param {string} id - The optional ID to be used as a base for the panelset ID.
+     * @returns {string} - The generated unique panelset ID.
+     */
+    const uniquePanelsetId = id => {
+      const panelsetNumber = () => (++panelsetIdx).toString().padStart(3, '0')
+
+      if (typeof id === 'undefined' || id === '') {
+        id = 'panelset_' + panelsetNumber()
+      } else if (panelsetIds.includes(id)) {
+        id = id + '_' + panelsetNumber()
+      }
+
+      panelsetIds.push(id)
+      return id
+    }
+
+    /**
+     * Generates a unique panel ID based on the provided name, by appending an
+     * increasing integer to the name to make it unique.
+     *
+     * @param {string} name - The name to generate the panel ID from.
+     * @returns {string} The unique panel ID.
+     */
+    const uniquePanelId = name => {
+      name = encodeURIComponent(name.toLowerCase().replace(/[\s]/g, '-'))
+      if (Object.keys(panelIds).includes(name)) {
+        name += ++panelIds[name]
+      } else {
+        panelIds[name] = 1
+      }
+      return name
+    }
+
+    /**
+     * Identifies the panel name based on the given item, taking into account
+     * the various ways that panel names can be specified in R Markdown, Quarto,
+     * or revealjs.
+     *
+     * @param {HTMLElement} item - The item to identify the panel name from.
+     * @returns {string} The identified panel name or undefined if no name can
+     * be identified.
+     */
+    const identifyPanelName = item => {
+      let name = 'Panel'
+
+      // If the item doesn't have a parent element, then we've already processed
+      // it, probably because we're in an Rmd, and it's been removed from the DOM
+      if (!item.parentElement) {
+        return
+      }
+
+      if (item.matches('.panel')) {
+        if (item.dataset.name) return item.dataset.name
+        if (item.getAttribute('name')) return item.getAttribute('name')
+      }
+
+      // In R Markdown when header-attrs.js is present, we may have found a
+      // section header but the class attributes won't be duplicated on the <hX> tag
+      if (
+        (item.tagName === 'SECTION' || item.classList.contains('section')) &&
+        /^H[1-6]/.test(item.children[0].tagName)
+      ) {
+        name = item.children[0].textContent
+        item.classList.remove('panel-name')
+        item.removeChild(item.children[0])
+        return name
+      }
+
+      const nameDiv = item.querySelector('.panel-name')
+      if (!nameDiv) return name
+
+      // In remarkjs the .panel-name span might be in a paragraph tag
+      // and if the <p> is empty, we'll remove it
+      if (
+        nameDiv.tagName === 'SPAN' &&
+        nameDiv.parentNode.tagName === 'P' &&
+        nameDiv.textContent === nameDiv.parentNode.textContent
+      ) {
+        name = nameDiv.textContent
+        item.removeChild(nameDiv.parentNode)
+        return name
+      }
+
+      // If none of the above, remove the nameDiv and return the name
+      name = nameDiv.textContent
+      nameDiv.parentNode.removeChild(nameDiv)
+      return name
+    }
+
+    function getElementAttributes (el) {
+      return {
+        classes: Array.from(el.classList)
+          .filter(c => !/^level\d$/.test(c))
+          .toString(),
+        style: el.style.cssText,
+        dataset: el.dataset
+      }
+    }
+
+    /**
+     * Processes an original section of content and prepare data for the content
+     * panel the item will become.
+     *
+     * @param {HTMLElement} item - The panel item to process.
+     * @returns {Object|null} - An object containing the panel's name, content,
+     * id, active status, and other attributes. Returns null if the panel name
+     * cannot be identified.
+     */
+    const processPanelItem = item => {
+      const name = identifyPanelName(item)
+      if (!name) {
+        return null
+      }
+      return {
+        name,
+        content: item.children,
+        id: uniquePanelId(name),
+        active:
+          item.dataset &&
+          ['', 'true'].includes(item.dataset.active?.toLowerCase()),
+        ...getElementAttributes(item)
+      }
+    }
+
+    /**
+     * Retrieves the current panel from the URL parameters.
+     * @param {string} panelsetId - The ID of the panelset.
+     * @returns {string|null} - The current panel ID or null if not in the URL.
+     */
+    const getCurrentPanelFromUrl = panelsetId => {
+      const params = new URLSearchParams(window.location.search)
+      return params.get(panelsetId)
+    }
+
+    /**
+     * Returns the initial selected panel ID based on the provided panels and
+     * the ID of the corresponding panelset. The active panel is chosen
+     * following:
+     *
+     * 1. If the panselset appears in the URL, use the panel ID from the URL.
+     * 2. If there is an active panel, use the ID of the first active panel.
+     * 3. Use the ID of the first panel in the array.
+     *
+     * Note that groups are not considered here. If the panelset is part of a
+     * group, the group state will be updated after the initial panelset is
+     * created.
+     *
+     * @param {Array} panels - The array of panel objects.
+     * @param {string} panelsetId - The ID of the panelset specified in the URL.
+     * @returns {string} - The ID of the initial selected panel.
+     */
+    function getInitSelectedPanel (panels, panelsetId) {
+      const panelIds = panels.map(p => p.id)
+
+      const panelSelectedUrl = getCurrentPanelFromUrl(panelsetId)
+      if (panelSelectedUrl && panelIds.includes(panelSelectedUrl)) {
+        return panelSelectedUrl
+      }
+
+      const panelsActive = panels.filter(p => p.active)
+      if (panelsActive.length) {
+        return panelsActive[0].id
+      }
+
+      return panels[0].id
+    }
+
+    /**
+     * Creates a panel set element with header tabs and corresponding content
+     * sections.
+     *
+     * @param {Array} panels - An array of panel objects.
+     * @param {Object} options - An object containing optional parameters for
+     * the panel set.
+     * @param {string} options.id - The ID of the panel set element.
+     * @param {string} options.classes - Additional CSS classes to be applied to
+     * the panel set element.
+     * @param {string} options.style - Inline CSS styles to be applied to the
+     * panel set element.
+     * @param {Object} options.dataset - Custom data attributes to be added to
+     * the panel set element.
+     * @returns {HTMLElement} - The created panel set element.
+     */
+    const reflowPanelSet = (panels, { id, classes, style, dataset }) => {
+      const res = document.createElement('div')
+      res.classList = 'panelset' + (classes ? ' ' + classes : '')
+      res.id = uniquePanelsetId(id)
+      res.style.cssText = style
+      if (dataset) {
+        Object.keys(dataset).forEach(key => {
+          res.dataset[key] = dataset[key]
+        })
+      }
+
+      const panelSelected = getInitSelectedPanel(panels, res.id)
+
+      // create header row
+      const headerRow = document.createElement('ul')
+      headerRow.className = 'panel-tabs'
+      headerRow.setAttribute('role', 'tablist')
+      panels
+        .map((p, idx) => {
+          const thisPanelIsActive = panelSelected === p.id
+
+          const panelHeaderItem = document.createElement('li')
+          panelHeaderItem.id = res.id + '_' + p.id // #panelsetid_panelid
+          panelHeaderItem.className = 'panel-tab'
+          panelHeaderItem.setAttribute('role', 'tab')
+          if (thisPanelIsActive) {
+            panelHeaderItem.tabIndex = 0
+          }
+          panelHeaderItem.classList.toggle(
+            'panel-tab-active',
+            thisPanelIsActive
+          )
+          panelHeaderItem.setAttribute('aria-selected', thisPanelIsActive)
+
+          if (p.dataset) {
+            Object.keys(p.dataset).forEach(key => {
+              panelHeaderItem.dataset[key] = p.dataset[key]
+            })
+          }
+
+          const panelHeaderLink = document.createElement('a')
+          panelHeaderLink.href =
+            '?' + res.id + '=' + p.id + '#' + panelHeaderItem.id
+          panelHeaderLink.setAttribute('onclick', 'return false;')
+          panelHeaderLink.tabIndex = -1 // list item is tabable, not link
+          panelHeaderLink.innerHTML = p.name
+          panelHeaderLink.setAttribute('aria-controls', p.id)
+
+          panelHeaderItem.appendChild(panelHeaderLink)
+          return panelHeaderItem
+        })
+        .forEach(el => headerRow.appendChild(el))
+
+      res.appendChild(headerRow)
+
+      panels
+        .map((p, idx) => {
+          const thisPanelIsActive = panelSelected === p.id
+          const panelTag = inRevealjs() ? 'div' : 'section'
+          const panelContent = document.createElement(panelTag)
+          panelContent.classList = p.classes ? 'panel ' + p.classes : 'panel'
+          panelContent.style.cssText = p.style
+          panelContent.classList.toggle('panel-active', thisPanelIsActive)
+          panelContent.id = p.id
+          // https://www.w3.org/WAI/ARIA/apg/patterns/tabs/examples/tabs-automatic/
+          panelContent.setAttribute('role', 'tabpanel')
+          panelContent.setAttribute('aria-labelledby', p.id)
+          panelContent.tabIndex = 0
+          Array.from(p.content).forEach(el => panelContent.appendChild(el))
+          return panelContent
+        })
+        .forEach(el => res.appendChild(el))
+
+      return res
+    }
+
+    /*
+     * Update selected panel for panelset or delete panelset from query string
+     *
+     * @param panelset Panelset ID to update in the search params @param panel
+     * Panel ID of selected panel in panelset, or null to delete from search
+     * params @param params Current params object, or params from
+     * window.location.search
+     */
+
+    /**
+     * Updates the search parameters with the specified panelset and panel
+     * values. If a panel is provided, it sets the panelset and panel in the
+     * search parameters. If no panel is provided, it removes the panelset from
+     * the search parameters.
+     *
+     * @param {string} panelsetId - The ID of the panelset.
+     * @param {string} [panelId] - The ID of the panel (optional).
+     * @param {URLSearchParams} [params=new
+     * URLSearchParams(window.location.search)] - The search parameters object
+     * (optional).
+     * @returns {URLSearchParams} - The updated search parameters object.
+     */
+    function updateSearchParams (
+      panelsetId,
+      panelId,
+      params = new URLSearchParams(window.location.search)
+    ) {
+      if (panelId) {
+        params.set(panelsetId, panelId)
+      } else {
+        params.delete(panelsetId)
+      }
+      return params
+    }
+
+    /*
+     * Update the URL to match params
+     */
+    const updateUrl = params => {
+      if (typeof params === 'undefined') return
+      params = params.toString() ? '?' + params.toString() : ''
+      const { pathname, hash } = window.location
+      const uri = pathname + params + hash
+      window.history.replaceState(uri, '', uri)
+    }
+
+    /**
+     * Handles the click event on a panel tab within a panelset.
+     * @param {HTMLElement} clicked - The clicked element.
+     */
+    function handleClickedPanel (clicked) {
+      const panelset = clicked.closest('.panelset')
+      if (!panelset) return
+
+      clicked = clicked.closest('.panel-tab')
+      if (!clicked) return
+
+      togglePanel(panelset, clicked)
+    }
+
+    /**
+     * Handles keydown events for the `.panel-tabs` element within a panelset.
+     * This performs two actions: toggling the panel via space or enter and
+     * moving to the next or previous panel via arrow keys, depending on the
+     * panelset orientation.
+     *
+     * @see https://www.w3.org/WAI/ARIA/apg/patterns/tabs/examples/tabs-automatic/
+     *
+     * @param {HTMLElement} panelset - The panelset element.
+     * @param {KeyboardEvent} ev - The keydown event.
+     */
+    function handlePanelTabsKeydown (panelset, ev) {
+      const target = ev.currentTarget.querySelector('.panel-tab-active')
+
+      function stopEvent () {
+        ev.preventDefault()
+        if (inRemarkjs() || inRevealjs()) {
+          ev.stopPropagation()
+        }
+      }
+
+      if (ev.code === 'Space' || ev.code === 'Enter') {
+        togglePanel(panelset, ev.target)
+        stopEvent()
+        return
+      }
+
+      let direction
+
+      if (panelset.getAttribute('aria-orientation') === 'vertical') {
+        if (ev.code === 'ArrowUp') direction = 'prev'
+        if (ev.code === 'ArrowDown') direction = 'next'
+      }
+
+      if (
+        inRemarkSlide(panelset) ||
+        inRevealjs() ||
+        panelset.getAttribute('aria-orientation') === 'horizontal'
+      ) {
+        if (ev.code === 'ArrowLeft') direction = 'prev'
+        if (ev.code === 'ArrowRight') direction = 'next'
+      }
+
+      if (!direction) return
+
+      const newActive = toggleSibling(panelset, target, direction)
+      if (newActive) stopEvent()
+      return newActive
+    }
+
+    /**
+     * Finds a panel by name within a panelset. `name` is compared with the
+     * panel tab text content, case-insensitive and trimmed.
+     *
+     * @param {HTMLElement} panelset - The panelset element.
+     * @param {string} name - The name of the panel tab to find.
+     * @returns {HTMLElement|undefined} - The matching panel element, or
+     * undefined if not found.
+     */
+    function findPanelByName (panelset, name) {
+      const matches = Array.from(
+        panelset.querySelectorAll(':scope > .panel-tabs > .panel-tab')
+      ).filter(p => p.innerText.toLowerCase().trim() === name)
+
+      if (!matches) {
+        console.error(
+          `No panel with name "${name}" found in panelset ${panelset.id}`,
+          { panelset, name }
+        )
+        return
+      }
+
+      if (matches > 1) {
+        console.warn(
+          `Multiple panels with name "${name}" found in panelset ${panelset.id}`,
+          { panelset, name }
+        )
+      }
+      return matches[0]
+    }
+
+    /**
+     * Toggles the visibility of a panel in a panelset.
+     *
+     * @param {HTMLElement} panelset - The panelset element containing the
+     * panels.
+     * @param {HTMLElement|string} target - The target panel or panel name to
+     * toggle.
+     * @param {'string'} [update='all'] - The update mode for the
+     * panelset. Possible values are 'all', 'group', or 'url'.
+     */
+    function togglePanel (panelset, target, update = 'all', tabIndex = 0) {
+      // target is a .panel-tab element or a panel name
+      if (!(target instanceof window.HTMLElement)) {
+        target = findPanelByName(panelset, target)
+        if (!target) return
+      }
+
+      const tabs = panelset.querySelectorAll(
+        ':scope > .panel-tabs > .panel-tab'
+      )
+      const panels = panelset.querySelectorAll(':scope > .panel')
+
+      const targetPanelId = target.children[0].getAttribute('aria-controls')
+
+      // Set tab state
+      Array.from(tabs).forEach(t => {
+        t.classList.remove('panel-tab-active')
+        t.setAttribute('aria-selected', false)
+        t.removeAttribute('tabindex')
+      })
+
+      target.classList.add('panel-tab-active')
+      target.setAttribute('aria-selected', true)
+      target.tabIndex = tabIndex
+
+      Array.from(panels).forEach(p => {
+        const isActive = p.id === targetPanelId
+        p.classList.toggle('panel-active', isActive)
+        p.hidden = !isActive
+      })
+
+      // emit window resize event to trick html widgets into fitting to the panel width
+      window.dispatchEvent(new window.Event('resize'))
+
+      if (['all', 'group'].includes(update) && panelset.dataset.group) {
+        const group = panelset.dataset.group
+        const panel = target.innerText.toLowerCase().trim()
+
+        setStoredPanelGroupState(group, panel)
+
+        panelset.dispatchEvent(
+          new window.CustomEvent('panelset:group', {
+            bubbles: true,
+            detail: { group, panel }
+          })
+        )
+      }
+
+      // update query string
+      if (['all', 'url'].includes(update)) {
+        const params = updateSearchParams(panelset.id, targetPanelId)
+        updateUrl(params)
+      }
+    }
+
+    /**
+     * Toggles the sibling panel in the specified direction.
+     *
+     * @param {HTMLElement} panelset - The panelset element.
+     * @param {HTMLElement} target - The target panel element.
+     * @param {"next" | "prev"} [direction="next"] - The direction to toggle the
+     * sibling panel. Possible values are "next" and "prev".
+     */
+    function toggleSibling (panelset, target, direction = 'next') {
+      let sibling
+      switch (direction) {
+        case 'next':
+          sibling = target.nextSibling
+          break
+        case 'prev':
+          sibling = target.previousSibling
+          break
+      }
+
+      if (!sibling) return
+      const update = parseInt(target.tabIndex) < 0 ? 'url' : 'all'
+      togglePanel(panelset, sibling, update, target.tabIndex)
+      sibling.focus()
+      return sibling
+    }
+
+    /**
+     * Initializes a panel set from the original markup into a full panelset.
+     * This includes creating the panel tabs, rearranging content, adding event
+     * listeners, and synchronizing with a panel set group.
+     *
+     * @param {HTMLElement} panelset - The `.panelset` element to initialize.
+     * @returns {HTMLElement} - The new panelset element.
+     */
+    const initPanelSet = panelset => {
+      let panels = Array.from(panelset.querySelectorAll(':scope > .panel, :scope > .cell > .panel'))
+
+      const pandocSectionSelector = ':is(section, .section)[class*="level"]'
+      if (!panels.length) {
+        // we're in tabset-alike R Markdown or Quarto
+        const getSectionLevel = el => {
+          const levels = [...el.classList].filter(s => s.match(/^level/))
+          return levels.length ? levels[0].replace('level', '') : levels
+        }
+
+        // {.panelset} applied to a section heading
+        let panelsetLevel = getSectionLevel(panelset)
+
+        if (!panelsetLevel.length) {
+          // {.panelset} applied as a fenced div around subsections
+          const subSections = panelset.querySelectorAll(pandocSectionSelector)
+          if (!subSections.length) return
+
+          panelsetLevel = Array.from(subSections)
+            .map(getSectionLevel)
+            .map(x => parseInt(x))
+            .reduce((acc, x) => Math.min(acc, x), Infinity)
+
+          panelsetLevel = +panelsetLevel - 1
+        }
+
+        // move children that aren't inside a section up above the panelset
+        Array.from(panelset.children).forEach(function (el) {
+          if (el.matches(pandocSectionSelector)) return
+          panelset.parentElement.insertBefore(el, panelset)
+        })
+
+        // panels are all .sections with .level<panelsetLevel + 1>
+        const panelLevel = +panelsetLevel + 1
+        panels = Array.from(
+          panelset.querySelectorAll(`:is(section, .section).level${panelLevel}`)
+        )
+      }
+
+      if (!panels.length) return
+
+      // create content panels
+      const contents = panels.map(processPanelItem).filter(o => o !== null)
+
+      // create panelset
+      const panelsetAttrs = getElementAttributes(panelset)
+      const newPanelSet = reflowPanelSet(contents, {
+        id: panelset.id,
+        ...panelsetAttrs
+      })
+      newPanelSet.classList = panelset.classList
+
+      // set orientation
+      const isVertical = panelset.matches(
+        '.sideways, .vertical, [aria-orientation="vertical"]'
+      )
+      newPanelSet.setAttribute(
+        'aria-orientation',
+        isVertical ? 'vertical' : 'horizontal'
+      )
+
+      panelset.parentNode.insertBefore(newPanelSet, panelset)
+      panelset.parentNode.removeChild(panelset)
+
+      // click and touch events
+      const panelTabs = newPanelSet.querySelector('.panel-tabs')
+      ;['click', 'touchend'].forEach(eventType => {
+        panelTabs.addEventListener(eventType, function (ev) {
+          handleClickedPanel(ev.target)
+          ev.stopPropagation()
+        })
+      })
+      panelTabs.addEventListener('touchmove', function (ev) {
+        ev.preventDefault()
+      })
+
+      // key events
+      newPanelSet
+        .querySelector('.panel-tabs')
+        .addEventListener('keydown', ev => {
+          handlePanelTabsKeydown(newPanelSet, ev)
+        })
+
+      // synchronize with the panelset group
+      if (newPanelSet.dataset.group) {
+        window.addEventListener('panelset:group', ev => {
+          if (ev.target === newPanelSet) return
+          if (ev.detail.group !== newPanelSet.dataset.group) return
+          togglePanel(newPanelSet, ev.detail.panel, 'url')
+        })
+
+        const groupData = getStoredPanelSettings()
+        const currentPanelFromUrl = getCurrentPanelFromUrl(newPanelSet.id)
+
+        if (!currentPanelFromUrl && groupData[newPanelSet.dataset.group]) {
+          togglePanel(newPanelSet, groupData[newPanelSet.dataset.group], null)
+        }
+      }
+
+      return newPanelSet
+    }
+
+    const localStorageKey = 'panelset-data'
+
+    /**
+     * Retrieves or creates the stored panel settings from local storage.
+     * @returns {{['string']: 'string'} | {}} The stored panel settings, as an
+     * empty object or an object with group names as keys and the currently
+     * activated panel names as values.
+     */
+    function getStoredPanelSettings () {
+      const data = window.localStorage.getItem(localStorageKey)
+      if (!data) {
+        window.localStorage.setItem(localStorageKey, '{}')
+        return {}
+      }
+      if (data) {
+        return JSON.parse(data)
+      }
+    }
+
+    function setStoredPanelSettings (data) {
+      window.localStorage.setItem(localStorageKey, JSON.stringify(data))
+    }
+
+    /**
+     * Sets the stored panel group state in local storage. The group `name` is
+     * used as a key and is globally checked across pages in the same domain.
+     *
+     * @param {string} name - The name of the panel group.
+     * @param {any} value - The value to set for the panel group.
+     */
+    function setStoredPanelGroupState (name, value) {
+      const data = getStoredPanelSettings()
+      data[name] = value
+      setStoredPanelSettings(data)
+    }
+
+    // initialize panels
+    document
+      .querySelectorAll('[data-panelset="true"]')
+      .forEach(el => {
+        const isCell = el.classList.contains('cell')
+        const hasParentPanelset = el.parentElement.classList.contains('panelset')
+        if (!isCell || !hasParentPanelset) {
+          // We let `data-panelset="true"` create a new panelset, unless it's on
+          // a code cell that's already inside a panelset, in which case the
+          // panels will be folded into the parent panelset.
+          el.classList.add('panelset')
+        }
+      })
+
+    const panelsets = { atomic: [], nested: [] }
+    Array.from(document.querySelectorAll('.panelset')).forEach(el => {
+      if (el.querySelector('.panelset')) {
+        // push nested panelsets to the start of the list (inner -> outer)
+        panelsets.nested.unshift(el)
+      } else {
+        // put panelsets without nested panelsets at the beginning
+        panelsets.atomic.push(el)
+      }
+    })
+
+    // initialize atomic panelsets first, then nested panelsets
+    panelsets.atomic.forEach(initPanelSet)
+    panelsets.nested.forEach(initPanelSet)
+
+    if (inRemarkjs()) {
+      const getVisibleActivePanelInfo = () => {
+        const slidePanels = document.querySelectorAll(
+          '.remark-visible .panel-tab-active'
+        )
+
+        if (!slidePanels.length) return null
+
+        return slidePanels.map(panel => {
+          return {
+            panel,
+            panelId: panel.children[0].getAttribute('aria-controls'),
+            panelSetId: panel.parentNode.parentNode.id
+          }
+        })
+      }
+
+      slideshow.on('hideSlide', slide => {
+        // clear focus if we had a panel-tab selected
+        document.activeElement.blur()
+
+        // clear search query for panelsets in current slide
+        const params = [
+          ...document.querySelectorAll('.remark-visible .panelset')
+        ].reduce(function (params, panelset) {
+          return updateSearchParams(panelset.id, null, params)
+        }, new URLSearchParams(window.location.search))
+
+        updateUrl(params)
+      })
+
+      slideshow.on('afterShowSlide', slide => {
+        const slidePanels = getVisibleActivePanelInfo()
+
+        if (slidePanels) {
+          // only first panel gets focus
+          slidePanels[0].panel.focus()
+          // but still update the url to reflect all active panels
+          const params = slidePanels.reduce(function (
+            params,
+            { panelId, panelSetId }
+          ) {
+            return updateSearchParams(panelSetId, panelId, params)
+          },
+          new URLSearchParams(window.location.search))
+          updateUrl(params)
+        }
+      })
+    }
+
+    if (inRevealjs()) {
+      window.Reveal.on('slidechanged', function ({ currentSlide, previousSlide, ...data }) {
+        // clear focus from any active panel-tab in the previous slide
+        const previousActive = previousSlide.querySelector('.panelset .panel-tab:focus')
+        if (previousActive) {
+          previousActive.blur()
+          previousActive.removeAttribute('tabindex')
+        }
+
+        const previousPanelsets = previousSlide.querySelectorAll('.panelset')
+        if (previousPanelsets.length) {
+          // clear search query for panelsets in previous slide
+          const params = [
+            ...previousSlide.querySelectorAll('.panelset')
+          ].reduce(function (params, panelset) {
+            return updateSearchParams(panelset.id, null, params)
+          }, new URLSearchParams(window.location.search))
+
+          updateUrl(params)
+        }
+
+        const firstPanelset = currentSlide.querySelector('.panelset')
+        if (!firstPanelset) return
+
+        const panelIdFromUrl = getCurrentPanelFromUrl(firstPanelset.id)
+        const panelFromUrl = !panelIdFromUrl
+          ? null
+          : firstPanelset
+            .querySelector(`[aria-controls="${panelIdFromUrl}"]`)
+            ?.parentElement
+
+        const firstPanel = panelIdFromUrl
+          ? panelFromUrl
+          : firstPanelset.querySelector('.panel-tab-active')
+
+        if (!firstPanel) return
+        firstPanel.setAttribute('tabindex', '-1')
+        firstPanel.focus()
+
+        // update url for all panels on this slide
+        const params = [
+          ...currentSlide.querySelectorAll('.panelset')
+        ].reduce(function (params, panelset) {
+          return updateSearchParams(
+            panelset.id,
+            panelset.querySelector('.panel-active').id,
+            params
+          )
+        }, new URLSearchParams(window.location.search))
+
+        updateUrl(params)
+      })
+    }
+  })
+})()
diff --git a/docs/sitemap.xml b/docs/sitemap.xml
index aac761f7..79c16a8e 100644
--- a/docs/sitemap.xml
+++ b/docs/sitemap.xml
@@ -32,6 +32,10 @@
     <loc>https://yjunechoe.github.io/posts/2024-09-22-fetch-files-web/</loc>
     <lastmod>2024-09-22T18:49:08-04:00</lastmod>
   </url>
+  <url>
+    <loc>https://yjunechoe.github.io/posts/2023-06-11-row-relational-operations/</loc>
+    <lastmod>2024-09-22T19:50:35-04:00</lastmod>
+  </url>
   <url>
     <loc>https://yjunechoe.github.io/posts/2024-07-21-enumerate-possible-options/</loc>
     <lastmod>2024-09-01T17:53:55-04:00</lastmod>
@@ -60,10 +64,6 @@
     <loc>https://yjunechoe.github.io/posts/2023-07-09-x-y-problem/</loc>
     <lastmod>2023-07-10T04:24:43-04:00</lastmod>
   </url>
-  <url>
-    <loc>https://yjunechoe.github.io/posts/2023-06-11-row-relational-operations/</loc>
-    <lastmod>2023-06-11T00:51:42-04:00</lastmod>
-  </url>
   <url>
     <loc>https://yjunechoe.github.io/posts/2022-11-13-dataframes-jl-and-accessories/</loc>
     <lastmod>2022-11-15T09:59:05-05:00</lastmod>