friendly · August 15, 2022 18:23
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 <h1 class="title">Quarto: Test LaTeX newcommands in HTML doc</h1>
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 <p>In a Quarto document, I want to be able to use more extensive math LaTeX features than are typical for simple equations, using some extensions presumably provided by <code>mathjax</code>, particularly for matrix expressions. (I think, but am not sure, that the latest Quarto uses <code>mathjax</code> v 3.2. )</p>
 <p>As a simiple example, here I use a straightforward math equation with no special stuff, with <code>\mathbf{}</code> used for matrices and vectors. This works well and the equation appears nicely in the RStudio editor window. The source code is:</p>
 <div class="sourceCode" id="cb1"><pre class="sourceCode latex code-with-copy"><code class="sourceCode latex"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="ss">$$</span><span class="sc">\mathbf</span><span class="ss">{y} = </span><span class="sc">\mathbf</span><span class="ss">{X} </span><span class="sc">\;</span><span class="ss"> </span><span class="sc">\mathbf</span><span class="ss">{</span><span class="sc">\beta</span><span class="ss">} + </span><span class="sc">\mathbf</span><span class="ss">{u}, </span></span>
 <span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="sc">\quad\mbox</span><span class="ss">{   with   }</span><span class="sc">\quad</span><span class="ss"> </span></span>
 <span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="sc">\mathbf</span><span class="ss">{u} </span><span class="sc">\sim</span><span class="ss"> </span><span class="sc">\mathcal</span><span class="ss">{N} (0, </span><span class="sc">\sigma</span><span class="ss">^2 </span><span class="sc">\mathbf</span><span class="ss">{I}) ,</span></span>
 <span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="ss">$$</span></span>
 <span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <p><span class="math display">\[\mathbf{y} = \mathbf{X} \; \mathbf{\beta} + \mathbf{u},
 \quad\mbox{   with   }\quad
 \mathbf{u} \sim \mathcal{N} (0, \sigma^2 \mathbf{I}) ,
 \]</span></p>
 <p>However, in another version, Iâd like to show the size of matrices using subscripts.<br>
 This also works, but it fails if I try to include an equation number <code>(eq-mlm)</code>.</p>
 <div class="sourceCode" id="cb2"><pre class="sourceCode latex code-with-copy"><code class="sourceCode latex"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="ss">$$</span></span>
 <span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="sc">\mathbf</span><span class="ss">{Y}_{n </span><span class="sc">\times</span><span class="ss"> p} = </span></span>
 <span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="sc">\mathbf</span><span class="ss">{X}_{n </span><span class="sc">\times</span><span class="ss"> q} </span><span class="sc">\,</span><span class="ss"> </span><span class="sc">\mathbf</span><span class="ss">{B}_{q </span><span class="sc">\times</span><span class="ss"> p} + </span><span class="sc">\mathbf</span><span class="ss">{U}_{n </span><span class="sc">\times</span><span class="ss"> p} </span><span class="sc">\:\:</span><span class="ss"> ,</span></span>
 <span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="ss">$$</span></span>
 <span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <p><span class="math display">\[
 \mathbf{Y}_{n \times p} =
 \mathbf{X}_{n \times q} \, \mathbf{B}_{q \times p} + \mathbf{U}_{n \times p} \:\: ,
 \]</span></p>
 <section id="newcommand" class="level2">
 <h2 class="anchored" data-anchor-id="newcommand">\newcommand</h2>
 <p>Now, try to define some abbreviated latex commands for these math expressions. The <a href="https://quarto.org/docs/authoring/markdown-basics.html">Quarto authoring doc</a> says these should work</p>
 <blockquote class="blockquote">
 <p>For HTML math processed using MathJax (the default) you can use the <code>\def</code>, <code>\newcommand</code>, <code>\renewcommand</code>, <code>\newenvironment</code>, <code>\renewenvironment</code>, and <code>\let</code> commands to create your own macros and environments.</p>
 </blockquote>
 <div class="sourceCode" id="cb3"><pre class="sourceCode latex code-with-copy"><code class="sourceCode latex"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="ss">$$</span></span>
 <span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a><span class="sc">\renewcommand*</span><span class="ss">{</span><span class="sc">\vec</span><span class="ss">}[1]{</span><span class="sc">\mathbf</span><span class="ss">{#1}} </span></span>
 <span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a><span class="sc">\newcommand*</span><span class="ss">{</span><span class="sc">\mat</span><span class="ss">}[1]{</span><span class="sc">\mathbf</span><span class="ss">{#1}} </span></span>
 <span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a><span class="sc">\newcommand</span><span class="ss">{</span><span class="sc">\trans</span><span class="ss">}{^</span><span class="sc">\mathsf</span><span class="ss">{T}} </span></span>
 <span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a><span class="sc">\newcommand*</span><span class="ss">{</span><span class="sc">\diag</span><span class="ss">}[1]{</span><span class="sc">\mathrm</span><span class="ss">{diag}</span><span class="sc">\,</span><span class="ss"> #1}}</span></span>
 <span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a><span class="sc">\newcommand</span><span class="ss">{</span><span class="sc">\sizedmat</span><span class="ss">}[2]{</span><span class="sc">\underset</span><span class="ss">{</span><span class="sc">\mathbf</span><span class="ss">{#1}}{(#2)}}</span></span>
 <span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a><span class="ss">$$</span></span>
 <span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <!-- % \newcommand{\sizedmat}[2]{\mathord{\mathop{\mat{#1}}\limits_{(#2)}} -->
 <p>The docs say to include this in a <code>::: {.hidden}</code> div:</p>
 <div class="hidden">
 <p><span class="math display">\[
 \renewcommand*{\vec}[1]{\mathbf{#1}}
 \newcommand*{\mat}[1]{\mathbf{#1}}
 \newcommand{\trans}{^\mathsf{T}}
 \newcommand*{\diag}[1]{\mathrm{diag}\, #1}}
 \newcommand{\sizedmat}[2]{\underset{\mathbf{#1}}{(#2)}}
 \]</span></p>
 </div>
 <p>Then, I try to use them:</p>
 <div class="sourceCode" id="cb4"><pre class="sourceCode latex code-with-copy"><code class="sourceCode latex"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="ss">$$</span></span>
 <span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="ss">{</span><span class="sc">\sizedmat</span><span class="ss">{</span><span class="sc">\mat</span><span class="ss">{Y}}{n </span><span class="sc">\times</span><span class="ss"> p}} = </span></span>
 <span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a><span class="ss">{</span><span class="sc">\sizedmat</span><span class="ss">{</span><span class="sc">\mat</span><span class="ss">{X}}{n </span><span class="sc">\times</span><span class="ss"> q}} </span><span class="sc">\,</span><span class="ss"> </span></span>
 <span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a><span class="ss">{</span><span class="sc">\sizedmat</span><span class="ss">{</span><span class="sc">\mat</span><span class="ss">{B}}{q </span><span class="sc">\times</span><span class="ss"> p}} + </span></span>
 <span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a><span class="ss">{</span><span class="sc">\sizedmat</span><span class="ss">{</span><span class="sc">\mat</span><span class="ss">{U}}{n </span><span class="sc">\times</span><span class="ss"> p}} ,</span></span>
 <span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a><span class="ss">$$</span></span>
 <span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <p>This doesnât work, perhaps because the <code>\newcommand</code> block wasnât interpreted as equations. (Or, could this be because of the <code>\underset</code> ?)</p>
 <p><span class="math display">\[
 {\sizedmat{\mat{Y}}{n \times p}} =
 {\sizedmat{\mat{X}}{n \times q}} \,
 {\sizedmat{\mat{B}}{q \times p}} +
 {\sizedmat{\mat{U}}{n \times p}} ,
 \]</span></p>
 </section>
 <section id="other-mathjax-extensions" class="level2">
 <h2 class="anchored" data-anchor-id="other-mathjax-extensions">Other <code>mathjax</code> extensions</h2>
 <p>Letâs try <a href="https://github.com/andrewheiss/bayesf22.classes.andrewheiss.com">Andrew Heissâ nice equations</a> using the mathjax <code>mathtools</code> extension. This LaTeX defines some colors:</p>
 <div class="sourceCode" id="cb5"><pre class="sourceCode latex code-with-copy"><code class="sourceCode latex"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="ss">$$</span></span>
 <span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="sc">\require</span><span class="ss">{mathtools}</span></span>
 <span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="sc">\definecolor</span><span class="ss">{bayesred}{RGB}{147, 30, 24}</span></span>
 <span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="sc">\definecolor</span><span class="ss">{bayesblue}{RGB}{32, 35, 91}</span></span>
 <span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a><span class="sc">\definecolor</span><span class="ss">{bayesorange}{RGB}{218, 120, 1}</span></span>
 <span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a><span class="sc">\definecolor</span><span class="ss">{grey}{RGB}{128, 128, 128}</span></span>
 <span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a><span class="ss">{</span><span class="sc">\color</span><span class="ss">{bayesorange} P (</span><span class="sc">\text</span>{H}<span class="ss"> </span><span class="sc">\mid</span><span class="ss"> </span><span class="sc">\text</span>{E}<span class="ss">)} = </span><span class="sc">\frac</span></span>
 <span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a><span class="ss">{{</span><span class="sc">\color</span><span class="ss">{bayesred} P(</span><span class="sc">\text</span>{H}<span class="ss">)} </span><span class="sc">\times</span><span class="ss"> </span></span>
 <span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a><span class="ss">{</span><span class="sc">\color</span><span class="ss">{bayesblue}P(</span><span class="sc">\text</span>{E}<span class="ss"> </span><span class="sc">\mid</span><span class="ss"> </span><span class="sc">\text</span>{H}<span class="ss">)}}</span></span>
 <span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a><span class="ss">{</span><span class="sc">\color</span><span class="ss">{grey} {P(</span><span class="sc">\text</span>{E}<span class="ss">)}}</span></span>
 <span id="cb5-11"><a href="#cb5-11" aria-hidden="true" tabindex="-1"></a><span class="ss">$$</span></span>
 <span id="cb5-12"><a href="#cb5-12" aria-hidden="true" tabindex="-1"></a></span>
 <span id="cb5-13"><a href="#cb5-13" aria-hidden="true" tabindex="-1"></a></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="hidden">
 <p><span class="math display">\[
 \require{mathtools}
 \definecolor{bayesred}{RGB}{147, 30, 24}
 \definecolor{bayesblue}{RGB}{32, 35, 91}
 \definecolor{bayesorange}{RGB}{218, 120, 1}
 \definecolor{grey}{RGB}{128, 128, 128}
 {\color{bayesorange} P (\text{H} \mid \text{E})} = \frac
 {{\color{bayesred} P(\text{H})} \times
 {\color{bayesblue}P(\text{E} \mid \text{H})}}
 {\color{grey} {P(\text{E})}}
 \]</span></p>
 </div>
 <p>This uses these colors:</p>
 <div class="sourceCode" id="cb6"><pre class="sourceCode latex code-with-copy"><code class="sourceCode latex"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="ss">$$</span></span>
 <span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="ss">{</span><span class="sc">\color</span><span class="ss">{grey} </span><span class="sc">\overbracket</span><span class="ss">[0.25pt]{</span><span class="sc">\color</span><span class="ss">{bayesorange} P (</span><span class="sc">\text</span>{Unknown}<span class="ss"> </span><span class="sc">\mid</span><span class="ss"> </span><span class="sc">\text</span>{Data}<span class="ss">)}^{</span><span class="sc">\text</span>{Posterior}<span class="ss">}} = </span><span class="sc">\frac</span></span>
 <span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="ss">{{</span><span class="sc">\color</span><span class="ss">{grey} </span><span class="sc">\overbracket</span><span class="ss">[0.25pt]{</span><span class="sc">\color</span><span class="ss">{bayesred} P (</span><span class="sc">\text</span>{Unknown}<span class="ss">)}^{</span><span class="sc">\text</span>{Prior}<span class="ss">}} </span><span class="sc">\times</span><span class="ss"> </span></span>
 <span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="ss">{</span><span class="sc">\color</span><span class="ss">{grey} </span><span class="sc">\overbracket</span><span class="ss">[0.25pt]{</span><span class="sc">\color</span><span class="ss">{bayesblue} P (</span><span class="sc">\text</span>{Data}<span class="ss"> </span><span class="sc">\mid</span><span class="ss"> </span><span class="sc">\text</span>{Unknown}<span class="ss">)}^{</span><span class="sc">\text</span>{Likelihood}<span class="ss">}}}</span></span>
 <span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a><span class="ss">{{</span><span class="sc">\color</span><span class="ss">{grey} </span><span class="sc">\underbracket</span><span class="ss">[0.25pt]{{</span><span class="sc">\color</span><span class="ss">{grey} P(</span><span class="sc">\text</span>{E}<span class="ss">)}}_{</span><span class="sc">\text</span>{Average likelihood}<span class="ss">}}}</span></span>
 <span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a><span class="ss">$$</span></span>
 <span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <p>The result does not appear nicely in the RStudio editor window, but works fine in the output.</p>
 <p><span class="math display">\[
 {\color{grey} \overbracket[0.25pt]{\color{bayesorange} P (\text{Unknown} \mid \text{Data})}^{\text{Posterior}}} = \frac
 {{\color{grey} \overbracket[0.25pt]{\color{bayesred} P (\text{Unknown})}^{\text{Prior}}} \times
 {\color{grey} \overbracket[0.25pt]{\color{bayesblue} P (\text{Data} \mid \text{Unknown})}^{\text{Likelihood}}}}
 {{\color{grey} \underbracket[0.25pt]{{\color{grey} P(\text{E})}}_{\text{Average likelihood}}}}
 \]</span></p>
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 </body></html>
diff --git a/test-newcommand.qmd b/test-newcommand.qmd
 ---
 title: "Quarto: Test LaTeX newcommands in HTML doc"

 format:
  html:
    html-math-method: mathjax
 #    url: "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"
  pdf:
    documentclass: scrreprt
    include-in-header: latex-commands.tex
 ---

 In a Quarto document, I want to be able to use more extensive math LaTeX features than are
 typical for simple equations, using some extensions presumably provided by `mathjax`,
 particularly for matrix expressions. (I think, but am not sure, that the latest Quarto uses `mathjax` v 3.2. )

 As a simiple example, here I use a straightforward math equation with no special stuff, with `\mathbf{}` used
 for matrices and vectors. This works well and the equation appears nicely in the RStudio editor window. The source code is:

 ```latex
 $$\mathbf{y} = \mathbf{X} \; \mathbf{\beta} + \mathbf{u}, 
 \quad\mbox{   with   }\quad 
 \mathbf{u} \sim \mathcal{N} (0, \sigma^2 \mathbf{I}) ,
 $$
 ```

 $$\mathbf{y} = \mathbf{X} \; \mathbf{\beta} + \mathbf{u}, 
 \quad\mbox{   with   }\quad 
 \mathbf{u} \sim \mathcal{N} (0, \sigma^2 \mathbf{I}) ,
 $$

 However, in another version, I'd like to show the size of matrices using subscripts.  
 This also works, but it fails if I try to include an equation number `(eq-mlm)`.

 ```latex
 $$
 \mathbf{Y}_{n \times p} = 
 \mathbf{X}_{n \times q} \, \mathbf{B}_{q \times p} + \mathbf{U}_{n \times p} \:\: ,
 $$
 ```

 $$
 \mathbf{Y}_{n \times p} = 
 \mathbf{X}_{n \times q} \, \mathbf{B}_{q \times p} + \mathbf{U}_{n \times p} \:\: ,
 $$

 ## \newcommand

 Now, try to define some abbreviated latex commands for these math expressions.
 The [Quarto authoring doc](https://quarto.org/docs/authoring/markdown-basics.html) says these should work

 > For HTML math processed using MathJax (the default) you can use the `\def`, `\newcommand`, `\renewcommand`, `\newenvironment`, `\renewenvironment`, and `\let` commands to create your own macros and environments.

 ```latex
 $$
 \renewcommand*{\vec}[1]{\mathbf{#1}} 
 \newcommand*{\mat}[1]{\mathbf{#1}} 
 \newcommand{\trans}{^\mathsf{T}} 
 \newcommand*{\diag}[1]{\mathrm{diag}\, #1}}
 \newcommand{\sizedmat}[2]{\underset{\mathbf{#1}}{(#2)}}
 $$
 ```
 <!-- % \newcommand{\sizedmat}[2]{\mathord{\mathop{\mat{#1}}\limits_{(#2)}} -->

 The docs say to include this in a `::: {.hidden}` div:

 ::: {.hidden}
 $$
 \renewcommand*{\vec}[1]{\mathbf{#1}} 
 \newcommand*{\mat}[1]{\mathbf{#1}} 
 \newcommand{\trans}{^\mathsf{T}} 
 \newcommand*{\diag}[1]{\mathrm{diag}\, #1}}
 \newcommand{\sizedmat}[2]{\underset{\mathbf{#1}}{(#2)}}
 $$
 :::

 Then, I try to use them:


 ```latex
 $$
 {\sizedmat{\mat{Y}}{n \times p}} = 
 {\sizedmat{\mat{X}}{n \times q}} \, 
 {\sizedmat{\mat{B}}{q \times p}} + 
 {\sizedmat{\mat{U}}{n \times p}} ,
 $$
 ```

 This doesn't work, perhaps because the `\newcommand` block wasn't interpreted as equations.
 (Or, could this be because of the `\underset` ?) 

 $$
 {\sizedmat{\mat{Y}}{n \times p}} = 
 {\sizedmat{\mat{X}}{n \times q}} \, 
 {\sizedmat{\mat{B}}{q \times p}} + 
 {\sizedmat{\mat{U}}{n \times p}} ,
 $$

 ## Other `mathjax` extensions

 Let's try [Andrew Heiss' nice equations](https://github.com/andrewheiss/bayesf22.classes.andrewheiss.com) 
 using the mathjax `mathtools` extension.  This LaTeX defines some colors:

 ```latex
 $$
 \require{mathtools}
 \definecolor{bayesred}{RGB}{147, 30, 24}
 \definecolor{bayesblue}{RGB}{32, 35, 91}
 \definecolor{bayesorange}{RGB}{218, 120, 1}
 \definecolor{grey}{RGB}{128, 128, 128}
 {\color{bayesorange} P (\text{H} \mid \text{E})} = \frac
 {{\color{bayesred} P(\text{H})} \times 
 {\color{bayesblue}P(\text{E} \mid \text{H})}}
 {\color{grey} {P(\text{E})}}
 $$

 ```
 ::: {.hidden}

 $$
 \require{mathtools}
 \definecolor{bayesred}{RGB}{147, 30, 24}
 \definecolor{bayesblue}{RGB}{32, 35, 91}
 \definecolor{bayesorange}{RGB}{218, 120, 1}
 \definecolor{grey}{RGB}{128, 128, 128}
 {\color{bayesorange} P (\text{H} \mid \text{E})} = \frac
 {{\color{bayesred} P(\text{H})} \times 
 {\color{bayesblue}P(\text{E} \mid \text{H})}}
 {\color{grey} {P(\text{E})}}
 $$
 :::

 This uses these colors:

 ```latex
 $$
 {\color{grey} \overbracket[0.25pt]{\color{bayesorange} P (\text{Unknown} \mid \text{Data})}^{\text{Posterior}}} = \frac
 {{\color{grey} \overbracket[0.25pt]{\color{bayesred} P (\text{Unknown})}^{\text{Prior}}} \times 
 {\color{grey} \overbracket[0.25pt]{\color{bayesblue} P (\text{Data} \mid \text{Unknown})}^{\text{Likelihood}}}}
 {{\color{grey} \underbracket[0.25pt]{{\color{grey} P(\text{E})}}_{\text{Average likelihood}}}}
 $$
 ```

 The result does not appear nicely in the RStudio editor window, but works fine in the output.
 $$
 {\color{grey} \overbracket[0.25pt]{\color{bayesorange} P (\text{Unknown} \mid \text{Data})}^{\text{Posterior}}} = \frac
 {{\color{grey} \overbracket[0.25pt]{\color{bayesred} P (\text{Unknown})}^{\text{Prior}}} \times 
 {\color{grey} \overbracket[0.25pt]{\color{bayesblue} P (\text{Data} \mid \text{Unknown})}^{\text{Likelihood}}}}
 {{\color{grey} \underbracket[0.25pt]{{\color{grey} P(\text{E})}}_{\text{Average likelihood}}}}
 $$
	---
	title: "Quarto: Test LaTeX newcommands in HTML doc"

	format:
	html:
	html-math-method: mathjax
	# url: "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"
	pdf:
	documentclass: scrreprt
	include-in-header: latex-commands.tex
	---

	In a Quarto document, I want to be able to use more extensive math LaTeX features than are
	typical for simple equations, using some extensions presumably provided by `mathjax`,
	particularly for matrix expressions. (I think, but am not sure, that the latest Quarto uses `mathjax` v 3.2. )

	As a simiple example, here I use a straightforward math equation with no special stuff, with `\mathbf{}` used
	for matrices and vectors. This works well and the equation appears nicely in the RStudio editor window. The source code is:

	```latex
	$$\mathbf{y} = \mathbf{X} \; \mathbf{\beta} + \mathbf{u},
	\quad\mbox{ with }\quad
	\mathbf{u} \sim \mathcal{N} (0, \sigma^2 \mathbf{I}) ,
	$$
	```

	$$\mathbf{y} = \mathbf{X} \; \mathbf{\beta} + \mathbf{u},
	\quad\mbox{ with }\quad
	\mathbf{u} \sim \mathcal{N} (0, \sigma^2 \mathbf{I}) ,
	$$

	However, in another version, I'd like to show the size of matrices using subscripts.
	This also works, but it fails if I try to include an equation number `(eq-mlm)`.

	```latex
	$$
	\mathbf{Y}_{n \times p} =
	\mathbf{X}_{n \times q} \, \mathbf{B}_{q \times p} + \mathbf{U}_{n \times p} \:\: ,
	$$
	```

	$$
	\mathbf{Y}_{n \times p} =
	\mathbf{X}_{n \times q} \, \mathbf{B}_{q \times p} + \mathbf{U}_{n \times p} \:\: ,
	$$

	## \newcommand

	Now, try to define some abbreviated latex commands for these math expressions.
	The [Quarto authoring doc](https://quarto.org/docs/authoring/markdown-basics.html) says these should work

	> For HTML math processed using MathJax (the default) you can use the `\def`, `\newcommand`, `\renewcommand`, `\newenvironment`, `\renewenvironment`, and `\let` commands to create your own macros and environments.

	```latex
	$$
	\renewcommand*{\vec}[1]{\mathbf{#1}}
	\newcommand*{\mat}[1]{\mathbf{#1}}
	\newcommand{\trans}{^\mathsf{T}}
	\newcommand*{\diag}[1]{\mathrm{diag}\, #1}}
	\newcommand{\sizedmat}[2]{\underset{\mathbf{#1}}{(#2)}}
	$$
	```
	<!-- % \newcommand{\sizedmat}[2]{\mathord{\mathop{\mat{#1}}\limits_{(#2)}} -->

	The docs say to include this in a `::: {.hidden}` div:

	::: {.hidden}
	$$
	\renewcommand*{\vec}[1]{\mathbf{#1}}
	\newcommand*{\mat}[1]{\mathbf{#1}}
	\newcommand{\trans}{^\mathsf{T}}
	\newcommand*{\diag}[1]{\mathrm{diag}\, #1}}
	\newcommand{\sizedmat}[2]{\underset{\mathbf{#1}}{(#2)}}
	$$
	:::

	Then, I try to use them:


	```latex
	$$
	{\sizedmat{\mat{Y}}{n \times p}} =
	{\sizedmat{\mat{X}}{n \times q}} \,
	{\sizedmat{\mat{B}}{q \times p}} +
	{\sizedmat{\mat{U}}{n \times p}} ,
	$$
	```

	This doesn't work, perhaps because the `\newcommand` block wasn't interpreted as equations.
	(Or, could this be because of the `\underset` ?)

	$$
	{\sizedmat{\mat{Y}}{n \times p}} =
	{\sizedmat{\mat{X}}{n \times q}} \,
	{\sizedmat{\mat{B}}{q \times p}} +
	{\sizedmat{\mat{U}}{n \times p}} ,
	$$

	## Other `mathjax` extensions

	Let's try [Andrew Heiss' nice equations](https://github.com/andrewheiss/bayesf22.classes.andrewheiss.com)
	using the mathjax `mathtools` extension. This LaTeX defines some colors:

	```latex
	$$
	\require{mathtools}
	\definecolor{bayesred}{RGB}{147, 30, 24}
	\definecolor{bayesblue}{RGB}{32, 35, 91}
	\definecolor{bayesorange}{RGB}{218, 120, 1}
	\definecolor{grey}{RGB}{128, 128, 128}
	{\color{bayesorange} P (\text{H} \mid \text{E})} = \frac
	{{\color{bayesred} P(\text{H})} \times
	{\color{bayesblue}P(\text{E} \mid \text{H})}}
	{\color{grey} {P(\text{E})}}
	$$

	```
	::: {.hidden}

	$$
	\require{mathtools}
	\definecolor{bayesred}{RGB}{147, 30, 24}
	\definecolor{bayesblue}{RGB}{32, 35, 91}
	\definecolor{bayesorange}{RGB}{218, 120, 1}
	\definecolor{grey}{RGB}{128, 128, 128}
	{\color{bayesorange} P (\text{H} \mid \text{E})} = \frac
	{{\color{bayesred} P(\text{H})} \times
	{\color{bayesblue}P(\text{E} \mid \text{H})}}
	{\color{grey} {P(\text{E})}}
	$$
	:::

	This uses these colors:

	```latex
	$$
	{\color{grey} \overbracket[0.25pt]{\color{bayesorange} P (\text{Unknown} \mid \text{Data})}^{\text{Posterior}}} = \frac
	{{\color{grey} \overbracket[0.25pt]{\color{bayesred} P (\text{Unknown})}^{\text{Prior}}} \times
	{\color{grey} \overbracket[0.25pt]{\color{bayesblue} P (\text{Data} \mid \text{Unknown})}^{\text{Likelihood}}}}
	{{\color{grey} \underbracket[0.25pt]{{\color{grey} P(\text{E})}}_{\text{Average likelihood}}}}
	$$
	```

	The result does not appear nicely in the RStudio editor window, but works fine in the output.
	$$
	{\color{grey} \overbracket[0.25pt]{\color{bayesorange} P (\text{Unknown} \mid \text{Data})}^{\text{Posterior}}} = \frac
	{{\color{grey} \overbracket[0.25pt]{\color{bayesred} P (\text{Unknown})}^{\text{Prior}}} \times
	{\color{grey} \overbracket[0.25pt]{\color{bayesblue} P (\text{Data} \mid \text{Unknown})}^{\text{Likelihood}}}}
	{{\color{grey} \underbracket[0.25pt]{{\color{grey} P(\text{E})}}_{\text{Average likelihood}}}}
	$$