RMarkdown Latex Notes

99_rmarkdown.Rmd

# Appendix {.unnumbered #latex}

Ray's Formatting Notes: version 2024-11-07
https://gist.github.com/RaymondBalise/ee4b7da0a70087317dc52bf479a4e2b6

```{=html}
<style>
  .col2 {
    columns: 2 150px;         /* number of columns and width in pixels*/
    -webkit-columns: 2 150px; /* chrome, safari */
    -moz-columns: 2 150px;    /* firefox */
  }
  .col3 {
    columns: 3 100px;
    -webkit-columns: 3 100px;
    -moz-columns: 3 100px;
  }
</style>
```

## Markdown highlighting {.unnumbered}

| Formatting | Code         |
|:-----------|:-------------|
| **bold**   | \*\*bold\*\* |
| __bold__   | \_\_bold\_\_ |
| *italic*   | \*italic\*   |
| _italic_   | \_italic\_   |

## Text coloring {.unnumbered}

To add color you can use CSS or R code like this:

```{r, include=TRUE}
color_text <- function(x, color){
  if(knitr::is_latex_output())
    paste("\\textcolor{",color,"}{",x,"}",sep="")
  else if(knitr::is_html_output())
    paste("<font color='",color,"'>",x,"</font>",sep="")
  else
    x
}

red <- function(x){
  if(knitr::is_latex_output())
    paste("\\textcolor{",'red',"}{",x,"}",sep="")
  else if(knitr::is_html_output())
    paste("<font color='red'>",x,"</font>",sep="")
  else
    x
}
```

The strng `r red("This is colored with the red function")` comes from:

```{r eval=FALSE}
`r red("This is colored with the red function")`
```

The string `r color_text("This is colored with the color_text function set to mauve", "#E0B0FF")` comes from:

```{r eval=FALSE}
`r color_text("This is colored with the color_text function set to mauve", "#E0B0FF")`
```

## Section references {.unnumbered #x99.4}

Section [99.4](#x99.4) comes from `Section [99.4](#x99.4)`

## Footnotes {.unnumbered}

^[A footnote] comes from `^[A footnote]`

## Formatting Text {.unnumbered}

| Appearance                                               | Code                                                   |
|:---------------------------------------------------------|:-------------------------------------------------------|
| `r xfun::n2w(3, cap = TRUE)`                             | `xfun::n2w(3, cap = TRUE)`                             |
| `r scales::percent(0.1447, accuracy= .1)`                | `scales::percent(0.1447, accuracy= .1)`                |
| `r scales::pvalue(0.1447, accuracy= .001, add_p = TRUE)` | `scales::pvalue(0.1447, accuracy= .001, add_p =TRUE)`  |

## Figures {.unnumbered}

Name a figure chunk with a name like figure99-1 and include fig.cap="something" then reference it like this: `\@ref(fig:figure99-1)`

## Displaying Formula {.unnumbered}

### Formatting Text Font {.unnumbered}

To tweak the appearance of words use these formats:

| Formatting        | Looks like              | Code                    |
|:------------------|:------------------------|:------------------------|
| plain text        | $\text{text Pr}$        | `\text{text Pr}`        |
| bold Greek symbol | $\boldsymbol{\epsilon}$ | `\boldsymbol{\epsilon}` |
| typewriter        | $x\ \tt{sentence}\ x$   | `\tt{sentence}`         |
| teletype          | $x\ \texttt{blah}\ x$   | `\texttt{blah}`         |
| slide font        | $\sf{blah}$             | `\sf{blah}`             |
| bold              | $\mathbf{x}$            | `\mathbf{x}`            |
| plain             | $\mathrm{text Pr}$      | `\mathrm{text Pr}`      |
| cursive           | $\mathcal{S}$           | `\mathcal{S}`           |
| Blackboard bold   | $\mathbb{R}$            | `\mathbb{R}`            |

If you are using R Markdown, to get the cursive fonts to work correctly on Chromium based browsers (Chrome, Edge, Brave, etc.) you will need to open the .html file, find the line that has `</head>` and add this line just before that close header tag:

```
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS_CHTML.js"></script>
```

If you are using Quarto, to get the cursive fonts to work correctly tweak the YAML header to include:

```
format:
  html:
    html-math-method:  
      method: mathjax
      url: "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"
```

### Cursive/Calligraphic Letters {.unnumbered}

Thank you Layla: <https://gist.github.com/labouz/d2e012f638864b9af061afe648ce441b>

| Letters                                | Code                                   | Meaning                         |
|:---------------------------------------|:---------------------------------------|:--------------------------------|
| $\mathcal{B}$                          | `$\mathcal{B}$`                        | Basis                           |
| $\mathcal{O}$                          | `$\mathcal{O}$`                        | Used for Big-O notation         |
| $\mathcal{P}$                          | `$\mathcal{P}$`                        | Power set, probability function |
| $\mathcal{S}$                          | `$\mathcal{S}$ `                       | A set                           |
| $(\Omega, \mathcal{F}, \mathcal{P})$   | `$(\Omega, \mathcal{F}, \mathcal{P})$` | Probability space/triple        |

### Symbols {.unnumbered}

| Symbols                                     | Code                                      |
|:--------------------------------------------|:------------------------------------------|
| $\stackrel{\text{def}}{=}$                  | `\stackrel{\text{def}}{=}`                |
| $\nabla$                                    | `\nabla`                                  |
| $\partial$                                  | `\partial`                                |
| $\vert$  or use $\lvert a \rvert$           | `\vert \text{ or use } \lvert a \rvert` \ |
| $\Vert$                                     | `\Vert`                                   |
| $\mid$ in set notation; `\given` is missing | `\mid`                                    |

### Brackets and Parentheses {.unnumbered}

| Looks like                 | Code                          |
|:---------------------------|:------------------------------| 
|$\big( \Big( \bigg( \Bigg($ | \\big( \\Big( \\bigg( \\Bigg( | 
|$\big] \Big] \bigg] \Bigg]$ | \\big] \\Big] \\bigg] \\Bigg] | 

### Notation {.unnumbered}

Based on a great [website for an old class](https://web.archive.org/web/20200730033432/https://www.calvin.edu/~rpruim/courses/s341/S17/from-class/MathinRmd.html) that is no long live.

| Math                                                          | Code                                                               |
|:--------------------------------------------------------------|:-------------------------------------------------------------------|
| $x = y$                                                       | `$x = y$`                                                          |
| $x \approx y$                                                 | `$x \approx y$`                                                    |
| $f_k(X) \equiv Pr(X|Y = k)$                                   | `f_k(X) \equiv Pr(X|Y = k)`                                        |
| $x \lt y$                                                     | `$x < y$`                                                          |
| $x \gt y$                                                     | `$x > y$`                                                          |
| $x \le y$                                                     | `$x \le y$`                                                        |
| $x \ge y$                                                     | `$x \ge y$`                                                        |
| $x \neq y$                                                    | `$x \neq y$`                                                        |
| $P(\emptyset)=0$                                              | `P(\emptyset)=0`                                                        |
| $x \times y$                                                  | `$x \times y$`                                                     |
| $x^{n}$                                                       | `$x^{n}$`                                                          |
| $x_{n}$                                                       | `$x_{n}$`                                                          |
| $x_1, x_2, \dots, x_n$                                        | `$x_1, x_2, \dots, x_n$`                                           |
| $x_1 + x_2 + \cdots + x_n$                                    | `$x_1 + x_2 + \cdots + x_n$`                                       |
| $\overline{x}$                                                | `$\overline{x}$`                                                   |
| $\hat{x}$                                                     | `$\hat{x}$`                                                        |
| $\widehat{SE}$                                                | `$\widehat{SE}$`                                                   |
| $\tilde{x}$                                                   | `$\tilde{x}$`                                                      |
| $\frac{a}{b}$                                                 | `$\frac{a}{b}$`                                                    |
| $\displaystyle \frac{a}{b}$                                   | `$\displaystyle \frac{a}{b}$`                                      |
| $\binom{n}{k}$                                                | `$\binom{n}{k}$`                                                   |
| $x_{1} + x_{2} + \cdots + x_{n}$                              | `$x_{1} + x_{2} + \cdots + x_{n}$`                                 |
| $x_{1}, x_{2}, \dots, x_{n}$                                  | `$x_{1}, x_{2}, \dots, x_{n}$`                                     |
| $\mathbf{x} = \langle x_{1}, x_{2}, \dots, x_{n}\rangle$      | `$\mathbf{x} = \langle x_{1}, x_{2}, \dots, x_{n}\rangle$`         |
| $x \in A$                                                     | `$x \in A$`                                                        |
| $\lvert A \rvert$                                             | `$\lvert A \rvert$`                                                |
| $\big \langle x_i, x_{i'}\big \rangle$                        | `\big \langle x_i, x_{i'}\big \rangle`                             |
| $x \in A$                                                     | `$x \in A$`                                                        |
| $x \subset B$                                                 | `$x \subset B$`                                                    |
| $x \subseteq B$                                               | `$x \subseteq B$`                                                  |
| $A \cup B$                                                    | `$A \cup B$`                                                       |
| $A \cap B$                                                    | `$A \cap B$`                                                       |
| $X \sim {\sf Binom}(n, \pi)$                                  | `X \sim {\sf Binom}(n, \pi)$`                                      |
| $\mathrm{P}(X \le x) = {\tt pbinom}(x, n, \pi)$               | `$\mathrm{P}(X \le x) = {\tt pbinom}(x, n, \pi)$`                  |
| $P(A \mid B)$                                                 | `$P(A \mid B)$`                                                    |
| $\mathrm{P}(A \mid B)$                                        | `$\mathrm{P}(A \mid B)$`                                           |
| $\{1, 2, 3\}$                                                 | `$\{1, 2, 3\}$`                                                    |
| $\sin(x)$                                                     | `$\sin(x)$`                                                        |
| $\log(x)$                                                     | `$\log(x)$`                                                        |
| $\exp(x)$                                                     | `$\exp(x)$`                                                        |
| $\sum\limits_{k=0}^n$                                         | `$\sum\limits_{k=0}^n$`                                            |
| $\exp{\big(\sum_{i=1}^p x_i\big)}$                            | `$\exp{\big(\sum_{i=1}^p x_i\big)}$`                               |
| $\int_{a}^{b}$                                                | `$\int_{a}^{b}$`                                                   |
| $\left(\int_{a}^{b} f(x) \; dx\right)$                        | `$\left(\int_{a}^{b} f(x) \; dx\right)$`                           |
| $\left[\int_{-\infty}^{\infty} f(x) \; dx\right]$             | `$\left[\int_{\-infty}^{\infty} f(x) \; dx\right]$`                |
| $\left. F(x) \right|_{a}^{b}$                                 | `$\left. F(x) \right|_{a}^{b}$`                                    |
| $\sum_{x = a}^{b} f(x)$                                       | `$\sum_{x = a}^{b} f(x)$`                                          |
| $\prod_{x = a}^{b} f(x)$                                      | `$\prod_{x = a}^{b} f(x)$`                                         |
| $\lim_{x \to \infty} f(x)$                                    | `$\lim_{x \to \infty} f(x)$`                                       |
| $\displaystyle \lim_{x \to \infty} f(x)$                      | `$\displaystyle \lim_{x \to \infty} f(x)$`                         |
| $RMSE = \sqrt{\frac{1}{n}\sum_{i=1}^{n} (Y_n - \hat{Y}_i)^2}$ | `$RMSE = \sqrt{\frac{1}{n}\sum_{i=1}^{n} (Y_n - \hat{Y}_i)^2}$`    |
| $(\texttt{pop} - \overline{ \texttt{pop}})$                   | `$(\texttt{pop} - \overline{\texttt{pop}})$`                       |
| $\hat{f}(x) \leftarrow \hat{f}(x) + \lambda\hat{f}^b(x)$      | `\hat{f}(x) \leftarrow \hat{f}(x) + \lambda\hat{f}^b(x)`           |


#### Stacked text (for finding maximum): {.unnumbered}
To get text stacked below a word for optimization formulas use `\mathop` with `$$`

| Math                                                          | Code                                                               |
|:--------------------------------------------------------------|:-------------------------------------------------------------------|
| $$\mathop{\text{max}}_{k}(\hat{p}_{mk})$$                     | `$$\mathop{\text{max}}_{k}(\hat{p}_{mk})$$`                        |


#### Adjust position of limits:  {.unnumbered}
To have limits appear next to sigma or pi (not above):

| Math                                                          | Code                                                               |
|:--------------------------------------------------------------|:-------------------------------------------------------------------|
| $\sum\nolimits_{i=1}^{n}X_i.$                                 | `\sum\nolimits_{i=1}^{n}X_i.`                                      |

### Matrices {.unnumbered}

\begin{equation}
A = 
  \begin{bmatrix}
    1 & \cdots & 3\\
    \vdots & \ddots & \vdots\\
    7 & \cdots & 9
  \end{bmatrix}
\end{equation}

Comes from this code:

```
\begin{equation}
A = 
  \begin{bmatrix}
    1 & \cdots & 3\\
    \vdots & \ddots & \vdots\\
    7 & \cdots & 9
  \end{bmatrix}
\end{equation}
```

Options to surround the matrix:

| Type            | Code              |
|:----------------|:------------------|
| Nothing         | `\begin{matrix}`  |
| Parentheses     | `\begin{pmatrix}` |
| Square Brackets | `\begin{bmatrix}` |
| Curly brackets  | `\begin{Bmatrix}` |
| Pipes           | `\begin{vmatrix}` |
| Double Pipes    | `\begin{Vmatrix}` |

## Equations {.unnumbered}

These are formulas that appear with an equation number.

### Basic Equation {.unnumbered}

The names of equations can not include . or \_ but it can include -

    \begin{equation} 
      1 + 1 = 2 
      (\#eq:eq99-1)
    \end{equation} 

Which appears as:

\begin{equation} 
  1 + 1 = 2
  (\#eq:eq99-1)
\end{equation} 

The reference to the equation is \@ref(eq:eq99-1) which comes from this code `\@ref(eq:eq99-1)`

### Case-When Equation (Large Curly Brace) {.unnumbered}

Based on: <https://tex.stackexchange.com/questions/9065/large-braces-for-specifying-values-of-variables-by-condition> 

Case when formula: 

```{=tex}
\begin{equation} 
y =
\begin{cases}
  0, & \text{if}\ a=1 \\
  1, & \text{otherwise}
\end{cases}
  (\#eq:eq99-2)
\end{equation} 
```

Which comes from this code:

```{}
\begin{equation} 
  y =
  \begin{cases}
    0, & \text{if}\ a=1 \\
    1, & \text{otherwise}
  \end{cases}
  (\#eq:eq99-2)
\end{equation} 
```

The reference to equation is \@ref(eq:eq99-2) which comes from this code `\@ref(eq:eq99-2)`

### Alligned with Underbars {.unnumbered}

\begin{equation}
\begin{aligned}
\mathrm{E}(Y-\hat{Y})^2 & = \mathrm{E}[f(X) + \epsilon -\hat{f}(X)]^2 \\
                        & = \underbrace{[f(X) -\hat{f}(X)]^2}_{\mathrm{Reducible}} + \underbrace{\mathrm{var}(\epsilon)}_{\mathrm{Irreducible}} \\
\end{aligned}
(\#eq:eq99-3)
\end{equation}

Comes from this code:

```{}
\begin{equation}
\begin{aligned}
\mathrm{E}(Y-\hat{Y})^2 & = \mathrm{E}[f(X) + \epsilon -\hat{f}(X)]^2 \\
                        & = \underbrace{[f(X) -\hat{f}(X)]^2}_{\mathrm{Reducible}} + \underbrace{\mathrm{var}(\epsilon)}_{\mathrm{Irreducible}} \\
\end{aligned}
(\#eq:eq99-3)
\end{equation}
```

## Greek letters {.unnumbered}

Based on a great [website for an old class](https://web.archive.org/web/20200730033432/https://www.calvin.edu/~rpruim/courses/s341/S17/from-class/MathinRmd.html) that is no long live.

::: {.col2}

| Letters                   | Code                        |
|:--------------------------|:----------------------------|
| $\alpha A$                | `$\alpha A$`                |
| $\beta B$                 | `$\beta B$`                 |
| $\gamma \Gamma$           | `$\gamma \Gamma$`           |
| $\delta \Delta$           | `$\delta \Delta$`           |
| $\epsilon \varepsilon E$  | `$\epsilon \varepsilon E$`  |
| $\zeta Z \sigma$          | `$\zeta Z \sigma`           |
| $\eta H$                  | `$\eta H$`                  |
| $\theta \vartheta \Theta$ | `$\theta \vartheta \Theta$` |
| $\iota I$                 | `$\iota I$`                 |
| $\kappa K$                | `$\kappa K$`                |
| $\lambda \Lambda$         | `$\lambda \Lambda$`         |
| $\mu M$                   | `$\mu M$`                   |

| Letters                   | Code                        |
|:--------------------------|:----------------------------|
| $\nu N$                   | `$\nu N$`                   |
| $\xi\Xi$                  | `$\xi\Xi$`                  |
| $o O$                     | `$o O$ (omicron)`           |
| $\pi \Pi$                 | `$\pi \Pi$`                 |
| $\rho\varrho P$           | `$\rho\varrho P$`           |
| $\sigma \Sigma$           | `\sigma \Sigma$`            |
| $\tau T$                  | `$\tau T$`                  |
| $\upsilon \Upsilon$       | `$\upsilon \Upsilon$`       |
| $\phi \varphi \Phi$       | `$\phi \varphi \Phi$`       |
| $\chi X$                  | `$\chi X$`                  |
| $\psi \Psi$               | `$\psi \Psi$`               |
| $\omega \Omega$           | `$\omega \Omega$`           |
:::

i forked and tried to modify only realize you can't pr for a gist?? so i added a little section at the bottom on calligraphic letters
https://gist.github.com/labouz/d2e012f638864b9af061afe648ce441b

mathcal no longer works with chrome. I replaced it with mathscr

Add fix to mathcal on Chromium based browsers on Mac OS.