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RMarkdown Latex Notes
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.gitignore
.Rproj.user
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99_rmarkdown.Rmd
# Appendix {.unnumbered #latex}
Ray's Formatting Notes: version 2021-12-31
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} |
### 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: <https://www.calvin.edu/~rpruim/courses/s341/S17/from-class/MathinRmd.html>
| 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)` |
| $x \lt y$ | `$x < y$` |
| $x \gt y$ | `$x > y$` |
| $x \le y$ | `$x \le y$` |
| $x \ge y$ | `$x \ge y$` |
| $x \times y$ | `$x \times y$` |
| $x^{n}$ | `$x^{n}$` |
| $x_{n}$ | `$x_{n}$` |
| $x_1, x_2, \dots, x_n$ | `$x_1, x_2, \dots, x_n$` |
| $x_1 + x_2 + \cdots + x_n$ | `$x_1 + x_2 + \cdots + x_n$` |
| $\overline{x}$ | `$\overline{x}$` |
| $\hat{x}$ | `$\hat{x}$` |
| $\widehat{SE}$ | `$\widehat{SE}$` |
| $\tilde{x}$ | `$\tilde{x}$` |
| $\frac{a}{b}$ | `$\frac{a}{b}$` |
| $\displaystyle \frac{a}{b}$ | `$\displaystyle \frac{a}{b}$` |
| $\binom{n}{k}$ | `$\binom{n}{k}$` |
| $x_{1} + x_{2} + \cdots + x_{n}$ | `$x_{1} + x_{2} + \cdots + x_{n}$` |
| $x_{1}, x_{2}, \dots, x_{n}$ | `$x_{1}, x_{2}, \dots, x_{n}$` |
| $\mathbf{x} = \langle x_{1}, x_{2}, \dots, x_{n}\rangle$ | `$\mathbf{x} = \langle x_{1}, x_{2}, \dots, x_{n}\rangle$` |
| $x \in A$ | `$x \in A$` |
| $\lvert A \rvert$ | `$\lvert A \rvert$` |
| $\big \langle x_i, x_{i'}\big \rangle$ | `\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)$` |
| $\mathrm{P}(X \le x) = {\tt pbinom}(x, n, \pi)$ | `$\mathrm{P}(X \le x) = {\tt pbinom}(x, n, \pi)$` |
| $P(A \mid B)$ | `$P(A \mid B)$` |
| $\mathrm{P}(A \mid B)$ | `$\mathrm{P}(A \mid B)$` |
| $\{1, 2, 3\}$ | `$\{1, 2, 3\}$` |
| $\sin(x)$ | `$\sin(x)$` |
| $\log(x)$ | `$\log(x)$` |
| $\exp(x)$ | `$\exp(x)$` |
| $\exp{\big(\sum_{i=1}^p x_i\big)}$ | `$\exp{\big(\sum_{i=1}^p x_i\big)}$` |
| $\int_{a}^{b}$ | `$\int_{a}^{b}$` |
| $\left(\int_{a}^{b} f(x) \; dx\right)$ | `$\left(\int_{a}^{b} f(x) \; dx\right)$` |
| $\left[\int_{-\infty}^{\infty} f(x) \; dx\right]$ | `$\left[\int_{\-infty}^{\infty} f(x) \; dx\right]$` |
| $\left. F(x) \right|_{a}^{b}$ | `$\left. F(x) \right|_{a}^{b}$` |
| $\sum_{x = a}^{b} f(x)$ | `$\sum_{x = a}^{b} f(x)$` |
| $\prod_{x = a}^{b} f(x)$ | `$\prod_{x = a}^{b} f(x)$` |
| $\lim_{x \to \infty} f(x)$ | `$\lim_{x \to \infty} f(x)$` |
| $\displaystyle \lim_{x \to \infty} f(x)$ | `$\displaystyle \lim_{x \to \infty} f(x)$` |
| $RMSE = \sqrt{\frac{1}{n}\sum_{i=1}^{n} (Y_n - \hat{Y}_i)^2}$ | `$RMSE = \sqrt{\frac{1}{n}\sum_{i=1}^{n} (Y_n - \hat{Y}_i)^2}$` |
| $(\texttt{pop} - \overline{ \texttt{pop}})$ | `$(\texttt{pop} - \overline{\texttt{pop}})$` |
| $\hat{f}(x) \leftarrow \hat{f}(x) + \lambda\hat{f}^b(x)$ | `\hat{f}(x) \leftarrow \hat{f}(x) + \lambda\hat{f}^b(x)` |
#### Stacked text (for finding maximum):
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:
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: <https://www.calvin.edu/~rpruim/courses/s341/S17/from-class/MathinRmd.html>
::: {.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` |
| $\eta H$ | `$\eta H$` |
| $\theta \vartheta \Theta$ | `$\theta \vartheta \Theta$` |
| $\iota I$ | `$\iota I$` |
| $\kappa K$ | `$\kappa K$` |
| $\lambda \Lambda$ | `$\lambda \Lambda$` |
| $\mu M$ | `$\mu M$` |
| $\nu N$ | `$\nu N$` |
| $\xi\Xi$ | `$\xi\Xi$` |
| $o O$ | `$o O$ (omicron)` |
| $\pi \Pi$ | `$\pi \Pi$` |
| $\rho\varrho P$ | `$\rho\varrho P$` |
| $\sigma \Sigma$ | `\sigma \Sigma$` |
| $\tau T$ | `$\tau T$` |
| $\upsilon \Upsilon$ | `$\upsilon \Upsilon$` |
| $\phi \varphi \Phi$ | `$\phi \varphi \Phi$` |
| $\chi X$ | `$\chi X$` |
| $\psi \Psi$ | `$\psi \Psi$` |
| $\omega \Omega$ | `$\omega \Omega$` |
:::
## Calligraphic Letters {.unnumbered}
| letters | code |meaning |
|:--------------------------|:-------------------------|:-----------------|
| $\mathcal{S}$ | `$\mathcal{S}$ ` | A set |
| $\mathcal{B}$ | `$\mathcal{B}$` | Basis |
| $\mathcal{P}$ | `$\mathcal{P}$` | Power set, probability function |
| $\mathcal{O}$ | `$\mathcal{O}$` | Used for Big-O notation |
| $(\Omega, \mathcal{F}, \mathcal{P})$ | `$(\Omega, \mathcal{F}, \mathcal{P})$` |Probability space/triple|
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