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1 Markdown highlighting

1.1 Bold and Italic

Formatting	Code
bold	**bold**
bold	__bold__
italic	*italic*
italic	_italic_

1.2 Text coloring

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

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 string This is colored with the red function comes from:

`r red("This is colored with the red function")`

The string This is colored with the color_text function set to mauve comes from:

`r color_text("This is colored with the color_text function set to mauve", "#E0B0FF")`

1.3 Formatting Text

Appearance	Code
Three	xfun::n2w(3, cap = TRUE)
14.5%	scales::percent(0.1447, accuracy= .1)
p=0.145	scales::pvalue(0.1447, accuracy= .001, add_p =TRUE)

1.4 Text Font

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}

2 References

2.1 Section references

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

2.2 Footnotes

¹ comes from ^[A footnote]

2.3 Figures

See Figure 2.1.

Figure 2.1: The cars data.

Name a figure chunk with a name like cars-plot and include fig.cap = "The cars data." then reference it like this: \@ref(fig:cars-plot)

3 Displaying Formula

3.1 Symbols

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

3.2 Brackets and Parentheses

Looks like	Code
\(\big( \Big( \bigg( \Bigg(\)	\big( \Big( \bigg( \Bigg(
\(\big] \Big] \bigg] \Bigg]\)	\big] \Big] \bigg] \Bigg]

3.3 Notation

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)

3.4 Greek letters

Based on: https://www.calvin.edu/~rpruim/courses/s341/S17/from-class/MathinRmd.html

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$
\(\tau T\)	$\tau T$
\(\upsilon \Upsilon\)	$\upsilon \Upsilon$
\(\phi \varphi \Phi\)	$\phi \varphi \Phi$
\(\chi X\)	$\chi X$
\(\psi \Psi\)	$\psi \Psi$
\(\omega \Omega\)	$\omega \Omega$

3.5 Calligraphic Letters

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

3.5.1 Stacked text (for finding maximum):

To get text stacked below a word for optimization formulas use \mathop with $$

Math	Code
\[\mathop{\text{max}}_{k}(\hat{p}_{mk})\]	$$\mathop{\text{max}}_{k}(\hat{p}_{mk})$$

3.5.2 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.

3.6 Matrices

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

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}

3.7 Equations

These are formulas that appear with an equation number.

3.7.1 Basic Equation

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:

\[\begin{equation} 1 + 1 = 2 \tag{3.1} \end{equation}\]

The reference to the equation is (3.1) which comes from this code \@ref(eq:eq99-1)

3.7.2 Case-When Equation (Large Curly Brace)

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

Case when formula:

\[\begin{equation} y = \begin{cases} 0, & \text{if}\ a=1 \\ 1, & \text{otherwise} \end{cases} \tag{3.2} \end{equation} \]

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 (3.2) which comes from this code \@ref(eq:eq99-2)

3.7.3 Alligned with Underbars

\[\begin{equation} \begin{aligned} \mathrm{E}(Y-\hat{Y})^2 & = \mathrm{E}[f(X) + \epsilon -\hat{f}(X)]^2 \\ & = \underbrace{[f(X) -\hat{f}(X)]^2}_{\mathrm{Reducible}} + \underbrace{\mathrm{var}(\epsilon)}_{\mathrm{Irreducible}} \\ \end{aligned} \tag{3.3} \end{equation}\]

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}

3.8 Convert models to equations

Use equatiomatic package (Anderson, Heiss, and Sumners 2022) to show the equations corresponding to models fitted in R

fit <- lm(mpg ~ cyl + disp, mtcars)

Theoretical model:

equatiomatic::extract_eq(fit)

\[ \operatorname{mpg} = \alpha + \beta_{1}(\operatorname{cyl}) + \beta_{2}(\operatorname{disp}) + \epsilon \]

Actual coefficients

equatiomatic::extract_eq(fit, use_coefs = TRUE)

\[ \operatorname{\widehat{mpg}} = 34.66 - 1.59(\operatorname{cyl}) - 0.02(\operatorname{disp}) \]

Based on: https://bookdown.org/yihui/rmarkdown-cookbook/equatiomatic.html

4 Tham khảo

Nguồn: Ray’s Formatting Notes, version 2021-02-15 https://gist.github.com/RaymondBalise/ee4b7da0a70087317dc52bf479a4e2b6

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1. A footnote↩︎