Use space instead of tab for indentation for better compatability.
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| ---
comments: true
title: Jekyll Post Template
date: 2024-04-25 12:00:00
image:
path: PATH_TO_IMAGE
math: true
mermaid: false
categories: [CAT_1, CAT_2]
tags: [tag_1, tag_2]
---
|
Image
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| {: style="max-width: 700px; height: auto;"}
{: width="700" height="400" }
{: w="700" h="400"}
_Image Caption_
|
Prompt
Example line for tip prompt.
Example line for info prompt.
Example line for warning prompt.
Example line for danger prompt.
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| > Example line for tip prompt.
{: .prompt-tip }
> Example line for info prompt.
{: .prompt-info }
> Example line for warning prompt.
{: .prompt-warning }
> Example line for danger prompt.
{: .prompt-danger }
|
Mathematics
- User
\vert instead of | because it will start a table sometimes. - Use
$$ $$, \$$ $$, and \$\$ $$ to add in-line math eqations. (Kramdown Doc)
Block Math
Block math need a mandatory blank line before and after the $$ sign.
Single Equation
\[f(\lambda x_2 + (1 - \lambda) x_1) \leq \lambda f(x_2) + (1 - \lambda) f(x_1)\]
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| <Mandatory Blank Line>
$$
f(\lambda x_2 + (1 - \lambda) x_1) \leq \lambda f(x_2) + (1 - \lambda) f(x_1)
$$
<Mandatory Blank Line>
|
Mutiple Equations
\[\displaylines{ x = a + b \\ y = b + c }\]
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| <Mandatory Blank Line>
$$
\displaylines{ x = a + b \\ y = b + c }
$$
<Mandatory Blank Line>
|
Align Multiple Equations
\[\begin{align} D_{KL}(P^{*}(y|x_i) \vert \vert P(y|x_i; \Theta)) &= \sum_{y} P^*(y|x_i) log \frac{P^*(y|x_i)}{P(y|x_i; \Theta)} \\ &= \sum_{y} P^*(y|x_i)[logP^*(y|x_i) - logP(y|x_i; \Theta)] \nonumber\\ &= \sum_{y} P^*(y|x_i)logP^*(y|x_i) - \sum_{y} P^{*}(y|x_i)logP(y|x_i; \Theta) \end{align}\]
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| <Mandatory Blank Line>
$$
\begin{align}
D_{KL}(P^{*}(y|x_i) \vert \vert P(y|x_i; \Theta))
&= \sum_{y} P^*(y|x_i) log \frac{P^*(y|x_i)}{P(y|x_i; \Theta)} \\
&= \sum_{y} P^*(y|x_i)[logP^*(y|x_i) - logP(y|x_i; \Theta)] \nonumber\\
&= \sum_{y} P^*(y|x_i)logP^*(y|x_i) - \sum_{y} P^{*}(y|x_i)logP(y|x_i; \Theta)
\end{align}
$$
<Mandatory Blank Line>
|
Use \nonumber to disable the number behind equations.
System of Equations
\[V_i = \begin{cases} -1, \text{ Not firing} \\ +1, \text{ Firing at maximum rate} \\ \end{cases}\]
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| <Mandatory Blank Line>
$$
V_i =
\begin{cases}
-1, \text{ Not firing} \\
+1, \text{ Firing at maximum rate} \\
\end{cases}
$$
<Mandatory Blank Line>
|
Matrix
\[\textbf{W} = \sum_s \begin{bmatrix} 0 & w_{12} & w_{13} & \dots & w_{1N} \\ w_{21} & 0 & w_{23} & w_{24} & w_{2N} \\ w_{31} & w_{32} & 0 & w_{34} & w_{3N} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ w_{N1} & w_{N2} & w_{N3} & \dots & 0 \\ \end{bmatrix}_{s=1, 2, 3, \dots, n}\]
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| <Mandatory Blank Line>
$$
\textbf{W} = \sum_s \textbf{V}^{(s)}(\textbf{V}^{(s)})^T = \sum_s
\begin{bmatrix}
0 & w_{12} & w_{13} & \dots & w_{1N} \\
w_{21} & 0 & w_{23} & w_{24} & w_{2N} \\
w_{31} & w_{32} & 0 & w_{34} & w_{3N} \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
w_{N1} & w_{N2} & w_{N3} & \dots & 0 \\
\end{bmatrix}_{s=1, 2, 3, \dots, n}
$$
<Mandatory Blank Line>
|
Arrows
\[\xleftarrow[\text{Text Below}]{\text{Text Above}}\] \[\xrightarrow[\text{Text Below}]{\text{Text Above}}\]
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| <Mandatory Blank Line>
$$
\xleftarrow[\text{Text Below}]{\text{Text Above}}
$$
<Mandatory Blank Line>
$$
\xrightarrow[\text{Text Below}]{\text{Text Above}}
$$
<Mandatory Blank Line>
|
Underbrace
\[\underbrace{\begin{bmatrix} v_1 \\ v_2 \\ v_3 \\ v_4 \end{bmatrix}}_{v} =\underbrace{\begin{bmatrix} r_1 \\ r_2 \\ r_3 \\ r_4 \end{bmatrix}}_{r} + \gamma \underbrace{ \begin{bmatrix} 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \end{bmatrix}}_{P} \underbrace{\begin{bmatrix} v_1 \\ v_2 \\ v_3 \\ v_4 \end{bmatrix}}_{v}\]
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| $$
\underbrace{\begin{bmatrix} v_1 \\ v_2 \\ v_3 \\ v_4 \end{bmatrix}}_{v}
=\underbrace{\begin{bmatrix} r_1 \\ r_2 \\ r_3 \\ r_4 \end{bmatrix}}_{r}
+ \gamma \underbrace{
\begin{bmatrix}
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
1 & 0 & 0 & 0
\end{bmatrix}}_{P}
\underbrace{\begin{bmatrix} v_1 \\ v_2 \\ v_3 \\ v_4 \end{bmatrix}}_{v}
$$
|
Display Modes
Default display math mode
\[\sum_{a} \pi (a \vert s) = 1\]
Force in-line math mode
\[\textstyle \sum_{a} \pi (a \vert s) = 1\]
- Defualt in-line math mode: \(\sum_{a} \pi (a \vert s) = 1\)
- Force display math mode: \(\displaystyle \sum_{a} \pi (a \vert s) = 1\)
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| Default display math mode
<Mandatory Blank Line>
$$
\sum_{a} \pi (a \vert s) = 1
$$
<Mandatory Blank Line>
Force in-line math mode
<Mandatory Blank Line>
$$
\textstyle \sum_{a} \pi (a \vert s) = 1
$$
<Mandatory Blank Line>
- Defualt in-line math mode: $$ \sum_{a} \pi (a \vert s) = 1 $$
- Force display math mode: $$ \displaystyle \sum_{a} \pi (a \vert s) = 1 $$
|
Fonts
\[\begin{align} &\text{mathbb: } \mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ &\text{mathcal: } \mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ &\text{mathfrak: } \mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ &\text{mathrm: } \mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ &\text{mathbf: } \mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ &\text{mathsf: } \mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ &\text{mathtt: } \mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \end{align}\]
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| $$
\begin{align}
&\text{mathbb: } \mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
&\text{mathcal: } \mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
&\text{mathfrak: } \mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
&\text{mathrm: } \mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
&\text{mathbf: } \mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
&\text{mathsf: } \mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
&\text{mathtt: } \mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\end{align}
$$
|
Dots
- \ldots for horizontal dots on the line
- \cdots for horizontal dots above the line
- \vdots for vertical dots
- \ddots for diagonal dots
\[\Sigma=\left[ \begin{array}{ccc} \sigma_{11} & \cdots & \sigma_{1n} \\ \vdots & \ddots & \vdots \\ \sigma_{n1} & \cdots & \sigma_{nn} \end{array} \right]\]
$$
\Sigma=\left[
\begin{array}{ccc}
\sigma_{11} & \cdots & \sigma_{1n} \\
\vdots & \ddots & \vdots \\
\sigma_{n1} & \cdots & \sigma_{nn}
\end{array}
\right]
$$
