hexo中常用的一些语法记录

简要记录Latex的常用基本语法

$$sum = \sum_{b}^{a}x^2\ \pi\ \alpha\ \sqrt\pi\$$ $$\begin{equation*} \int_{-X}^{Y} \exp(z)\, dz \end{equation*}$$

$\textbf{HelloWorld}!$

$\sum_{i=1}^n a_i=0$

BP算法

训练集 $\left\{\left(x^{(1)}, y^{(1)}\right), \ldots,\left(x^{(m)}, y^{(m)}\right)\right\}$

设 $\Delta_{i j}^{(l)}=0(\text { for all } l, i, j)$

$\begin{array}{l}{\text {For } i=1 \text { to } m}\end{array}$

$$\begin{array}{l}{\text { Set } a^{(1)}=x^{(i)}} \\ {\text { Perform forward propagation to compute } a^{(l)} \text { for } l=2,3, \ldots, L} \\ {\text { Using } y^{(i)}, \text { compute } \delta^{(L)}=a^{(L)}-y^{(i)}} \\ {\text { Compute } \delta^{(L-1)}, \delta^{(l+1)}, \ldots, \delta^{(2)}} \\ {\Delta_{i j}^{(l)} :=\Delta_{i j}^{(l)}+a_{j}^{(l)} \delta_{i}^{(l+1)}}\end{array}$$

$\begin{array}{l}{D_{i j}^{(l)} :=\frac{1}{m} \Delta_{i j}^{(l)}+\lambda \Theta_{i j}^{(l)}} & {\text { if } j \neq 0} \\ {D_{i j}^{(l)} :=\frac{1}{m} \Delta_{i j}^{(l)}} & {\text { if } j=0}\end{array}$

其中 $\frac{\partial}{\partial \Theta_{i j}^{(l)}} J(\Theta)=D_{i j}^{(l)}$

$$f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases}$$

$c(u)=\begin{cases} \sqrt\frac{1}{N}，u=0\\ \sqrt\frac{2}{N}， u\neq0\end{cases} $

$$\begin{aligned} &\vec{R_1}=[na\vec{e_x},ma\vec{e_y},la\vec{e_z}]& \nonumber\\ &\vec{R_2}=[(n+0.5)a\vec{e_x},(m+0.5)a\vec{e_y},la\vec{e_z}]& \nonumber \\ &\vec{R_3}=[(n+0.5)a\vec{e_x},ma\vec{e_y},(l+0.5)a\vec{e_z}]& \nonumber \\ &\vec{R_4}=[na\vec{e_x},(m+0.5)a\vec{e_y},(l+0.5)a\vec{e_z}]& \nonumber\\ \end{aligned}\\$$ $$\begin{aligned}\\ y&=kx+b \\ x^2+b&=y\\ \end{aligned}\\$$ $$\begin{aligned}&\\ \frac{1}{1+x}=\sum_{n=0}^{\infty}(-1)^nx^n\\ \end{aligned}$$

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在markdown中使用html语法

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