Contents
Latex Useful Snippets
Set-Up
\documentclass[12pt]{article}
\usepackage{arxiv}
\usepackage{subfig}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{hyperref}
\usepackage{url}
\usepackage{booktabs}
\usepackage{amsfonts}
\usepackage{nicefrac}
\usepackage{microtype}
\usepackage{lipsum}
\usepackage[title]{appendix}
\usepackage{graphicx}
\usepackage{graphics}
\usepackage{multirow}
\usepackage{epigraph}
\usepackage{xparse}
\usepackage{amsmath}
\usepackage{svg}
\usepackage{booktabs}
\usepackage{hyperref}
\usepackage{listings,multicol}
\usepackage{xcolor}
\usepackage{algorithm,algorithmic}
\usepackage{cite}
\hypersetup{urlcolor=black}
\definecolor{airforceblue}{rgb}{0.36, 0.54, 0.66}
\hypersetup{
colorlinks=true,
citecolor=black,
urlcolor= airforceblue
}
\newenvironment{conditions}
{\par\vspace{\abovedisplayskip}\noindent\begin{tabular}{>{$}l<{$} @{${}={}$} l}}
{\end{tabular}\par\vspace{\belowdisplayskip}}
\definecolor{codegreen}{rgb}{0,0.6,0}
\definecolor{codegray}{rgb}{0.5,0.5,0.5}
\definecolor{codepurple}{rgb}{0.58,0,0.82}
\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
\lstdefinestyle{mystyle}{
backgroundcolor=\color{backcolour},
commentstyle=\color{codegreen},
keywordstyle=\color{magenta},
numberstyle=\tiny\color{codegray},
stringstyle=\color{codepurple},
basicstyle=\ttfamily\footnotesize,
breakatwhitespace=false,
breaklines=true,
captionpos=b,
keepspaces=true,
numbers=left,
numbersep=5pt,
showspaces=false,
showstringspaces=false,
showtabs=false,
tabsize=2
}
\lstset{style=mystyle}
\let\oldquote\quote
\let\endoldquote\endquote
\RenewDocumentEnvironment{quote}{om}
{\oldquote}
{\par\nobreak\smallskip
\hfill(#2\IfValueT{#1}{~---~#1})\endoldquote
\addvspace{\bigskipamount}}
Equations with conditions
In order to reference the equation, then just use \ref{example} when writing in the body of the document.
\vspace{-0.2cm}
\begin{align}
\ \hat v(s, w) = \sum_{i=1}^{d}w_{i}x_{i}(s) \label{example}
\end{align}
\vspace{-0.4cm}
where:
\begin{conditions}
$w_{i}$ & Weight vector \\
$x_{i}$ & Feature representation via RBF\\
\end{conditions}
\vspace{-0.2cm}
Multiple Equations
\vspace{-0.2cm}
\begin{align}
\ d_{1} = \dfrac{ln(\dfrac{80}{90}) + (0.17 + \dfrac{0.2^{2}}{2})(2)}{0.2\sqrt{2}} = 0.927
\ d_{2} = d_{1} - 0.2\sqrt{2} = 0.6442
\\ C(S,t) = 80\mathcal{N}(0.927) - 90e^{(-0.17(2))}\mathcal{N}(0.6442) = \$18.42
\label{eq:3}
\vspace{-0.3cm}
\end{align}
PNG Image
\vspace{-0.3cm}
\begin{figure}[ht!]%
\centering
\includegraphics[width=6.5cm]{images/best_j.png}%
\vspace{-0.2cm}
\caption{Number of Basis Functions vs Residual Error}%
\vspace{-0.3cm}
\end{figure}
Images in row
\begin{figure}[ht!]%
\centering
\hspace{-0.6cm}
\subfloat[Tabular Method]{\includegraphics[width=5cm]{images/q_table.png}}%
\label{fig:example2}%
\subfloat[Tabular RBF Approximation]{\includegraphics[width=5cm]{images/rbf.png}}%
\label{fig:example3}%
\subfloat[Q Learning RBF Approximation]{\includegraphics[width=5cm]{images/q_rbf.png}}%
\vspace{-0.2cm}
\caption{Cost-to-go function}%
\label{fig:example4}%
\vspace{-0.25cm}
\end{figure}
SVG Images
\vspace{-0.3cm}
\begin{figure}[ht!]%
\centering
\includesvg[width=15.5cm]{images/ARprocess.svg}%
\vspace{-0.4cm}
\caption{Autoregressive Process with slowly changing parameters}%
\vspace{-0.3cm}
\end{figure}
Tables
Standard
{
\begin{table}[h!]
\centering
\begin{tabular}{|c|c|c|c|}
\hline
Specifics & Stock 1 & Stock 2 \\
\hline
Weight & 70\% & 30\% \\
Expected Return & 15\% & 18\% \\
Standard Deviation & 20\% & 17\% \\
\hline
\end{tabular}
\caption{Stocks Parameters}
\label{five}
\end{table}
}
Multirow, multicolumns
\vspace{-0.3cm}
{
\begin{table}[h!]
\centering
\begin{tabular}{|c|c|c|c|c|c|}
\hline
\multirow{2}{*}{Coefficient} & \multicolumn{5}{c|}{Percentage Error (\%)} \\\cline{2-6}
& First Estimate & Second Estimate & Third Estimate & Fourth Estimate & Fifth Estimate \\
\hline
First Coefficient (1.4) & 4.683 & 4.687 & 4.690 & 4.689 & 4.689 &
Second Coefficient (-0.7) & 2.175 & 2.182 & 2.187 & 2.187 & 2.186 &
\hline
\end{tabular}
\caption{Linear Kalman filter estimated percentage errors}
\label{table:1}
\vspace{-0.8cm}
\end{table}
}
Listings
Standard
\begin{lstlisting}[language=Python, caption=Helper functions]
def two_assets_variance(w, std, corr):
return (w[0]**2)*(std[0]**2)+(w[1]**2)*(std[1]**2)+2*w[0]*w[1]*std[0]*std[1]*corr
def var_to_std(var):
return np.sqrt(var)
def portfolio_return(weight, ret):
port_ret = 0
for i in range(len(weight)):
port_ret += weight[i]*ret[i]
return port_ret
\end{lstlisting}
Multicolumn
\vspace{-0.3cm}
\begin{figure}[ht!]%
\centering
\begin{lstlisting}[numbers=left,xleftmargin=0.5em, multicols=2]
Input: X, Y, N, beta
th_n1_n1 = np.random.randn(len(X[0]),1)
P_n1_n1 = 0.001 * np.eye(len(X[0]))
R = 0.2 * np.std(X[0:10])
Q = beta * np.eye(len(X[0]))
for n in range(0, N):
x = X[n].reshape(len(X[n]), 1)
th_n_n1 = th_n1_n1.copy()
P_n_n1 = P_n1_n1 + Q
yh = sigmoid(th_n_n1.T @ x)
en = Y[n] - yh
f = sigmoid_derivative(yh) * x
den = f.T @ P_n1_n1 @ f + R
kn = (P_n1_n1 @ f) / den
th_n_n = th_n_n1 + kn * en
I_mat = np.eye(len(X[0]))
P_n_n = (I_mat - kn @ f.T) @ P_n_n1
th_n1_n1 = th_n_n.copy()
P_n1_n1 = P_n_n.copy()
return th_n_n\end{lstlisting}
\caption{Extended Kalman Filter Pseudocode}
\vspace{-0.3cm}
\end{figure}
Algorithm
\begin{algorithm}
\caption{Calculate $y = x^n$}
\label{alg1}
\vspace*{-.5cm}
\begin{multicols}{2}
\begin{algorithmic}[1]
\REQUIRE $n \geq 0 \vee x \neq 0$
\ENSURE $y = x^n$
\STATE $y \Leftarrow 1$
\IF{$n < 0$}
\STATE $X \Leftarrow 1 / x$
\STATE $N \Leftarrow -n$
\ELSE
\STATE $X \Leftarrow x$
\STATE $N \Leftarrow n$
\ENDIF
\WHILE{$N \neq 0$}
\IF{$N$ is even}
\STATE $X \Leftarrow X \times X$
\STATE $N \Leftarrow N / 2$
\ELSE[$N$ is odd]
\STATE $y \Leftarrow y \times X$
\STATE $N \Leftarrow N - 1$
\ENDIF
\ENDWHILE
\end{algorithmic}
\end{multicols}
\vspace*{-.4cm}
\end{algorithm}
Bibliography
\bibliographystyle{unsrt}
\begin{thebibliography}{1}
\vspace{-0.2cm}
\bibitem{one}
Arulampalam, MS, Maskell, S, Gordon, N &Tim Clapp, T.
\newblock A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian
Bayesian Tracking, IEEE Trans. Signal Processing 50(2), 174-188, 2002.
\bibitem{data}
Rain in Australia, Joe Young.
\newblock Kaggle.
\newblock Accessed at: {\em
\href{https://www.kaggle.com/jsphyg/weather-dataset-rattle-package}
{https://www.kaggle.com/jsphyg/weather-dataset-rattle-package}},
March 2020.
\end{thebibliography}
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