twilight.sty

% In a project, always first use the following mandatory packages
% \usepackage{graphicx, amssymb, amsmath, amsthm, dsfont, tikz, pgfplots, hyperref, xcolor, enumitem, fancyhdr, xparse, geometry, bbm, calligra, environ, comment, twilight}
\RequirePackage{graphicx}
\RequirePackage{amssymb, amsmath, amsthm, dsfont}
\RequirePackage{tikz}
\RequirePackage{pgfplots}
\RequirePackage{hyperref}
\RequirePackage{xcolor}
\RequirePackage{enumitem}
\RequirePackage{fancyhdr}
\RequirePackage{xparse}
\RequirePackage{geometry}
\RequirePackage{bbm}
\RequirePackage{calligra}
\RequirePackage{environ}
\RequirePackage{comment}

\usepgfplotslibrary{fillbetween}
\usetikzlibrary{patterns}

\pgfplotsset{compat=1.18}

% Follow British English: No Indentation
\setlength\parindent{0pt}

% Title Page Setup
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Example Usage:                                    %
% \def\CourseTitle{ExampleCourse}                   %
% \def\CourseAuthor{ExampleAuthor}                  %
% \def\CourseDate{Fall 20xx Semester}               %
% \CoursePage                                       %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\CoursePage}{
    \begin{center}\LARGE \CourseTitle\end{center}
    \begin{center}\Large ---\ \CourseAuthor\ --- \\ \CourseDate\end{center}
    \phantom{}\hrule\phantom{}
}


% Review Mode
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% use \begin{reviewmode}{1} to turn on and {0} to turn off              %
% When in review mode, all proofs are replaced with 10 empty lines      %
%    that allow you to print down and work by hand on the class-proofs  %
% In all cases, use \begin{visibleproof}...\end{visibleproof} to make   %
%    certain proofs always visible, no matter of the parameter given    %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\NewEnviron{reviewmode}[1]{%
    \let\visibleproof\proof
    \let\endvisibleproof\endproof
    \ifnum#1=1
        \RenewEnviron{proof}{\phantom{}\\ \\ \\ \\ \\ \\ \\ \\ \\ \\}{}
    \fi
    \BODY
    \let\proof\visibleproof
    \let\endproof\endvisibleproof
}


% Color Definitions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Usage: \textcolor{NavyBlue}{lorum ipsum}          %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\definecolor{NavyBlue}{RGB}{0,0,128}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Citation of the code below                                                                            %
% TITLE: How to trim the spaces for `\BODY` in `\NewEnviron`                                            %
% SUBTITLE: I'm not sure what the purpose of ansproofbase is. Just set the color at the outset. ...     %
% AUTHOR: egreg @ Tex StackExchange                                                                     %
% DATE: Jan 28th, 2024                                                                                  %
% AVAILABILITY: https://tex.stackexchange.com/a/711780/315951                                           %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Begin of Borrowed Code
\ExplSyntaxOn

\NewDocumentEnvironment{ansproof}{O{\proofname}+b}{%
  \par\color{NavyBlue}
  \begin{proof}[#1]
  \twilight_if_empty:nF { #2 } { #2 }
  \end{proof}
}{}

\prg_new_protected_conditional:Nnn \twilight_if_empty:n { T,F,TF }
 {
  \tl_set:Nn \l_tmpa_tl { #1 }
  \tl_replace_all:Nnn \l_tmpa_tl { \par } { }
  \tl_if_blank:VTF \l_tmpa_tl { \prg_return_true: } { \prg_return_false: }
 }

\ExplSyntaxOff
% End of Borrowed Code



% Mathematical Notations
\newcommand{\pf}[2]{\dfrac{\partial #1}{\partial #2}} % Partial Derivative
\newcommand{\df}[2]{\dfrac{\text{d} #1}{\text{d} #2}} % Derivative
% Number Sets
\newcommand{\R}{\mathds{R}}
\newcommand{\N}{\mathds{N}}
\newcommand{\Q}{\mathds{Q}}
\newcommand{\C}{\mathds{C}}
\newcommand{\Z}{\mathds{Z}}
\newcommand{\E}{\mathbb{E}}
\newcommand{\I}{\mathbb{I}}
% Calligraphic Letters
\newcommand{\Ac}{\mathcal{A}}
\newcommand{\Bc}{\mathcal{B}}
\newcommand{\Cc}{\mathcal{C}}
\newcommand{\Dc}{\mathcal{D}}
\newcommand{\Ec}{\mathcal{E}}
\newcommand{\Fc}{\mathcal{F}}
\newcommand{\Gc}{\mathcal{G}}
\newcommand{\Hc}{\mathcal{H}}
\newcommand{\Ic}{\mathcal{I}}
\newcommand{\Jc}{\mathcal{J}}
\newcommand{\Kc}{\mathcal{K}}
\newcommand{\Lc}{\mathcal{L}}
\newcommand{\Mc}{\mathcal{M}}
\newcommand{\Nc}{\mathcal{N}}
\newcommand{\Oc}{\mathcal{O}}
\newcommand{\Pc}{\mathcal{P}}
\newcommand{\Qc}{\mathcal{Q}}
\newcommand{\Rc}{\mathcal{R}}
\newcommand{\Sc}{\mathcal{S}}
\newcommand{\Tc}{\mathcal{T}}
\newcommand{\Uc}{\mathcal{U}}
\newcommand{\Vc}{\mathcal{V}}
\newcommand{\Wc}{\mathcal{W}}
\newcommand{\Xc}{\mathcal{X}}
\newcommand{\Yc}{\mathcal{Y}}
\newcommand{\Zc}{\mathcal{Z}}
% Bold & Italic Letters
\newcommand{\av}{\boldsymbol{a}}
\newcommand{\bv}{\boldsymbol{b}}
\newcommand{\cv}{\boldsymbol{c}}
\newcommand{\dv}{\boldsymbol{d}}
\newcommand{\ev}{\boldsymbol{e}}
\newcommand{\fv}{\boldsymbol{f}}
\newcommand{\gv}{\boldsymbol{g}}
\newcommand{\hv}{\boldsymbol{h}}
\newcommand{\iv}{\boldsymbol{i}}
\newcommand{\jv}{\boldsymbol{j}}
\newcommand{\kv}{\boldsymbol{k}}
\newcommand{\lv}{\boldsymbol{l}}
\newcommand{\mv}{\boldsymbol{m}}
\newcommand{\nv}{\boldsymbol{n}}
\newcommand{\ov}{\boldsymbol{o}}
\newcommand{\pv}{\boldsymbol{p}}
\newcommand{\qv}{\boldsymbol{q}}
\newcommand{\rv}{\boldsymbol{r}}
\newcommand{\sv}{\boldsymbol{s}}
\newcommand{\tv}{\boldsymbol{t}}
\newcommand{\uv}{\boldsymbol{u}}
\newcommand{\vv}{\boldsymbol{v}}
\newcommand{\wv}{\boldsymbol{w}}
\newcommand{\xv}{\boldsymbol{x}}
\newcommand{\yv}{\boldsymbol{y}}
\newcommand{\zv}{\boldsymbol{z}}
\newcommand{\Av}{\boldsymbol{A}}
\newcommand{\Bv}{\boldsymbol{B}}
\newcommand{\Cv}{\boldsymbol{C}}
\newcommand{\Dv}{\boldsymbol{D}}
\newcommand{\Ev}{\boldsymbol{E}}
\newcommand{\Fv}{\boldsymbol{F}}
\newcommand{\Gv}{\boldsymbol{G}}
\newcommand{\Hv}{\boldsymbol{H}}
\newcommand{\Iv}{\boldsymbol{I}}
\newcommand{\Jv}{\boldsymbol{J}}
\newcommand{\Kv}{\boldsymbol{K}}
\newcommand{\Lv}{\boldsymbol{L}}
\newcommand{\Mv}{\boldsymbol{M}}
\newcommand{\Nv}{\boldsymbol{N}}
\newcommand{\Ov}{\boldsymbol{O}}
\newcommand{\Pv}{\boldsymbol{P}}
\newcommand{\Qv}{\boldsymbol{Q}}
\newcommand{\Rv}{\boldsymbol{R}}
\newcommand{\Sv}{\boldsymbol{S}}
\newcommand{\Tv}{\boldsymbol{T}}
\newcommand{\Uv}{\boldsymbol{U}}
\newcommand{\Vv}{\boldsymbol{V}}
\newcommand{\Wv}{\boldsymbol{W}}
\newcommand{\Xv}{\boldsymbol{X}}
\newcommand{\Yv}{\boldsymbol{Y}}
\newcommand{\Zv}{\boldsymbol{Z}}
% Bold Letters (Vectors, Matrices, Tensors, etc.)
\newcommand{\ab}{\mathbf{a}}
\newcommand{\bb}{\mathbf{b}}
\newcommand{\cb}{\mathbf{c}}
\newcommand{\db}{\mathbf{d}}
\newcommand{\eb}{\mathbf{e}}
\newcommand{\fb}{\mathbf{f}}
\newcommand{\gb}{\mathbf{g}}
\newcommand{\hb}{\mathbf{h}}
\newcommand{\ib}{\mathbf{i}}
\newcommand{\jb}{\mathbf{j}}
\newcommand{\kb}{\mathbf{k}}
\newcommand{\lb}{\mathbf{l}}
\newcommand{\mb}{\mathbf{m}}
\newcommand{\nb}{\mathbf{n}}
\newcommand{\ob}{\mathbf{o}}
\newcommand{\pb}{\mathbf{p}}
\newcommand{\qb}{\mathbf{q}}
\newcommand{\rb}{\mathbf{r}}
\renewcommand{\sb}{\mathbf{s}}  % If you want to use the original \sb, you need to use \renewcommand
\newcommand{\ub}{\mathbf{u}}
\newcommand{\vb}{\mathbf{v}}
\newcommand{\wb}{\mathbf{w}}
\newcommand{\xb}{\mathbf{x}}
\newcommand{\yb}{\mathbf{y}}
\newcommand{\zb}{\mathbf{z}}
\newcommand{\Ab}{\mathbf{A}}
\newcommand{\Bb}{\mathbf{B}}
\newcommand{\Cb}{\mathbf{C}}
\newcommand{\Db}{\mathbf{D}}
\newcommand{\Eb}{\mathbf{E}}
\newcommand{\Fb}{\mathbf{F}}
\newcommand{\Gb}{\mathbf{G}}
\newcommand{\Hb}{\mathbf{H}}
\newcommand{\Ib}{\mathbf{I}}
\newcommand{\Jb}{\mathbf{J}}
\newcommand{\Kb}{\mathbf{K}}
\newcommand{\Lb}{\mathbf{L}}
\newcommand{\Mb}{\mathbf{M}}
\newcommand{\Nb}{\mathbf{N}}
\newcommand{\Ob}{\mathbf{O}}
\newcommand{\Pb}{\mathbf{P}}
\newcommand{\Qb}{\mathbf{Q}}
\newcommand{\Rb}{\mathbf{R}}
\newcommand{\Sb}{\mathbf{S}}
\newcommand{\Tb}{\mathbf{T}}
\newcommand{\Ub}{\mathbf{U}}
\newcommand{\Vb}{\mathbf{V}}
\newcommand{\Wb}{\mathbf{W}}
\newcommand{\Xb}{\mathbf{X}}
\newcommand{\Yb}{\mathbf{Y}}
\newcommand{\Zb}{\mathbf{Z}}
\newcommand{\zerob}{\mathbf{0}} % Zero Vector
\newcommand{\oneb}{\mathbf{1}} % Vector of Ones
\newcommand{\phib}{\boldsymbol{\phi}} % Feature Vector
\newcommand{\Phib}{\boldsymbol{\Phi}} % Feature Matrix
\newcommand{\mub}{\boldsymbol{\mu}}
\newcommand{\xib}{\boldsymbol{\xi}}
\newcommand{\sigmab}{\boldsymbol{\sigma}}
\newcommand{\Sigmab}{\boldsymbol{\Sigma}}
\newcommand{\alphab}{\boldsymbol{\alpha}}
\newcommand{\betab}{\boldsymbol{\beta}}
\newcommand{\gammab}{\boldsymbol{\gamma}}
\newcommand{\deltab}{\boldsymbol{\delta}}
\newcommand{\Deltab}{\boldsymbol{\Delta}}
\newcommand{\Lambdab}{\boldsymbol{\Lambda}}
\newcommand{\lambdab}{\boldsymbol{\lambda}}
\newcommand{\T}{\top} % Transpose of a Matrix
\newcommand{\idc}{\mathbbm{1}}
\NewDocumentCommand{\norm}{m o}{\IfNoValueTF{#2} {\ensuremath{\left|\left|#1\right|\right|}} {\ensuremath{\left\|#1\right\|_{#2}}}}
\newcommand{\djunion}{\perp\kern-5pt\perp} % Disjoint Union
\newcommand{\sjt}{\textnormal{subject to}}
\newcommand{\st}{\textnormal{s.t.}}
\newcommand{\opt}[1]{{{#1}^*}}
% Machine Learning and Statistics Symbols
\NewDocumentCommand{\ith}{o m o}{
    \IfNoValueTF{#3} {
        \IfNoValueTF{#1} {{#2^{(i)}}} {{#2^{(#1)}}}
    } {
        \IfNoValueTF{#1} {{#2^{(i)}_{#3}}} {{#2^{(#1)}_{#3}}}
    }
}
\newcommand{\xnor}{\text{XNOR}}
\newcommand{\VC}{\text{VC}}
% Real Analysis Symbols
\newcommand{\bdry}[1]{\partial#1} % Boundary
\newcommand{\itrr}[1]{{#1^o}} % Interior
\newcommand{\clsr}[1]{\bar{#1}} % Closure
% Machine Learning, Matrix Notations
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\sign}{sign}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\diag}{\textbf{diag}}
% Real Analysis Notations
\DeclareMathOperator{\interior}{interior}
\DeclareMathOperator{\closure}{closure}
\DeclareMathOperator{\boundary}{boundary}
\DeclareMathOperator{\exterior}{exterior}
\newcommand{\seqn}[1]{\left\{#1_n\right\}} %Standard Sequence
\newcommand{\sseqn}[1]{\left\{#1_{n_k}\right\}} %Standard Subsequence
% Theorem Notes Taking
\newtheorem{theorem}{Theorem}
\newtheorem{define}{Definition}
\newtheorem{corollary}{Corollary}
\newtheorem{lemma}{Lemma}
\newtheorem{prop}{Properties}
\newtheorem{axiom}{Axiom}
\newtheorem{program}{Program} % For Optimization Problems

% Tikz Commands

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Draw a Point in TikzPicture                              %
% Example Usage                                            %
% \drawPt{(1,1.5)} % draw a point at (1,1.5)               %
% \drawPt{(1,1.5)}[A] % same & with label A                %
% \drawPt{(1,1.5)}[A][below] % same & label below the node %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\NewDocumentCommand{\drawPt}{m o o}{%
    \IfNoValueTF{#3} {
        \IfNoValueTF{#2} {
            \draw[fill=white] #1 circle (1.5pt) node[below] {};
        } {
            \draw[fill=white] #1 circle (1.5pt) node[below] {#2};
        }
    } {
        \draw[fill=white] #1 circle (1.5pt) node[#3] {#2};
    }
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Draw points in TikzPicture w/o label                     %
% Example Usage                                            %
% \drawPts{(1,1.5), (2,3), (5,7)}                          %
% draw three points, respectively at the coordinate given  %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\drawPts}[1]{
    \foreach \coor in {#1} {
        % Draw circles at the points
        \edef\temp{\noexpand\draw[fill=white] \coor circle (1.5pt);}
        \temp
    }
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Citation of the code below                        %
% TITLE: PGF/TikZ Manual                            %
% SUBTITLE: Pattern Library                         %
% AUTHOR: Mark Wibrow                               %
% DATE: Jan 8th, 2024                               %
% AVAILABILITY: https://tikz.dev/library-patterns   %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Begin of Borrowed Code

% How to use "mylines" pattern
% Example Usage:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{tikzpicture}                                           %
%   \begin{axis} [axis lines=center, axis on top, axis equal]   %
%     \addplot [draw=none, domain=-2:0, name path=p1] {x+2};    %
%     \addplot [draw=none, domain=-0.5:1.5, name path=p2] {x-1};%
%\addplot[pattern={mylines[size=5pt,line width=.8pt,angle=45]}, %
%        pattern color=blue!40] fill between[of=p5 and p6];     %
%   \end{axis}                                                  %
%\end{tikzpicture}                                              %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\usetikzlibrary {patterns.meta}
\tikzdeclarepattern{
  name=mylines,
  parameters={
      \pgfkeysvalueof{/pgf/pattern keys/size},
      \pgfkeysvalueof{/pgf/pattern keys/angle},
      \pgfkeysvalueof{/pgf/pattern keys/line width},
  },
  bounding box={
    (0,-0.5*\pgfkeysvalueof{/pgf/pattern keys/line width}) and
    (\pgfkeysvalueof{/pgf/pattern keys/size},
0.5*\pgfkeysvalueof{/pgf/pattern keys/line width})},
  tile size={(\pgfkeysvalueof{/pgf/pattern keys/size},
\pgfkeysvalueof{/pgf/pattern keys/size})},
  tile transformation={rotate=\pgfkeysvalueof{/pgf/pattern keys/angle}},
  defaults={
    size/.initial=5pt,
    angle/.initial=45,
    line width/.initial=.4pt,
  },
  code={
      \draw [line width=\pgfkeysvalueof{/pgf/pattern keys/line width}]
        (0,0) -- (\pgfkeysvalueof{/pgf/pattern keys/size},0);
  },
}

% End of Borrowed Code