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% package information --------------------------------------------------------------------------------------------------

\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{cora-macs}[2024-12-11] % Should match the version on CTAN.

% Authors: Tobias Ladner, Lukas Koller
% TUM - Cyber-Physical Systems Group
% Website: https://www.ce.cit.tum.de/cps

% Based on: https://www.overleaf.com/learn/latex/Writing_your_own_package

% required packages ----------------------------------------------------------------------------------------------------

% general packages
\RequirePackage{xifthen}
\RequirePackage{xstring}
\RequirePackage{amsfonts}
\RequirePackage{keyval}

% color
\RequirePackage{xcolor}

% tikz
\RequirePackage{tikzscale}
\RequirePackage{pgfplots}
\RequirePackage{mathtools}
\RequirePackage{graphics}
\usepgfplotslibrary{external}


% pre-processing -------------------------------------------------------------------------------------------------------

% for better logging
\newcommand{\DeclareCORAOption}[2]{
  \DeclareOption{#1}{
  % display information
    \PackageInfo{cora-macs}{Loading '#1' option..}
    % content
    #2
  }
}

% nice to have
\providecommand{\R}{\ensuremath{\mathbb{R}}}
\providecommand{\N}{\ensuremath{\mathbb{N}}}

% all sets should be written in mathcal
\newcommand{\contSet}[1]{\ensuremath{\mathcal{#1}}}

% CORA macro
\providecommand{\CORA}[0]{{\color{black}C\color{red!90!black}O\color{black}RA}}

% declare options ------------------------------------------------------------------------------------------------------

\DeclareCORAOption{sets}{ %                                                                          --- continuous sets
% contSet ---

% formatting
  \newcommand{\neghphantom}[1]{\settowidth{\dimen0}{#1}\hspace*{-\dimen0}}

  % short-hand notation (including nice punctuation for large sets)
  \newcommand{\shortContSet}[3][]{\ensuremath{% \defContSet[punctuation]{abbreviation}{cs parameters of set}
    \left&lt;#2\right&gt;_{#3\,}%
    \ifthenelse{\isempty{#1}}% add abbreviation
    {} % none given
    {\neghphantom{\scriptsize #3}#1\neghphantom{#1}\hphantom{\scriptsize #3}}
  }}
  \newcommand{\defContSet}[2]{\left\{ #1 \ \middle|\ #2 \right\}}
  \newcommand{\defContSetSplit}[2]{\left\{ #1 \vphantom{#2} \ \right| \\ &amp;\qquad \left. \vphantom{#1} #2 \right\}}

  % interval ---
  \providecommand{\I}{\contSet{I}}
  \newcommand{\shortI}[2]{\ensuremath{\left[#1,#2\right]}}

  % zonotope ---
  \providecommand{\Z}{\contSet{Z}}
  \newcommand{\shortZ}[3][]{\shortContSet[#1]{#2,#3}{Z}}
  \newcommand{\defZ}{\left\{ c + \sum_{i=1}^{p} \beta_i G_{(\cdot,i)} ~\middle|~ \beta_i \in [-1,1] \right\}}

  % polynomial zonotope ---
  \providecommand{\PZ}{\contSet{PZ}}
  \newcommand{\shortPZ}[5][]{\shortContSet[#1]{#2,#3,#4,#5}{PZ}}
  \newcommand{\defPZmain}{c + \sum_{i=1}^h \left(\prod_{k=1}^p \alpha_k^{E_{(k,i)}}\right) G_{(\cdot, i)} + \sum_{j=1}^{q} \beta_j G_{I(\cdot, j)}}
  \newcommand{\defPZcond}{\alpha_k, \beta_j \in \left[-1,1\right]}
  \newcommand{\defPZ}{\defContSet{\defPZmain}{\defPZcond}}
  \newcommand{\defPZSplit}{\defContSetSplit{\defPZmain}{\defPZcond}}
}


\DeclareCORAOption{operations}{ %                                                                         --- operations

% define monospace operator including inline operator
  \newcommand{\operator}[3][]{%
    \text{\normalfont\small#2}%
    \IfSubStr{#1}{inline}% if inline
    {(#3)}% no \left/\right
    {\left(#3\right)}}
  \newcommand{\operatortt}[3][]{\operator[#1]{{\ensuremath{\mathtt{#2}}}}{#3}}

  % enclosure
  \newcommand{\opEnclose}[3][]{\operatortt[#1]{enclose}{#2,#3}}
  \newcommand{\opEnclosePrime}[3][]{\operatortt[#1]{enclose}{#2,#3}}
  \newcommand{\opIntervalEnclosure}[2][]{\operatortt[#1]{interval}{#2}}
  \newcommand{\opBoxEnclosure}[2][]{\operatortt[#1]{box}{#2}}
  \newcommand{\opBound}[2][]{\operatortt[#1]{bound}{#1}}
  \newcommand{\opZonotopeEnclosure}[2][]{\operatortt[#1]{zonotope}{#2}}
  \newcommand{\opZonoEnclosure}[2][]{\operatortt[#1]{zono}{#2}}
  \newcommand{\opPolyZonotopeEnclosure}[2][]{\operatortt[#1]{polyZonotope}{#2}}
  \newcommand{\opPolyZonoEnclosure}[2][]{\operatortt[#1]{polyZono}{#2}}

  % further operations
  \newcommand{\opProject}[2][]{\operatortt{project}{#2}}

  % operations that should be stantard latex operations
  \providecommand{\diag}[2][]{\operator[#1]{diag}{#2}}
  \providecommand{\Diag}[2][]{\operator[#1]{Diag}{#2}}
  \providecommand{\mod}[3][]{\operator[#1]{mod}{#2,#3}}
  \newcommand{\dia}[2][]{\operator[#1]{dia}{#2}}
  \newcommand{\sign}[2][]{\operator[#1]{sign}{#2}}
}


\DeclareCORAOption{nn}{ %                                                                            --- neural networks

% neural network
  \newcommand{\NN}[0]{\ensuremath{\Phi}}
  \newcommand{\numLayers}[0]{\ensuremath{\kappa}}
  \newcommand{\numNeurons}[0]{\ensuremath{n}}

  % layers
  \newcommand{\nnLayerName}[2][]{\ensuremath{L_{#2}^\text{#1}}}
  \newcommand{\nnLayer}[3][]{\ensuremath{\nnLayerName[#1]{#2}\left(#3\right)}}
  \newcommand{\nnActFun}{\ensuremath{\phi}}
  \newcommand{\actfun}{\nnActFun} % remove?

  % point propagation
  \newcommand{\nnInput}[0]{\ensuremath{x}}
  \newcommand{\nnHidden}[0]{\ensuremath{h}}
  \newcommand{\nnOutput}[0]{\ensuremath{y}}
  \newcommand{\nnGrad}{\ensuremath{g}}

  % set propagation
  \newcommand{\nnInputSet}[0]{\contSet{X}}
  \newcommand{\nnHiddenSet}[0]{\contSet{H}}
  \newcommand{\nnHiddenSetExact}[0]{\nnHiddenSet^*}
  \newcommand{\nnOutputSet}[0]{\contSet{Y}}
  \newcommand{\nnOutputSetExact}[0]{\nnOutputSet^*}
  \newcommand{\nnGradSet}{\contSet{G}}

  % set-based training
  \newcommand{\nnTarget}{\ensuremath{t}}
  \newcommand{\regrSub}{MSE}
  \newcommand{\ceSub}{CE}
  \newcommand{\pointLoss}{\ensuremath{E}}
  \newcommand{\setLoss}{\ensuremath{\widetilde{E}}}

  % other
  \newcommand{\nnPertRadius}{\epsilon}

  % specification
  \newcommand{\unsafeSet}[0]{\contSet{S}}

}

%

\DeclareCORAOption{colors}{%                                                                                  --- colors

% cora colors (see CORAcolor in cora)                                                                    --- cora colors
  \definecolor{CORAcolorReachSet}{rgb}{0.2706, 0.5882, 1.0000}     % blue
  \definecolor{CORAcolorReachSet2}{rgb}{0.6902, 0.8235, 1.0000}    % light-blue
  \definecolor{CORAcolorInitialSet}{rgb}{1, 1, 1}                  % white
  \definecolor{CORAcolorFinalSet}{rgb}{0.9000, 0.9000, 0.9000}     % light-gray
  \definecolor{CORAcolorSimulations}{rgb}{0.0000, 0.0000, 0.0000}  % black
  \definecolor{CORAcolorUnsafe}{rgb}{0.9451, 0.5529, 0.5686}       % red
  \definecolor{CORAcolorUnsafeLight}{rgb}{0.9059, 0.7373, 0.7373}  % light red
  \definecolor{CORAcolorSafe}{rgb}{0.4706, 0.7725, 0.4980}         % light green
  \definecolor{CORAcolorUnknown}{rgb}{0.9290, 0.6940, 0.1250}      % yellow
  \colorlet{CORAcolorInvariant}{CORAcolorSafe}                     % light green

  % default colors (also default matlab colors)
  \definecolor{CORAcolorBlue}{rgb}{0, 0.4470, 0.7410}
  \definecolor{CORAcolorRed}{rgb}{0.8500, 0.3250, 0.0980}
  \definecolor{CORAcolorYellow}{rgb}{0.9290, 0.6940, 0.1250}
  \definecolor{CORAcolorPurple}{rgb}{0.4940, 0.1840, 0.5560}
  \definecolor{CORAcolorGreen}{rgb}{0.4660, 0.6740, 0.1880}
  \definecolor{CORAcolorLightBlue}{rgb}{0.3010, 0.7450, 0.9330}
  \definecolor{CORAcolorDarkRed}{rgb}{0.6350, 0.0780, 0.1840}

  % define order of colors (see useCORAcolors in cora)
  \colorlet{CORAcolor1}{CORAcolorBlue}
  \colorlet{CORAcolor2}{CORAcolorRed}
  \colorlet{CORAcolor3}{CORAcolorYellow}
  \colorlet{CORAcolor4}{CORAcolorPurple}
  \colorlet{CORAcolor5}{CORAcolorGreen}
  \colorlet{CORAcolor6}{CORAcolorLightBlue}
  \colorlet{CORAcolor7}{CORAcolorDarkRed}

  \definecolor{CORAcolorHighlight1}{rgb}{1.0000,0.6824,0.2980} % 'CORA:highlight1 (orange)'
  \definecolor{CORAcolorHighlight2}{rgb}{0.3804,0.6275,1.0000} % 'CORA:highlight2 (lightblue)'

  %                                                                                                       --- TUM colors
  \definecolor{TUMblue}{rgb}{0.00, 0.40, 0.74}
  \definecolor{TUMgray}{rgb}{0.85, 0.85, 0.86}
  \definecolor{TUMpantone285C}{rgb}{0.00, 0.45, 0.81}
  \definecolor{TUMpantone300C}{RGB}{27, 94, 170} %uncorrected TUMpantone300C
  \definecolor{lightblue}{rgb}{0.7529,0.8118,0.9333}

}


\DeclareCORAOption{tikz}{ %                                                                                     --- tikz

% groupplots
  \usepgfplotslibrary{groupplots}
  \usetikzlibrary{pgfplots.groupplots}
  \usetikzlibrary{matrix}
  \usetikzlibrary{patterns}
  \usetikzlibrary{arrows,arrows.meta}

  % main packages
  \pgfplotsset{compat=1.18}

  % tikz externalize
  \providecommand{\includetikzinternalpath}{./figures/externalize}
  \providecommand{\includetikzupdatepath}[1]{\renewcommand{\includetikzinternalpath}[1]{##1}}
  \tikzexternalize[prefix=\includetikzinternalpath/]
  % include tikz
  \providecommand{\includetikzinternalusetikz}[1]{%
    \tikzset{external/export next=\CORAtikzexternalize}
    \tikzsetnextfilename{\CORAtikzname{#1}}%
    \input{#1.tikz}%
  }
  % reuse externalized pdf
  \providecommand{\includetikzinternalusepdf}[1]{%
    \IfSubStr{\CORAtikzexternalize}{true}{
    % include pdf if exists
      \IfFileExists{{\includetikzinternalpath/\CORAtikzname{#1}.pdf}}{
      % include pdf
        \includegraphics{\includetikzinternalpath/\CORAtikzname{#1}.pdf}
      }{
      % show error message
        \texttt{
          \tiny  \sloppy
          The file ''\expandafter\detokenize\expandafter{\includetikzinternalpath}/\expandafter\detokenize\expandafter{\CORAtikzname{#1}}.pdf`` does not exist and has to be exported first.
          Please re-compile with tikz externalize and shell escape enabled.
          Check the documentation for details.
        }
      }
    }{
    % call tikz
      \includetikzinternalusetikz{#1}
    }
  }
  % set up commands for tikz options (default: false)
  \providecommand{\CORAtikzname}[1]{#1}
  \providecommand{\CORAtikzexternalize}{true}
  \providecommand{\CORAtikzsetupoptions}[1]{
  % option 'animate': externalize with overlaynumber
    \IfSubStr{#1}{animate}{
    % have overlay number in name to have each overlay as separate pdf
      \renewcommand{\CORAtikzname}[1]{##1-animate-\overlaynumber}
      \mode&lt;handout&gt;{
        % additionally have one pdf for handout mode
        \renewcommand{\CORAtikzname}[1]{##1-animate-handout}
      }
    }{
      \renewcommand{\CORAtikzname}[1]{##1}
    }
    % option 'noexternalize'/'noexport': whether figure should be externalized
    \IfSubStr{#1}{noexternalize}{
      \renewcommand{\CORAtikzexternalize}{false}
    }{
      \IfSubStr{#1}{noexport}{
        \renewcommand{\CORAtikzexternalize}{false}
      }{
        \renewcommand{\CORAtikzexternalize}{true}
      }
    }
  }
  % main command to include tikz
  \providecommand{\includetikz}[2][]{\texttt{Not yet initialized}}
  % make tikz/pdf selectable
  \providecommand{\CORAexternalizeusetikz}{\renewcommand{\includetikz}[2][]{\CORAtikzsetupoptions{##1}\includetikzinternalusetikz{##2}}}
  \providecommand{\CORAexternalizeusepdf}{\renewcommand{\includetikz}[2][]{\CORAtikzsetupoptions{##1}\includetikzinternalusepdf{##2}}}
  \CORAexternalizeusetikz

  \tikzset {external/optimize=true}
  % ensure
  \makeatletter
  \providecommand*{\overlaynumber}{\number\beamer@slideinframe}
  \makeatother

  % styling
  \pgfplotsset{every axis/.append style={
    ylabel near ticks,
    xlabel near ticks,
  }}
  \tikzset{
    &gt;={Stealth[length=1mm]},
  }

  % frame animations - in-/visible on for tikz objects
  \tikzset{
    alt/.code args={&lt;#1&gt;#2#3}{%
    \alt&lt;#1&gt;{\pgfkeysalso{#2}}{\pgfkeysalso{#3}} % \pgfkeysalso doesn't change the path
  },
  invisible/.style={opacity=0},
  visible on/.style={alt={#1{}{invisible}}},
  invisible on/.style={alt={#1{invisible}{}}},
}

% tikz neural networks
\tikzset{
  pics/nn/.style n args={4}{code={ % args: number of layers, list of hidden neurons, size of neuron, distance between neurons
    \pgfmathsetmacro{\d}{#4};
    \pgfmathsetmacro{\hn}{#1};
    \foreach[count=\i] \h in {#2} { % draw network
      \foreach \ii in {1,...,\h} { % draw layer
        \node[circle,fill=CORAcolorBlue!75,draw=CORAcolorBlue,thick,inner sep={#3}] (l\i-\ii) at ({1.0cm*(\i-1-0.5*(\hn-1))},{\d*(\ii-0.5*(\h+1))}) {}; % \d*(\ii-1+0.5*Mod(\h,2))
      };
    };
    % connect neurons
    \foreach[count=\i] \hi in {#2} { %
      \foreach[count=\j] \hj in {#2} { %
        \pgfmathtruncatemacro{\dji}{\j-\i};
        \ifnum\dji=1
        \foreach \ii in {1,...,\hi} { %
          \foreach \jj in {1,...,\hj} { %
            \draw (l\i-\ii.east) -- (l\j-\jj.west); %
          };
        };
        \fi
      };
    };
  },
  },
  neuron label/.style n args={1}{label={[font=\footnotesize,text=white]center:#1}},
  pics/zono3/.style n args={2}{code={\filldraw (0,-{#1}) -- (-{#2},-{#1}) -- (-{#2},0) -- (0,{#1}) -- ({#2},{#1}) -- ({#2},0) -- cycle;}},
  pics/lossArrows3/.style n args={2}{code={\draw (0,0) -- ({0.5*#2},{0.5*#1}) -- ({0.5*#2},{#1}) -- ({#2},{#1});}},
}

\pgfplotsset{
  enclosurefunction/.style={color=black, forget plot},
  enclosureset/.style={color=CORAcolorGreen, forget plot},
  enclosuresetbounds/.style={color=CORAcolorGreen, dashed, forget plot},
  enclosureinputbounds/.style={color=TUMgray, dashed, forget plot},
  enclosurepolynomial/.style={color=CORAcolorBlue, forget plot},
  enclosureerror/.style={color=CORAcolorRed, forget plot},
}

}

% process options ------------------------------------------------------------------------------------------------------

\ProcessOptions\relax

% post-processing ------------------------------------------------------------------------------------------------------
</pre></body></html>