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% package information --------------------------------------------------------------------------------------------------
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{cora-macs}[2024-10-25]
% 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 ----------------------------------------------------------------------------------------------------
\RequirePackage{xifthen}
\RequirePackage{xstring}
\RequirePackage{amsfonts}
\RequirePackage{xcolor}
% 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}}}
% process 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<#2\right>_{#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| \\ &\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
\newcommand{\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_{#1}^\text{#2}}}
\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}}
% other
\newcommand{\nnPertRadius}{\epsilon}
% specification
\newcommand{\unsafeSet}[0]{\contSet{S}}
}
% --- colors
\DeclareCORAOption{colors}{ % --- cora colors
% cora colors (see CORAcolor in cora)
\definecolor{CORAcolorReachSet}{rgb}{0.2706, 0.5882, 1.0000} % blue
\definecolor{CORAcolorReachSet2}{rgb}{0.6902, 0.8235, 1.0000} % light-blue
\definecolor{CORAcolorOnitialSet}{rgb}{1, 1, 1} % white
\definecolor{CORAcolorFinalSet}{rgb}{0.9000, 0.9000, 0.9000} % light-gray
\definecolor{CORAcolorSimulations}{rgb}{0.9000, 0.9000, 0.9000} % 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
\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)'
}
\DeclareCORAOption{tumcolors}{ % ---- 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}
}
% process all options
\ProcessOptions\relax
% post-processing ------------------------------------------------------------------------------------------------------
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