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393 lines
17 KiB
393 lines
17 KiB
3 years ago
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% https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=2ahUKEwiwv6SOxr3gAhVp6KYKHUAfBMUQFjABegQIHBAC&url=http%3A%2F%2Fctan.math.washington.edu%2Ftex-archive%2Fmacros%2Flatex%2Fcontrib%2Fglossaries%2Fglossaries-user.pdf&usg=AOvVaw31Aw4LHCUnYYR1r6HL9_ZG
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\newcommand*{\sym}[4]{
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\newglossaryentry{#1}{type=symbols,name={$#2$},sort={#3},description={#4}}
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}
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% \newglossaryentry{}{type=symbols,name=$$,sort=,description={}}
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% \macsym{macro}{name}{sort}{description}
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% -----------------------------------------------------------------------------
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% Mathematics basics
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% -----------------------------------------------------------------------------
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% Define new math operators
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\DeclareMathOperator{\imag}{im}
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%\DeclareMathOperator{\kern}{kern} %somewhere already defined
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\DeclareMathOperator{\essinf}{ess-inf}
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\DeclareMathOperator*{\esssup}{ess-sup}
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\DeclareMathOperator{\dist}{dist}
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\DeclareMathOperator{\diag}{diag}
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\DeclareMathOperator{\graph}{graph}
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\DeclareMathOperator{\sign}{sign}
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\DeclareMathOperator{\rank}{rank}
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\DeclareMathOperator{\sat}{sat}
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\DeclareMathOperator{\spec}{spec}
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\DeclareMathOperator{\loc}{loc}
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\DeclareMathOperator{\grad}{grad}
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\DeclareMathOperator{\fin}{fin}
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\DeclareMathOperator{\vol}{vol}
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\DeclareMathOperator{\col}{col}
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\DeclareMathOperator{\row}{row}
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\DeclareMathOperator{\lin}{lin}
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\DeclareMathOperator{\step}{step}
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% Abbreviate sets, compact sets (of numbers, ...)
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\newcommand{\F}{\mathbb{F}}
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\sym{sy:F}{\F}{F}{sets of fett numbers ...}
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\newcommand{\X}{\mathbb{X}}
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\sym{sy:X}{\X}{X}{sets of XXX numbers ...}
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\newcommand{\N}{\mathbb{N}}
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\newcommand{\B}{\mathbb{B}}
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\newcommand{\Z}{\mathbb{Z}}
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\newcommand{\Q}{\mathbb{Q}}
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\newcommand{\R}{\mathbb{R}}
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\newcommand{\Rp}{\mathbb{R}_{\geq 0}}
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\newcommand{\Rsp}{\mathbb{R}_{> 0}}
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%\newcommand{\C}{\mathbb{C}}
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\newcommand{\Cn}{\mathbb{C}_{< 0}}
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\newcommand{\Czp}{\mathbb{C}_{\geq 0}}
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% compact set
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\newcommand{\cset}[1]{\mathfrak{#1}}
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% open set
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\newcommand{\oset}[1]{\mathcal{#1}}
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% function set
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\newcommand{\fset}[1]{\mathcal{#1}}
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% system class
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\newcommand{\sclass}[1]{\mathcal{#1}}
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% operator class
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\newcommand{\oclass}[1]{\mathcal{#1}}
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% boundary set
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\newcommand{\bset}[1]{\mathcal{#1}}
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% for defining a set
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\newcommand{\setdef}[2]{\left\{\ #1\ \left|\vphantom{#1}\ #2\ \right.\right\}}
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% function spaces
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\newcommand{\Lp}[1]{\fset{L}^{#1}}
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\newcommand{\Lone}{\fset{L}^{1}}
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\newcommand{\Loneloc}{\fset{L}^{1}_{\loc}}
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\newcommand{\Ltwo}{\fset{L}^{2}}
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\newcommand{\Linf}{\fset{L}^{\infty}}
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\newcommand{\Linfloc}{\fset{L}^{\infty}_{\loc}}
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\newcommand{\Ck}{\fset{C}^{k}}
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\newcommand{\Czero}{\fset{C}}
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\newcommand{\Cone}{\fset{C}^{1}}
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\newcommand{\Ctwo}{\fset{C}^{2}}
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\newcommand{\Cinf}{\fset{C}^{\infty}}
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\newcommand{\Wkinf}{\fset{W}^{k,\infty}}
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\newcommand{\Woneinf}{\fset{W}^{1,\infty}}
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\newcommand{\Wtwoinf}{\fset{W}^{2,\infty}}
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% Norms
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% norm ||.||
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\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}
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% ||.||_infty
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\newcommand{\esnorm}[1]{\lVert #1 \rVert_{\infty}}
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\newcommand{\Wnorm}[3]{\lVert #3 \rVert_{#1,#2}}
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\newcommand{\Lnorm}[2]{\lVert #2 \rVert_{\fset{L}^{#1}}}
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% limits
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\newcommand{\limtoinfty}[1]{\lim_{#1 \to \infty}}
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\newcommand{\limtozero}[1]{\lim_{#1 \to 0}}
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\newcommand{\limto}[2]{\lim_{#1 \to #2}}
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% General
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% lapace
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\newcommand{\laplaceT}[1]{\mathscr{L}\left\{#1\right\}}
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\newcommand{\laplaceIT}[1]{\mathscr{L}^{-1}\left\{#1\right\}}
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% myVector = \mv
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\newcommand{\mv}[1]{\boldsymbol{#1}}
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% myMatrix = \mm
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\newcommand{\mm}[1]{\boldsymbol{#1}}
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% myOperator = \mO
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\newcommand{\mo}[1]{\boldsymbol{\mathfrak{#1}}}
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% inner product <.,.>
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\newcommand{\iproduct}[2]{\langle #1,\, #2 \rangle}
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% myEnergy = \me
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\newcommand{\me}[1]{\boldsymbol{\mathcal{#1}}}
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% Dimensions e.g. [Nm]
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\newcommand{\di}[1]{\left[\rm{#1}\right]}
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% Differentiation
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\newcommand{\fdiff}[2]{\frac{\textrm{d}^{#1}}{\textrm{d}{#2}^{#1}}\,}
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\newcommand{\fpartial}[2]{\frac{\partial^{#1}}{\partial #2^{#1}}\,}
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\newcommand{\fpartials}[3]{\dfrac{\partial^{#1}{#3}}{\partial #2^{#1}}\,}
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% Hackl
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\newcommand{\Sonelin}{\sclass{S}_1^{\lin}}
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\newcommand{\Stwolin}{\sclass{S}_2^{\lin}}
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\newcommand{\Sone}{\sclass{S}_1}
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\newcommand{\Stwo}{\sclass{S}_2}
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\newcommand{\gsc}{\varsigma}
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\newcommand{\myref}{\rm{ref}}
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\newcommand{\yref}{y_{\rm{ref}}}
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\newcommand{\Yref}{Y_{\rm{ref}}}
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\newcommand{\pF}{\psi}
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%\newtheoremstyle{break}
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%{\topsep}{\topsep}{\itshape}{}{\bfseries}
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%{:}{\newline}{}
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%\theoremstyle{break}
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\newtheorem{theorem}{Theorem}[section]
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\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{definition}[theorem]{Definition}
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\newtheorem{example}[theorem]{Example}
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%\newtheorem{proposition}[theorem]{Proposition}
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%\newtheorem{lemma}[theorem]{Lemma}
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%\newtheorem{claim}[theorem]{Claim}
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%\newtheorem{assumption}[theorem]{Assumption}
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%\newtheorem{motivation}[theorem]{Motivation}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% (RE-)DEFINE NEW MATH EXPRESSIONS for ELECTRICAL DRIVES and DRIVES CONTROL
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% PS-Frag
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%\newcommand{\psf}[1]{\psfrag{#1}[cc][cc][1][0]{$#1$}}
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% Real- und Imaginäranteil
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\newcommand{\Rea}[1]{\operatorname{\mathfrak{Re}}\{#1\}}
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\newcommand{\Ima}[1]{\operatorname{\mathfrak{Im}}\{#1\}}
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% General
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\newcommand{\einhalb}{\dfrac{1}{2}}
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% Linear Algebra
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\newcommand{\tr}{\mathrm{tr}}
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%\newcommand{\diag}{diag}
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\newcommand{\transpose}[1]{{#1}^\top}
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\newcommand{\inv}[1]{{#1}^{-1}}
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\newcommand{\oneV}{\mv{1}} % unity vector e.g. 1_3 = (1,1,1)^\top
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\newcommand{\oneM}{\mm{I}} % unity vector e.g. 1_3 = (1,1,1)^\top
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% Differentiation
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\newcommand{\ddtsmall}{\tfrac{{\rm d}}{{\rm d}t}}
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\newcommand{\ddt}{\dfrac{{\rm d}}{{\rm d}t}}
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\newcommand{\ddp}[1]{\frac{\partial}{\partial #1}}
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% Optimierung
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\newcommand{\argmin}[1]{\underset{#1}{\arg\min}}
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\newcommand{\argmax}[1]{\underset{#1}{\max}}
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% Integration
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\newcommand{\intd}{~d}
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% Stochastic
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\newcommand{\Erwartungswert}[1]{E[#1]}
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\newcommand{\Varianz}[1]{Var[#1]}
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% Hidden Markov Model
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\newcommand{\xkhat}[2] {\hat{\mv{x}}_{\mv{#1}#2}}
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\newcommand{\xkkhat}[2]{\hat{x}_{\text{#1},\text{#2}}}
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\newcommand{\xk}[1]{\mv{x_{\text{#1}}}}
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\newcommand{\xkk}[2]{x_{\text{#1},\text{#2}}}
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\newcommand{\yk}[1]{\mv{y_{\text{#1}}}}
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\newcommand{\ykk}[2]{y_{\text{#1},\text{#2}}}
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\newcommand{\p}[1]{p\left(#1\right)}
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\newcommand{\phat}[1]{\hat{p}\left(#1\left)}
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\newcommand{\pk}[2]{p_{\text{#1}}(#2)}
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\newcommand{\px}[1]{p(\xk{#1})}
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\newcommand{\py}[1]{p(\yk{#1})}
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\newcommand{\pxx}[2]{p(\xk{#1}|\xk{#2})}
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\newcommand{\pxy}[2]{p(\xk{#1}|\yk{#2})}
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\newcommand{\pyx}[1]{p(\yk{#1}|\xk{#1})}
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\newcommand{\pxxy}[3]{p(\xk{#1},\xk{#2}|\yk{#3})}
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\newcommand{\Likelihood}[2]{L_{#1}(#2)}
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\newcommand{\LogLikelihood}[2]{\mathcal{L}_{#1}(#2)}
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\newcommand{\MatrixML}[1]{\mm{\hat{#1}_{ML}}}
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% Particle Filter
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\newcommand{\xkp}[2]{\mv{x_{\text{#1}}}^{(#2)}}
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\newcommand{\xkps}[1]{\mv{x_{\text{#1}}}^{(s)}}
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\newcommand{\ykp}[2]{\mv{y_{\text{#1}}}^{(#2)}}
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\newcommand{\pxxp}[3]{p(\xk{#1}|\xkp{#2}{#3})}
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\newcommand{\pxxps}[3]{p(\mv{x_{#1}^{s}}|\xkp{#2}{#3})}
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\newcommand{\pyxp}[2]{p(\yk{#1}|\xkp{#1}{#2})}
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\newcommand{\wkp}[2]{\mathit{w}_{#1}^{(#2)}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\opensymdef
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%\losstring - Wenn output ein Makro enthält, dann ein \losstring am Anfang einfügen.
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% Syntax \newsym Befehl
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%\newsym[ description ]{ macroname }{ output }
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% Basics:
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%\newsym[set of natural numbers]{N}{\mathbb{N}}
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%\newsym[set of integer numbers]{Z}{\mathbb{Z}}
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%\newcommand{\R}{\mathbb{R}}
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\DeclarePairedDelimiter{\parens}{\lparen}{\rparen} % (round) parentheses \parens{...} (no auto-size) and \parens*{...} (auto-size), useful for combination with functions f\parens{args}
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\DeclarePairedDelimiter{\bracks}{\lbrack}{\rbrack} % [square] brackets
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\DeclarePairedDelimiter{\curls}{\{}{\}} % curly braces
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\DeclarePairedDelimiter\abs{\lvert}{\rvert} % abs()
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\newcommand{\mvbegin}[1]{\begin{bmatrix}#1\end{bmatrix}} % Vector content - begin[ ]end
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\newcommand{\mmbegin}[1]{\begin{bmatrix}#1\end{bmatrix}} % Matrix content - begin[ ]end
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\newcommand{\mrbegin}[2]{\left[ \begin{array}{*{#1}{r}}#2\end{array} \right] } % Matrix content - columns right aligned, number of columns in first argument
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\newcommand{\simpleeq}[1]{\begin{IEEEeqnarray}{rCl}#1\end{IEEEeqnarray}} % Einfache Gleichung mit Inhalt
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\newcommand{\mtbegin}[1]{\parens*{#1}} % Tupel - begin ( )end
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\newcommand{\msbegin}[1]{\curls*{#1}} % Set - begin { }end
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\newcommand{\counterset}[1]{\bracks{#1}} % counter set {1, ..., N}, written as [N]
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\newcommand{\normbegin}[1]{\left\Vert{#1}\right\Vert} % Norm
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\newcommand{\rechtsoffen}[1]{\left[#1\right)} % Rechtsoffenes Intervall
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\newcommand{\linkssoffen}[1]{\left(#1\right]} % Linksoffenes Intervall
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\newcommand{\closedSetR}[1]{\bracks{#1}} % Geschlossene Menge [0,pi]
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\newcommand{\del}{\partial} % Partielle Ableitung
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\newcommand{\trans}[1]{{#1}^T} % Transpose
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\newcommand{\pinv}[1]{{#1}^{+}} % Pseudo-Inverse
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%\newcommand{\norm}[1]{\left\lvert#1\right\rvert} % Absolute value
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\newcommand{\dimR}[1]{\R^{#1}} % Dimension of real vector R^(a)
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\newcommand{\dimRTwo}[2]{\R^{#1\times#2}} % Dimension of real vector R^(a x b)
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\newcommand{\dif}{\mathrm{d}} % Derivative operator d
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\newcommand{\matfun}[3][]{\mm{#2}_{#1}\parens*{#3}} % Matrix function R_a(u) = \matfun[a]{R}{u}
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\newcommand{\const}{\text{const.}} % const.
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\newcommand{\sinBr}[1]{\sin{\left(#1\right)}} % \sin() with braces
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\newcommand{\cosBr}[1]{\cos{\left(#1\right)}} % \cos() with braces
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\newcommand{\diagBr}[1]{\symdiag\curls{#1}} % Diagonal matrix diag{vector}
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\newcommand{\nullV}{\mv{0}} % Nullvektor
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\DeclareMathOperator{\signOp}{\text{sign}} % sign operator
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\newcommand{\signBr}[1]{\signOp\parens*{#1}} % sign(#1) with parentheses
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\newcommand{\expBr}[1]{\exp\parens*{#1}} % exp(#1) with parentheses
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%\newsym[cost function]{costFun}{J} % Cost function
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\newcommand{\costFunBr}[1]{\costFun\parens*{#1}} % Cost function J(#1) with parentheses
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\newcommand{\costFunSubBr}[2]{\costFun_{#1}\parens*{#2}} % Cost function J_#1(#2) with subscript and parentheses
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% some constants:
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%\newsym[generic constant]{constA}{c} % a generic constant c
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% calculus:
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\DeclareMathOperator{\diff}{\mathrm{d}\!} % non-italic differential
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\DeclareMathOperator{\supp}{\mathrm{supp}\!} % non-italic differential
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% basic probability tools:
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%\newcommand{\klBr}[2]{\klOp \parens*{#1 \mid\mid #2}} % old version of KL(#1 || #2) without automatic resizing of ||
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\DeclarePairedDelimiterX{\infdivx}[2]{(}{)}{#1\;\delimsize\|\;#2} % helper for (1 || 2)
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\newcommand{\klBr}{\kl\infdivx*} % KL(#1 || #2), starred version for automatic sizing; usage: \klBr{p}{q}
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\newcommand{\elboBr}[1]{\elbo\parens*{#1}}
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\newcommand{\est}[1]{\hat{#1}} % estimated value of some parameter, label etc.
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\newcommand{\apr}[1]{\widetilde{#1}} % approximate parameter, usually for an approximating density \pdfq
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\newcommand{\suchThat}{s.t.} % text to add constraints to an optimization problem (english: s.t.); [Papageorgiou2012, p. 11]: "unter Berücksichtigung von (u.B.v.)"; [Papageorgiou2012, p. 12, p. 67] "wobei"
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% -----------------------------------------------------------------------------
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% Application variables and constants
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% -----------------------------------------------------------------------------
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% parameter estimation:
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%\newsym[iteration number]{iteration}{i}
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% -----------------------------------------------------------------------------
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||
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% Units
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||
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% -----------------------------------------------------------------------------
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||
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\newcommand{\mathSymbolWithUnit}[2]{ \SI[parse-numbers = false, number-math-rm = \ensuremath]{#1}{\bracks{#2}} } % math symbol with unit, e.g. \varphi [rad]; do not use $
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||
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% -----------------------------------------------------------------------------
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% Lists
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||
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% -----------------------------------------------------------------------------
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||
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||
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% Itemize with smaller indentation and item spacing:
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||
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\newcommand{\myitemize}[1]{\begin{itemize}[leftmargin=3.5mm,listparindent=0mm, itemindent=0mm, parsep=0mm, itemsep=0mm]#1\end{itemize}}
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||
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\newenvironment{myindentpar}[1]%
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||
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{\begin{list}{}%
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||
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{\setlength{\leftmargin}{#1}}%
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||
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\item[]%
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||
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}
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||
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{\end{list}}
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||
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||
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|
% -----------------------------------------------------------------------------
|
||
|
|
% Editing helpers
|
||
|
|
% -----------------------------------------------------------------------------
|
||
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|
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||
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% Mark text sections for easy recognition:
|
||
|
|
\newcommand{\fixme}[1]{\hl{#1}}
|
||
|
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\newcommand{\texttodo}[1]{\textcolor{orange}{#1}}
|
||
|
|
\newcommand{\textfixme}[1]{\textcolor{red}{#1}}
|
||
|
|
\newcommand{\textcaution}[1]{\textcolor{red}{#1}}
|
||
|
|
\newcommand{\textinfo}[1]{\textcolor{blue}{#1}}
|
||
|
|
|
||
|
|
% Quotes:
|
||
|
|
\newcommand{\deqq}[1]{\glqq{}#1\grqq} % german quotation
|
||
|
|
\newcommand{\enqq}[1]{``#1''} % english quotation
|
||
|
|
\newcommand{\citebeamer}[1]{\begin{small}#1\end{small}}
|
||
|
|
|
||
|
|
% References to figures, tables etc.:
|
||
|
|
\newcommand{\figref}[1]{Figure\;\ref{#1}} % Reference to figure, middle of a sentence
|
||
|
|
\newcommand{\Figref}[1]{Figure\;\ref{#1}} % Reference to figure, beginning of a sentence
|
||
|
|
\newcommand{\fullsubfigref}[1]{Fig.\;\ref*{#1}} % Reference to figure and subfigure, middle of a sentence; the subcaption package needs \ref*
|
||
|
|
\newcommand{\Fullsubfigref}[1]{Figure\;\ref*{#1}} % Reference to figure and subfigure, beginning of a sentence; the subcaption package needs \ref*
|
||
|
|
\newcommand{\tabref}[1]{Table\;\ref{#1}} % Reference to table, middle of a sentence
|
||
|
|
\newcommand{\Tabref}[1]{Table\;\ref{#1}} % Reference to table, middle of a sentence
|
||
|
|
\newcommand{\lstref}[1]{Listing\;\ref{#1}} % Reference to code listing, middle of a sentence
|
||
|
|
\newcommand{\Lstref}[1]{Listing\;\ref{#1}} % Reference to code listing, beginning of a sentence
|
||
|
|
\newcommand{\defref}[1]{Def.\;\ref{#1}} % Reference to definition, middle of a sentence
|
||
|
|
\newcommand{\Defref}[1]{Def.\;\ref{#1}} % Reference to definition, beginning of a sentence
|
||
|
|
\newcommand{\chref}[1]{Chapter\;\ref{#1}} % Reference to chapter, middle of a sentence
|
||
|
|
\newcommand{\Chref}[1]{Chapter\;\ref{#1}} % Reference to chapter, beginning of a sentence
|
||
|
|
\newcommand{\secref}[1]{Section\;\ref{#1}} % Reference to section, middle of a sentence
|
||
|
|
\newcommand{\Secref}[1]{Section\;\ref{#1}} % Reference to section, beginning of a sentence
|
||
|
|
\newcommand{\appref}[1]{Appendix\;\ref{#1}} % Reference to appendix, middle of a sentence
|
||
|
|
\newcommand{\Appref}[1]{Appendix\;\ref{#1}} % Reference to appendix, beginning of a sentence
|
||
|
|
\newcommand{\algoref}[1]{Alg.\;\ref{#1}} % Reference to an algorithm, middle of a sentence
|
||
|
|
\newcommand{\Algoref}[1]{Alg.\;\ref{#1}} % Reference to an algorithm, beginning of a sentence
|
||
|
|
\newcommand{\algolineref}[1]{Line\;\ref{#1}} % Reference to a line of an algorithm, middle of a sentence
|
||
|
|
\newcommand{\Algolineref}[1]{Line\;\ref{#1}} % Reference to a line of an algorithm, beginning of a sentence
|
||
|
|
% use \algref{labelAlgo}{labelLine} to reference algorithm and line at once
|
||
|
|
|
||
|
|
%\newcommand{\matlab}{\textsc{Matlab}\textsuperscript{\textregistered}} % MATLAB
|
||
|
|
\newcommand{\writeMatlab}{\textsc{Matlab}} % MATLAB
|
||
|
|
%\newcommand{\simulink}{\textsc{Simulink}\textsuperscript{\textregistered}} % SIMULINK
|
||
|
|
\newcommand{\writeSimulink}{\textsc{Simulink}} % SIMULINK
|
||
|
|
\newcommand{\writeFunction}[1]{\texttt{#1}} % Programming function name, e.g. quadprog
|
||
|
|
|
||
|
|
% tikz individual externalization:
|
||
|
|
\newcommand{\mytikzexton}{\tikzexternalenable} % turn externalization on for the rest of the document
|
||
|
|
\newcommand{\mytikzextoff}{\tikzexternaldisable} % turn externalization off for the rest of the document
|
||
|
|
|
||
|
|
% macros for plot axis labels with default values to be overwritten in individual plots:
|
||
|
|
\newcommand\figureXLabel{Default XLabel}
|
||
|
|
\newcommand\figureYLabel{Default YLabel}
|
||
|
|
\newcommand\figureZLabel{Default ZLabel}
|
||
|
|
|
||
|
|
\newcommand{\tabitem}{~~\llap{\textbullet}~~}
|
||
|
|
|
||
|
|
% -----------------------------------------------------------------------------
|
||
|
|
% Finish
|
||
|
|
% -----------------------------------------------------------------------------
|
||
|
|
%\closesymdef
|