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files/macro.tex

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+% theorem styles
+\theoremstyle{plain}
+\newtheorem{theorem}{Theorem}[section]
+\newtheorem{corollary}{Corollary}[theorem]
+\newtheorem{lemma}[theorem]{Lemma}
+\newtheorem{proposition}[theorem]{Proposition}
+
+\theoremstyle{definition}
+\newtheorem{definition}[theorem]{Definition}
+\newtheorem{remark}[theorem]{Remark}
+
+% brackets
+\newcommand{\round}[1]{\left( #1 \right)}
+\newcommand{\curly}[1]{\left\lbrace #1 \right\rbrace}
+\newcommand{\squarebrack}[1]{\left\lbrack #1 \right\rbrack}
+
+% sums
+\newcommand{\sumi}[2]{\sum\limits_{i=#1}^{#2}}
+\newcommand{\sumj}[2]{\sum\limits_{j=#1}^{#2}}
+\newcommand{\sumk}[2]{\sum\limits_{k=#1}^{#2}}
+\newcommand{\sump}[2]{\sum\limits_{p=#1}^{#2}}
+\newcommand{\suml}[2]{\sum\limits_{l=#1}^{#2}}
+\newcommand{\sumn}[2]{\sum\limits_{n=#1}^{#2}}
+\newcommand{\summ}[2]{\sum\limits_{m=#1}^{#2}}
+\newcommand{\sumt}[2]{\sum\limits_{t=#1}^{#2}}
+
+\newcommand{\Sum}{\sum_{i = 1}^{n}}
+\newcommand{\Sumi}[1]{\sum\limits_{i = 1}^{#1}}
+\newcommand{\Sumt}[1]{\sum\limits_{t = 1}^{#1}}
+
+% norms
+\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}
+\newcommand{\norm}[2]{\left\lVert#2\right\rVert_{#1}}
+\newcommand{\esqnorm}[1]{\left\lVert#1\right\rVert_2^2}
+\newcommand{\enorm}[1]{\left\lVert#1\right\rVert_2}
+\newcommand{\infnorm}[1]{\left\lVert#1\right\rVert_\infty}
+\newcommand{\opnorm}[1]{\left\lVert#1\right\rVert_\text{op}}
+\newcommand{\normF}[1]{\left\lVert#1\right\rVert_{\text{F}}}
+\newcommand{\inner}[1]{\left\langle#1\right\rangle}
+
+% bold numbers
+\newcommand{\zero}{\mathbf{0}}
+\newcommand{\one}{\mathbf{1}}
+
+% bold small english vectors
+\newcommand{\avec}{\mathbf{a}}
+\newcommand{\bvec}{\mathbf{b}}
+\newcommand{\cvec}{\mathbf{c}}
+\newcommand{\dvec}{\mathbf{d}}
+\newcommand{\e}{\mathbf{e}}
+\newcommand{\f}{\mathbf{f}}
+\newcommand{\g}{\mathbf{g}}
+\newcommand{\h}{\mathbf{h}}
+\newcommand{\ivec}{\mathbf{i}}
+\newcommand{\jvec}{\mathbf{j}}
+\newcommand{\kvec}{\mathbf{k}}
+\newcommand{\lvec}{\mathbf{l}}
+\newcommand{\m}{\mathbf{m}}
+\newcommand{\n}{\mathbf{n}}
+\newcommand{\ovec}{\mathbf{o}}
+\newcommand{\p}{\mathbf{p}}
+\newcommand{\q}{\mathbf{q}}
+\newcommand{\rvec}{\mathbf{r}}
+\newcommand{\s}{\mathbf{s}}
+\newcommand{\tvec}{\mathbf{t}}
+\newcommand{\uvec}{\mathbf{u}}
+\newcommand{\vvec}{\mathbf{v}}
+\newcommand{\w}{\mathbf{w}}
+\newcommand{\x}{\mathbf{x}}
+\newcommand{\y}{\mathbf{y}}
+\newcommand{\z}{\mathbf{z}}
+
+% bold capital english matrices
+\newcommand{\A}{\mathbf{A}}
+\newcommand{\B}{\mathbf{B}}
+\newcommand{\C}{\mathbf{C}}
+\newcommand{\D}{\mathbf{D}}
+\newcommand{\Emat}{\mathbf{E}}
+\newcommand{\F}{\mathbf{F}}
+\newcommand{\G}{\mathbf{G}}
+\newcommand{\Hmat}{\mathbf{H}}
+\newcommand{\I}{\mathbf{I}}
+\newcommand{\J}{\mathbf{J}}
+\newcommand{\K}{\mathbf{K}}
+\newcommand{\Lmat}{\mathbf{L}}
+\newcommand{\M}{\mathbf{M}}
+\newcommand{\N}{\mathbf{N}}
+\newcommand{\Omat}{\mathbf{O}}
+\newcommand{\Pmat}{\mathbf{P}}
+\newcommand{\Q}{\mathbf{Q}}
+\newcommand{\Rmat}{\mathbf{R}}
+\newcommand{\Smat}{\mathbf{S}}
+\newcommand{\T}{\mathbf{T}}
+\newcommand{\U}{\mathbf{U}}
+\newcommand{\V}{\mathbf{V}}
+\newcommand{\W}{\mathbf{W}}
+\newcommand{\X}{\mathbf{X}}
+\newcommand{\Y}{\mathbf{Y}}
+\newcommand{\Z}{\mathbf{Z}}
+
+% bold capital greek matrices
+\newcommand{\SIGMA}{\mathbf{\Sigma}}
+\newcommand{\LAMBDA}{\mathbf{\Lambda}}
+
+% capital mathcal
+\newcommand{\Acal}{\mathcal{A}}
+\newcommand{\Bcal}{\mathcal{B}}
+\newcommand{\Ccal}{\mathcal{C}}
+\newcommand{\Dcal}{\mathcal{D}}
+\newcommand{\Ecal}{\mathcal{E}}
+\newcommand{\Fcal}{\mathcal{F}}
+\newcommand{\Gcal}{\mathcal{G}}
+\newcommand{\Hcal}{\mathcal{H}}
+\newcommand{\Ical}{\mathcal{I}}
+\newcommand{\Jcal}{\mathcal{J}}
+\newcommand{\Kcal}{\mathcal{K}}
+\newcommand{\Lcal}{\mathcal{L}}
+\newcommand{\Mcal}{\mathcal{M}}
+\newcommand{\Ncal}{\mathcal{N}}
+\newcommand{\Ocal}{\mathcal{O}}
+\newcommand{\Pcal}{\mathcal{P}}
+\newcommand{\Qcal}{\mathcal{Q}}
+\newcommand{\Rcal}{\mathcal{R}}
+\newcommand{\Scal}{\mathcal{S}}
+\newcommand{\Tcal}{\mathcal{T}}
+\newcommand{\Ucal}{\mathcal{U}}
+\newcommand{\Vcal}{\mathcal{V}}
+\newcommand{\Wcal}{\mathcal{W}}
+\newcommand{\Xcal}{\mathcal{X}}
+\newcommand{\Ycal}{\mathcal{Y}}
+\newcommand{\Zcal}{\mathcal{Z}}
+
+% small greek bold vectors
+\newcommand{\alphavec}{\boldsymbol{\alpha}}
+\newcommand{\betavec}{\boldsymbol{\beta}}
+\newcommand{\gammavec}{\boldsymbol{\gamma}}
+\newcommand{\deltavec}{\boldsymbol{\delta}}
+\newcommand{\epsvec}{\boldsymbol{\epsilon}}
+\newcommand{\etavec}{\boldsymbol{\eta}}
+\newcommand{\nuvec}{\boldsymbol{\nu}}
+\newcommand{\tauvec}{\boldsymbol{\tau}}
+\newcommand{\rhovec}{\boldsymbol{\rho}}
+\newcommand{\lmbda}{\boldsymbol{\lambda}}
+\newcommand{\muvec}{\boldsymbol{\mu}}
+\newcommand{\thetavec}{\boldsymbol{\theta}}
+
+% complexity notations
+\newcommand{\BigO}[1]{\mathcal{O}\round{#1}}
+\newcommand{\BigOmega}[1]{\Omega\round{#1}}
+
+% Set notations
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\Rd}[1]{\mathbb{R}^{#1}}
+\newcommand{\Natural}{\mathbb{N}}
+\newcommand{\Integer}{\mathbb{Z}}
+\newcommand{\Rational}{\mathbb{Q}}
+
+% Probability
+\newcommand{\E}[1]{\mathbb{E}\squarebrack{#1}}
+\newcommand{\Exp}[2]{\mathbb{E}_{#1}\squarebrack{#2}}
+\newcommand{\Prob}[1]{P\curly{#1}}
+
+% math shortcuts
+\newcommand{\inv}[1]{\frac{1}{#1}}
+\newcommand{\indicator}[2]{\mathbbm{1}_{#1}\round{#2}}
+\newcommand{\Tr}[1]{\text{Tr}\squarebrack{#1}}
+
+% others
+\newcommand{\BOX}[1]{\fbox{\parbox{\linewidth}{\centering#1}}}
+\newcommand{\textequal}[1]{\stackrel{#1}{=}}
+\newcommand{\textleq}[1]{\stackrel{#1}{\leq}}
+\newcommand{\textgeq}[1]{\stackrel{#1}{\geq}}