\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{textcase}
\usepackage{paralist}
\usepackage{soul}

\newcommand{\mat}[1]{\boldsymbol{#1}}
\renewcommand{\vec}[1]{\boldsymbol{\mathrm{#1}}}
\newcommand{\vecalt}[1]{\boldsymbol{#1}}

\newcommand{\conj}[1]{\overline{#1}}

\newcommand{\normof}[1]{\|#1\|}
\newcommand{\onormof}[2]{\|#1\|_{#2}}

\newcommand{\itr}[2]{#1^{(#2)}}
\newcommand{\itn}[1]{^{(#1)}}

\newcommand{\eps}{\varepsilon}
\newcommand{\kron}{\otimes}

\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\trace}{trace}
\DeclareMathOperator{\tvec}{vec}

\newcommand{\prob}{\mathbb{P}}
\newcommand{\probof}[1]{\prob\left\{ #1 \right\}}

\newcommand{\pmat}[1]{\begin{pmatrix} #1 \end{pmatrix}}
\newcommand{\bmat}[1]{\begin{bmatrix} #1 \end{bmatrix}}
\newcommand{\spmat}[1]{\left(\begin{smallmatrix} #1 \end{smallmatrix}\right)}
\newcommand{\sbmat}[1]{\left[\begin{smallmatrix} #1 \end{smallmatrix}\right]}

\newcommand{\RR}{\mathbb{R}}
\newcommand{\CC}{\mathbb{C}}

\providecommand{\eye}{\mat{I}}
\providecommand{\mA}{\ensuremath{\mat{A}}}
\providecommand{\mB}{\ensuremath{\mat{B}}}
\providecommand{\mC}{\ensuremath{\mat{C}}}
\providecommand{\mD}{\ensuremath{\mat{D}}}
\providecommand{\mE}{\ensuremath{\mat{E}}}
\providecommand{\mF}{\ensuremath{\mat{F}}}
\providecommand{\mG}{\ensuremath{\mat{G}}}
\providecommand{\mH}{\ensuremath{\mat{H}}}
\providecommand{\mI}{\ensuremath{\mat{I}}}
\providecommand{\mJ}{\ensuremath{\mat{J}}}
\providecommand{\mK}{\ensuremath{\mat{K}}}
\providecommand{\mL}{\ensuremath{\mat{L}}}
\providecommand{\mM}{\ensuremath{\mat{M}}}
\providecommand{\mN}{\ensuremath{\mat{N}}}
\providecommand{\mO}{\ensuremath{\mat{O}}}
\providecommand{\mP}{\ensuremath{\mat{P}}}
\providecommand{\mQ}{\ensuremath{\mat{Q}}}
\providecommand{\mR}{\ensuremath{\mat{R}}}
\providecommand{\mS}{\ensuremath{\mat{S}}}
\providecommand{\mT}{\ensuremath{\mat{T}}}
\providecommand{\mU}{\ensuremath{\mat{U}}}
\providecommand{\mV}{\ensuremath{\mat{V}}}
\providecommand{\mW}{\ensuremath{\mat{W}}}
\providecommand{\mX}{\ensuremath{\mat{X}}}
\providecommand{\mY}{\ensuremath{\mat{Y}}}
\providecommand{\mZ}{\ensuremath{\mat{Z}}}
\providecommand{\mLambda}{\ensuremath{\mat{\Lambda}}}
\providecommand{\mPbar}{\bar{\mP}}

\providecommand{\ones}{\vec{e}}
\providecommand{\va}{\ensuremath{\vec{a}}}
\providecommand{\vb}{\ensuremath{\vec{b}}}
\providecommand{\vc}{\ensuremath{\vec{c}}}
\providecommand{\vd}{\ensuremath{\vec{d}}}
\providecommand{\ve}{\ensuremath{\vec{e}}}
\providecommand{\vf}{\ensuremath{\vec{f}}}
\providecommand{\vg}{\ensuremath{\vec{g}}}
\providecommand{\vh}{\ensuremath{\vec{h}}}
\providecommand{\vi}{\ensuremath{\vec{i}}}
\providecommand{\vj}{\ensuremath{\vec{j}}}
\providecommand{\vk}{\ensuremath{\vec{k}}}
\providecommand{\vl}{\ensuremath{\vec{l}}}
\providecommand{\vm}{\ensuremath{\vec{l}}}
\providecommand{\vn}{\ensuremath{\vec{n}}}
\providecommand{\vo}{\ensuremath{\vec{o}}}
\providecommand{\vp}{\ensuremath{\vec{p}}}
\providecommand{\vq}{\ensuremath{\vec{q}}}
\providecommand{\vr}{\ensuremath{\vec{r}}}
\providecommand{\vs}{\ensuremath{\vec{s}}}
\providecommand{\vt}{\ensuremath{\vec{t}}}
\providecommand{\vu}{\ensuremath{\vec{u}}}
\providecommand{\vv}{\ensuremath{\vec{v}}}
\providecommand{\vw}{\ensuremath{\vec{w}}}
\providecommand{\vx}{\ensuremath{\vec{x}}}
\providecommand{\vy}{\ensuremath{\vec{y}}}
\providecommand{\vz}{\ensuremath{\vec{z}}}
\providecommand{\vpi}{\ensuremath{\vecalt{\pi}}}


\providecommand{\tA}{\ensuremath{\mat{\tilde{A}}}}
\providecommand{\tB}{\ensuremath{\tilde{\mat{B}}}}
\providecommand{\tC}{\ensuremath{\tilde{\mat{C}}}}
\providecommand{\tD}{\ensuremath{\tilde{\mat{D}}}}
\providecommand{\tE}{\ensuremath{\tilde{\mat{E}}}}
\providecommand{\tF}{\ensuremath{\tilde{\mat{F}}}}
\providecommand{\tG}{\ensuremath{\tilde{\mat{G}}}}
\providecommand{\tH}{\ensuremath{\tilde{\mat{H}}}}
\providecommand{\tI}{\ensuremath{\tilde{\mat{I}}}}
\providecommand{\tJ}{\ensuremath{\tilde{\mat{J}}}}
\providecommand{\tK}{\ensuremath{\tilde{\mat{K}}}}
\providecommand{\tL}{\ensuremath{\tilde{\mat{L}}}}
\providecommand{\tM}{\ensuremath{\tilde{\mat{M}}}}
\providecommand{\tN}{\ensuremath{\tilde{\mat{N}}}}
\providecommand{\tO}{\ensuremath{\tilde{\mat{O}}}}
\providecommand{\tP}{\ensuremath{\tilde{\mat{P}}}}
\providecommand{\tQ}{\ensuremath{\tilde{\mat{Q}}}}
\providecommand{\tR}{\ensuremath{\tilde{\mat{R}}}}
\providecommand{\tS}{\ensuremath{\tilde{\mat{S}}}}
\providecommand{\tT}{\ensuremath{\tilde{\mat{T}}}}
\providecommand{\tU}{\ensuremath{\tilde{\mat{U}}}}
\providecommand{\tV}{\ensuremath{\tilde{\mat{V}}}}
\providecommand{\tW}{\ensuremath{\tilde{\mat{W}}}}
\providecommand{\tX}{\ensuremath{\tilde{\mat{X}}}}
\providecommand{\tY}{\ensuremath{\tilde{\mat{Y}}}}
\providecommand{\tZ}{\ensuremath{\tilde{\mat{Z}}}}

\providecommand{\tx}{\ensuremath{\tilde{\vec{x}}}}
\providecommand{\tb}{\ensuremath{\tilde{\vec{b}}}}

\providecommand{\sF}{\ensuremath{\mathcal{F}}}
\providecommand{\sI}{\ensuremath{\mathcal{I}}}
\providecommand{\sP}{\ensuremath{\mathcal{P}}}
\providecommand{\sC}{\ensuremath{\mathcal{C}}}
\providecommand{\Tr}{\ensuremath{T}}
\providecommand{\mAc}{\ensuremath{\mA^{(\text{cur})}}}
\providecommand{\vbc}{\ensuremath{\vb^{(\text{cur})}}}
\makeatother


\usepackage{xspace}
\newcommand{\datacbuckle}{\texttt{cbuckle}\xspace}
\newcommand{\databcsstk}{\texttt{bcsstk18}\xspace}
\newcommand{\datagyro}{\texttt{gyro\textunderscore m}\xspace}
\newcommand{\datainline}{\texttt{inline\textunderscore 1}\xspace}
\newcommand{\dataconsph}{\texttt{consph}\xspace}
\newcommand{\dataldoor}{\texttt{ldoor}\xspace}
\newcommand{\origiter}{\texttt{orig\textunderscore{iter}}\xspace}
\newcommand{\dataminsurfo}{\texttt{minsurfo}\xspace}
\newcommand{\datasdkq}{\texttt{s3dkq4m2}\xspace}