newcmds.tex

\long\def\symbolfootnote[#1]#2{\begingroup%
\def\thefootnote{\fnsymbol{footnote}}\footnote[#1]{#2}\endgroup}

%-----------------------------------------------------------------------
%\newcommand{\hiddensubsection}[1]{
%\stepcounter{subsection}
%\subsection*{\arabic{section}.\arabic{subsection}\hspace{1em}{#1}}}

%\newcommand{\hiddensection}[1]{
%\stepcounter{section}
%\section*{\arabic{section}.\arabic{section}\hspace{1em}{#1}}}

\newcommand{\Probab}[1]{\mbox{}{\mathbb{P}}\left[#1\right]}
\newcommand{\Exp}{\mbox{}{\bf{E}}}
\newcommand{\Expect}[1]{\mbox{}{\mathbb{E}}\left[#1\right]}
\newcommand{\Varnce}[1]{\mbox{}{\bf{Var}}\left[#1\right]}
\newcommand{\Trace }[1]{\mbox{}{\mathrm{Tr}}\left(#1\right)}
%\newcommand{\diag  }[1]{\mbox{}{\textrm{diag}}\left(#1\right)}
\newcommand{\Sqrt  }[1]{\mbox{}\left(#1\right)^{1/2}}
\newcommand{\Qdrt  }[1]{\mbox{}\left(#1\right)^{1/4}}
\newcommand{\FNormB }[1]{\mbox{}\left\|#1\right\|_{\mathrm{F}}  }
\newcommand{\FNormBS}[1]{\mbox{}\left\|#1\right\|_{\mathrm{F}}^2}
\newcommand{\FNorm }[1]{\mbox{}\|#1\|_\mathrm{F}  }
\newcommand{\FNormS}[1]{\mbox{}\|#1\|_\mathrm{F}^2}
\newcommand{\FNormF}[1]{\mbox{}\|#1\|_\mathrm{F}^4}
\newcommand{\FNormQ}[1]{\mbox{}\left\|#1\right\|_\mathrm{F}^4}
\newcommand{\TNormB }[1]{\mbox{}\left\|#1\right\|_2  }
\newcommand{\TNormBS}[1]{\mbox{}\left\|#1\right\|_2^2}
\newcommand{\TNorm }[1]{\mbox{}\|#1\|_2  }
\newcommand{\TNormS}[1]{\mbox{}\|#1\|_2^2}
\newcommand{\TNormF}[1]{\mbox{}\|#1\|_2^4}
\newcommand{\TNormQ}[1]{\mbox{}\left\|#1\right\|_2^4}
\newcommand{\XNormB }[1]{\mbox{}\left\|#1\right\|_{\xi}  }
\newcommand{\XNormBS}[1]{\mbox{}\left\|#1\right\|_{\xi}^2}
\newcommand{\XNorm }[1]{\mbox{}\|#1\|_{\xi}  }
\newcommand{\XNormS}[1]{\mbox{}\|#1\|_{\xi}^2}
\newcommand{\PNorm }[1]{\mbox{}\|#1\|_{p}  }
\newcommand{\PNormS}[1]{\mbox{}\|#1\|_{p}^2}
\newcommand{\XNormQ}[1]{\mbox{}\left\|#1\right\|_{\xi}^4}
\newcommand{\VTNorm }[1]{\mbox{}\left|#1\right|  }
\newcommand{\VTNormS}[1]{\mbox{}\left|#1\right|^2}
\newcommand{\VTNormQ}[1]{\mbox{}\left|#1\right|^4}
\newcommand{\VTTNorm }[1]{\mbox{}\left|#1\right|_2  }
\newcommand{\VTTNormS}[1]{\mbox{}\left|#1\right|_2^2}
\newcommand{\VTTNormQ}[1]{\mbox{}\left|#1\right|_2^4}
\newcommand{\MCNorm}[1]{\mbox{}\|#1\|_{1 \rightarrow 2}}
\newcommand{\MCNormS}[1]{\mbox{}\|#1\|_{1 \rightarrow 2}^2}
\newcommand{\INorm}[1]{\mbox{}\|#1\|_\infty}

%\newtheorem{theorem}{\bf Theorem}[]
%\newtheorem{lemma}[theorem]{Lemma}
%\newtheorem{definition}[theorem]{Definition}
%\newtheorem{proposition}[theorem]{Proposition}
%\newtheorem{corollary}[theorem]{Corollary}
%\newtheorem{axiom}[theorem]{Axiom}

\newcommand{\qedsymb}{\hfill{\rule{2mm}{2mm}}}

\newcommand{\transp}{^{\textsc{T}}}
\newcommand{\trace}{\text{\rm Tr}}
\newcommand{\mat}[1]{{\ensuremath{\bm{\mathrm{#1}}}}}
\newcommand{\dvc}{\ensuremath{d_{\small \sf VC}}}
\newcommand{\abs }[1]{\left|#1\right|}
\newcommand{\EE}[1]{\ensuremath{\mathbb{E}\left[#1\right] } }
\newcommand{\condE}[2]{\ensuremath{\mathbf{E}_{#1}\left[{#2}\right] } }
\newcommand{\var}[1]{\text{Var}\ensuremath{\left[#1\right] } }
\newcommand{\lambdamax}[1]{\ensuremath{\lambda_{\mathrm{max}}\left(#1\right)}}
\renewcommand{\vec}[1]{\ensuremath{\bm{#1}}}


\renewcommand{\const}[1]{\ensuremath{\mathrm{#1}}}
% Pseudo-inverse of a matrix
\newcommand{\pinv}[1]{ {#1}^\dagger}

\def\gammab{{\bm{\gamma}}}
\def\kappab{{\bm{\kappa}}}
\def\sig{{\bm{\Sigma}}}
\def\sigplus{{\bm{\Sigma}^{+}}}
\def\siginv{{\bm{\Sigma}^{-1}}}
\def\bet{{\bm{\beta}}}
\def\one{{\bm{1}}}
\def\exp{\hbox{\rm exp}}
\def\rank{\hbox{\rm rank}}
\newcommand{\stablerank}[1]{\operatorname{sr}\left(#1\right)}

\def\cond{\hbox{\rm \bf{k}}}

\def\col{\hbox{\rm col}}
\def\ker{\hbox{\rm ker}}
\def\ahat{{\hat\a}}
\def\b{{\mathbf b}}
\def\e{{\mathbf e}}
\def\expe{{\mathrm e}}
\def\q{{\mathbf q}}
\def\rb{{\mathbf r}}
\def\s{{\mathbf s}}
\def\u{{\mathbf u}}
\def\v{{\mathbf v}}
\def\d{{\mathbf \delta}}
\def\xhat{{\hat\x}}
\def\yhat{{\hat\y}}
\def\A{\matA}
\def\B{\matB}
\def\C{\matC}
\def\Ahat{\hat\matA}
\def\Atilde{\tilde\matA}
\def\Btilde{\tilde\matB}
\def\Stilde{\tilde\matS}
\def\Utilde{\tilde\matU}
\def\Vtilde{\tilde\matV}
\def\E{{\cl E}}
\def\G{{\cl G}}
\def\hset{{\cl H}}
\def\Q{{\bm{Q}}}
\def\U{{\bm{U}}}
\def\V{{\bm{V}}}
\def\win{\hat{\w}}
\def\wopt{\w^*}
\def\matAhat{\hat\mat{A}}
\def\matA{\mat{A}}
\def\matB{\mat{B}}
\def\matC{\mat{C}}
\def\matD{\mat{D}}
\def\matE{\mat{E}}
\def\matG{\mat{G}}
\def\matH{\mat{H}}
\def\matI{\mat{I}}
\def\matM{\mat{M}}
\def\matP{\mat{P}}
\def\matQ{\mat{Q}}
\def\matR{\mat{R}}
\def\matS{\mat{S}}
\def\matT{\mat{T}}
\def\matU{\mat{U}}
\def\matV{\mat{V}}
\def\matW{\mat{W}}
\def\matX{\mat{X}}
\def\matY{\mat{Y}}
\def\matZ{\mat{Z}}
\def\matSig{\mat{\Sigma}}
\def\matTh{\mat{\Theta}}
\def\matOmega{\mat{\Omega}}
\def\matPsi{\mat{\Psi}}
\def\matGam{\mat{\Gamma}}
\def\w{{\mathbf{w}}}
\def\ein{{\cl E_{\text{\rm in}}}}
\def\eout{{\cl E}}
\def\scl{{\textsc{l}}}
\def\scu{{\textsc{u}}}
\def\phiu{{\overline{\phi}}}
\def\psiu{{\overline{\psi}}}
\def\phil{{\underbar{\math{\phi}}}}
\DeclareMathSymbol{\Prob}{\mathbin}{AMSb}{"50}
%\DeclareMathSymbol{\Exp}{\mathbin}{AMSb}{"45}
\newcommand\remove[1]{}

\def\nnz{{ \rm nnz }}

\def\mvec#1#2{[#1_1,\ldots ,#1_#2]}
\def\msum#1#2#3{$$\sm_{#1=#2}^#3$$}
\def\mint#1#2{$$\int_#1^#2$$}
\def\math#1{$#1$}
\def\mathd#1{$$#1\eqa$$}
\def\mand#1{$$#1$$}
%\def\v#1{{\mathbf #1}}
\def\frac#1#2{{#1\over #2}}
\def\ital#1{{\it #1}}
\def\mld#1{\begin{equation}
#1
\end{equation}}
\def\eqar#1{\begin{eqnarray}
#1
\end{eqnarray}}
\def\eqan#1{\begin{eqnarray*}
#1
\end{eqnarray*}}

%\DeclareSymbolFont{AMSb}{U}{msb}{m}{n}
%\DeclareMathSymbol{\N}{\mathbin}{AMSb}{"4E}
%\DeclareMathSymbol{\Z}{\mathbin}{AMSb}{"5A}
\DeclareMathSymbol{\R}{\mathbin}{AMSb}{"52}
%\DeclareMathSymbol{\Q}{\mathbin}{AMSb}{"51}
%\DeclareMathSymbol{\I}{\mathbin}{AMSb}{"49}
%\ DeclareMathSymbol{\C}{\mathbin}{AMSb}{"43}

%\def\R{{\mathbf R\hspace*{-1.65ex}\rule{0.08ex}{1.35ex}\hspace*{1.65ex}}}
\def\Nat{{\mathbf N\hspace*{-1.89ex}\rule{0.07ex}{1.5ex}\hspace*{1.89ex}\hspace*{-1.7ex}\rule{0.1ex}{1.5ex}\hspace*{1.7ex}\hspace*{-.6ex}\rule{0.1ex}{1.5ex}\hspace*{.6ex}}}
%\def\Q{{\mathbf Q\hspace*{-1.35ex}\raise.15ex\hbox{\rule{0.095ex}{1.35ex}}\hspace*{1.4ex}}}
%\def\C{{\mathbf C\hspace*{-1.25ex}\raise.15ex\hbox{\rule{0.095ex}{1.35ex}}\hspace*{1.25ex}}}
\def\qed{\hfill\rule{2mm}{2mm}}
\def\sm{\sum\limits}
\def\choose#1#2{\left({{#1}\atop{#2}}\right)}
\def\cl#1{{\cal #1}}
\def\prob#1{{P\left[{#1}\right]}}
%\def\implies{\Rightarrow}
\def\mathbox#1{{\fbox{\math{#1}}}}
\def\mandbox#1{{\fbox{\math{\displaystyle #1}}}}
\newcommand{\argmin}{\operatorname*{argmin}}
%\def\argmin{\mathop{\hbox{argmin}}\limits}
\def\argmax{\mathop{\hbox{argmax}}\limits}

\def\mbf#1{{\mbox{\boldmath{$#1$}}}}
\def\h{{\mathbf h}}
\def\m{{\mathbf m}}
\def\x{{\mathbf x}}
\def\y{{\mathbf y}}
\def\z{{\mathbf z}}
\def\X{{\mathbf X}}
\def\Y{{\mathbf Y}}
%\def\Z{{\mathbf Z}}
\def\a{{\mathbf a}}
\def\b{{\mathbf b}}
\def\exp#1{{\left\langle#1\right\rangle}}
\def\E#1{{{\mathbf E}\left[#1\right]}}
%\def\mod#1{{\left|#1\right|}}
\def\norm#1{{\|#1\|}}
\def\floor#1{{\left\lfloor\,#1\,\right\rfloor}}
\def\ceil#1{{\left\lceil\,#1\,\right\rceil}}
\def\r#1{{(\ref{#1})}}
\def\rot#1{{\rotatebox{90}{#1\ }}}

\newcommand{\stitle}[1]{\begin{center}{\bf\color[named]{Red}#1}\\[-.8em]\rule{\linewidth}{1pt}\end{center}}
\newcommand{\myv}[1]{{ \bf #1} }
\newcommand{\mym}[1]{{ \bf #1} }
\newcommand{\red}[1]{{\color[named]{Red} #1}}
\newcommand{\blue}[1]{{\color[named]{Blue} #1}}
\newcommand{\green}[1]{{\color[named]{Green} #1}}
\newcommand{\light}[1]{{\color[rgb]{0.7,0.7,0.7} #1}}
\newcommand{\dark}[1]{{\color[rgb]{0,0,0} #1}}


\def\qn#1{{{#1}?\hfill\bf\math{\bigcirc} 1\qquad\math{\bigcirc} 2\qquad\math{\bigcirc} 3\qquad\math{\bigcirc} 4\qquad\math{\bigcirc} 5}}

\def\dotfil{\leaders\hbox to 1.5mm{.}\hfill}
%\newcounter{rmnum}
%\def\RN#1{\count0=#1\uppercase\expandafter{\romannumeral\count0}}
\def\RN#1{\setcounter{rmnum}{#1}\uppercase\expandafter{\romannumeral\value{rmnum}}}
\def\rn#1{\setcounter{rmnum}{#1}\expandafter{\romannumeral\value{rmnum}}}
\def\lequal{{\buildrel{\scriptscriptstyle <}\over{\scriptscriptstyle =}}}
\def\gequal{\ {\buildrel{\scriptstyle >}\over{\scriptstyle =}}\ }
\def\econd#1#2{\ {\buildrel{\scriptstyle #1}\over{\scriptstyle #2}}\ }

\def\smileyface{{
\begin{picture}(13,13)
\allinethickness{1.5pt}
\put(6.5,3.5){\circle{13}}
\put(3.9,5.5){\circle*{1.25}}
\put(8.7,5.5){\circle*{1.25}}
\put(1.7,0){\spline(2,2.5)(4.7,0)(7,2.5)}
\end{picture}
}}
\def\sadface{{
\begin{picture}(13,13)
\allinethickness{1.5pt}
\put(6.5,3.5){\circle{13}}
\put(3.9,5.5){\circle*{1.25}}
\put(8.7,5.5){\circle*{1.25}}
\put(1.7,0.5){\spline(2.5,0)(5,2.5)(7.5,0)}
\end{picture}
}}