%%%%%%%%%%%%%%%%%%
% LaTeX macros.tex
% 27 Apr 2003: \def replaced by \newcommand
% 17 Aug 2005: \Frac fixed (needs {} around #1 and #2).
%              \Newcommand, \pmat, \bmat  introduced.
%              NB: \Newcommand doesn't work with commands that have [] arguments.
% 05 Sep 2005: Added innerproduct
% 08 Dec 2005: Realized that \providecommand already does what we were
%              trying to do with \Newcommand.
% 11 Dec 2005: Revived \Newcommand to overload commands from other packages.
%%%%%%%%%%%%%%%%%%

%\newcommand{\proof{\penalty 25\noindent{\bf Proof.}\nobreak\hskip 1em\ignorespaces}

%\newcommand{\emptybox}{\ \vbox{\hrule\hbox{\vrule height1.3ex\hskip0.8ex\vrule}\hrule}}
\newcommand{\emptybox}{\vbox{\hrule height0.6pt\hbox{\vrule height1.3ex width0.6pt\hskip0.8ex%
   \vrule width0.6pt}\hrule height0.6pt}} % SIAM \endproof

\newcommand{\noproof}{\hspace{.5em}\blackslug}
\newcommand{\m}{\phantom-}
\newcommand{\mm}[1]{\hbox{$#1$}}                 % math mode
\newcommand{\mtx}[2]{\renewcommand{\arraystretch}{1.2}%
      \left(\! \begin{array}{#1}#2\end{array}\! \right)}
% The next two are better than \mtx.
\newcommand{\pmat}[1]{{\renewcommand{\arraystretch}{1.1}%
   \begin{pmatrix}#1\end{pmatrix}}}  % Need \usepackage{amsmath}
\newcommand{\bmat}[1]{{\renewcommand{\arraystretch}{1.1}%
   \begin{bmatrix}#1\end{bmatrix}}}
\newcommand{\smat}[1]{{\renewcommand{\arraystretch}{1.1}%
   \left[\begin{smallmatrix}#1\end{smallmatrix}\right]}}
   
% Does anyone know how to do this with \newcommand?
\ifx   \innerprod\undefined%
   \def\innerprod(#1,#2){\langle#1,#2\rangle} % Must be called as \innerproduct(A,B)
\fi

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Replace commands defined in other packages%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\Newcommand}[2]%
   {\ifx#1\undefined \newcommand{#1}{#2} \else \renewcommand{#1}{#2} \fi}
\ifx\mod\undefined
  \newcommand{\mod}[1]{|#1|}
\else
  \renewcommand{\mod}[1]{|#1|}
\fi
\Newcommand{\Re} {\mathbb{R}}           % Need \usepackage{amssymb}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Commands defined in other packages%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\providecommand{\det}  {\mathop{\mathrm{det}}}
\providecommand{\diag} {\mathop{\mathrm{diag}}}
\providecommand{\dim}  {\mathop{\mathrm{dim}}}
\providecommand{\exp}  {\mathop{\mathrm{exp}}}
\providecommand{\Frac}[2]{{\etxtstyle{\frac{#1}{#2}}}}
%\providecommand{\mod}[1]{|#1|}
\providecommand{\rank} {\mathop{\mathrm{rank}}}
\providecommand{\Range}{\mathop{\mathrm{range}}}
%\providecommand{\Re}   {\mathbb{R}}           % Need \usepackage{amssymb}
\providecommand{\Co}   {\mathbb{C}}           % Need \usepackage{amssymb}
\providecommand{\vec}  {\mathop{\mathrm{vec}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\be}{\begin{enumerate}}
\newcommand{\ee}{\end{enumerate}}
\newcommand{\tild}{\raisebox{-0.5ex}{\~{}}}
\newcommand{\st}{:}
\newcommand{\abs}[1]{|#1|}
\newcommand{\argmin}{\mathop{\mathrm{argmin}}}
\newcommand{\argmax}{\mathop{\mathrm{argmax}}}
\newcommand{\conv}{\mathop{\mathrm{conv}}}
\newcommand{\eig}{\mathop{\mathrm{eig}}}
\newcommand{\mv}[1]{\mathtt{#1}}
\newcommand{\mtt}[1]{\mathtt{#1}}
\newcommand{\T}{^T\!}
\newcommand\Tinv{^{-T}\!}
\newcommand{\und}[1]{$\underline{\hbox{#1}}$}
\newcommand{\gge}{\succeq}
\newcommand{\twonorm}[1]{\norm{#1}_2}
\newcommand{\onenorm}[1]{\norm{#1}_1}
\newcommand{\infnorm}[1]{\norm{#1}_{\infty}}
\newcommand{\dualnorm}[1]{\norm{#1}_D}
\newcommand{\disp}{\displaystyle}
\newcommand{\super}{\scriptstyle}
\newcommand{\superplus}{^{+}}
\newcommand{\superminus}{^{-}}
\newcommand{\ur}{\mbox{\bf u}}
%\newcommand{\Re}{I\!\!R}
\newcommand{\sgap}{\;}
\newcommand{\mgap}{\;\;}
\newcommand{\bgap}{\;\;\;}
\newcommand{\subject}{\hbox{\rm subject to}}
\newcommand{\minimize}[1]{{\displaystyle\minim_{#1}}}
\newcommand{\minimizearg}[2]{{\displaystyle\minim_{#1 \in \Re^{#2}}}}
\newcommand{\maximizearg}[2]{{\displaystyle\maxim_{#1 \in \Re^{#2}}}}
\newcommand{\minimizetwoarg}[4]{{\displaystyle\minim_{#1 \in \Re^{#2},%
                                                  #3 \in \Re^{#4}}}}
\newcommand{\maximizetwoarg}[4]{{\displaystyle\maxim_{#1 \in \Re^{#2},%
                                                  #3 \in \Re^{#4}}}}
\newcommand{\maximize}[1]{{\displaystyle\maxim_{#1}}}
\newcommand{\eval}[2]{\left.#1\right|_{\alpha=#2}} % alpha     suffix
\newcommand{\evaluate}[2]{\left.#1\right|_{#2}}    % arbitrary suffix

\newcommand{\Bigp}[1]{\bigl(#1\bigr)}
\newcommand{\tmat}[2]{(\, #1 \ \ #2 \,)}
\newcommand{\tmatt}[3]{(\, #1 \ \  #2 \ \  #3\,)}
\newcommand{\tmattt}[4]{(\, #1 \ \  #2 \ \  #3 \ \  #4\,)}
\newcommand{\tmatttt}[5]{(\, #1 \ \  #2 \ \  #3 \ \  #4 \ \  #5\,)}

\newcommand{\mat}[2]{\Bigp{\; #1 \quad #2 \;}}
\newcommand{\matt}[3]{\Bigp{\; #1 \quad #2 \quad #3\;}}
\newcommand{\mattt}[4]{\Bigp{\; #1 \quad #2 \quad #3 \quad #4\;}}
\newcommand{\matttt}[5]{\Bigp{\; #1 \quad #2 \quad #3 \quad #4 \quad #5\;}}
\newcommand{\Cpp}{C\raise3pt\hbox{\tiny++}}
\newcommand{\blackslug}{\hbox{\hskip 1pt \vrule width 4pt height 6pt depth 1.5pt
  \hskip 1pt}}
\newcommand{\boxit}[1]{\vbox{\hrule\hbox{\vrule\hskip 3pt
  \vbox{\vskip 3pt #1 \vskip 3pt}\hskip 3pt\vrule}\hrule}}
\newcommand{\cross}{\scriptscriptstyle\times}
\newcommand{\maxim}{\mathop{\mathrm{maximize}}}
\newcommand{\minim}{\mathop{\mathrm{minimize}}}
\newcommand{\cond}{\mathrm{cond}}
\newcommand{\defined}{\buildrel{\scriptscriptstyle\triangle}\over=}
\newcommand{\definedas}{\defined}
\newcommand{\sep}{\mathop{\mathrm{sep}}}
\newcommand{\In}{\mathop{\mathrm{In}\,}}
\newcommand{\boundary}{\mathop{\mathrm{bnd}}}
\newcommand{\interior}{\mathop{\mathrm{int}}}
\newcommand{\Null}{\mathop{\mathrm{null}}}
\newcommand{\Rank}{\mathop{\mathrm{rank}}}
\newcommand{\op}{\mathop{\mathrm{op}}}
\newcommand{\re}{\mathop{\mathrm{re}}}
\newcommand{\range}{\mathop{\mathrm{range}}}
\newcommand{\sign}{\mathop{\mathrm{sign}}}
\newcommand{\sgn}{\mathop{\mathrm{sgn}}}
\newcommand{\Span}{\mbox{\rm span}}
\newcommand{\trace}{\mathop{\mathrm{trace}}}
\newcommand{\drop}{^{\null}}
\newcommand{\etal}{et al.}  %%% No italics!!  Also, must say \etal\
\newcommand{\float}{fl}
\newcommand{\Grad}{\nabla\!}
%\newcommand{\grad}{\nabla}   % Already defined
\newcommand{\Hess}{\nabla^2\!}
\newcommand{\half}  {{\textstyle\frac12}}
\newcommand{\third} {{\textstyle\frac13}}
\newcommand{\fourth}{{\textstyle\frac14}}
\newcommand{\sixth}{{\textstyle\frac16}}
\newcommand{\inv}{^{-1}}
\newcommand{\invsq}{^{-2}}
\newcommand{\limk}{\lim_{k\to\infty}}
\newcommand{\modd}[1]{\biggl|#1\biggr|}
\newcommand{\Mod}[1]{\left|#1\right|}
\newcommand{\normm}[1]{\biggl\|#1\biggr\|}
\newcommand{\norm}[1]{\|#1\|}
\newcommand{\pinv}{^\dag}                   %  pseudoinverse
\newcommand{\seql}[2]{\{\hthinsp#1\hthinsp\}_{#2}}
\newcommand{\seq}[1]{\seql{#1}{k\ge0}}
\newcommand{\Seq}[1]{\{\hthinsp#1\hthinsp\}}
\newcommand{\Set}[1]{\{\, #1 \,\}}
\newcommand{\spose}[1]{\hbox to 0pt{#1\hss}}
\newcommand{\sub}[1]{^{\null}_{#1}}
\newcommand{\till}{\,{:}\,}                 %  Matlab i = 1:n as i = 1\till n
\newcommand{\words}[1]{\hbox{\quad#1\quad}}
\newcommand{\wordss}[1]{\hbox{\qquad#1\qquad}}
\newcommand{\Words}[1]{\quad\mbox{#1}\quad}
\newcommand{\Wordss}[1]{\qquad\mbox{#1}\qquad}
\newcommand{\tsb}[1]{\textbf{\textsf{#1}}}

\providecommand{\text}[1]{\hbox{\quad#1\quad}}
\newcommand{\textt}[1]{\hbox{\qquad#1\qquad}}
\newcommand{\ntext}[1]{\noalign{\vskip 2pt\hbox{#1}\vskip 2pt}}
%\newcommand{\enddef}{{$\null$}}
\newcommand{\xint}{{x_{\rm int}}}

%%% Fixed-size glue, only for math mode

\newcommand{\hthinsp}{\mskip  1   mu}    %           thin space
\newcommand{\pthinsp}{\mskip  2   mu}    %           thin space
\newcommand{\pmedsp }{\mskip  2.75mu}    %         medium space
\newcommand{\pthiksp}{\mskip  3.5 mu}    %          thick space
\newcommand{\nthinsp}{\mskip -2   mu}
\newcommand{\nmedsp }{\mskip -2.75mu}
\newcommand{\nthiksp}{\mskip -3.5 mu}

%%% Specially lowered subscripts (see \sub above)

\newcommand{\Asubk}{A\sub{\nthinsp k}}
\newcommand{\Bsubk}{B\sub{\nthinsp k}}
\newcommand{\Fsubk}{F\sub{\nmedsp k}}
\newcommand{\Gsubk}{G\sub{\nthinsp k}}
\newcommand{\Hsubk}{H\sub{\nthinsp k}}
\newcommand{\HsubB}{H\sub{\nthinsp \scriptscriptstyle{B}}}
\newcommand{\HsubS}{H\sub{\nthinsp \scriptscriptstyle{S}}}
\newcommand{\HsubBS}{H\sub{\nthinsp \scriptscriptstyle{BS}}}
\newcommand{\Hz}{H\sub{\nthinsp \scriptscriptstyle{Z}}}
\newcommand{\Jsubk}{J\sub{\nmedsp k}}
\newcommand{\Psubk}{P\sub{\nthiksp k}}
\newcommand{\Qsubk}{Q\sub{\nthinsp k}}
\newcommand{\Vsubk}{V\sub{\nmedsp k}}
\newcommand{\Vsubone}{V\sub{\nmedsp 1}}
\newcommand{\Vsubtwo}{V\sub{\nmedsp 2}}
\newcommand{\Ysubk}{Y\sub{\nmedsp k}}
\newcommand{\Wsubk}{W\sub{\nthiksp k}}
\newcommand{\Zsubk}{Z\sub{\nthinsp k}}
\newcommand{\Zsubi}{Z\sub{\nthinsp i}}

%%% Subscripts

\newcommand{\subfr}{_{\scriptscriptstyle{\it FR}}}
\newcommand{\subfx}{_{\scriptscriptstyle{\it FX}}}
\newcommand{\fr}{_{\scriptscriptstyle{\it FR}}}
\newcommand{\fx}{_{\scriptscriptstyle{\it FX}}}
\newcommand{\submax}{_{\max}}
\newcommand{\submin}{_{\min}}
\newcommand{\subminus}{_{\scriptscriptstyle -}}
\newcommand{\subplus }{_{\scriptscriptstyle +}}

\newcommand{\A}{_{\scriptscriptstyle A}}
\newcommand{\B}{_{\scriptscriptstyle B}}
%\newcommand{\BS}{_{\scriptscriptstyle BS}}
\newcommand{\C}{_{\scriptscriptstyle C}}
\newcommand{\D}{_{\scriptscriptstyle D}}
\newcommand{\E}{_{\scriptscriptstyle E}}
\newcommand{\F}{_{\scriptscriptstyle F}}
\newcommand{\G}{_{\scriptscriptstyle G}}
\newcommand{\I}{_{\scriptscriptstyle I}}
\newcommand{\w}{_w}
%\newcommand{\k}{_k}
\newcommand{\kp}[1]{_{k+#1}}
\newcommand{\km}[1]{_{k-#1}}
%\newcommand{\j}{_j}
\newcommand{\jp}[1]{_{j+#1}}
\newcommand{\jm}[1]{_{j-#1}}
%\newcommand{\i}{_i}
\newcommand{\ip}[1]{_{i+#1}}
\newcommand{\im}[1]{_{i-#1}}
\newcommand{\K}{_{\scriptscriptstyle K}}
\renewcommand{\L}{_{\scriptscriptstyle L}}
\newcommand{\M}{_{\scriptscriptstyle M}}
\newcommand{\N}{_{\scriptscriptstyle N}}
%\newcommand{\subb}{\B}
%\newcommand{\subc}{\C}
%\newcommand{\subm}{\M}
%\newcommand{\subf}{\F}
%\newcommand{\subn}{\N}
%\newcommand{\subh}{\H}
%\newcommand{\subk}{\K}
%\newcommand{\subt}{_{\scriptscriptstyle T}}
%\newcommand{\subr}{\R}
%\newcommand{\subz}{\Z}
\newcommand{\J}{_{\scriptscriptstyle J}}
%\newcommand{\O}{_{\scriptscriptstyle O}}
\renewcommand{\P}{_{\scriptscriptstyle P}}
\newcommand{\Q}{_{\scriptscriptstyle Q}}
%\newcommand{\R}{_{\scriptscriptstyle R}}
\let\Sec=\S
\renewcommand{\S}{_{\scriptscriptstyle S}}
\renewcommand{\N}{_{\scriptscriptstyle N}}
\Newcommand{\R}{_{\scriptscriptstyle R}}
\newcommand{\U}{_{\scriptscriptstyle U}}
\newcommand{\V}{_{\scriptscriptstyle V}}
\newcommand{\W}{_{\scriptscriptstyle W}}
\newcommand{\X}{_{\scriptscriptstyle X}}
\newcommand{\Y}{_{\scriptscriptstyle Y}}
\newcommand{\Z}{_{\scriptscriptstyle Z}}

%%% Superscript stars

\newcommand{\superstar}{^{\raise 0.5pt\hbox{$\nthinsp *$}}}
\newcommand{\SUPERSTAR}{^{\raise 0.5pt\hbox{$*$}}}
\newcommand{\shrink}{\mskip -7mu}  %%% Less space after \xstar if followed by , or .

\newcommand{\alphastar}{\alpha\superstar}
\newcommand{\sigmastar}{\sigma\superstar}
\newcommand{\gammastar}{\gamma\superstar}
\newcommand{\lamstar  }{\lambda\superstar}
\newcommand{\lamstarT }{\lambda^{\raise 0.5pt\hbox{$\nthinsp *$}T}}
\newcommand{\lambdastar}{\lamstar}
\newcommand{\nustar}{\nu\superstar}
\newcommand{\mustar}{\mu\superstar}
\newcommand{\pistar}{\pi\superstar}
\newcommand{\thetastar}{\theta\superstar}

\newcommand{\cstar}{c\superstar}
\newcommand{\dstar}{d\SUPERSTAR}
\newcommand{\fstar}{f\SUPERSTAR}
\newcommand{\gstar}{g\superstar}
\newcommand{\hstar}{h\superstar}
\newcommand{\mstar}{m\superstar}
\newcommand{\pstar}{p\superstar}
\newcommand{\sstar}{s\superstar}
\newcommand{\ustar}{u\superstar}
\newcommand{\vstar}{v\superstar}
\newcommand{\wstar}{w\superstar}
\newcommand{\xstar}{x\superstar}
\newcommand{\ystar}{y\superstar}
\newcommand{\zstar}{z\superstar}

\newcommand{\Astar}{A\SUPERSTAR}
\newcommand{\Bstar}{B\SUPERSTAR}
\newcommand{\Cstar}{C\SUPERSTAR}
\newcommand{\Fstar}{F\SUPERSTAR}
\newcommand{\Gstar}{G\SUPERSTAR}
\newcommand{\Hstar}{H\SUPERSTAR}
\newcommand{\Jstar}{J\SUPERSTAR}
\newcommand{\Kstar}{K\SUPERSTAR}
\newcommand{\Mstar}{M\SUPERSTAR}
\newcommand{\Qstar}{Q\SUPERSTAR}
\newcommand{\Ustar}{U\SUPERSTAR}
\newcommand{\Vstar}{V\SUPERSTAR}
\newcommand{\Wstar}{W\SUPERSTAR}
\newcommand{\Xstar}{X\SUPERSTAR}
\newcommand{\Zstar}{Z\SUPERSTAR}

%%% bars, hats, tildes  (\skew4 is the default)

\newcommand{\alphabar}{\skew3\bar\alpha}
\newcommand{\alphahat}{\skew3\hat\alpha}
\newcommand{\alphatilde}{\skew3\tilde\alpha}
\newcommand{\betabar}{\skew{2.8}\bar\beta}
%\newcommand{\betahat}{\skew{2.8}\widehat\beta}
\newcommand{\betahat}{\skew6\hat\beta}
\newcommand{\betatilde}{\skew6\tilde\beta}
\newcommand{\delbar}{\bar\delta}
\newcommand{\deltilde}{\skew5\tilde\delta}
\newcommand{\deltabar}{\delbar}
\newcommand{\deltatilde}{\deltilde}
\newcommand{\epsbar}{\skew3\bar\epsilon}
\newcommand{\lambar}{\bar\lambda}
\newcommand{\etabar}{\bar\eta}
\newcommand{\etahat}{\hat\eta}
\newcommand{\gammabar}{\bar\gamma}
%\newcommand{\lamhat}{\skew{2.8}\widehat\lambda}
%\newcommand{\lamhat}{\skew{3.8}\widehat\lambda}
\newcommand{\lamhat}{\widehat\lambda}
\newcommand{\lamtilde}{\widetilde\lambda}
\newcommand{\lambdabar}{\lambar}
\newcommand{\lambdahat}{\lamhat}
\newcommand{\mubar}{\skew3\bar \mu}
\newcommand{\muhat}{\skew3\widehat \mu}
\newcommand{\mutilde}{\widetilde\mu}
\newcommand{\nubar}{\skew3\bar\nu}
\newcommand{\nuhat}{\skew3\widehat\nu}
\newcommand{\nutilde}{\skew3\tilde\nu}
\newcommand{\omegabar}{\bar\omega}
\newcommand{\varphihat}{\widehat\varphi}
\newcommand{\varphibar}{\bar\varphi}
\newcommand{\pibar}{\skew1\bar\pi}
\newcommand{\pihat}{\skew1\widehat \pi}
\newcommand{\sigmabar}{\skew{2.8}\bar\sigma}
\newcommand{\sigmahat}{\skew3\hat\sigma}
%\newcommand{\sigmahat}{\widehat\sigma}
\newcommand{\sigmatilde}{\skew{2.8}\tilde\sigma}
\newcommand{\rhobar}{\bar\rho}
%\newcommand{\rhohat}{\skew2\widehat\rho}
\newcommand{\rhohat}{\skew{3.5}\hat\rho}
\newcommand{\taubar}{\bar\tau}
\newcommand{\tautilde}{\tilde\tau}
\newcommand{\tauhat}{\widehat\tau}
\newcommand{\thetabar}{\bar\theta}
\newcommand{\thetahat}{\hat\theta}
\newcommand{\xibar}{\skew4\bar\xi}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  Math italic and calligraphic fonts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\providecommand{\varGamma}  {{\mathit\Gamma}}
\providecommand{\varDelta}  {{\mathit\Delta}}
\providecommand{\varTheta}  {{\mathit\Theta}}
\providecommand{\varLambda} {{\mathit\Lambda}}
\providecommand{\varXi}     {{\mathit\Xi}}
\providecommand{\varPi}     {{\mathit\Pi}}
\providecommand{\varSigma}  {{\mathit\Sigma}}
\providecommand{\varUpsilon}{{\mathit\Upsilon}}
\providecommand{\varPhi}    {{\mathit\Phi}}
\providecommand{\varPsi}    {{\mathit\Psi}}
\providecommand{\varOmega}  {{\mathit\Omega}}

\newcommand{\Deltait}{\varDelta}
\newcommand{\Gammait}{\varGamma}
\newcommand{\Gammabarit}{\skew5\bar\Gammait}
\newcommand{\Lambdait}{\varLambda}
\newcommand{\Lamhatit}{\skew5\widehat\Lambdait}
\newcommand{\Lambarit}{\skew5\bar\Lambdait}
\newcommand{\Omegait}{\varOmega}
\newcommand{\Omegaitbar}{\skew5\bar\Omegait}
\newcommand{\Piit}{\varPi}
\newcommand{\Pibarit}{\bar\varPi}
\newcommand{\Pihatit}{\skew5\widehat\varPi}
\newcommand{\Piitbar}{\skew5\bar\Piit}
\newcommand{\Phiit}{\varPhi}
\newcommand{\Psiit}{\varPsi}
\newcommand{\Sigmait}{\varSigma}
\newcommand{\Thetait}{\varTheta}
\newcommand{\Upsilonit}{\varUpsilon}
\newcommand{\Xiit}{\varXi}

\newcommand{\setA}{\mathcal{A}}
\newcommand{\setD}{\mathcal{D}}
\newcommand{\setE}{\mathcal{E}}
\newcommand{\setF}{\mathcal{F}}
\newcommand{\setG}{\mathcal{G}}
\newcommand{\setI}{\mathcal{I}}
\newcommand{\setJ}{\mathcal{J}}
\newcommand{\setP}{\mathcal{P}}
\newcommand{\setS}{\mathcal{S}}
\newcommand{\setU}{\mathcal{U}}
\newcommand{\setV}{\mathcal{V}}
\newcommand{\setW}{\mathcal{W}}

\newcommand{\suba}{_a}
\newcommand{\subb}{_b}
\newcommand{\subc}{_c}
\newcommand{\sube}{_e}
\newcommand{\subf}{_f}
\newcommand{\subi}{_i}
\newcommand{\subm}{_m}
\newcommand{\subw}{_w}
\newcommand{\subA}{_{\scriptscriptstyle A}}
\newcommand{\subB}{_{\scriptscriptstyle B}}
\newcommand{\subC}{_{\scriptscriptstyle C}}
\newcommand{\subE}{_{\scriptscriptstyle E}}
\newcommand{\subF}{_{\scriptscriptstyle F}}
\newcommand{\subI}{_{\scriptscriptstyle I}}
\newcommand{\subM}{_{\scriptscriptstyle M}}
\newcommand{\subg}{_{\scriptscriptstyle G}}
\newcommand{\subl}{_{\scriptscriptstyle L}}
\newcommand{\subn}{_{\scriptscriptstyle N}}
\newcommand{\subh}{_{\scriptscriptstyle H}}
\newcommand{\subk}{_{\scriptscriptstyle K}}
\newcommand{\subt}{_{\scriptscriptstyle T}}
\newcommand{\subp}{_{\scriptscriptstyle P}}
\newcommand{\subq}{_{\scriptscriptstyle Q}}
\newcommand{\subr}{_{\scriptscriptstyle R}}
\newcommand{\subs}{_{\scriptscriptstyle S}}
\newcommand{\subv}{_{\scriptscriptstyle V}}
\newcommand{\subW}{_{\scriptscriptstyle W}}
\newcommand{\subz}{_{\scriptscriptstyle Z}}

\newcommand{\Ascr}{{\mathcal A}}
\newcommand{\Bscr}{{\mathcal B}}
\newcommand{\Cscr}{{\mathcal C}}
\newcommand{\Fscr}{{\mathcal F}}
\newcommand{\Dscr}{{\mathcal D}}
\newcommand{\Gscr}{{\mathcal G}}
\newcommand{\Gscrbar}{{\mathcal\Gbar}}
\newcommand{\Hscr}{{\mathcal H}}
\newcommand{\Iscr}{{\mathcal I}}
\newcommand{\Jscr}{{\mathcal J}}
\newcommand{\Kscr}{{\mathcal K}}
\newcommand{\Kscrbar}{{\mathcal\Kbar}}
\newcommand{\Lscr}{{\mathcal L}}
\newcommand{\Mscr}{{\mathcal M}}
\newcommand{\lscr}{\ell}
\newcommand{\lscrbar}{\ellbar}
\newcommand{\Oscr}{{\mathcal O}}
\newcommand{\Pscr}{{\mathcal P}}
\newcommand{\Qscr}{{\mathcal Q}}
\newcommand{\Sscr}{{\mathcal S}}
\newcommand{\Tscr}{{\mathcal T}}
\newcommand{\Uscr}{{\mathcal U}}
\newcommand{\Vscr}{{\mathcal V}}
\newcommand{\Wscr}{{\mathcal W}}
%\newcommand{\Mscr}{{\mathcal M}}
\newcommand{\Nscr}{{\mathcal N}}
\newcommand{\Rscr}{{\mathcal R}}
\newcommand{\Xscr}{{\mathcal X}}

\newcommand{\abar}{\skew3\bar a}
\newcommand{\ahat}{\skew2\widehat a}
\newcommand{\atilde}{\skew2\widetilde a}
\newcommand{\Abar}{\skew7\bar A}
\newcommand{\Ahat}{\widehat A}
\newcommand{\Atilde}{\widetilde A}
\newcommand{\bbar}{\skew3\bar b}
\newcommand{\bhat}{\skew2\widehat b}
\newcommand{\btilde}{\skew2\widetilde b}
\newcommand{\Bbar}{\bar B}
\newcommand{\Bhat}{\skew4\widehat B}
\newcommand{\cbar}{\skew5\bar c}
\newcommand{\chat}{\skew3\widehat c}
\newcommand{\ctilde}{\widetilde c}
\newcommand{\Cbar}{\bar C}
\newcommand{\Chat}{\widehat C}
\newcommand{\Ctilde}{\widetilde C}
\newcommand{\dbar}{\bar d}
\newcommand{\dhat}{\widehat d}
\newcommand{\dtilde}{\widetilde d}
\newcommand{\Dbar}{\bar D}
\newcommand{\Dhat}{\widehat D}
\newcommand{\Dtilde}{\widetilde D}
\newcommand{\ehat}{\skew3\widehat e}
\newcommand{\ebar}{\bar e}
\newcommand{\Ebar}{\bar E}
\newcommand{\Ehat}{\widehat E}
\newcommand{\fbar}{\bar f}
\newcommand{\fhat}{\widehat f}
\newcommand{\ftilde}{\widetilde f}
\newcommand{\Fbar}{\bar F}
\newcommand{\Fhat}{\widehat F}
\newcommand{\gbar}{\skew{4.3}\bar g}
%\newcommand{\ghat}{\skew{4.3}\widehat g}
\newcommand{\ghat}{\skew{4.3}\hat g}
\newcommand{\gtilde}{\skew{4.5}\widetilde g}
\newcommand{\Gbar}{\bar G}
\newcommand{\Ghat}{\widehat G}
%\newcommand{\hbar}{\skew{4.2}\bar h}
\newcommand{\hhat}{\skew2\widehat h}
\newcommand{\htilde}{\skew3\widetilde h}
\newcommand{\Hbar}{\skew5\bar H}
\newcommand{\Hhat}{\widehat H}
\newcommand{\Htilde}{\widetilde H}
\newcommand{\Ibar}{\skew5\bar I}
\newcommand{\Itilde}{\widetilde I}
\newcommand{\Jbar}{\skew6\bar J}
\newcommand{\Jhat}{\widehat J}
\newcommand{\Jtilde}{\widetilde J}
\newcommand{\kbar}{\skew{4.4}\bar k}
\newcommand{\Khat}{\widehat K}
\newcommand{\Kbar}{\skew{4.4}\bar K}
\newcommand{\Ktilde}{\widetilde K}
\newcommand{\ellbar}{\bar \ell}
\newcommand{\lhat}{\skew2\widehat l}
\newcommand{\lbar}{\skew2\bar l}
\newcommand{\Lbar}{\skew{4.3}\bar L}
\newcommand{\Lhat}{\widehat L}
\newcommand{\Ltilde}{\widetilde L}
\newcommand{\mbar}{\skew2\bar m}
\newcommand{\mhat}{\widehat m}
\newcommand{\mtilde}{\widetilde m}
\newcommand{\Mbar}{\skew{4.4}\bar M}
\newcommand{\Mhat}{\widehat M}
\newcommand{\Mtilde}{\widetilde M}
\newcommand{\Nbar}{\skew{4.4}\bar N}
\newcommand{\Ntilde}{\widetilde N}
\newcommand{\nbar}{\skew2\bar n}
\newcommand{\pbar}{\skew2\bar p}
%\newcommand{\phat}{\skew2\widehat p}
\newcommand{\phat}{\skew2\hat p}
\newcommand{\ptilde}{\skew2\widetilde p}
\newcommand{\Pbar}{\skew5\bar P}
\newcommand{\Phat}{\widehat P}
\newcommand{\Ptilde}{\skew5\widetilde P}
\newcommand{\qbar}{\bar q}
\newcommand{\qhat}{\skew2\widehat q}
\newcommand{\qtilde}{\widetilde q}
\newcommand{\Qbar}{\bar Q}
\newcommand{\Qhat}{\widehat Q}
\newcommand{\Qtilde}{\widetilde Q}
\newcommand{\rbar}{\skew3\bar r}
\newcommand{\rhat}{\skew3\widehat r}
\newcommand{\rtilde}{\skew3\widetilde r}
\newcommand{\Rbar}{\skew5\bar R}
\newcommand{\Rhat}{\widehat R}
\newcommand{\Rtilde}{\widetilde R}
\newcommand{\sbar}{\bar s}
%\newcommand{\shat}{\widehat s}
\newcommand{\shat}{\skew3\hat s}
\newcommand{\Stilde}{\widetilde S}
\newcommand{\stilde}{\widetilde s}
\newcommand{\Shat}{\widehat S}
\newcommand{\Sbar}{\skew2\bar S}
\newcommand{\tbar}{\bar t}
\newcommand{\ttilde}{\widetilde t}
\newcommand{\that}{\widehat t}
\newcommand{\Tbar}{\bar T}
\newcommand{\That}{\widehat T}
\newcommand{\Ttilde}{\widetilde T}
\newcommand{\ubar}{\skew3\bar u}
\newcommand{\uhat}{\skew3\widehat u}
\newcommand{\utilde}{\skew3\tilde u}
\newcommand{\Ubar}{\skew2\bar U}
\newcommand{\Uhat}{\widehat U}
\newcommand{\Utilde}{\widetilde U}
\newcommand{\vbar}{\skew3\bar v}
\newcommand{\vhat}{\skew3\widehat v}
\newcommand{\vtilde}{\skew3\widetilde v}
\newcommand{\Vbar}{\skew2\bar V}
\newcommand{\Vhat}{\widehat V}
\newcommand{\Vtilde}{\widetilde V}
\newcommand{\wbar}{\skew3\bar w}
\newcommand{\what}{\skew3\widehat w}
\newcommand{\wtilde}{\skew3\widetilde w}
\newcommand{\Wbar}{\skew3\bar W}
\newcommand{\What}{\widehat W}
\newcommand{\Wtilde}{\widetilde W}
\newcommand{\xbar}{\skew{2.8}\bar x}
\newcommand{\xhat}{\skew{2.8}\widehat x}
\newcommand{\xtilde}{\skew3\widetilde x}
\newcommand{\Xhat}{\widehat X}
\newcommand{\ybar}{\skew3\bar y}
\newcommand{\yhat}{\skew3\widehat y}
\newcommand{\ytilde}{\skew3\widetilde y}
\newcommand{\Ytilde}{\widetilde Y}
\newcommand{\Ybar}{\skew2\bar Y}
\newcommand{\Yhat}{\widehat Y}
\newcommand{\zbar}{\skew{2.8}\bar z}
\newcommand{\zhat}{\skew{2.8}\widehat z}
\newcommand{\ztilde}{\skew{2.8}\widetilde z}
\newcommand{\Zbar}{\skew5\bar Z}
\newcommand{\Zhat}{\widehat Z}
\newcommand{\Ztilde}{\widetilde Z}

\providecommand{\Matlab}{{\sc Matlab}}

\providecommand{\AMPL  }{{\small AMPL}}
\providecommand{\CUTE  }{{\small CUTE}}
\providecommand{\CUTEr }{{\small CUTE}r}
\providecommand{\GAMS  }{{\small GAMS}}
\providecommand{\Knossos} {{\small K}nossos}
\providecommand{\LANCELOT}{{\small LANCELOT}}

\providecommand{\LPOPT }{{\small LPOPT}}
\providecommand{\LSSOL }{{\small LSSOL}}
\providecommand{\LUSOL }{{\small LUSOL}}
\providecommand{\MINOS }{{\small MINOS}}
\providecommand{\NLSSOL}{{\small NLSSOL}}
\providecommand{\NPSOL }{{\small NPSOL}}
\providecommand{\QPOPT }{{\small QPOPT}}
\providecommand{\QPSOL }{{\small QPSOL}}
\providecommand{\SNOPT }{{\small SNOPT}}
\providecommand{\SQOPT }{{\small SQOPT}}

\providecommand{\CGM   }{{\small CGM}}
%\providecommand{\GMRES }{{\small GMRES}}
%\providecommand{\LSQR  }{{\small LSQR}}
%\providecommand{\MINRES}{{\small MINRES}}
%\providecommand{\SYMMLQ}{{\small SYMMLQ}}
\newcommand{\CG}       {{\small CG}\xspace} % Need \usepackage{xspace}
\newcommand{\CGLS}     {{\small CGLS}\xspace}
\newcommand{\RRLS}     {{\small RRLS}\xspace}
\newcommand{\LSQR}     {{\small LSQR}\xspace}
\newcommand{\GMRES}    {{\small GMRES}\xspace}
\newcommand{\LSMR}     {{\small LSMR}\xspace}
\newcommand{\MINRES}   {{\small MINRES}\xspace}
\newcommand{\MINRESQLP}{{\small MINRES-QLP}\xspace}
\newcommand{\SYMMLQ}   {{\small SYMMLQ}\xspace}
\newcommand{\SQMR}     {{\small SQMR}\xspace}
\newcommand{\MATLAB}   {{\small MATLAB}\xspace}
\newcommand{\FORTRAN}  {{\small FORTRAN}\xspace}
\newcommand{\SymOrtho} {\text{SymOrtho}\xspace}


%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End:
