mathshortcuts.sty

这是移动机器人同时定位与地图创建的第三部分

% mathshortcuts.sty
%-----------------------------------------------------------------
%    History:
%    Date            Who         What
%    -----------     -------     -----------------------------
%    2002            rme         Created and written.
%    10-31-2003      rme         Rewrote array definitions.
%    11-05-2003      rme         Removed array definitions, use
%                                amsmath \begin{bmatrix} environment
%    11-05-2003      rme         Added \leftexp
%    08-18-2004      rme         Added \normalcov, \normalinfo, \pdf
%    09-04-2004      rme         Added \symbolfootnote
%    12-04-2004      mrw         Added \argmax command
%    05-13-2005      mrw         Added \argmin command	

\ProvidesPackage{mathshortcuts}
\usepackage{ifthen}
\usepackage{amsmath}

% symbol footnot: syntax \symbolfootnote[1]{text}
% 1 - *
% 2 - dagger
% 3 - double dagger
% 4 - ...9 see page 175 of latex manual
\long\def\symbolfootnote[#1]#2{\begingroup%
\def\thefootnote{\fnsymbol{footnote}}\footnote[#1]{#2}\endgroup}

% argmax function
\providecommand{\argmax}[1]{{\hbox{$\underset{#1}{\mbox{argmax}}\;$}}}
\providecommand{\argmin}[1]{{\hbox{$\underset{#1}{\mbox{argmin}}\;$}}}

% normal cov: syntax \normalcov[optional]{u}{P}
\providecommand{\normalcov}[3][-9876]{
  \ifthenelse{\equal{#1}{-9876}}
  % print N(u,P)
  {\ensuremath{\mathcal{N}\bigl({#2},{#3}\bigr)}}
  % print N(x;u,P)
  {\ensuremath{\mathcal{N}\bigl({#1};{#2},{#3}\bigr)}}
}

% normal info: syntax \normalinfo[optional]{u}{P}
\providecommand{\normalinfo}[3][-9876]{
  \ifthenelse{\equal{#1}{-9876}}
  % print N(u,P)
  {\ensuremath{\mathcal{N}^{-1}\bigl({#2},{#3}\bigr)}}
  % print N(x;u,P)
  {\ensuremath{\mathcal{N}^{-1}\bigl({#1};{#2},{#3}\bigr)}}
}

% pdf
\providecommand{\pdf}[2][-9876]{
  \ifthenelse{\equal{#1}{-9876}}
  % print p(x)
  {\ensuremath{p\left({#2}\right)}}
  % print p(x|y)
  {\ensuremath{p\left({#1}~\vert~{#2}\right)}}
}

% bold vector
\providecommand{\bvec}[1]{\ensuremath{\boldsymbol{\mathrm{#1}}}}
% homogenous vector
\providecommand{\hvec}[1]{\ensuremath{\underline{\boldsymbol{\mathrm{#1}}}}}
% mean vector
\providecommand{\mvec}[1]{\ensuremath{\overline{\boldsymbol{\mathrm{#1}}}}}
% matrix
\providecommand{\mat}[1]{\ensuremath{\mathrm{#1}}}
% skew-symmetric matrix
\providecommand{\skewsym}[1]{\ensuremath{[{#1}]_{\times}}}
% identity matrix
\providecommand{\eye}[1]{\ensuremath{\mat{I}_{#1\times#1}}}
% zeros matrix
\providecommand{\zeros}[2]{\ensuremath{0_{#1\times#2}}}
% absolute
\providecommand{\abs}[1]{\ensuremath{\lvert#1\rvert}}
% norm
\providecommand{\norm}[1]{\ensuremath{\left\lVert#1\right\rVert}}
% left sub/sup script
\providecommand{\leftexp}[2]{\ensuremath{{\vphantom{#2}}{#1}{#2}}}
% parenthesis
\providecommand{\paren}[1]{\ensuremath{\hspace{-2pt}\left({#1}\right)}}
% rotx
\providecommand{\rotx}[1]{
  \ensuremath{
    \begin{bmatrix}
      1 & 0                           & 0 \\
      0 & \hphantom{-}\cos\paren{#1}  & \sin\paren{#1} \\
      0 & -\sin\paren{#1}             & \cos\paren{#1}
    \end{bmatrix}
  }
}
% roty
\providecommand{\roty}[1]{
  \ensuremath{
    \begin{bmatrix}
      \cos\paren{#1} & 0 & -\sin\paren{#1} \\
      0              & 1 & 0               \\
      \sin\paren{#1} & 0 & \hphantom{-}\cos\paren{#1}
    \end{bmatrix}
  }
}
% rotz
\providecommand{\rotz}[1]{
  \ensuremath{
    \begin{bmatrix}
      \hphantom{-}\cos\paren{#1}  & \sin\paren{#1} & 0 \\
      -\sin\paren{#1}             & \cos\paren{#1} & 0 \\
      0                           & 0              & 1
    \end{bmatrix}
  }
}
% rotxyz
\providecommand{\rotxyz}[3]{
  \ensuremath{
    \begin{bmatrix}
      % row 1
      \cos\paren{#3}\cos\paren{#2} & 
      -\sin\paren{#3}\cos\paren{#1}+\cos\paren{#3}\sin\paren{#2}\sin\paren{#1} &
      \hphantom{-}\sin\paren{#3}\sin\paren{#1}+\cos\paren{#3}\sin\paren{#2}\cos\paren{#1} \\
      % row 2
      \sin\paren{#3}\cos\paren{#2} &
      \hphantom{-}\cos\paren{#3}\cos\paren{#1}+\sin\paren{#3}\sin\paren{#2}\sin\paren{#1} &
      -\cos\paren{#3}\sin\paren{#1}+\sin\paren{#3}\sin\paren{#2}\cos\paren{#1} \\
      % row 3
      -\sin\paren{#2} &
      \cos\paren{#2}\sin\paren{#1} &
      \cos\paren{#2}\cos\paren{#1} 
    \end{bmatrix}
  }
}

\DeclareMathOperator{\atan}{tan^{-1}}  % atan
\DeclareMathOperator{\atantwo}{atan2}  % atan2
\DeclareMathOperator{\asin}{sin^{-1}}  % asin
\DeclareMathOperator{\acos}{cos^{-1}}  % acos