information-theory-operators.tex

\usepackage{amssymb,mathtools}
\usepackage{mleftright}

% mathrm differential with space before for integral notation
\newcommand{\dee}{\mathop{\mathrm{d}\!}}

% Middle bar resize for \set{}: https://tex.stackexchange.com/a/460/19048
\makeatletter
\newcommand{\my@set}[1]{\left\lbrace #1\right\rbrace}
\newcommand{\my@cset}[2]{%
 \left\lbrace #1\vphantom{#2}\right\vert%
 \left.\vphantom{#1}#2\right\rbrace}
\def\my@first#1|#2\relax{#1}
\def\my@second#1|#2\relax{#2}
\newcommand{\set}[1]{%
\edef\my@given{#1}
\edef\my@start{\my@first#1|\relax}%
\ifx\my@start\my@given%
\my@set{#1}
\else
\edef\my@last{\my@second#1\relax}%
\my@cset{\my@start}{\my@last}%
\fi}

% KL operator: (use \KL{p}{q} or \KL*{p}{q} for resizing version)
\DeclarePairedDelimiterX{\infdivx}[2]{(}{)}{#1\,\delimsize\|\,#2}
\newcommand{\KL}{D_{\mathrm{KL}}\infdivx}

% Simple information theory operators (such as \I{X:Y} for mutual information):
\DeclarePairedDelimiterX{\parens}[1]{(}{)}{#1}
\newcommand{\I}{\operatorname{I}\parens}

% %%%% An alternate way to do \I{X:Y}
% \newcommand{\op}[2]{\operatorname{#1}({#2})} % to make various operators
% \newcommand\I[1]{\op{I}{#1}}
% \newcommand{\II}[1]{\op{II}{#1}}
% \newcommand\T[1]{\op{T}{#1}}
% \newcommand\B[1]{\op{B}{#1}}
% % My Expectation and entropy operators
% \DeclareMathOperator*{\EV}{\mathbb{E}}
% \newcommand\E[2]{\EV_{#1}\left[{#2}\right]} % Expectation
% \renewcommand\H[1]{\op{H}{#1}} % Entropy
% %%%%

% For better spacing in something like \H{X:Y|Z}
\DeclareMathSymbol{:}{\mathop}{operators}{"3A} % colon behave as operator instead of relation
\DeclareMathSymbol{|}{\mathbin}{symbols}{"6A} % pipe behave as bin relation instead of ord


% Expectation operator implementation from https://tex.stackexchange.com/a/266485/19048
% BEGIN
\makeatletter
\newcommand*{\E}{%
  \def\E@sub{}%
  \def\E@sup{}%
  \E@scripts%
}
\newcommand*{\E@scripts}{%
  \@ifnextchar_\E@subscript{%
    \@ifnextchar^\E@supscript\E@finish%
  }%
}
\def\E@subscript_#1{%
  \ifx\E@sub\@empty%
    \def\E@sub{#1}%
  \else
    \errmessage{E already has a subscript}%
  \fi
  \E@scripts%
}
\def\E@supscript^#1{%
  \ifx\E@sup\@empty%
    \def\E@sup{#1}%
  \else
    \errmessage{E already has a superscript}%
  \fi
  \E@scripts%
}
\newcommand*{\E@finish}[1]{%
  \mathbb{E}%
  \ifx\E@sub\@empty\else _{\E@sub}\fi
  \ifx\E@sup\@empty\else ^{\E@sup}\fi
  \mleft[#1\mright]%
}
\makeatother
% END

% Entropy operator that can take optional subscript for conditional entropy
% BEGIN
\makeatletter
\renewcommand*{\H}{%
  \def\H@sub{}%
  % \def\H@sup{}%
  \H@scripts%
}
\newcommand*{\H@scripts}{%
  \@ifnextchar_\H@subscript{%
    \@ifnextchar^\H@supscript\H@finish%
  }%
}
\def\H@subscript_#1{%
  \ifx\H@sub\@empty%
    \def\H@sub{#1}%
  \else
    \errmessage{H already has a subscript}%
  \fi
  \H@scripts%
}
% \def\H@supscript^#1{%
%   \ifx\H@sup\@empty
%     \def\H@sup{#1}%
%   \else
%     \errmessage{E already has a superscript}%
%   \fi
%   \H@scripts
% }
\newcommand*{\H@finish}[1]{%
  \mathrm{H}%
  \ifx\H@sub\@empty\else _{\H@sub}\fi
  % \ifx\H@sup\@empty\else ^{\H@sup}\fi
  \mleft(#1\mright)%
}
\makeatother
% END