56

A common notation used for information divergence is D(P||Q). I hope to get something like D(S||Q) where S=||P||/2. I wonder if it is possible to display it nicely ? In such a way that the middle double bar has the right height. I tried 

$D \left( \frac{\|P\|}{2} \right| \left| Q \right)$

The above do not work as the middle bar are not of the same vertical height but its closest to what I hope to achieved. Using just \| instead of \right| \left| for the middle double bar results in a short middle double bar.

Does anyone has a good idea on how to achieve that. Thanks Else, I could just create a new notation.

-- Update -- I managed to find out how to do it with this useful operator \middle

$D \left( \frac{\|P\|}{2} \middle\| Q \right)$

Hope someone else may find this useful.

shunjie
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  • I'd rather recommend not using auto scaling unless it is absolutely necessary. Try you construction as part of the text, using P^2 instead of P. The fences will become too large. – daleif Dec 31 '13 at 23:11
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    We'd like to keep answers separate from questions, so you should write a separate answer instead of editing your answer into the question. Self-answers are perfectly admissible, and a well-written answer may earn you additional reputation. Welcome to TeX.SX! – Adam Liter Dec 31 '13 at 23:24

4 Answers4

56

This double bar should be treated as a binary relation, so it will be distinguishable from other usages, such as a norm.

The simplest way to cope with the problem is to use mathtools facilities:

\documentclass{article}
\usepackage{mathtools}

\DeclarePairedDelimiterX{\infdivx}[2]{(}{)}{%
  #1\;\delimsize\|\;#2%
}
\newcommand{\infdiv}{D\infdivx}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}


\begin{document}

\begin{gather}
D\left(P \middle\| Q\right) \rlap{\quad\itshape WRONG!} \\
% normal size
\infdiv{P}{Q} \\
% fixed size delimiters
\infdiv[\bigg]{\frac{\norm{P}}{2}}{Q} \\
% extensible delimiters
\infdiv*{\frac{\norm{P}}{2}}{Q}
\end{gather}

\end{document}

enter image description here

Note that number 1 is wrong in two respects: there is an unwanted space between the "D" and the left parenthesis; the two bars are too near the symbols, making for ambiguity.

egreg
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13

In MathJax use $\lVert$ and $\rVert$. The capital v gives you double bars while the lower case v in $\lvert$ gives you single vertical bars. But it's not clear to me what to you is the "right" height.

Also, you have $\vert$ and $\Vert$.

Since you mention using a vertical bar as a binary relation, you may want $\mid$ which is kerned to sit midway between its neighbours. But that has no double-bar version so finally, you have the option of $\mathrel{\Vert}$ which is both double-bar and kerned to the centre.

it's a hire car baby
  • 231
  • I don't think your last edit is correct. \vert and \Vert are declared as \mathord, not \mathbin. – campa Dec 23 '20 at 11:52
  • @campa thanks, you may be right because I don't fully understand your comment. What aspect of what I put is untrue? The part about the kerning? This might be wrong. Also I started out thinking of $\mid$ and then changed when I realsed there is no $\Mid$. – it's a hire car baby Dec 23 '20 at 18:14
  • The bit about spacing is incorrect. \mid has the spacing of a binary relation, but \vert is an ordinary symbol. And as you say there is indeed no Mid. (I was wrong too, I wrote \mathbin but actually meant \mathrel.) Bottom line: \vert and \Vert are not kerned. \mid is, and for thr double bar you must either do \mathrel{\Vert}, or insert spacong manually (as egreg did) or define your own macro \Mid. – campa Dec 23 '20 at 18:37
  • THanks @campa . Is that all accurate now? IF so I will prune these comments. – it's a hire car baby Dec 23 '20 at 18:55
  • So... what is the best command? (1) \infdiv by @egreg, or (2) \mathrel{\Vert} by @it's a hire car baby ? – Ommo Aug 17 '23 at 09:45
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    @limone "the best" can be an ambiguous criterion but if you mean the best for the original poster, they ultimately declared in the question that they found \middle to work best for their purposes. That might well be the same as my \mid. – it's a hire car baby Aug 17 '23 at 10:50
  • Thanks a lot @it'sahirecarbaby! Yes, you are right, I did not define the term "best".. I meant the command that, from a mathematical point of view, is the clearest and most correct one, and that does not create any ambiguity... :-) – Ommo Aug 17 '23 at 11:03
2

Using \parallel gives a nice result.  Latex code:D_{KL}(q(z|x,\phi)\parallel p(z))

KL divergence example

Charles Xu
  • 121
  • 3
    This is bad advise as \parallel cannot be scaled and thus the auto scaled version the OP shows last will not work. – daleif Mar 22 '22 at 09:45
0

An alternative is to use \Big\|. And instead of \Big one can use \big or \bigg, etc. depending on how much length you want.

Gaurav Saxena
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