Math & Science ⇒ numerical conditions

[kent]

I often should have liked to be able to test for numerical conditions in my PGF macros.
Let me illustrate with one simple example:
Let A and B be two given poinst where we have access to their coordinates, say A = (\xA,\yA) and B = (\xB,\yB).
I would then like to be able to check if A = B within some tolerance.
But how should I test to see, say, for \dx = \xB-\xA that abs(\dx) < \eps for a small defined value of \eps (i.e 0.0005)?
As far as I know the Latex \ifthenelse cannot be used.
Kent Holing, NORWAY

[mas]

Looking at the pgf manual, Section 90, you can see that there is a pgfmath library which has commands to do what you need. I am just pasting below from the manual (page 939):

90.2
Comparison and logical functions
In addition to the commands described in Section 89.3.5, the following command was provided by Christian
Feuersänger:
\pgfmathapproxequalto{<x>}{<y>}
Defines \pgfmathresult 1.0 if |<x>−<y>|< 0.0001, but 0.0 otherwise. As a side-effect, the global boolean
\ifpgfmathcomparison will be set accordingly.

[kent]

Thanks, I see I need to upgrade the PGF version I am using or could anybody supply the code needed/mentioned?

[Stefan Kottwitz]

Hi Kent!

It's probably good to update in any case. I remember you worked on an intersection topic, that also was solvable with PGF 3 aka TikZ 3. It provides a lot more features than PGF 2. Otherwise you may re-program already existing new features.

You may consider to update the whole TeX installation. LaTeX evolves, new features, packages, and bug fixes appear.

Stefan

[kent]

Since I recently got PGF 3.0 installed, I like to revisit the above.
What's wrong with the if statement below?

Code: Select all

\pgfmathapproxequalto{0.15}{0.1499999999};
\let\out\pgfmathresult;%here \out is 1.0 as it should
\ifthenelse{\ifpgfmathcomparison}{true}{false};%here I thought I should get true
% since I thought \ifpgfmathcomparison is true since \out is 1.0

Kent

[kent]

By using \let\outt\pgfmathint{\out} I transformed 1.0 to 1 and I could then use \ifthenelse{\outt>0} etc..
But, I still wonder how to use the boolean \ifpgfmathcomparison.

[cgnieder]

\ifpgfmathcomparison can be checked like any boolean defined with \newif:

Code: Select all

\documentclass{article}

\usepackage{tikz,etoolbox,ifthen}

\begin{document}

\pgfmathapproxequalto{0.15}{0.1499999999}

% standard TeX:
\ifpgfmathcomparison
  true%
\else
  false%
\fi

% etoolbox:
\ifbool{pgfmathcomparison}{true}{false}

% ifthen:
\ifthenelse{\boolean{pgfmathcomparison}}{true}{false}

\end{document}

[kent]

One more question, how do I compare numerically numbers in if statements such that
if(2.3>5.7}{false}{true}?

[kent]

Reading the manuals more carefully, I managed to resolve myself. Sorry, for bothering you with this.