How do I use pgfmathdeclarefunction to create define a new pgf function?

Question

I'd like to define new function for pgf so I can use it in pgfplots. I'm trying to create a unit pulse function p(x) which has a value of 1 from x=0 to x=1, and 0 elsewhere.

I read the pgf manual on Customizing the Mathematical Engine (section 65, page 541), but I'm probably misunderstanding something =P

This code doesn't work:

\documentclass{minimal}
\usepackage{pgfplots}

\pgfmathdeclarefunction{p}{1}{%
  \pgfmathand{\pgfmathless{#1}{1}} {\pgfmathgreater{#1}{0}}%
}

\begin{document}

\begin{tikzpicture}
  \begin{axis}
    \addplot {p(x)};
  \end{axis}
\end{tikzpicture}

\end{document}

Answer 1

I got it to work by using pgfmathparse inside of pgfmathdeclarefunction (I don't know if that's how you're supposed to do it, but I'm satisfied for now)

I can also define it locally using declare function.

\documentclass{letter}
\usepackage{pgfplots}
\usepackage{setspace}
\doublespacing

\pgfmathdeclarefunction{p}{1}{%
  \pgfmathparse{and(#1>0, #1<1)}%
}

\begin{document}

My pgf version is: \pgfversion

p(0.2) is \pgfmathparse{p(0.2)}\pgfmathresult

p(2) is \pgfmathparse{p(2)}\pgfmathresult

Plot of p(x):

\begin{tikzpicture}
  \begin{axis}
    \addplot[domain=-5:5, samples=50]{p(x)};
  \end{axis}
\end{tikzpicture}

Using declare function to define localp(x):

\begin{tikzpicture}
[
  declare function={
    localp(\t) = and(\t > 0, \t < 1);
  }
]
  \begin{axis}
    \addplot[domain=-5:5, samples=50]{localp(x)};
  \end{axis}
\end{tikzpicture}

\end{document}

Answer 2

I think I can provide some more insight into the questions here.

The good news at first: providing \begin{axis}[use fpu=false] will enable you to use all custom math functions (as long as they work in pgf, I guess).

Now the details: Let me summarize the state of the discussion: When we use custom math functions in pgfplots, we have

1. the solution containing `\pgf@x=#1pt` leads to

   
   ! Illegal unit of measure (pt inserted).
    
                      Y
   l.24      \addplot[domain=-5:5, samples=50]{double(x)};
   

2. The solution with `\pgfmathmultiply{#1}{#1}` worked
3. The solution(s) with `\pgfmathparse` worked as well
4. The solution with `\pgfmathand{\pgfmathless{#1}{1}}{\pgfmathgreater{#1}{0}}` failed (in my case something strange with `! Extra else`

The problem is caused by the fact that PGFPlots has the initial configuration 'use fpu=true'. The fpu is a PGF library; it replaces the math module by something like single precision floating points.

As long as user contributed math functions rely only on high-level math functions (like \pgfmathparse or \pgfmathmultiply as above), the codebase will transparently use the FPU - and everything is consistent.

But as soon as you employ TeX registers, things become different: Writing \pgf@x=#1pt means that the first argument is interpreted as a fixed point number in the range -16000...16000 (roughly). With use fpu=true, both is essentially violated: the fpu has neither fixed point numbers nor is it restricted to this data range. The error message arises because (at the point of this writing), floating point numbers are stored like 1Y1.0e1 where the Y separates "flags" from mantissa. The Y is the first character where \pgf@x=#1pt bails out. Note, however, that the FPU is smart enough to detect if the RETURN VALUE of a custom function is a TeX register number or a float. But I am unaware of any way of asking "will the function handle floats?".

So, as already mentioned, use fpu=false disables the FPU; pgfplots will then operate with fixed point numbers in the range -16000...16000 and all the math functions should work.

The other solution is to use the basic layer math functions like \pgfmathmultiply. Note that unless I am mistaken, \pgfmathmultiply will also invoke \pgfmathparse (which is expensive). Use \pgfmathmultiply@ to suppress argument parsing (which, however, needs a \makeatletter before defining the custom function).

Unfortunately, I am unaware of why the \pgfmathand{} {} solution fails. Does it work in PGF?

I hope this helps here.

Answer 3

I suggest this very simple code:

\documentclass{minimal}
\usepackage{tikz}
\makeatletter
\pgfmathdeclarefunction{p}{1}{\edef\pgfmathresult{\ifdim#1pt<\z@0\else\ifdim#1pt>1pt 0\else1\fi\fi}}
\makeatother
\begin{document}
\begin{tikzpicture}
\draw[very thin,color=gray] (-2,-2) grid (2,2);
\draw[color=blue] plot (\x,{p(\x)});
\end{tikzpicture}
\end{document}

Answer 4

@Altermundus Thanks for that example code. I tried using a shortened version for an example. It seems like it works in pgf, but not in pgfplots.

Compiling this example code, I get

My pgf version is: 2.10

test(2.5) is 2

but no plot. I get a bunch of errors at the \addplot line: "Illegal unit of measure (pt inserted)" "Paragraph ended before \pgfflt@readlowlevelfloat was complete"

\documentclass{minimal}
\usepackage{pgfplots}

\makeatletter
\pgfmathdeclarefunction{test}{1}{%
  \begingroup%
    \pgfmath@xa=#1pt\relax%
    \pgfmathparse{int(\pgfmath@xa)}%
    \pgfmath@smuggleone\pgfmathresult%
  \endgroup%
}%
\makeatother

\begin{document}

My pgf version is: \pgfversion

test(2.5) is \pgfmathparse{test(2.5)}\pgfmathresult

\begin{tikzpicture}
  \begin{axis}
    \addplot[domain=-2:2, samples=10]{test(x)};
  \end{axis}
\end{tikzpicture}

\end{document}

Answer 5

I modified my answer with only an example from the pgfmanual (the first one for \pgfmathdeclarefunction. This example from the pgfmanual works with pgf and not with pgfplots (why ???)

The part with pgfplots gives Latex Error: ./add_func_pgfplots.tex:77 Illegal unit of measure (pt inserted).

\documentclass{minimal}
\usepackage{pgfplots}
\makeatletter
\pgfmathdeclarefunction{double}{1}{%
 \begingroup 
  \pgf@x=#1pt\relax 
  \multiply\pgf@x by2\relax 
  \pgfmathreturn\pgf@x
 \endgroup 
}
\makeatother 
\begin{document}
\pgfmathparse{double(44.3)}\pgfmathresult 

 \begin{tikzpicture} 
   \draw plot [domain=0:5, samples=144, smooth] (\x,{double(\x)}); 
\end{tikzpicture} 

\begin{tikzpicture}
  \pgfmathdouble{1}
   \let\ra\pgfmathresult
   \draw (0,0) circle (\ra);% \ra is fine
 %  \begin{axis}
 %    \addplot[domain=-5:5, samples=50]{double(x)};
 %  \end{axis}  
\end{tikzpicture}

\end{document}

But this code works

 \documentclass{scrartcl}
 \usepackage{pgfplots}

\begin{document}

My pgf version is: \pgfversion 

\pgfmathdeclarefunction{double}{1}{
\begingroup
\pgfmathmultiply{#1}{#1} % instead of \pgfmathparse{#1*#1} from kristi
\endgroup 
} 

\begin{tikzpicture}
  \begin{axis}
   \addplot[domain=-5:5, samples=50]{double(x)};
 \end{axis}   
\end{tikzpicture}

\end{document}  

The main problem with \pgfmathparse is the code is slow if we need to make a lot of loops