[Tex/LaTex] pgf-tikz problem with ‘declare function’

pgfmathtikz-pgf

I need to make a plot of a non-linear functions. To get familiar with the 'declare function' capability of pgf-tikz, I tried the following code:

\documentclass[10pt]{article}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\begin{document}
  \thispagestyle{empty}
    \begin{tikzpicture}[scale=2.0,
      declare function={
        func(\x,\a) = 1.0/(\x^\a);
      }]
% draw grid  
      \draw[very thin,color=gray] (0.0,0.0) grid (2.0,2.0); 
% draw axes 
      \draw[->] (0.0,0.0) -- (2.0,0.0) node[right] {$x$};
      \draw[->] (0.0,0.0) -- (0.0,2.0) node[above] {$y$};     
% draw functions
      \draw[blue]  plot[domain=0.5:2.0,samples=100] (\x,{func(\x,1.0)});
      \draw[red]   plot[domain=0.8:2.0,samples=100] (\x,{func(\x,2.0)}); 
      \draw[green] plot[domain=0.5:2.0,samples=100] (\x,{func(\x,0.5)}); 
  \end{tikzpicture}
\end{document}

enter image description here

So what I expect to see are three lines corresponding to 1/x, 1/x^2, and 1/sqrt(x). The last function call did not give the correct function. Since I'm new to using the math functionality of pgf-tikz, I suspect I'm doing something wrong or I'm overlooking something. I'd be glad to get some pointers that

  • help me fix this problem; and

  • get some advice about how to best/better approach this problem.

The function I will need to plot is going to be more complicated, but also smooth and under some limits approaches 1/x.

Best Answer

TikZ Solution:

I believe there are some limitations in using the internal math engine with power type functions (but for some reason works just fine with pgfplots as in the solution below), but if you change your definition from func(\x,\a) = 1.0/(\x^\a) to:

func(\t,\a) = 1.0/(exp((\a)*ln(\t)));

you get (and also added very thick option to \draw):

enter image description here

##Pgfplots Solution:

However, I would recommend that you use pgfplots for graphing. As per Consistently specify a Function and use it for computation and plotting, I would recommend that you use the approach suggest there to define the function:

\def\func(#1,#2){1.0/((#1)^(#2))}

This method will allow you to be able to use this one definition for:

  1. Computation of values to:
  1. Graphing using pgfplot
  2. Graphing using pgfplots/gnuplot

enter image description here

\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}

\def\func(#1,#2){1.0/((#1)^(#2))}%

\begin{document}
\begin{tikzpicture}
\begin{axis}[
    domain=0.5:2.0, samples=100,
    every axis plot post/.style= ultra thick]
    \addplot [blue] {\func(x,1.0)};%
    \addplot [red]  {\func(x,2.0)};%
    \addplot [green]{\func(x,0.5)};
\end{axis}
\end{tikzpicture}
\end{document}
Related Question