Plotting multiple functions in pgfplots

Question

I have a function that I want to graph. However, there are 10 variations of it with 5 different constants each. I do not want to simply plug in a number 50 times. Is there an easier way to do this? Also, the graph comes out strangely. Is there an alternative to pgfplotsthat I use to generate an image and then just use includegraphics, preferably something with vector graphics so that it is of the highest quality. Thank you.

\documentclass[letterpaper]{article}
\usepackage{pgfplots} \pgfplotsset{width=10cm,compat=1.16}

\begin{document}


\[ y^{\prime} ( t ) = \frac{\lambda \phi ( \beta - \alpha )}{t \left[ 1 + ( t/\gamma)^{-\phi} \right]^\lambda \left[ 1 + (t/\gamma)^{\phi} \right]} \] 


\begin{figure}[htbp!]
  \centering
  \begin{tikzpicture}
     \begin{axis}[
      legend pos=north east,
      title = {},
      xlabel = {time},
      ylabel = {temperature},
      xmin = 0, xmax = 15,
      ymin = 0, ymax = 8,
      xtick = {0, 5, 10, 15},
      ytick = {0, 2, 4, 6, 8},
    ]

      \addplot[black, no marks, domain=0.01:15, smooth]{(1.86*3.38*(42.2 - 23.3))/(x*(1 + (x/3.15)^(-3.38))^(1.86)*(1 + (x/3.15)^(3.38)))};
      \addlegendentry{fitted function}

      \addplot[red, no marks, domain=0.01:15, smooth]{(12*3.01*(43.6 - 23.8))/(x*(1 + (x/1.38)^(-3.01))^(12)*(1 + (x/1.38)^(3.01)))};
      \addlegendentry{fitted function2}

    \end{axis}
  \end{tikzpicture}

\end{figure}

\end{document}

@marmot Thank you, but an example please? Also any suggestions for making the graph look better or other options? Edit. I spoke too soon. I think I can figure out the declare function. Though example would be nice in case I screw it up. — Ilyankor, Jan 28 '19 at 04:54
Off-topic. There is no difference between ^\prime and '; the latter makes the code easy to write. — manooooh, Jan 28 '19 at 06:50

score 2 · Accepted Answer · 2019-01-28T05:56:39.937

You can declare functions with the key declare function. (The TikZ library math has additional means to define functions, but this does not harmonize that well with pgfplots because pgfplots uses fpu.) Here is an example. This reproduces your plot with a declared function.

\documentclass[letterpaper]{article}
\usepackage{pgfplots} 
\pgfplotsset{width=10cm,compat=1.16}

\begin{document}


\[ y^{\prime} ( t ) = \frac{\lambda \phi ( \beta - \alpha )}{t \left[ 1 + ( t/\gamma)^{-\phi} \right]^\lambda \left[ 1 + (t/\gamma)^{\phi} \right]} \] 


\begin{figure}[htbp!]
  \centering
  \begin{tikzpicture}[declare function={f(\x,\alpha,\beta,\gamma,\lambda,\phi)=%
  (\lambda*\phi*( \beta - \alpha ))/(\x*pow( 1 + pow( \x/\gamma,-\phi),\lambda) 
  *( 1 + pow(\x/\gamma,\phi)));}]
     \begin{axis}[
      legend pos=north east,
      title = {},
      xlabel = {time},
      ylabel = {temperature},
      xmin = 0, xmax = 15,
      ymin = 0, ymax = 8,
      xtick = {0, 5, 10, 15},
      ytick = {0, 2, 4, 6, 8},
    ]

      \addplot[black, no marks, domain=0.01:15, smooth]
      {f(x,23.3,42.2,3.15,1.86,3.38)};
      %\addplot[black, no marks, domain=0.01:15, smooth]{(1.86*3.38*(42.2 - 23.3))/(x*(1 + (x/3.15)^(-3.38))^(1.86)*(1 + (x/3.15)^(3.38)))};
      \addlegendentry{fitted function}

      \addplot[red, no marks, domain=0.01:15, smooth]
      {f(x,23.8,43.6,1.38,12,3.01)};
      %\addplot[red, no marks, domain=0.01:15, smooth]{(12*3.01*(43.6 - 23.8))/(x*(1 + (x/1.38)^(-3.01))^(12)*(1 + (x/1.38)^(3.01)))};
      \addlegendentry{fitted function2}


    \end{axis}
  \end{tikzpicture}
\end{figure}
\end{document}

Plotting multiple functions in pgfplots

1 Answers1