在 pgfplots 中绘制多个函数

Question

我有一个要绘制的函数。但是，它有 10 个变体，每个变体有 5 个不同的常数。我不想简单地插入一个数字 50 次。有没有更简单的方法可以做到这一点？此外，图表看起来很奇怪。有没有其他方法pgfplots可以生成图像，然后直接使用includegraphics，最好是带有矢量图形的东西，这样它的质量最高。谢谢。

\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}

Answer 1

您可以使用键声明函数declare function。（Ti钾Z 库math有其他定义函数的方法，但这与 不太协调，pgfplots因为pgfplots使用fpu。）这是一个例子。这将使用声明的函数重现您的图。

\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}