Tikz/addplot 与 gnuplot - 函数 x^(-2/3) 的图形

Question

我想绘制函数图形x^(-2/3)在域 1:2 和 -2:-0.1 中。但对于负数，我遇到了错误（见下文）。我不知道如何为 tikz 命令 \addplot 中使用的 gnuplot 设置数字格式“%.7e”。也许问题出在其他地方。

接下来，我发现 gnuplot 无法绘制函数 x^(-2/3)，只能绘制 x^(-0.6666)。我收到消息空 y 范围 [1:1]

Xelatex 错误：

set format "%.7e";; set samples 100; set dummy x; plot [x=-2:-0.1] x**(-0.666); ^ 
%%"example.pgf-plot.gnuplot", line 2: all points y value undefined!

代码：

\documentclass{scrbook}

\usepackage{tikz,pgfplots}

\begin{document}

  \begin{tikzpicture}[thick,scale=0.7, 
      every node/.style={transform shape} ]


    \begin{axis}[
      xmin = -1.5, xmax = 2.5, ymin = 0, ymax = 3.5,  % osy
      domain = -1:3.5,
      restrict y to domain=0:3,
      axis equal image,
      axis x line = middle,
      axis y line = middle,
      xlabel={$x$}, ylabel={$y$},
      ]

      \addplot[color=red, samples=100, smooth, ultra thick, unbounded coords=jump, no markers, 
               domain = 0.1:2] gnuplot{x^(-0.666)};

      \addplot[color=red, samples=100, smooth, ultra thick, unbounded coords=jump, no markers, 
               domain = -2:-0.1] gnuplot{x^(-0.666)};


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

该图形应该关于 y 轴对称，但事实并非如此。

Answer 1

的情节y=x^(-2/3)是不关于 y 轴对称（也许你其实是在策划y=1/(cuberoot(x^2))？）。

对于负值x，您将得到一个复杂的结果。您可以使用 gnuplot 函数提取结果的实部real，然后绘制该图：

如果你真的想画图（在正域中y=1/(cuberoot(x^2))等于），你可以使用。这会给你一个关于 y 轴对称的函数：x^(2/3)1/(x^2)^(1./3)

---

\documentclass{scrbook}

\usepackage{tikz,pgfplots}

\begin{document}

  \begin{tikzpicture}[thick,scale=0.7, 
      every node/.style={transform shape} ]


    \begin{axis}[
      xmin = -2.5, xmax = 2.5, ymin = -3.5, ymax = 3.5,  % osy
      restrict y to domain=-3:3,
      axis equal image,
      axis x line = middle,
      axis y line = middle,
      xlabel={$x$}, ylabel={$y$},
      ]

      \addplot[color=red, samples=100, smooth, ultra thick, unbounded coords=jump, no markers, 
               domain = 0.1:2] gnuplot{x^(-2.0/3)};

      \addplot[color=red, samples=100, smooth, ultra thick, unbounded coords=jump, no markers, 
               domain = -2:-0.1] gnuplot{real(x^(-2.0/3))};


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

---

\documentclass{scrbook}

\usepackage{tikz,pgfplots}

\begin{document}

  \begin{tikzpicture}[thick,scale=0.7, 
      every node/.style={transform shape} ]


    \begin{axis}[
      xmin = -2.5, xmax = 2.5, ymin = -3.5, ymax = 3.5,  % osy
      restrict y to domain=-3:3,
      axis equal image,
      axis x line = middle,
      axis y line = middle,
      xlabel={$x$}, ylabel={$y$},
      ]

      \addplot[color=red, samples=100, smooth, ultra thick, unbounded coords=jump, no markers, 
               domain = 0.1:2] gnuplot{1/((x^2)^(1./3))};

      \addplot[color=red, samples=100, smooth, ultra thick, unbounded coords=jump, no markers, 
               domain = -2:-0.1] gnuplot{1/(x^2)^(1./3)};


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