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如何绘制多条曲线并命名？

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如何绘制多条曲线并命名？

我需要绘制多条曲线来说明运行时间，但其中一些曲线不起作用，而且我不知道如何在图中命名这些曲线。

\documentclass{standalone}
\usepackage{pgfplots}
\tikzset{>=stealth}
\begin{document}
\begin{tikzpicture}
  \begin{axis}[
    xmin=0,xmax=10,
    ymin=0,ymax=10,
    axis lines=center,
    axis line style=->]
    \addplot[->] expression[domain=0:10,samples=100]{x^(2)} ; 
  \addplot[->] expression[domain=0:10,samples=100]{\sqrt(x)} ;  
     \addplot[->] expression[domain=0:10,samples=100]{x!} ; 

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

我仍然需要绘制常数、对数和指数，但现在我如何让代码工作，以及如何在每条曲线旁边显示名称？（解释所有这些的额外材料也会有所帮助）

答案1

您可以在这里看到开始使用 pgfplots 所需要了解的内容：

\documentclass{standalone}
\usepackage{pgfplots}
\tikzset{>=stealth}
\begin{document}
\begin{tikzpicture}
  \begin{axis}[
    xmin=0,xmax=6.9,
    ymin=0,ymax=30,
    axis lines=center,
    axis line style=->]
    \addplot[dashed,red] expression[domain=0:5,samples=100]{(x)^2} ; \addlegendentry{$x^2$}
  \addplot[-,green] expression[domain=0:5,samples=100]{sqrt(x)} ;  \addlegendentry{$\sqrt{x}$}
     \addplot[dotted,blue] expression[domain=0:5,samples=100]{x!} ; \addlegendentry{$x!$}

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

正如@Stefan Pinnow 所说，域对于阶乘来说太大了，所以我必须改变它......

结果如下：

在此处输入图片描述

答案2

不幸的是，你在问题中并没有非常精确地说明你真正想要实现的目标，所以在我的回答中，我假设你想坚持给定的轴限制。

正如问题下方的评论中所述，如果不改变“某些东西”而只用 进行纠正，\sqrt(x)您sqrt(x)会得到“维度过大”的错误，因为x!函数产生的值的大小为10^6，而轴极限为10。

也不清楚如何你想要“命名曲线”。如果你指的是添加图例，那么请查看koleygr 的答案。如果你想添加名字在图表本身，这就是我在这里展示的内容。我在这里也使用了“硬”情况，在“图表末尾”添加名称，即 at pos=1。如果标签应该出现在“图表中间”的某个地方，请随意pos向标签nodes 添加相应的语句。

有关更多详细信息，请查看代码中的注释。（如果还有不清楚的地方，请随时询问。）

% used PGFPlots v1.15
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
    \pgfplotsset{
        /tikz/>=stealth,
        % use this `compat' level or higher to use Lua for calculations
        % (this is not required though)
        compat=1.12,
        % ---------------------------------------------------------------------
        % please skip this block for now
        % (copied from <https://tex.stackexchange.com/a/375348>)
        /pgf/declare function={
            % declare the main function(s)
            f(\x) = sqrt(\x);
            % state (or calculate) the lower and upper boundaries (the domain values)
            lb = 0;
            ub = 10;
            %
            % ---------------
            %%% nonlinear spacing: <https://stackoverflow.com/a/39140096>
            % "non-linearity factor"
            a = 0.4;
            % function to use for the nonlinear spacing
            Y(\x) = exp(a*\x);
            % rescale to former limits
            X(\x) = (Y(\x) - Y(lb))/(Y(ub) - Y(lb)) * (ub - lb) + lb;
        },
        % ---------------------------------------------------------------------
    }
\begin{document}
\begin{tikzpicture}
    \begin{axis}[
        % use the above defined variables here as well, so you only have to
        % change them in one place, if you would like to change these values
        xmin=lb,xmax=ub,
        ymin=0,ymax=10,
        axis lines=center,
        axis line style=->,
        % move common options here
        % also use the above defined variables here
        domain=lb:ub,
        % you don't want to show markers
        no markers,
        % show the plots "smoothly"
        smooth,
        % because the label nodes will be outside the axis "rectangle" they
        % would be clipped, so we disable clipping
        clip=false,
    ]
%        % Using these two functions have some downsides ...
%        \addplot+ [domain=0:4] {x^2};
%        \addplot {sqrt(x)};

        % Instead of increasing the number of samples "to make it look good",
        % we use nonlinear sampling instead.
        % (For more details have a look at <https://tex.stackexchange.com/a/375348>)
        \addplot ({X(x)},{f(X(x))})
            % add a label (node)
            % (the default position is at `pos=1.0`)
            node [right] {$\sqrt{x}$}
        ;

        % Because $x^2$ is the inverse function of $\sqrt{x}$ we simply
        % exchange the $x$ and $y$ arguments of the previous `\addplot'.
        % By doing that we also avoid that the function looks bad and we don't
        % have to increase the number of `samples'
        \addplot ({f(X(x))},{X(x)})
            node [above]{$x^2$}
        ;

        % Here we also use the minimalistic approach.
        \addplot+ [
            % Because values only change at integer x values, we can use
            % `const plot'.
            const plot,
            % $4!$ already yields $24$ and so we don't need a higher max
            % `domain' value.
            domain=0:4,
            % Use a number of samples that assures that also samples are at
            % integer x values to give a right result. This makes $5$ at minimum.
            samples=5,
            % So the plot stops at $y = 10$ use the following key--value.
            % (Otherwise, because we use `clip=false' the line would be drawn
            %  up to 24.)
            restrict y to domain*=0:10,
        ] {x!}
            node [above] {$x!$}
        ;
    \end{axis}
\end{tikzpicture}
\end{document}

该图显示了上述代码的结果

答案3

也许您对对数-对数图感兴趣？

输出

残酷阴谋

在此处输入图片描述

受限y域

和\addplot+[mark=none,const plot,restrict y to domain=0:42] {x!};

仅显示exp(0)=1和之间的值exp(42)~10^17。

我认为这足以说明相对增长的观点。

实际上：设置ymax更好。

在此处输入图片描述

代码

残酷阴谋

\documentclass[12pt,tikz,border=0pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.14}
\begin{document}
\begin{tikzpicture}
  \begin{loglogaxis}
    [
      %domain=2:30,
      ymin=1,
      axis lines = center,
      samples at ={1,2,...,100},
      grid=both,
      legend entries={$y=x!$,$y=x^2$,$y=\sqrt{x}$},
      every axis legend/.append style=
      {
        at={(current axis.above origin)},
        anchor=north west, xshift=1cm, yshift=-1mm,
        draw=none,
        cells={anchor=west},
        %font=\scriptsize,
      }
    ]
    \addplot+[mark=none,const plot] {x!};
    \addplot+[mark=none] {x^2};
    \addplot+[mark=none] {sqrt(x)};
  \end{loglogaxis}
\end{tikzpicture}
\end{document}

受限域

\documentclass[12pt,tikz,border=0pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.14}
\begin{document}
\begin{tikzpicture}
  \begin{loglogaxis}
    [
      height=13cm,
      ymin=1,
      ymax=exp(40),
      hide obscured x ticks=false,
      hide obscured y ticks=false,
      axis lines = center,
      samples at ={1,2,...,100},
      grid=both,
      legend entries={$y=x!$,$y=\exp(x)$,$y=x^2$,$y=\sqrt{x}$,$y=\ln(x)$},
      every axis legend/.append style=
      {
        at={(current axis.above origin)},
        anchor=north west, xshift=3mm, yshift=-1mm,
        draw=none,
        cells={anchor=west},
        %font=\scriptsize,
      },
    ]
    \addplot+[mark=none,const plot,] {x!}; 
    \addplot+[mark=none] {exp(x)}; 
    \addplot+[mark=none] {x^2};
    \addplot+[mark=none] {sqrt(x)};
    \addplot+[mark=none] {ln(x)}; 
  \end{loglogaxis}
\end{tikzpicture}
\end{document}

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