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在特定区间绘制反函数

tag-icon • tag-icon tikz-pgf
在特定区间绘制反函数

我想画这个

因此，我创建了这个代码

\documentclass[border=12pt]{standalone}
\usepackage{tikz,tkz-base,tkz-tab}
\usetikzlibrary{positioning}
\usepackage{pifont}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\begin{document}
            \begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1cm,y=1cm]
                \begin{axis}[scale=1.3, x=1cm, y=1cm, axis lines=middle, xmin=-3.5, xmax=7, ymin=-3, ymax=6, xtick={-3,...,6}, ytick={-2,...,5},]
                    \draw[line width=1pt, color=blue, smooth, samples=100, domain=0:6.5] plot(\x,{2 *\x * ln \x - 2*\x });
                    \draw[line width=1pt, color=blue, smooth, samples=100, domain=-2:6] plot({2 *\x * ln \x - 2*\x ,\x});
                    \draw[line width=1pt, color=black, smooth, samples=100, domain=-1.2:6] plot(\x,{\x});
                    \draw[color=red , thick,<->] (0.3,-2)--(1.7,-2);
                    \draw[line width=0.1pt, color=black, dashed](1,0)|-(0,-2);
                    \draw[line width=0.1pt, color=black, dashed](4.4816,0)|-(0,4.4816);
                    \node[black, rotate=45] at (3,3.4) {$(\Delta):y = x$}; % y = x
                    \node[black] at (4.4816,0) {{\tiny \ding{53}}};
                    \node[left,yshift=-1mm] at (0,4.6) {{\small $e^{\frac{3}{2}}$}};
                    \node[left,yshift=-2.5mm] at (4.8,0) {{\small $e^{\frac{3}{2}}$}};
                    \node[left,yshift=-2mm] at (2.9,-0.1) {{\small $e$}};
                    \node[black] at (0,4.4816) {{\tiny \ding{53}}};
                    \node[black] at (2.7182,0) {{\tiny \ding{53}}};
                    \draw[color=red , thick, ->] (0,0)--(0,-0.9);
                    \draw[color=red , thick, ->] (-2,1)--(-2,1.7);
                    \begin{scriptsize}
                        \draw[color=blue] (2.8,1.4) node {$(C_f)$};
                    \end{scriptsize}
                \end{axis}
            \end{tikzpicture}
\end{document}

但它没有给我相同的结果 + 我得到了一些错误，我不知道如何修复它们

答案1

分析、调试……：

  • 全部评论
  • 逐步评论
  • 做一些代码格式化和注释
  • 揭示 4 个未使用的包

你的问题是，你不能通过简单地“交换”变量来计算逆：

  • \draw[line width=1pt, color=blue, smooth, samples=100, domain=-2:6] plot({2 *\x * ln \x - 2*\x ,\x});

建议：

  • 通过删除内联计算\draw
  • 存储为（表格）数据
  • 读取所述数据，包括交换列和不交换列
  • 情节
  • pgfplot更加一致地使用

在此处输入图片描述

\documentclass[border=12pt]{standalone}
                            %\usepackage{tikz,tkz-base,tkz-tab}
\usepackage{tikz}
                            %\usetikzlibrary{positioning}
\usepackage{pifont}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}


\begin{document}
 \begin{tikzpicture}[line cap=round,line join=round,%>=triangle 45,
                    x=1cm,y=1cm]
    \begin{axis}[scale=1.3, x=1cm, y=1cm, axis lines=middle, 
                xmin=-3.5, xmax=7, ymin=-3, ymax=6, 
                xtick={-3,...,6}, ytick={-2,...,5},]
                
        % ~~~ function C_f ~~~~~~~~~~~~~~~~
        \draw[line width=1pt, color=blue, smooth, samples=100, domain=0:6.5] plot(\x,{2 *\x * ln \x - 2*\x });
        
        % ~~~ "inverse" ~~~ No ~~~~~~~~~~~~~~~
%       \draw[line width=1pt, color=blue, smooth, samples=100, domain=-2:6] plot({2 *\x * ln \x - 2*\x ,\x});

        % ~~~ diagonal ~~~~~~~~~~
        \draw[line width=1pt, color=black, smooth, samples=100, domain=-1.2:6] plot(\x,{\x});
            
        % ~~~ labels, marks etc. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        \draw[color=red , thick,<->] (0.3,-2)--(1.7,-2);
        \draw[line width=0.1pt, color=black, dashed](1,0)|-(0,-2);
        \draw[line width=0.1pt, color=black, dashed](4.4816,0)|-(0,4.4816);
        
        \node[black, rotate=45] at (3,3.4) {$(\Delta):y = x$}; % y = x
        \node[black] at (4.4816,0) {{\tiny \ding{53}}};
        \node[left,yshift=-1mm] at (0,4.6) {{\small $e^{\frac{3}{2}}$}};
        \node[left,yshift=-2.5mm] at (4.8,0) {{\small $e^{\frac{3}{2}}$}};
        \node[left,yshift=-2mm] at (2.9,-0.1) {{\small $e$}};
        \node[black] at (0,4.4816) {{\tiny \ding{53}}};
        \node[black] at (2.7182,0) {{\tiny \ding{53}}};
        
        \draw[color=red , thick, ->] (0,0)--(0,-0.9);
        \draw[color=red , thick, ->] (-2,1)--(-2,1.7);
        \begin{scriptsize}
            \draw[color=blue] (2.8,1.4) node {$(C_f)$};
        \end{scriptsize}
    \end{axis}
 \end{tikzpicture}
\end{document}

答案2

以下是如何在 中执行此操作的草图pgfplots，其中显示了大多数（并非全部）必需的功能。目前，在情节范围tikz内使用超出了我的范围 ;-) 请根据需要进行改进。coordinate system

关键思想：

  • 将所需的 3 个函数计算为数据表（在本例中为手动）
  • 打开主电网
  • 根据需要贴上一些标签和标记

暗示：

  • \addplot ... ;似乎定义了一条路径
  • 这就是为什么你可以在它后面放置任意数量的节点
  • 这是放置文本、符号等的一种方式。

将函数数据保存为fnc.dat：

x   y
0   0
0.1 -0.6605170
0.5 -1.6931472
1.0 -2.
1.5 -1.7836047
2.0 -1.2274113
2.5 -0.4185463
3.0 0.5916737
3.5 1.7693408 
4.0 3.0903549
4.5 4.5366966
5.0 6.0943791
5.5 7.7522290

仅交换数据并保存为inv.dat：

x               y
0               0   
-0.6605170      0.1 
-1.6931472      0.5 
-2.             1.0 
-1.7836047      1.5 
-1.2274113      2.0 
-0.4185463      2.5 
0.5916737       3.0 
1.7693408       3.5 
3.0903549       4.0 
4.5366966       4.5 
6.0943791       5.0 
7.7522290       5.5

因为它非常简单所以我们也保存它lin.dat，或者在 pgfplots 中计算它：

x   y
-3 -3
7  7

结果

\documentclass[10pt,border=3mm,tikz]{standalone}
\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}

 \begin{axis}[
    title={$C_f(x)$ and its inverse},
    xlabel={$x$}, 
    ylabel={$y$}, 
    grid=major,
 ]
    % ~~~ function ~~~~~~~~~~~~~~~~~~~~~~~~
    \addplot[blue ] table {fnc.dat} 
        %~~~  marking zero ~~~~
        node[pos=.38,circle,draw] {}
        % ~~~ putting text ~~~~~~
        node[pos=.38,xshift=5mm,yshift=-3mm] {$(e,0)$}
        % ~~~ name of the curve ~~~~~~~
        [xshift=15pt]%  moving the label to right of curve
        node[pos=.5] {$(C_f)$};
        
    % ~~~ inverse ~~~~~~~~~~~~~~~~~~~~~~~~
    \addplot[black] table {inv.dat}
        [yshift=4mm,xshift=-2mm]
        node[pos=.3] {inverse};
        
    % ~~~ linear ~~~~~~~~~~~~~~~~~~~~~~~~
    \addplot[green!80!black!100] table {lin.dat}% could be calculated 
        %~~~  marking intersection ~~~~
        node[pos=.74,circle,draw] {}
        % ~~~ putting text ~~~~~~
        node[pos=.74,xshift=8mm,yshift=-3mm] {$(e^{1.5},e^{1.5})$}
        % ~~~ name of the curve ~~~~~~~~~~      
        [yshift=3mm]
        node[pos=.45,sloped] {$(\Delta):y = x$};
 \end{axis}
\end{tikzpicture}

\end{document}

答案3

使用tzplot：

反函数：tzfn'

在此处输入图片描述

\documentclass{standalone} 

\usepackage{tzplot}

\begin{document}

\begin{tikzpicture}[font=\scriptsize]
\tzhelplines[thick](-4,-3)(8,8)
\tzaxes(-4,-3)(8,8){$x$}{$y$}
\tzshoworigin
\tzticks{-3,-2,-1,1,2,...,7}{-2,-1,1,2,...,7}
\def\Gx{2*\x*ln(\x)-2*\x}
\def\ray{\x}
\tzfn\ray[-2:7]{$y=x$}[r]
\tzfn[blue]\Gx[.001:5]{$g$}[a]
\tzfn'[red]\Gx[1:5]{$g^{-1}$}[r] % inverse function
\end{tikzpicture}

\end{document}

完整代码

在此处输入图片描述

\documentclass{standalone} 

\usepackage{tzplot}

\begin{document}

\begin{tikzpicture}[font=\scriptsize]
\tzhelplines(-4,-3)(8,8)
\tzaxes(-4,-3)(8,8){$x$}{$y$}
\tzshoworigin
\tzticks{-3,-2,-1,1,2,...,7}{-2,-1,1,2,...,7}
% graphs
\def\Gx{2*\x*ln(\x)-2*\x}
\def\ray{\x}
\tzfn\ray[-2:7]{$y=x$}[r]
\tzfn[blue]"Gx"\Gx[.001:5]{$g$}[a]
\tzfn'[red]"iGx"\Gx[1:5]{$g^{-1}$}[r] % inverse function
% slopes and intersections
\tzXpoint*{Gx}{iGx}(X)
\tzslopeat[<->,red]{Gx}{1}{1cm}
\tzline+[->,red,thick](-2,1)(0,.5) % ad hoc
\tzproj*(1,-2)
\tzXpoint*[blue]{Gx}{axes}(ex){$e$}[b]  % y-intercept
\tzXpoint*[red]{iGx}{axes}(ey){$e$}[l]  % x-intercept
\end{tikzpicture}

\end{document}

答案4

感谢你们

我实际上通过将域名从 更改为domain=-2:6来解决这个问题domain=1:6

我在交换变量时忘记交换域

\documentclass[border=12pt]{standalone}
                            %\usepackage{tikz,tkz-base,tkz-tab}
\usepackage{tikz}
                            %\usetikzlibrary{positioning}
\usepackage{pifont}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}


\begin{document}
 \begin{tikzpicture}[line cap=round,line join=round,%>=triangle 45,
                    x=1cm,y=1cm]
    \begin{axis}[scale=1.3, x=1cm, y=1cm, axis lines=middle, 
                xmin=-3.5, xmax=7, ymin=-3, ymax=6, 
                xtick={-3,...,6}, ytick={-2,...,5},]
                
        % ~~~ function C_f ~~~~~~~~~~~~~~~~
        \draw[line width=1pt, color=blue, smooth, samples=100, domain=0:6.5] plot(\x,{2 *\x * ln \x - 2*\x });
        
       \draw[line width=1pt, color=blue, smooth, samples=100, domain=1:6] plot({2 *\x * ln \x - 2*\x ,\x});

        % ~~~ diagonal ~~~~~~~~~~
        \draw[line width=1pt, color=black, smooth, samples=100, domain=-1.2:6] plot(\x,{\x});
            
        % ~~~ labels, marks etc. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        \draw[color=red , thick,<->] (0.3,-2)--(1.7,-2);
        \draw[line width=0.1pt, color=black, dashed](1,0)|-(0,-2);
        \draw[line width=0.1pt, color=black, dashed](4.4816,0)|-(0,4.4816);
        
        \node[black, rotate=45] at (3,3.4) {$(\Delta):y = x$}; % y = x
        \node[black] at (4.4816,0) {{\tiny \ding{53}}};
        \node[left,yshift=-1mm] at (0,4.6) {{\small $e^{\frac{3}{2}}$}};
        \node[left,yshift=-2.5mm] at (4.8,0) {{\small $e^{\frac{3}{2}}$}};
        \node[left,yshift=-2mm] at (2.9,-0.1) {{\small $e$}};
        \node[black] at (0,4.4816) {{\tiny \ding{53}}};
        \node[black] at (2.7182,0) {{\tiny \ding{53}}};
        
        \draw[color=red , thick, ->] (0,0)--(0,-0.9);
        \draw[color=red , thick, ->] (-2,1)--(-2,1.7);
        \begin{scriptsize}
            \draw[color=blue] (2.8,1.4) node {$(C_f)$};
        \end{scriptsize}
    \end{axis}
 \end{tikzpicture}
\end{document}

在此处输入图片描述

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