使用 tikz 和 pgfplots 包绘制近似函数

Question

我怎样才能正确地绘制10^9*ln(1+10^{-9}/(x+2))从-1到的图1？

\documentclass{article}
    \usepackage{tikz}
    \usepackage{pgfplots}
    \begin{document}
    \begin{tikzpicture}[scale=0.7]
        \begin{axis}[
            xmin=-2.1,
            xmax=1.39,
            ymin=-1.25,
            ymax=1.25,
            unit vector ratio={1 1},
            axis lines=center,
            %axis equal image,
            xlabel={$x$},
            xlabel style={anchor=west},
            ylabel={$f(x)$},
            ylabel style={anchor=south},
            samples=200,
            ]
%
            \addplot[
                color=blue,
                domain=-1:1,
                ] {1/(x+2)};
            \addplot[
                color=red,
                domain=-1:1,
                ] {10^9*ln(1+1/(10^9*(x+2))};
        \end{axis}
    \end{tikzpicture}
\end{document}

Answer 1

正如 caverac 指出的那样他的回答这很可能是因为 (La)TeX 的计算限制。除了使用 gnuplot 作为计算引擎外，您还可以使用 Lua，方法是添加compat1.12 或更高级别，并使用 LuaLaTeX 进行编译，以获得正确/所需的结果。

% used PGFPlots v1.16
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
    % use this `compat' level or higher to make use of Lua for the computations
    % (in case it is used LuaLaTeX as engine)
    \pgfplotsset{compat=1.12}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[
        xmin=-2.1,
        xmax=1.39,
        ymin=-1.25,
        ymax=1.25,
        unit vector ratio={1 1},
        axis lines=center,
        %axis equal image,
        xlabel={$x$},
        xlabel style={anchor=west},
        ylabel={$f(x)$},
        ylabel style={anchor=south},
        samples=51,     % (decreased number of samples)
        domain=-1:1,    % (moved common `\addplot' option here)
        no markers,     % (you used the default colors, thus adding this options
                        %  gives the same result)
    ]
        % (removed optional `\addplot' arguments)
        \addplot {1/(x+2)};
        % (slightly rewritten formula (and balanced braces))
        \addplot {1e9 * ln(1 + 1e-9/(x+2))};
    \end{axis}
\end{tikzpicture}
\end{document}

Answer 2

我认为问题在于精度，您可以gnuplot使用更精确的数值引擎

\documentclass{article}

\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}

\begin{document}
  \begin{tikzpicture}[scale=0.7]
    \begin{axis}[
      xmin=-2.1,
      xmax=1.39,
      ymin=-1.25,
      ymax=1.25,
      unit vector ratio={1 1},
      axis lines=center,
      %axis equal image,
      xlabel={$x$},
      xlabel style={anchor=west},
      ylabel={$f(x)$},
      ylabel style={anchor=south},
      samples=200,
      ]
      %
      \addplot[
        color=blue,
        domain=-1:1,
      ] {1/(x+2)};
      \addplot gnuplot[
        color=red,
        domain=-1:1,
      ] {10^9*log(1+10^(-9)/(x+2))};
    \end{axis}
  \end{tikzpicture}
\end{document}