pgfplots 能否绘制诸如 $f(x) = x^2 \sin(1/x) + x/2$ 之类的函数？

Question

我试图在区间 $[-0.05,0.05]$ 上绘制标题中描述的函数，但我得到的只是一条直线：

这是我的代码：

\documentclass[a4paper,11pt,finnish]{report}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
    clip=false,
    axis line style = thick,
    axis x line = middle,
    axis y line = middle,
    ticks = none,
    xlabel=$x$,
    xlabel style ={anchor=west},
    ylabel=$y$,
    ylabel style ={anchor=south}
    ]
    \addplot[domain=-0.05:-0.01,samples=1000] {x^2 * sin(1/x) + x/2};
    \addplot[domain=0.01:0.05,samples=1000] {x^2 * sin(1/x) + x/2}
        node [pos = 0.95,above left] {$f(x)$};
    \node at(axis cs: 0,0) [circle,fill,scale=0.3]  {};
\end{axis}
\end{tikzpicture}
\end{document}

我想看看这个间隔内函数的波动情况。这仅仅是精度问题，还是其他问题？

Answer 1

sin使用度数。您可以使用gnuplot（需要-shell-escape）；请注意，对于gnuplot，sin需要弧度。

\documentclass[a4paper,11pt]{report}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
    clip=false,
    axis line style = thick,
    axis x line = middle,
    axis y line = middle,
    ticks = none,
    xlabel=$x$,
    xlabel style ={anchor=west},
    ylabel=$y$,
    ylabel style ={anchor=south}
    ]
    \addplot [domain=-0.05:-0.01,samples=1000] gnuplot {x^2 * sin(1/x) + x/2};
    \addplot [domain=0.01:0.05,samples=1000] gnuplot {x^2 * sin(1/x) + x/2}
        node [pos = 0.95,above left] {$f(x)$};
    \node at(axis cs: 0,0) [circle,fill,scale=0.3]  {};
\end{axis}
\end{tikzpicture}
\end{document}

或者你可以转换成弧度：

\documentclass[a4paper,11pt]{report}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
    clip=false,
    axis line style = thick,
    axis x line = middle,
    axis y line = middle,
    ticks = none,
    xlabel=$x$,
    xlabel style ={anchor=west},
    ylabel=$y$,
    ylabel style ={anchor=south}
    ]
    \addplot [domain=-0.05:-0.01,samples=1000] {x^2 * sin((1/x)r) + x/2};
    \addplot [domain=0.01:0.05,samples=1000] {x^2 * sin((1/x)r) + x/2}
        node [pos = 0.95,above left] {$f(x)$};
    \node at(axis cs: 0,0) [circle,fill,scale=0.3]  {};
\end{axis}
\end{tikzpicture}
\end{document}

Answer 2

与此同时，这里有一种使用 MetaPost 的方法，可能会对它感兴趣，它可以显示它是哪种曲线。为方便起见，代码包含在 LuaLaTeX 程序中。

顺便说一句，无论是使用 PGFplots、MetaPost 还是其他任何工具，都应注意为 x 选择足够小的增量（如果整个 x 轴上的增量相同）。例如，10^(-3) 就不够小。

\documentclass[border=3mm]{standalone}
\usepackage{luatex85, luamplib}
    \mplibsetformat{metafun}
    \mplibnumbersystem{double}
\begin{document}
\begin{mplibcode}
beginfig(1);
    u = 100cm; v = 200cm; 
    xmax = .05; xstep = .05*1E-3; ymax = .0275; 
    drawarrow (-xmax*u, 0) -- (xmax*u, 0); label.bot(btex $x$ etex, (xmax*u, 0));
    drawarrow (0, -ymax*v) -- (0, ymax*v); label.lft(btex $y$ etex, (0, ymax*v));
    path curve;
    curve = function(2, "x", "x**2 * sin(1/x) + .5x", xstep, xmax, xstep) xyscaled (u, v);
    draw curve; draw curve rotated 180; 
endfig;
\end{mplibcode}
\end{document}