PGFPlots – How to Plot a Summation of Cosine Wave Using LuaTeX and luaCode

Question

I need to draw a wave that is the summation of these cosine waves

This is my attempt in LuaLaTeX:

\documentclass{article}

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

\usepackage{luacode}
\begin{luacode*}

function p(x)
    assert(x == math.floor(x), "x must be an integer")
    res = 0
    for W = 0, 4000 do
        res = res + (1/2) * (1 + math.cos(2*math.pi*x*W))
    end
    tex.sprint(res)
end
\end{luacode*}

\begin{document}

\begin{tikzpicture}[
  declare function={p(\n) = \directlua{p(\n)};}
  ]
  \begin{axis}[
    use fpu=false, % very important!
    xlabel=$x$, ylabel=$p(x)$,
    samples at={0,...,21},
    only marks,
    ]
    \addplot {p(x)};
  \end{axis}
\end{tikzpicture}

\end{document}

The shape of the graph I expect held a central absolute maximum, with local maximums that decrease as the central maximum moves away

The graph show nothing

Answer 1

I'm still not one of the cool kidz who use LuaLaTeX these days. This solution will be done in plain LaTeX, i.e. pdflatex.

I used the tikzmath library of TikZ, no PGFPlots needed. Also, I don't know whether you really needed the 1+ in the summation, since it will only shift the graph up, but customise the following as you wish. Maybe \n = 6.

\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{math}

\begin{document}

\begin{tikzpicture}[scale=.5]
    \tikzmath{
        function f(\x, \n) {
            %\y = \n+1;
            \y = 0;
            for \i in {0,...,\n} {
                \y = \y + cos(deg(2 * pi * \x) * \i);
            };
            \y = \y / 2;
            return \y;
        };
    }
    \draw[->] (-5,0) -- (5,0) node[below] {\(x\)};
    \draw[->] (0,-1) -- (0,4) node[left] {\(p(x)\)};
    \draw[domain=-4:4, samples=201, smooth] plot (\x, {f(\x,6)});
\end{tikzpicture}

\end{document}

---

Answer to comment: This should actually work, you only need to add use fpu=false, as you said (see also this question).

\documentclass[convert]{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{math}

\begin{document}

\begin{tikzpicture}[scale=.5]
    \tikzmath{
        function f(\x, \n) {
            %\y = \n+1;
            \y = 0;
            for \i in {0,...,\n} {
                \y = \y + cos(deg(2 * pi * \x) * \i);
            };
            \y = \y / 2;
            return \y;
        };
    }
    \begin{axis}[use fpu=false]
        \addplot[domain=-4:4, samples=201] {f(x,6)};
    \end{axis}
\end{tikzpicture}

\end{document}