[Tex/LaTex] Plotting greatest integer function (floor)

pstrickstikz-pgf

How can one plot y=1/floor(1/x) in pstricks? where floor is the greatest integer function. i.e. floor(2.5)=2 and floor(-0.5)=-1.

I need to generate something like what I generated in sage:

enter image description here

But I do not want vertical lines; I also need to put some disk and fdisk for the points.

Best Answer

Somewhat crudely done with MetaPost. Coding can certainly be optimized.

EDIT I've improved the coding (I think). The result remains the same, except for the filled dots which are now really of the same size than the empty ones.

input latexmp; setupLaTeXMP(textextlabel=enable, mode=rerun);

vardef dot expr z =
  image(filldraw fullcircle scaled 3bp shifted z;)
enddef;

vardef emptydot expr z = 
  save circle; path circle; circle = fullcircle scaled 3bp shifted z;
  unfill circle; circle
enddef;

beginfig(1);
n := 200;
u := 8cm;
xmax := 1.1; ymax := xmax;
drawarrow -(u*xmax, 0) -- (u*xmax, 0);
drawarrow -(0, u*ymax) -- (0, u*ymax);
label.bot("$x$", (u*xmax, 0)); label.lft("$y$", (0, u*ymax));

drawoptions(withcolor red);
draw (-xmax*u, -u) -- (-u, -u);
for i = 1 upto n:
  draw ((u/(i+1), u/i) -- (u/i, u/i)); draw (-u/i, -u/(i+1)) -- (-u/(i+1), -u/(i+1));
endfor;

drawoptions(withcolor black);
draw (u, 0) -- (u, u) dashed evenly; draw (0, u) -- (u/2, u) -- (u/2, 0) dashed evenly;
draw dot(u, u) withcolor red; draw emptydot(u/2, u) withcolor red;
label.bot("$1$", (u, 0)); label.bot ("$\frac{1}{2}$", (u/2, 0)); label.lft("$1$", (0, u));

draw (-u, 0) -- (-u, -u) -- (0, -u) dashed evenly;
draw dot(-u, -u) withcolor red;
label.top("$-1$", (-u, 0)); label.rt("$-1$", (0, -u)); 

for i = 2 upto 5:
  draw (u/(i+1), 0) -- (u/(i+1), u/i) -- (0, u/i) dashed evenly;
  draw dot(u/i, u/i) withcolor red; draw emptydot(u/(i+1), u/i) withcolor red;
  label.bot("$\frac{1}{" & decimal (i+1) & "}$", (u/(i+1), 0));
  label.lft("$1/" & decimal i & "$", (0, u/i));
  %
  draw (-u/i, 0) -- (-u/i, -u/i) -- (0, -u/i) dashed evenly;
  draw dot(-u/i, -u/i) withcolor red; draw emptydot(-u/(i-1), -u/i) withcolor red;
  label.top("$\frac{-1}{" & decimal i & "}$", (-u/i, 0));
  label.rt("$-1/" & decimal i & "$", (0, -u/i));
endfor;

draw emptydot(origin) withcolor red; label.lrt("$O$", origin);
endfig;
end.

enter image description here

`TikZ` Solution:

I believe there are some limitations in using the internal math engine with power type functions (but for some reason works just fine with pgfplots as in the solution below), but if you change your definition from func(\x,\a) = 1.0/(\x^\a) to:

func(\t,\a) = 1.0/(exp((\a)*ln(\t)));

you get (and also added very thick option to \draw):

enter image description here

##Pgfplots Solution:

However, I would recommend that you use pgfplots for graphing. As per Consistently specify a Function and use it for computation and plotting, I would recommend that you use the approach suggest there to define the function:

\def\func(#1,#2){1.0/((#1)^(#2))}

This method will allow you to be able to use this one definition for:

Computation of values to:

Define a piecewise function as in Defining a Piecewise Function for PGFplots,
Compute values of individual points as in this example where I label a specific point given the x value
be able to use it as any other built in math function and define a translation as in the green curve

Graphing using pgfplot
Graphing using pgfplots/gnuplot

enter image description here

\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}

\def\func(#1,#2){1.0/((#1)^(#2))}%

\begin{document}
\begin{tikzpicture}
\begin{axis}[
    domain=0.5:2.0, samples=100,
    every axis plot post/.style= ultra thick]
    \addplot [blue] {\func(x,1.0)};%
    \addplot [red]  {\func(x,2.0)};%
    \addplot [green]{\func(x,0.5)};
\end{axis}
\end{tikzpicture}
\end{document}

[Tex/LaTex] Plotting Trigonometric Functions

Here is something that should get you going.

\documentclass[border=2mm]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
grid=both,
domain=-2*pi:2*pi,
samples=200,
no marks,
xticklabels={-2$\pi$,-1.5$\pi$,...$\pi$,2$\pi$},
xtick={-6.2832,-4.7124,...,6.2832},
x post scale=1.5
]
\addplot {2*sin(deg(x))+0.8*sin(pi*deg(x))};
\end{axis}
\end{tikzpicture}
\end{document}

enter image description here

Best Answer

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[Tex/LaTex] pgf-tikz problem with ‘declare function’

TikZ Solution:

[Tex/LaTex] Plotting Trigonometric Functions

Related Question

`TikZ` Solution: