Ygthkb

I would like to plot a bump function in a similar way as its done in Loring W. Tu's Book 'An introduction to Manifolds' (page 129, fig. 13.4), however it never quite works the way I want. Here is my MWE:

documentclass[border=10pt]{standalone} 



usepackage{pgfplots}

usepackage{tikz}

pgfplotsset{%

every x tick/.style={black, thick},

every y tick/.style={black, thick},

every tick label/.append style = {font=footnotesize},

every axis label/.append style = {font=footnotesize},

compat=1.12

  }

begin{document}

begin{tikzpicture}

begin{axis}[xmin=-1.2, xmax=2, ymin=-0.7, ymax=1.2,



 xtick = {-1,0,1}, ytick = { 1},

 scale=0.4, restrict y to domain=-1.5:1.2,

 axis x line=center, axis y line= center,

 samples=40]





 addplot[black, samples=100, smooth, domain=-1.2:0, thick]

   plot (x, { 0 });



 addplot[black, samples=100, smooth, domain=0:1, thick, label={x}]

   plot (x, { exp( -1/x)/(exp (-1/x)+exp(1/(x-1))) });





 addplot[black, thick, samples=100, smooth, domain=1:2]

   plot (x, {1} );



 end{axis}

 end{tikzpicture}



  end{document}

My main problem with this result is, that the "plateau" is already attained before x=1, which really doesn't look like it's right. Changing sample sizes to higher than 100 will immediately yield dimension errors. Any tips?

Welcome to TeX.SE! I do not have that book but often people use tanh for that.

documentclass[border=10pt]{standalone} 



usepackage{pgfplots}

usepackage{tikz}

pgfplotsset{%

every x tick/.style={black, thick},

every y tick/.style={black, thick},

every tick label/.append style = {font=footnotesize},

every axis label/.append style = {font=footnotesize},

compat=1.12

  }

begin{document}

begin{tikzpicture}

begin{axis}[xmin=-1.2, xmax=2, ymin=-0.7, ymax=1.2,

 xtick = {-1,0,1}, ytick = { 1},

 scale=0.4, restrict y to domain=-1.5:1.2,

 axis x line=center, axis y line= center,

 samples=40]





 addplot[black, samples=100, smooth, domain=-1.2:2, thick]

   plot (x, {0.5*(1+tanh(5*(x-0.5)))});

end{axis}

end{tikzpicture}

end{document}

Of course, you can vary the width of the step by playing with the prefactor, which is 5 above.

documentclass[border=10pt,tikz]{standalone} 

usepackage{pgfplots}

pgfplotsset{%

every x tick/.style={black, thick},

every y tick/.style={black, thick},

every tick label/.append style = {font=footnotesize},

every axis label/.append style = {font=footnotesize},

compat=1.12

  }

begin{document}

foreach X in {2,2.2,...,6,5.8,5.6,...,2.2}

{begin{tikzpicture}

begin{axis}[xmin=-1.2, xmax=2, ymin=-0.7, ymax=1.2,

 xtick = {-1,0,1}, ytick = { 1},

 scale=0.4, restrict y to domain=-1.5:1.2,

 axis x line=center, axis y line= center,

 samples=40,

 title={$f(x)=left[1+tanhbigl(

 pgfmathprintnumber[precision=1,fixed,zerofill]{X}(x-1/2)bigr)right]/2$}]



 addplot[black, samples=100, smooth, domain=-1.2:2, thick]

   plot (x, {0.5*(1+tanh(X*(x-0.5)))});

end{axis}

end{tikzpicture}}

end{document}

The plots in proferred answers do not look like what I understand to be a bump function; rather, the plots of the derivatives of the indicated functions would be bump functions. The following directly produces a bump function plot, with support the interval $[-1,1]$:

documentclass[border=10pt]{standalone} 



usepackage{pgfplots}

usepackage{tikz}

pgfplotsset{%

  every x tick/.style={black, thin},

  every y tick/.style={black, thick},

  every tick label/.append style = {font=footnotesize},

  every axis label/.append style = {font=footnotesize},

  compat=1.12

 }

begin{document}

begin{tikzpicture}

begin{axis}[xmin=-1.2, xmax=1.2, ymin=-0.2, ymax=1.2,

  xtick = {-1,0,1}, ytick = { 1},

  scale=0.4, restrict y to domain=-0.2:1.2,

  axis x line=center, axis y line= center,

  samples=40]

addplot[black, samples=100, smooth, domain=-1.2:-1, thick]

   plot (x, { 0 });

addplot[black, samples=100, smooth, domain=-1:1, thick, label={x}]

   plot (x, {exp(1-1/(1-x^2)});

addplot[black, thick, samples=100, smooth, domain=1:1.2]

   plot (x, {0} );

end{axis}

end{tikzpicture}



end{document}

(I'm unsure how to avoid the apparent gap in the graph immediately to the right of $x=-1$.)