Plotting a bump function












3















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?










share|improve this question



























    3















    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?










    share|improve this question

























      3












      3








      3








      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?










      share|improve this question














      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?







      tikz-pgf pgfplots






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked Feb 23 at 16:04









      rhodeltarhodelta

      182




      182






















          2 Answers
          2






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          oldest

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          3














          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}


          enter image description here



          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}


          enter image description here






          share|improve this answer


























          • great answer, exactly what I needed thanks a lot!

            – rhodelta
            Feb 23 at 16:23






          • 1





            @ArtificialStupidity Well, fixed it, but do you think that is important here?

            – marmot
            Feb 23 at 16:29






          • 1





            Yes. It is important for me. :-) Thank you for fixing!

            – The Inventor of God
            Feb 23 at 16:59



















          2














          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}


          Bump function



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






          share|improve this answer
























          • The gap will disappear once you plot addplot[black, samples=101, smooth, domain=-1.2:1.2, thick, label={x}] plot (x, {ifthenelse(abs(x)>1,0,exp(1-1/(1-x^2))}); instead of three plots.

            – marmot
            Feb 23 at 17:15











          • @marmot: but why does the middle of the 3-part plot code fail to fill in just to the right of -1, even if I use samples=101 for that portion? Is this just due to a rounding error?

            – murray
            Feb 24 at 22:44











          • No, the function is not defined there. LaTeX does not take limits. So you ask it to evaluate exp(1-1/(1-x^2)) at x=-1 and when LaTeX parses this, it just sees an infinity resulting from -1/(1-x^2) while it does not care whether or not the infinity means that the exponential will vanish. As a consequence, it drops this coordinate, and starts the plot at the next point. If you draw everything in one stretch, it will still drop these coordinates, but then connect two "well-behaved" points, so that there won't be a gap.

            – marmot
            Feb 24 at 22:57











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          2 Answers
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          oldest

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          2 Answers
          2






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          3














          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}


          enter image description here



          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}


          enter image description here






          share|improve this answer


























          • great answer, exactly what I needed thanks a lot!

            – rhodelta
            Feb 23 at 16:23






          • 1





            @ArtificialStupidity Well, fixed it, but do you think that is important here?

            – marmot
            Feb 23 at 16:29






          • 1





            Yes. It is important for me. :-) Thank you for fixing!

            – The Inventor of God
            Feb 23 at 16:59
















          3














          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}


          enter image description here



          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}


          enter image description here






          share|improve this answer


























          • great answer, exactly what I needed thanks a lot!

            – rhodelta
            Feb 23 at 16:23






          • 1





            @ArtificialStupidity Well, fixed it, but do you think that is important here?

            – marmot
            Feb 23 at 16:29






          • 1





            Yes. It is important for me. :-) Thank you for fixing!

            – The Inventor of God
            Feb 23 at 16:59














          3












          3








          3







          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}


          enter image description here



          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}


          enter image description here






          share|improve this answer















          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}


          enter image description here



          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}


          enter image description here







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Feb 23 at 16:37

























          answered Feb 23 at 16:11









          marmotmarmot

          105k4126241




          105k4126241













          • great answer, exactly what I needed thanks a lot!

            – rhodelta
            Feb 23 at 16:23






          • 1





            @ArtificialStupidity Well, fixed it, but do you think that is important here?

            – marmot
            Feb 23 at 16:29






          • 1





            Yes. It is important for me. :-) Thank you for fixing!

            – The Inventor of God
            Feb 23 at 16:59



















          • great answer, exactly what I needed thanks a lot!

            – rhodelta
            Feb 23 at 16:23






          • 1





            @ArtificialStupidity Well, fixed it, but do you think that is important here?

            – marmot
            Feb 23 at 16:29






          • 1





            Yes. It is important for me. :-) Thank you for fixing!

            – The Inventor of God
            Feb 23 at 16:59

















          great answer, exactly what I needed thanks a lot!

          – rhodelta
          Feb 23 at 16:23





          great answer, exactly what I needed thanks a lot!

          – rhodelta
          Feb 23 at 16:23




          1




          1





          @ArtificialStupidity Well, fixed it, but do you think that is important here?

          – marmot
          Feb 23 at 16:29





          @ArtificialStupidity Well, fixed it, but do you think that is important here?

          – marmot
          Feb 23 at 16:29




          1




          1





          Yes. It is important for me. :-) Thank you for fixing!

          – The Inventor of God
          Feb 23 at 16:59





          Yes. It is important for me. :-) Thank you for fixing!

          – The Inventor of God
          Feb 23 at 16:59











          2














          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}


          Bump function



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






          share|improve this answer
























          • The gap will disappear once you plot addplot[black, samples=101, smooth, domain=-1.2:1.2, thick, label={x}] plot (x, {ifthenelse(abs(x)>1,0,exp(1-1/(1-x^2))}); instead of three plots.

            – marmot
            Feb 23 at 17:15











          • @marmot: but why does the middle of the 3-part plot code fail to fill in just to the right of -1, even if I use samples=101 for that portion? Is this just due to a rounding error?

            – murray
            Feb 24 at 22:44











          • No, the function is not defined there. LaTeX does not take limits. So you ask it to evaluate exp(1-1/(1-x^2)) at x=-1 and when LaTeX parses this, it just sees an infinity resulting from -1/(1-x^2) while it does not care whether or not the infinity means that the exponential will vanish. As a consequence, it drops this coordinate, and starts the plot at the next point. If you draw everything in one stretch, it will still drop these coordinates, but then connect two "well-behaved" points, so that there won't be a gap.

            – marmot
            Feb 24 at 22:57
















          2














          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}


          Bump function



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






          share|improve this answer
























          • The gap will disappear once you plot addplot[black, samples=101, smooth, domain=-1.2:1.2, thick, label={x}] plot (x, {ifthenelse(abs(x)>1,0,exp(1-1/(1-x^2))}); instead of three plots.

            – marmot
            Feb 23 at 17:15











          • @marmot: but why does the middle of the 3-part plot code fail to fill in just to the right of -1, even if I use samples=101 for that portion? Is this just due to a rounding error?

            – murray
            Feb 24 at 22:44











          • No, the function is not defined there. LaTeX does not take limits. So you ask it to evaluate exp(1-1/(1-x^2)) at x=-1 and when LaTeX parses this, it just sees an infinity resulting from -1/(1-x^2) while it does not care whether or not the infinity means that the exponential will vanish. As a consequence, it drops this coordinate, and starts the plot at the next point. If you draw everything in one stretch, it will still drop these coordinates, but then connect two "well-behaved" points, so that there won't be a gap.

            – marmot
            Feb 24 at 22:57














          2












          2








          2







          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}


          Bump function



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






          share|improve this answer













          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}


          Bump function



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







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered Feb 23 at 16:57









          murraymurray

          2,1671031




          2,1671031













          • The gap will disappear once you plot addplot[black, samples=101, smooth, domain=-1.2:1.2, thick, label={x}] plot (x, {ifthenelse(abs(x)>1,0,exp(1-1/(1-x^2))}); instead of three plots.

            – marmot
            Feb 23 at 17:15











          • @marmot: but why does the middle of the 3-part plot code fail to fill in just to the right of -1, even if I use samples=101 for that portion? Is this just due to a rounding error?

            – murray
            Feb 24 at 22:44











          • No, the function is not defined there. LaTeX does not take limits. So you ask it to evaluate exp(1-1/(1-x^2)) at x=-1 and when LaTeX parses this, it just sees an infinity resulting from -1/(1-x^2) while it does not care whether or not the infinity means that the exponential will vanish. As a consequence, it drops this coordinate, and starts the plot at the next point. If you draw everything in one stretch, it will still drop these coordinates, but then connect two "well-behaved" points, so that there won't be a gap.

            – marmot
            Feb 24 at 22:57



















          • The gap will disappear once you plot addplot[black, samples=101, smooth, domain=-1.2:1.2, thick, label={x}] plot (x, {ifthenelse(abs(x)>1,0,exp(1-1/(1-x^2))}); instead of three plots.

            – marmot
            Feb 23 at 17:15











          • @marmot: but why does the middle of the 3-part plot code fail to fill in just to the right of -1, even if I use samples=101 for that portion? Is this just due to a rounding error?

            – murray
            Feb 24 at 22:44











          • No, the function is not defined there. LaTeX does not take limits. So you ask it to evaluate exp(1-1/(1-x^2)) at x=-1 and when LaTeX parses this, it just sees an infinity resulting from -1/(1-x^2) while it does not care whether or not the infinity means that the exponential will vanish. As a consequence, it drops this coordinate, and starts the plot at the next point. If you draw everything in one stretch, it will still drop these coordinates, but then connect two "well-behaved" points, so that there won't be a gap.

            – marmot
            Feb 24 at 22:57

















          The gap will disappear once you plot addplot[black, samples=101, smooth, domain=-1.2:1.2, thick, label={x}] plot (x, {ifthenelse(abs(x)>1,0,exp(1-1/(1-x^2))}); instead of three plots.

          – marmot
          Feb 23 at 17:15





          The gap will disappear once you plot addplot[black, samples=101, smooth, domain=-1.2:1.2, thick, label={x}] plot (x, {ifthenelse(abs(x)>1,0,exp(1-1/(1-x^2))}); instead of three plots.

          – marmot
          Feb 23 at 17:15













          @marmot: but why does the middle of the 3-part plot code fail to fill in just to the right of -1, even if I use samples=101 for that portion? Is this just due to a rounding error?

          – murray
          Feb 24 at 22:44





          @marmot: but why does the middle of the 3-part plot code fail to fill in just to the right of -1, even if I use samples=101 for that portion? Is this just due to a rounding error?

          – murray
          Feb 24 at 22:44













          No, the function is not defined there. LaTeX does not take limits. So you ask it to evaluate exp(1-1/(1-x^2)) at x=-1 and when LaTeX parses this, it just sees an infinity resulting from -1/(1-x^2) while it does not care whether or not the infinity means that the exponential will vanish. As a consequence, it drops this coordinate, and starts the plot at the next point. If you draw everything in one stretch, it will still drop these coordinates, but then connect two "well-behaved" points, so that there won't be a gap.

          – marmot
          Feb 24 at 22:57





          No, the function is not defined there. LaTeX does not take limits. So you ask it to evaluate exp(1-1/(1-x^2)) at x=-1 and when LaTeX parses this, it just sees an infinity resulting from -1/(1-x^2) while it does not care whether or not the infinity means that the exponential will vanish. As a consequence, it drops this coordinate, and starts the plot at the next point. If you draw everything in one stretch, it will still drop these coordinates, but then connect two "well-behaved" points, so that there won't be a gap.

          – marmot
          Feb 24 at 22:57


















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