File:Binary entropy plot.svg

From Infogalactic: the planetary knowledge core
Jump to: navigation, search
Original file ‎(SVG file, nominally 300 × 300 pixels, file size: 1 KB)

Summary

<a href="https://en.wikipedia.org/wiki/Information_entropy" class="extiw" title="en:Information entropy">en:Information entropy</a> of a <a href="https://en.wikipedia.org/wiki/Bernoulli_trial" class="extiw" title="en:Bernoulli trial">en:Bernoulli trial</a> X. If X can assume values 0 and 1, entropy of X is defined as H(X) = -Pr(X=0) log2 Pr(X=0) - Pr(X=1) log2 Pr(X=1). It has value if Pr(X=0)=1 or Pr(X=1)=1. The entropy reaches maximum when Pr(X=0)=Pr(X=1)=1/2 (the value of entropy is then 1). The image was created in the following steps. First I have created a DVI version starting from a LaTeX/Pstricks source. Here is the code:

<span class="c">%Plot of information entropy of bernoulli variable</span>
<span class="c">%</span>
<span class="c">%latex binary_entropy_plot; dvips binary_entropy_plot</span>
<span class="c">%open .ps file in gimp, choose strong antialias in both text and graphics,</span>
<span class="c">%resulution 500, color mode, crop, scale to 45%, save as .png</span>
<span class="k">\documentclass</span><span class="na">[12pt]</span><span class="nb">{</span>article<span class="nb">}</span>
<span class="k">\usepackage</span><span class="nb">{</span>pst-plot<span class="nb">}</span>
<span class="k">\begin</span><span class="nb">{</span>document<span class="nb">}</span>
<span class="k">\psset</span><span class="nb">{</span>unit=4cm<span class="nb">}</span>        
<span class="k">\begin</span><span class="nb">{</span>pspicture<span class="nb">}</span>(0,0)(1.01,1)
<span class="k">\psgrid</span><span class="na">[gridlabels=0pt,gridcolor=lightgray,subgriddiv=10,subgridcolor=lightgray]</span>(0,0)(0,0)(1,1)
<span class="k">\newrgbcolor</span><span class="nb">{</span>myblue<span class="nb">}{</span>0 0 0.7<span class="nb">}</span>
<span class="k">\psaxes</span><span class="na">[arrows=->,arrowsize=2pt 4,Dx=0.5,Dy=0.5]</span>(0,0)(0,0)(1.1,1.1)
<span class="k">\psplot</span><span class="na">[plotstyle=curve,plotpoints=100,linewidth=1.8pt,linecolor=myblue]</span><span class="nb">{</span>0.0001<span class="nb">}{</span>0.9999<span class="nb">}{</span>-1 x x log 2 log div mul 1 x sub 1 x sub log 2 log div mul add mul<span class="nb">}</span>
<span class="k">\rput</span>(0.5,-0.22)<span class="nb">{</span><span class="s">$</span><span class="nv">\Pr</span><span class="o">(</span><span class="nb">X</span><span class="o">=</span><span class="m">1</span><span class="o">)</span><span class="s">$</span><span class="nb">}</span>
<span class="k">\rput</span><span class="nb">{</span>90<span class="nb">}</span>(-0.28,0.5)<span class="nb">{</span><span class="s">$</span><span class="nb">H</span><span class="o">(</span><span class="nb">X</span><span class="o">)</span><span class="s">$</span><span class="nb">}</span>
<span class="k">\end</span><span class="nb">{</span>pspicture<span class="nb">}</span>
<span class="k">\end</span><span class="nb">{</span>document<span class="nb">}</span>

compile it with latex to get the DVI. Then it was converted to PS with dvips. Finally it was converted to SVG using <a href="https://en.wikipedia.org/wiki/en:Wikipedia:WikiProject_Electronics/Ps2svg.sh" class="extiw" title="w:en:Wikipedia:WikiProject Electronics/Ps2svg.sh">ps2svg.sh</a>; it needed some post-processing with Inkscape

Licensing

Lua error in package.lua at line 80: module 'strict' not found.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current15:02, 4 January 2017Thumbnail for version as of 15:02, 4 January 2017300 × 300 (1 KB)127.0.0.1 (talk)<p><a href="https://en.wikipedia.org/wiki/Information_entropy" class="extiw" title="en:Information entropy">en:Information entropy</a> of a <a href="https://en.wikipedia.org/wiki/Bernoulli_trial" class="extiw" title="en:Bernoulli trial">en:Bernoulli trial</a> <i>X</i>. If <i>X</i> can assume values 0 and 1, entropy of <i>X</i> is defined as <i>H</i>(<i>X</i>) = -Pr(<i>X</i>=0) log<sub>2</sub> Pr(<i>X</i>=0) - Pr(<i>X</i>=1) log<sub>2</sub> Pr(<i>X</i>=1). It has value if Pr(<i>X</i>=0)=1 or Pr(<i>X</i>=1)=1. The entropy reaches maximum when Pr(<i>X</i>=0)=Pr(<i>X</i>=1)=1/2 (the value of entropy is then 1). The image was created in the following steps. First I have created a DVI version starting from a LaTeX/Pstricks source. Here is the code: </p> <div class="mw-highlight mw-content-ltr" dir="ltr"><pre><span class="c">%Plot of information entropy of bernoulli variable</span> <span class="c">%</span> <span class="c">%latex binary_entropy_plot; dvips binary_entropy_plot</span> <span class="c">%open .ps file in gimp, choose strong antialias in both text and graphics,</span> <span class="c">%resulution 500, color mode, crop, scale to 45%, save as .png</span> <span class="k">\documentclass</span><span class="na">[12pt]</span><span class="nb">{</span>article<span class="nb">}</span> <span class="k">\usepackage</span><span class="nb">{</span>pst-plot<span class="nb">}</span> <span class="k">\begin</span><span class="nb">{</span>document<span class="nb">}</span> <span class="k">\psset</span><span class="nb">{</span>unit=4cm<span class="nb">}</span> <span class="k">\begin</span><span class="nb">{</span>pspicture<span class="nb">}</span>(0,0)(1.01,1) <span class="k">\psgrid</span><span class="na">[gridlabels=0pt,gridcolor=lightgray,subgriddiv=10,subgridcolor=lightgray]</span>(0,0)(0,0)(1,1) <span class="k">\newrgbcolor</span><span class="nb">{</span>myblue<span class="nb">}{</span>0 0 0.7<span class="nb">}</span> <span class="k">\psaxes</span><span class="na">[arrows=->,arrowsize=2pt 4,Dx=0.5,Dy=0.5]</span>(0,0)(0,0)(1.1,1.1) <span class="k">\psplot</span><span class="na">[plotstyle=curve,plotpoints=100,linewidth=1.8pt,linecolor=myblue]</span><span class="nb">{</span>0.0001<span class="nb">}{</span>0.9999<span class="nb">}{</span>-1 x x log 2 log div mul 1 x sub 1 x sub log 2 log div mul add mul<span class="nb">}</span> <span class="k">\rput</span>(0.5,-0.22)<span class="nb">{</span><span class="s">$</span><span class="nv">\Pr</span><span class="o">(</span><span class="nb">X</span><span class="o">=</span><span class="m">1</span><span class="o">)</span><span class="s">$</span><span class="nb">}</span> <span class="k">\rput</span><span class="nb">{</span>90<span class="nb">}</span>(-0.28,0.5)<span class="nb">{</span><span class="s">$</span><span class="nb">H</span><span class="o">(</span><span class="nb">X</span><span class="o">)</span><span class="s">$</span><span class="nb">}</span> <span class="k">\end</span><span class="nb">{</span>pspicture<span class="nb">}</span> <span class="k">\end</span><span class="nb">{</span>document<span class="nb">}</span> </pre></div> <p>compile it with <i>latex</i> to get the DVI. Then it was converted to PS with <i>dvips</i>. Finally it was converted to SVG using <a href="https://en.wikipedia.org/wiki/en:Wikipedia:WikiProject_Electronics/Ps2svg.sh" class="extiw" title="w:en:Wikipedia:WikiProject Electronics/Ps2svg.sh">ps2svg.sh</a>; it needed some post-processing with Inkscape </p>
  • You cannot overwrite this file.

The following 2 pages link to this file:

Retrieved from "https://infogalactic.com/w/index.php?title=File:Binary_entropy_plot.svg&oldid=723431866"