[Gzz-commits] manuscripts/Paper Makefile paper.tex zipfarea.mp

[Tuomas J. Lukka]

CVSROOT:        /cvsroot/gzz
Module name:    manuscripts
Changes by:     Tuomas J. Lukka <address@hidden>        03/03/24 11:24:27

Modified files:
        Paper          : Makefile paper.tex zipfarea.mp 

Log message:
        Illustrate zipf's law

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/manuscripts/Paper/Makefile.diff?tr1=1.6&tr2=1.7&r1=text&r2=text
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/manuscripts/Paper/paper.tex.diff?tr1=1.52&tr2=1.53&r1=text&r2=text
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/manuscripts/Paper/zipfarea.mp.diff?tr1=1.2&tr2=1.3&r1=text&r2=text

Patches:
Index: manuscripts/Paper/Makefile
diff -u manuscripts/Paper/Makefile:1.6 manuscripts/Paper/Makefile:1.7
--- manuscripts/Paper/Makefile:1.6      Fri Mar 21 06:37:51 2003
+++ manuscripts/Paper/Makefile  Mon Mar 24 11:24:27 2003
@@ -6,7 +6,7 @@
 LATEXCMD=
 endif
 
-all: pipe.1 perceptual-model.eps pipeline.eps buoyoing.1 buoyoing.5 zipf.ps
+all: pipe.1 perceptual-model.eps pipeline.eps buoyoing.1 buoyoing.5 zipf.ps 
zipfarea.1
        latex "${LATEXCMD} paper"
        BIBINPUTS=..:$$BIBINPUTS bibtex paper
        latex "${LATEXCMD} paper"
@@ -17,6 +17,9 @@
 
 buoyoing.1 buoyoing.5: buoyoing.mp
        TEX=latex mpost buoyoing
+
+zipfarea.1: zipfarea.mp
+       mpost zipfarea.mp
 
 # doesn't work because of .ps screenshots
 pdf: perceptual-model.pdf pipeline.pdf
Index: manuscripts/Paper/paper.tex
diff -u manuscripts/Paper/paper.tex:1.52 manuscripts/Paper/paper.tex:1.53
--- manuscripts/Paper/paper.tex:1.52    Sun Mar 23 15:16:05 2003
+++ manuscripts/Paper/paper.tex Mon Mar 24 11:24:27 2003
@@ -1248,15 +1248,16 @@
 \centering
 %\fbox{\vbox{\vskip 3in}}
 \ifpics
-\includegraphics[width=6cm]{zipf}
+\includegraphics[width=6cm]{zipfarea.1}
 \fi
 \caption{
 \label{fig-zipf}
-Idealized representation of typical document usage pattern according
-to Zipf's law:
-the solid curve represents the access count as a function of rank
-for 100 documents (only the first 15 shown)
-and the dotted curve represents the cumulative proportion of accesses.
+Zipf's law concretized: why remembering 15 textures helps.
+In real life, accesses to documents often follow Zipf's law, meaning that
+some documents get accessed far more often than most.
+Each square represents a document, and the area of each square is scaled
+to its rate of accesses.
+The diagram shows 2000 documents weighted with Zipf's law with exponent 1.1.
 The 15 most important documents account XXX\% of the accesses.
 }
 \end{figure}
Index: manuscripts/Paper/zipfarea.mp
diff -u manuscripts/Paper/zipfarea.mp:1.2 manuscripts/Paper/zipfarea.mp:1.3
--- manuscripts/Paper/zipfarea.mp:1.2   Mon Mar 24 05:20:35 2003
+++ manuscripts/Paper/zipfarea.mp       Mon Mar 24 11:24:27 2003
@@ -1,3 +1,6 @@
+
+prologues := 2;
+
 beginfig(1);
 
 
@@ -5,9 +8,14 @@
 
 path ucircle;
 ucircle := fullcircle shifted (.5,.5);
+show bbox(ucircle);
 
 h = 250;
 
+numeric coords[]x;
+numeric coords[]y;
+numeric coords[]h;
+
 vardef getcoord(expr s, e) =
     save tp;
     save cp;
@@ -20,24 +28,77 @@
     xpart(urcorner(tp))
 enddef;
 
+ncircles = 0;
+
+nsteps = 5;
+
+vardef drawcircle(expr rad, cmi, cmc) =
+    fill unitsquare scaled rad shifted (cmi,cmc) withcolor (uniformdeviate(1), 
uniformdeviate(1), uniformdeviate(1));
+    draw unitsquare scaled rad shifted (cmi,cmc) withpen pencircle scaled 1pt;
+enddef;
+
 vardef addcircle(expr rad) =
     save cmi, cmc;
     save cur;
-    cmi := 1000;
-    for i = 0 upto h / rad:
-       cur := getcoord(i*rad, (i+1)*rad);
-%      show i,cur;
-       if cur < cmi:
-           cmi := cur;
-           cmc := i * rad;
-       fi
+    save rmost;
+    save npie;
+    numeric cmi;
+    numeric rmost[];
+    numeric npie;
+    npie := h / (rad/nsteps) - nsteps + 1;
+    for j = 0 upto npie:
+       rmost[j] := 0; 
     endfor;
-    draw ucircle scaled rad shifted (cmi,cmc);
+    for i = 1 upto ncircles:
+       for j = floor(coords[i].y / (rad/nsteps) - nsteps + 1) upto 
floor((coords[i].y+coords[i].h) / (rad/nsteps)):
+%          show "LOOP:",i, coords[i].x,rmost[j];
+           if (j >= 0) and (j <= npie):
+               if (rmost[j] < coords[i].x):
+    %          show "SET";
+                   rmost[j] := coords[i].x;
+               fi;
+           fi
+       endfor
+    endfor;
+    cmi := 2000;
+    for j = 0 upto npie:
+%      show cmi;
+%      show rmost[j];
+       if (not known cmi) or (cmi > rmost[j]):
+           cmi := rmost[j];
+           cmc := j * (rad/nsteps);
+       fi;
+    endfor;
+
+    drawcircle(rad, cmi, cmc);
+
+    ncircles := ncircles +1;
+    coords[ncircles].x := cmi + rad;
+    coords[ncircles].y := cmc;
+    coords[ncircles].h := rad;
+%    show "Placed",cmi,cmc,rad;
+enddef;
+
+curx = 0;
+cury = 0;
+maxrad = 0;
+
+vardef addvarcircle(expr rad) = 
+    if cury + rad > h:
+       curx := curx + maxrad;
+       cury := 0;
+       maxrad := 0;
+    fi;
+    drawcircle(rad, curx, cury);
+    if rad > maxrad:
+       maxrad := rad;
+    fi;
+    cury := cury + rad;
 enddef;
 
-for i = 1 upto 100:
+for i = 1 upto 2000:
 %    draw fullcircle scaled (mrad/((i**1.01)**.5)) shifted (.02*mrad*i,100);
-    addcircle(mrad / ((i**1.01)**.5));
+    addvarcircle(mrad / ((i**1.05)**.5));
 endfor;
 
 picture p;