imported>Dmitrii Kouznetsov |
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| == Summary == | | == Summary == |
| {{Image_Details|user
| | Importing file |
| |description = Explicit plot of the [[Tania function]], <math>y=\mathrm{Tania}(x)</math>
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| |author = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
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| |date-created = 2011 September 22
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| |pub-country = Japan
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| |notes
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| |versions = http://tori.ils.uec.ac.jp/TORI/index.php/File:TaniaPlot.png
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| }}
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| == Licensing ==
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| {{CC|by|3.0}}
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| | |
| ==Source==
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| === [[C++]] generator of the curve===
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| #include <math.h>
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| #include <stdio.h>
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| #include <stdlib.h>
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| #define DB double
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| #define DO(x,y) for(x=0;x<y;x++)
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| using namespace std;
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| #include <complex>
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| typedef complex<double> z_type;
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| #define Re(x) x.real()
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| #define Im(x) x.imag()
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| #define I z_type(0.,1.)
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| | |
| z_type ArcTania(z_type z) {return z + log(z) - 1. ;}
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| z_type ArcTaniap(z_type z) {return 1. + 1./z ;}
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| z_type TaniaTay(z_type z) { int n; z_type s;
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| s=1.+z*(.5+z*(1./16.+z*(-1./192.+z*(-1./3072.+z*(1.3/6144.+z*(-4.7/147456.
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| //+z*(7.3/4128768.) //some reserve term
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| )))))); DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
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| z_type TaniaNega(z_type z){int n;z_type s=exp(z-exp(z)+1.);
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| DO(n,4) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
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| z_type TaniaBig(z_type z){int n;z_type s=z; s=z-log(s)+1.;
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| DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
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| z_type TaniaS(z_type z){int n; z_type s,t=z+z_type(2.,-M_PI);t*=2./9.; t=I*sqrt(t);
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| s=-1.+t*(3.+t*(-3.+t*(.75+t*(.3+t*(.9/16.+t*(-.3/7.+t*(-12.51/224. //+t*(-.9/28.)
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| )))))));
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| DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
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| z_type Tania(z_type z){ z_type t;
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| if( fabs(Im(z))< M_PI && Re(z)<-2.51) return TaniaNega(z);
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| if( abs(z)>7. || Re(z)>3.8 ) return TaniaBig(z);
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| if( Im(z) > .7 ) return TaniaS(z);
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| if( Im(z) < -.7) return conj(TaniaS(conj(z)));
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| return TaniaTay(z);
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| }
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| | |
| void ado(FILE *O, int X, int Y)
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| { fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%');
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| fprintf(O,"%c%cBoundingBox: 0 0 %d %d\n",'%','%',X,Y);
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| fprintf(O,"/M {moveto} bind def\n");
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| fprintf(O,"/L {lineto} bind def\n");
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| fprintf(O,"/S {stroke} bind def\n");
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| fprintf(O,"/s {show newpath} bind def\n");
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| fprintf(O,"/C {closepath} bind def\n");
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| fprintf(O,"/F {fill} bind def\n");
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| fprintf(O,"/o {.1 0 360 arc C S} bind def\n");
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| fprintf(O,"/times-Roman findfont 20 scalefont setfont\n");
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| fprintf(O,"/W {setlinewidth} bind def\n");
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| fprintf(O,"/RGB {setrgbcolor} bind def\n");}
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| | |
| #define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
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| #define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);
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| main(){ int j,k,m,n; DB x,y, a;
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| FILE *o;o=fopen("taniaplot.eps","w");ado(o,808,408);
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| fprintf(o,"404 4 translate\n 100 100 scale\n");
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| for(m=-4;m<5;m++){ M(m,0)L(m,4)}
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| for(n=0;n<5;n++){ M(-4,n)L(4,n)}
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| fprintf(o,".01 W 0 0 0 RGB S\n");
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| // for(n=0;n<380;n++){y=.02+.01*n; x=ArcTania(y); if(n==0)M(x,y) else L(x,y) }
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| for(n=0;n<82;n++){ x=-4.03+.1*n; y=Re(Tania(x)); if(n==0)M(x,y) else L(x,y) }
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| fprintf(o,".03 W 0 .5 0 RGB S\n");
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| fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
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| system("epstopdf taniaplot.eps");
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| system( "open taniaplot.pdf"); //these 2 commands may be specific for macintosh
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| getchar(); system("killall Preview");// if run at another operational sysetm, may need to modify
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| }
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| ===[[Latex]] generator of the lables===
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| % Gerenator of TaniaPlot.png
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| % Save the paragraph below as TaniaPlot.tex
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| % After the latexing and generation TaniaPlot.pdf
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| %> convert TaniaPlot.pdf TaniaPlot.png
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| % Copyleft 2011 by Dmitrii Kouznetsov
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| \documentclass[12pt]{article} %
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| \usepackage{geometry} %
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| \usepackage{graphicx} %
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| \usepackage{rotating} %
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| \paperwidth 810pt %
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| \paperheight 426pt %
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| \topmargin -103pt %
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| \oddsidemargin -96pt %
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| \textwidth 1200pt %
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| \textheight 600pt %
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| \pagestyle {empty} %
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| \newcommand \sx {\scalebox} %
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| \newcommand \rot {\begin{rotate}} %
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| \newcommand \ero {\end{rotate}} %
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| \newcommand \ing {\includegraphics} %
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| \begin{document} %
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| \sx{1}{ \begin{picture}(808,410) %
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| \put(1,9){\ing{taniaplot}} %
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| \put(388,394){\sx{2.8}{$y$}} %
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| \put(388,303){\sx{2.8}{$3$}} %
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| \put(388,203){\sx{2.8}{$2$}} %
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| \put(388,103){\sx{2.8}{$1$}} %
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| \put( 86,-9){\sx{2.5}{$-3$}} %
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| \put(186,-9){\sx{2.5}{$-2$}} %
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| \put(286,-9){\sx{2.5}{$-1$}} %
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| \put(400,-9){\sx{2.5}{$0$}} %
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| \put(500,-9){\sx{2.5}{$1$}} %
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| \put(600,-9){\sx{2.5}{$2$}} %
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| \put(700,-9){\sx{2.5}{$3$}} %
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| \put(796,-9){\sx{2.5}{$x$}} %
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| \put(560,214){\rot{37}\sx{4}{$y=\mathrm{Tania}(x)$}\ero} %
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| \end{picture} %
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| } %
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| \end{document}
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