File:TaniaPlot.png

Summary

Title / Description	Explicit plot of the Tania function, ${\displaystyle y=\mathrm {Tania} (x)}$
Citizendium author & Copyright holder	Copyright © Dmitrii Kouznetsov. See below for licence/re-use information.
Date created	2011 September 22
Country of first publication	Japan
Notes	You can edit this page and add notes here which may be useful to people who wish to re-use this media.
Other versions	http://tori.ils.uec.ac.jp/TORI/index.php/File:TaniaPlot.png
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Licensing

   

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Source

C++ generator of the curve

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
using namespace std;
#include <complex>
typedef complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)

z_type ArcTania(z_type z) {return z + log(z) - 1. ;}

z_type ArcTaniap(z_type z) {return 1. + 1./z ;}

z_type TaniaTay(z_type z) { int n; z_type s;
s=1.+z*(.5+z*(1./16.+z*(-1./192.+z*(-1./3072.+z*(1.3/6144.+z*(-4.7/147456.
//+z*(7.3/4128768.) //some reserve term
)))))); DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }

z_type TaniaNega(z_type z){int n;z_type s=exp(z-exp(z)+1.);
DO(n,4) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }

z_type TaniaBig(z_type z){int n;z_type s=z; s=z-log(s)+1.;
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }

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);
s=-1.+t*(3.+t*(-3.+t*(.75+t*(.3+t*(.9/16.+t*(-.3/7.+t*(-12.51/224. //+t*(-.9/28.)
)))))));
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }

z_type Tania(z_type z){ z_type t;
if( fabs(Im(z))< M_PI && Re(z)<-2.51) return TaniaNega(z);
if( abs(z)>7. || Re(z)>3.8 ) return TaniaBig(z);
if( Im(z) > .7 ) return TaniaS(z);
if( Im(z) < -.7) return conj(TaniaS(conj(z)));
return TaniaTay(z);
}

void ado(FILE *O, int X, int Y)
{      fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%');
       fprintf(O,"%c%cBoundingBox: 0 0 %d %d\n",'%','%',X,Y);
       fprintf(O,"/M {moveto} bind def\n");
       fprintf(O,"/L {lineto} bind def\n");
       fprintf(O,"/S {stroke} bind def\n");
       fprintf(O,"/s {show newpath} bind def\n");
       fprintf(O,"/C {closepath} bind def\n");
       fprintf(O,"/F {fill} bind def\n");
       fprintf(O,"/o {.1 0 360 arc C S} bind def\n");
       fprintf(O,"/times-Roman findfont 20 scalefont setfont\n");
       fprintf(O,"/W {setlinewidth} bind def\n");
       fprintf(O,"/RGB {setrgbcolor} bind def\n");}

#define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);

main(){ int j,k,m,n; DB x,y, a;
FILE *o;o=fopen("taniaplot.eps","w");ado(o,808,408);
fprintf(o,"404 4 translate\n 100 100 scale\n");
for(m=-4;m<5;m++){ M(m,0)L(m,4)}
for(n=0;n<5;n++){ M(-4,n)L(4,n)}
fprintf(o,".01 W 0 0 0 RGB S\n");
// for(n=0;n<380;n++){y=.02+.01*n; x=ArcTania(y); if(n==0)M(x,y) else L(x,y) }
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) }
fprintf(o,".03 W 0 .5 0 RGB S\n");
fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
      system("epstopdf taniaplot.eps");
      system(    "open taniaplot.pdf"); //these 2 commands may be specific for macintosh
getchar(); system("killall Preview");// if run at another operational sysetm, may need to modify
}

Latex generator of the lables

% Gerenator of TaniaPlot.png  

% Save the paragraph below as  TaniaPlot.tex  

% After the latexing and generation TaniaPlot.pdf  

%> convert TaniaPlot.pdf TaniaPlot.png  

% Copyleft 2011 by Dmitrii Kouznetsov  

\documentclass[12pt]{article} % 

\usepackage{geometry} % 

\usepackage{graphicx} % 

\usepackage{rotating} % 

\paperwidth 810pt % 

\paperheight 426pt % 

\topmargin -103pt % 

\oddsidemargin -96pt % 

\textwidth 1200pt % 
 
\textheight 600pt % 

\pagestyle {empty} % 

\newcommand \sx {\scalebox} % 

\newcommand \rot {\begin{rotate}} % 
 
\newcommand \ero {\end{rotate}} % 

\newcommand \ing {\includegraphics} % 

\begin{document} % 

\sx{1}{ \begin{picture}(808,410) % 

\put(1,9){\ing{taniaplot}} % 

\put(388,394){\sx{2.8}{$y$}} % 

\put(388,303){\sx{2.8}{$3$}} % 

\put(388,203){\sx{2.8}{$2$}} % 

\put(388,103){\sx{2.8}{$1$}} % 

\put( 86,-9){\sx{2.5}{$-3$}} % 

\put(186,-9){\sx{2.5}{$-2$}} % 

\put(286,-9){\sx{2.5}{$-1$}} % 

\put(400,-9){\sx{2.5}{$0$}} % 

\put(500,-9){\sx{2.5}{$1$}} % 

\put(600,-9){\sx{2.5}{$2$}} % 

\put(700,-9){\sx{2.5}{$3$}} % 

\put(796,-9){\sx{2.5}{$x$}} % 

\put(560,214){\rot{37}\sx{4}{$y=\mathrm{Tania}(x)$}\ero} % 

\end{picture} % 

} % 

\end{document}