File:AuZexLamPlotT.jpg
Explicit plot of functions AuZex (thick black curve) and LambertW (thin red curve).
See AuZex approximation for details.
C++ generator of curves
// Files Tania.cin, LambertW.cin, AuZex.cin, ado.cin should be loaded to the working directory in order to compile the code below.
#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.)
#include "Tania.cin" // need for LambertW #include "LambertW.cin" // need for AuZex // #include "SuZex.cin" #include "AuZex.cin" #include "ado.cin" #define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y); #define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; FILE *o;o=fopen("AuZexLam.eps","w"); ado(o,1204,404);
fprintf(o,"2 202 translate\n 100 100 scale\n");
fprintf(o,"1 setlinejoin 2 setlinecap\n");
for(n=-4;n<3;n++) {M(0,n)L(12,n)}
for(m=0;m<13;m++) {M(m,-2)L(m,2)}
M(M_E,0)L(M_E,1) fprintf(o,".01 W S\n");
// DO(m,1300){y=-2. +.01*m; x=Re(suzex(y)); if(m==0) M(x,y) else L(x,y) if(x>12) break;} fprintf(o,".06 W 0 1 1 RGB S\n");
DO(m,700){x=.38 +.02*m; y=Re(auzex(x)); if(m==0) M(x,y) else L(x,y) if(x>12.03) break;} fprintf(o,".023 W 0 0 0 RGB S\n");
DO(m,700){x=-.03 +.02*m; y=Re(LambertW(x)); if(m==0) M(x,y) else L(x,y) if(x>12.03) break;} fprintf(o,".011 W 1 0 0 RGB S\n");
fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o);
system("epstopdf AuZexLam.eps");
system( "open AuZexLam.pdf"); //for macintosh
getchar(); system("killall Preview"); // For macintosh
}
Latex generator of labels
% Copyleft 2012 by Dmitrii Kouznetsov%<br>
\documentclass[12pt]{article}
\usepackage{geometry}
\usepackage{graphicx} %<br
\usepackage{rotating}
\paperwidth 1208pt
\paperheight 405pt
\topmargin -108pt
\oddsidemargin -73pt
\textwidth 1300pt
\textheight 900pt
\pagestyle {empty}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing {\includegraphics}
\parindent 0pt
\begin{document}%<br>
{\begin{picture}(1204,404)
\put(0,0){\ing{AuZexLam}} \put(13,387){\sx{2.9}{$y$}}
%\put(209,378){\sx{3.1}{$\mathrm e$}}
\put(13,292){\sx{2.8}{$1$}}
\put(13,192){\sx{2.8}{$0$}}
\put(-1,092){\sx{2.8}{$-\!1$}}
\put(267,184){\sx{2.9}{$\mathrm e$}}
\put( 95, 176){\sx{2.8}{$1$}}
\put(195,176){\sx{2.8}{$2$}}
\put(295,176){\sx{2.8}{$3$}}
\put(396,176){\sx{2.8}{$4$}}
\put(496,176){\sx{2.8}{$5$}}
\put(597,176){\sx{2.8}{$6$}}
\put(698,176){\sx{2.8}{$7$}}
\put(798,176){\sx{2.8}{$8$}}
\put(898,176){\sx{2.8}{$9$}}
\put(990,176){\sx{2.8}{$10$}}
\put(1090,176){\sx{2.8}{$11$}}
% \put(300,-9){\sx{2.5}{$0$}}
\put(1189,180){\sx{2.9}{$x$}}
\put(25,240){\sx{2.7}{\rot{17}$y\!=\!\mathrm{LambertW}(x)$\ero}}
\put(914,334){\sx{3.4}{$y\!=\!\mathrm{AuZex}(x)$}}
\end{picture}
}
\end{document}
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:50, 20 June 2013 | | 2,508 × 841 (169 KB) | Maintenance script (talk | contribs) | Importing image file |
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