File:SuZexPlot511T.jpg

Explicit plot of function SuZex in comparison to its transfer function zex$(z)\!=\!z\,\exp(z)$:

$y\!=\!\mathrm{SuZex}(x)$ and

$y\!=\!\mathrm{zex}(x)$

C++ generator of curves
// Files ado.cin. SuZexCoef20.cin, SuZexTay2008co.cin, SuZexTay0co.cin, SuZex.cin

//should be loaded to the working directory in order to compile the code below.

using namespace std; typedef complex z_type;
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x=0; m--){ s*=L; s+=a[n][m]; } c[n]=s; } s=c[20]/z; for(n=19;n>=0;n--){ s+=c[n]; s/=z;} return s; }
 * 1) include "SuZexCoef20.cin"

z_type suzex2008t12(z_type z){ int n,m=80; z_type s; #include "SuZexTay2008co.cin" s=c[m]; for(n=m-1;n>=0;n--){ s*=z; s+=c[n];} return s;}

z_type SuZexTay0(z_type z){ int n,m=96; z_type s; #include "SuZexTay0co.cin" s=SuZexTay0co[m]; for(n=m-1;n>=0;n--){ s*=z; s+=SuZexTay0co[n];} return s;}

z_type suzex(z_type z){int m,n; z_type s; if( abs(z) < 1.6 )                  return SuZexTay0(z) ; // I made the Taylor expansion for this case if( Re(z)>0 && fabs(Im(z))<1.5){n=int(Re(z)+.5); s=SuZexTay0(z-(0.+n)); DO(m,n) s=zex(s); return s;} z+=-1.1259817765745026;    // WARNING! ARGUEMENT CHANGES ITS VALUE! if( abs(z+12.) < 8.1 )              return suzex2008t12(z+12.) ; // I made the Taylor expansion for this case if( Re(z)<-12. || fabs(Im(z)) > 8. ) return suzexo(z); // definitely, |z|>8 n= int(Re(z)+12.); s=suzex2008t12(z+12.-(0.+n)); DO(m,n) s=zex(s); return s; } // Copyleft 2012 by Dmitrii Kouznetsov */


 * 1) include "SuZex.cin"
 * 1) include "ado.cin"
 * 2) define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
 * 3) 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, cu,cd; DB x1=-1.1259817765745026; //DO(n,8){ y=Re(suzex(x1)); x=y-1.; x1+=-1.2*x; printf("%18.16f %18.16f\n", x1,y);} getchar; FILE *o;o=fopen("SuZexPlot511.eps","w"); ado(o,504,1104); fprintf(o,"303 101 translate\n 100 100 scale\n"); fprintf(o,"1 setlinejoin 2 setlinecap\n"); for(m=-3;m<3;m++) {M(m,-1)L(m,16)} for(n=-1;n<17;n++) {M(-3,n)L(2,n)} M(0,M_E)L(1,M_E) M(0,-1./M_E)L(-1,-1./M_E) fprintf(o,".006 W S\n"); // DO(m,130){x=-3.02 +.1*m; y=Re(suzex(x)); if(m==0) M(x,y) else L(x,y) if(y>10) break;} fprintf(o,".03 W 0 0 1 RGB S\n"); // DO(m,130){x=-10.+.1*m; y=-1./(x+x1);  if(m==0) M(x,y) else L(x,y) if(y>10) break;}  fprintf(o,".01 W 0 0 0 RGB S\n"); // DO(m,130){x=-2.+.1*m; y=exp(x);      if(m==0) M(x,y) else L(x,y) if(y>10) break;}  fprintf(o,".01 W .5 0 0 RGB S\n"); DO(m,130){x=-3.02+.1*m; y=Re(zex(x));   if(m==0) M(x,y) else L(x,y) if(y>10) break;}  fprintf(o,".01 W 0 0 0 RGB S\n"); // fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o); system("epstopdf SuZexPlot511.eps"); system(   "open SuZexPlot511.pdf"); //for macintosh getchar; system("killall Preview"); // For macintosh }

Latex generator of labels
% % % file SuZexPlot.pdf should be generated with the code above in order to compile the Latex document below. % % Copyleft 2012 by Dmitrii Kouznetsov % \documentclass[12pt]{article} % \usepackage{geometry} % \usepackage{graphicx} % \usepackage{rotating} % \paperwidth 508pt % \paperheight 1104pt % \topmargin -96pt % \oddsidemargin -81pt % \textwidth 1200pt % \textheight 1200pt % \pagestyle {empty} % \newcommand \sx {\scalebox} % \newcommand \rot {\begin{rotate}} % \newcommand \ero {\end{rotate}} % \newcommand \ing {\includegraphics} % \parindent 0pt% \pagestyle{empty} % \begin{document} % \begin{picture}(1202,1102) % %\put(10,10){\ing{ExpQ2plot}} % \put(322,1090){\sx{4}{$y$}} % \put(292,372){\sx{4}{$\mathrm e$}} % \put(315, 62){\sx{4}{$-\!1/\mathrm e$}} % \put(325,998){\sx{4}{$9$}} % \put(325,898){\sx{4}{$8$}} % \put(325,798){\sx{4}{$7$}} % \put(325,698){\sx{4}{$6$}} % \put(325,598){\sx{4}{$5$}} % \put(325,498){\sx{4}{$4$}} % \put(325,398){\sx{4}{$3$}} % \put(325,298){\sx{4}{$2$}} % \put(325,198){\sx{4}{$1$}} % %\put(325,098){\sx{4}{$0$}} % % \put(078,116){\sx{4}{$-\!2$}} % \put(178,116){\sx{4}{$-\!1$}} % \put(304,116){\sx{4}{$0$}} % \put(404,116){\sx{4}{$1$}} % \put(490,116){\sx{4}{$x$}} % % \put(12,188){\sx{4}{\rot{0}$y\!=\!\mathrm{SuZex}(x)$\ero}} % \put(358,162){\sx{4}{\rot{0}$y\!=\!x\mathrm{e}^x$\ero}} % %\put(10,10){\ing{ExpQ2plot}} % \put(10,10){\ing{SuZexPlot511}} % \end{picture} % \end{document} % %