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.

#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 zex(z_type z) { return z*exp(z);}

z_type suzexo(z_type z){ int n,m; z_type L=log(-z); z_type c[21]; z_type s;
#include "SuZexCoef20.cin"
c[0]=-1.; c[1]=.5*L;
for(n=2;n<21;n++){ s=a[n][n]; 
                   for(m=n-1; m>=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; }

 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
*/

#include "SuZex.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, 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
}

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