File:Arknemmap11.jpg

#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 std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"

// global varaibles
DB NEMTSOVp=1.; //will be changed by nemsingu
DB NEMTSOVq=1.; //will be changed by nemsingu
DB NEMTSOVR; // Re(s) such that nemtsov'(s)=0
DB NEMTSOVI; // Im(s) such that nemtsov'(s)=0
DB NEMTSOVr; // should be assigned by memsingu
DB NEMTSOVi; // should be assigned by memsingu

z_type nempq(z_type z){ return z*(1.+z*z*(NEMTSOVp+z*NEMTSOVq)); }
z_type nempq1(z_type z){ return 1.+z*z*(3.*NEMTSOVp+z*(4*NEMTSOVq)); }

z_type arcnem0pq(z_type z){
z_type p=NEMTSOVp; // WARNING: global variable
z_type q=NEMTSOVq; // WARNING: global variable
z_type P=p+4.*q*z; z_type PP=P*P; z_type PPP=PP*P;
z_type Q=q-p*p*z; z_type QQ=Q*Q;
z_type r=729.*QQ + 108.*PPP;
z_type R=sqrt(r);
//z_type R=-I*sqrt(-r);
z_type s3=27.*q - 27.*p*p*z + R;
z_type s=pow(s3,1./3.);
z_type B0=pow(2.,1./3.)*P/(q*s);
z_type B1=pow(54.,-1./3.)*s/q ;
z_type B=B1-B0;
z_type c=0.25*p*p/(q*q)+B;
z_type C=sqrt(c);
// z_type C=I*sqrt(-c);
return -.25*p/q - .5*C + .5*sqrt( 0.5*p*p/(q*q) - B + (.25*p*p*p+2.*q*q)/(q*q*q*C) ) ;
}

z_type arcnemRpq(z_type z){
//#include"arcnem2.txt"
z_type p=NEMTSOVp; // WARNING: global variable.
z_type q=NEMTSOVq; // WARNING: global variable.
z_type P=p+4.*q*z; z_type PP=P*P; z_type PPP=PP*P;
z_type Q=q-p*p*z; z_type QQ=Q*Q;
z_type r=729.*QQ + 108.*PPP;
//z_type R=sqrt(r);
z_type R=I*sqrt(-r);
z_type s3=27.*q - 27.*p*p*z + R;
z_type s=pow(s3,1./3.);
z_type B0=pow(2.,1./3.)*P/(q*s);
z_type B1=pow(54.,-1./3.)*s/q ;
z_type B=B1-B0;
z_type c=0.25*p*p/(q*q)+B;
z_type C=sqrt(c);
//z_type C=I*sqrt(-c);
return -.25*p/q - .5*C + .5*sqrt( 0.5*p*p/(q*q) - B + (.25*p*p*p+2.*q*q)/(q*q*q*C) ) ;
}

z_type nemsingu(z_type p,z_type q){ z_type a=sqrt(pow(p,3) + 4.*pow(q,2));
z_type s= z_type(1.,-sqrt(3.)) * ( p + pow(-pow(p,3)+4.*(a-2.*q)*q,1./3.) )
* ( -p + pow(pow(p,3) - 4.*a*q + 8.*pow(q,2),1./3.) )
/ ( 8.*q*pow( -pow(p,3) + 4.*(a-2.*q)*q ,1./3.) ) ;
NEMTSOVp=Re(p); // WARNING: NEMTSOVp is global variable.
NEMTSOVq=Re(q); // WARNING: NEMTSOVq is global variable.
z_type t=nempq(s); // mempq does not use NEMTSOVi .
NEMTSOVR=Re(s); // WARNING: NEMTSOVR is global variable.
NEMTSOVI=Im(s); // WARNING: NEMTSOVI is global variable.
NEMTSOVr=Re(t); // WARNING: NEMTSOVr is global variable.
NEMTSOVi=Im(t); // WARNING: NEMTSOVi is global variable.
return s; // Warning: tested only for real p,q.
}

z_type arknempq(z_type z){ DB x=Re(z); DB y=Im(z);
if(x>NEMTSOVr){ if(y> NEMTSOVi) return arcnemRpq(z);
                if(y<-NEMTSOVi) return conj(arcnemRpq(conj(z))); }
// if(x*x+y*y<.25*(NEMTSOVr*NEMTSOVr+NEMTSOVi*NEMTSOVi)) return arcnemo(z);
return arcnem0pq(z);}

z_type arknem(z_type z){z_type s,t,u; s=arknempq(z); // singe Newton iterate
t=z-nempq(s); u=nempq1(s); if(abs(t)>1.e-20 && abs(u)>.001 ) s+=t/u;
return s;}

//#include "arknem.cin"

int main(){ int Max; int j,k,m,n; DB x,y, p,q,P,Q, t, sr,si,tr,ti; z_type z,c,d,s;
P=1.; // WARNING: here p,q are already in use in two different meanings for graphics.
Q=1.; // WARNING: in this routine, the capital letters are used to denote coefficents
s=nemsingu(P,Q); //WARNING: it assign valies to global variables DB NEMTSOV@
tr=NEMTSOVr;
ti=NEMTSOVi;
printf("P,Q : %6.2lf RI: %6.2lf %20.16lf %20.16lf\n", P, Q,NEMTSOVR,NEMTSOVI);
printf("GLOBAL: %6.2lf ri: %6.2lf %20.16lf %20.16lf\n",NEMTSOVp,NEMTSOVq,NEMTSOVr,NEMTSOVi);
// arcnemogen(P,Q); DO(n,42) printf("nemins[%2d]= %30.14lf\n",n,ARCNEMo42[n]);
int M=801,M1=M+1;
int N=401,N1=N+1;
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
char v[M1*N1]; // v is working array
FILE *o;o=fopen("arknemmap1010.eps","w");ado(o,402,402);
fprintf(o,"201 201 translate\n 100 100 scale\n");
DO(m,M1) X[m]=-2.+.005*(m-.5);
DO(n,N1) Y[n]=-2.+.01*(n-.5);
for(m=-2;m<3;m++){ M(m,-2)L(m,2)}
for(n=-2;n<3;n++){ M(-2,n)L(2,n)}
fprintf(o,".003 W 0 0 0 RGB 2 setlinecap S\n");
M(tr, -2) L(tr, 2)
M(-2, ti) L(2, ti)
M(-2,-ti) L(2,-ti)
fprintf(o,".001 W 0 0 0 RGB S\n");
DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
DO(m,M1){x=X[m]; printf("run at x=%6.3f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
c=arknem(z);
//c=nempq(c);
//d=z;
//p=abs(c-d)/(abs(c)+abs(d)); p=-log(p)/log(10.); if(p>-85 && p<85) g[m*N1+n]=p;
p=Re(c); q=Im(c);
        if(p>-40 && p<40 &&
        q >-40 && q<40 ) { g[m*N1+n]=p; f[m*N1+n]=q; }
        }}
fprintf(o,"1 setlinejoin 1 setlinecap\n");
//#include"plofu.cin"
p=.1;q=.1;
for(m=-9;m<9;m++)for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N, (m+.1*n),-q,q);
                                                fprintf(o,".003 W 0 .6 0 RGB S\n");
for(m=0;m<19;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q);
                                                fprintf(o,".003 W .9 0 0 RGB S\n");
for(m=0;m<19;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q);
                                                fprintf(o,".003 W 0 0 .9 RGB S\n");
for(m= 1;m<20;m++) conto(o,f,w,v,X,Y,M,N,(0.-m),-p,p);fprintf(o,".008 W .8 0 0 RGB S\n");
for(m= 1;m<20;m++) conto(o,f,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".008 W 0 0 .8 RGB S\n");
                   conto(o,f,w,v,X,Y,M,N,(0. ),-p,p);fprintf(o,".008 W .5 0 .5 RGB S\n");
for(m=-21;m<22;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".008 W 0 0 0 RGB S\n");

/*
p=2; // Why does not it draw the circle "16" ?
conto(o,g,w,v,X,Y,M,N,16.,-4,4);fprintf(o,".002 W .3 0 .3 RGB S\n");
conto(o,g,w,v,X,Y,M,N,15.,-p,p);fprintf(o,".004 W 0 0 1 RGB S\n");
conto(o,g,w,v,X,Y,M,N,14.,-p,p);fprintf(o,".002 W 0 1 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,13.,-p,p);fprintf(o,".002 W 1 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,12.,-p,p);fprintf(o,".004 W 0 0 .6 RGB S\n");
conto(o,g,w,v,X,Y,M,N,11.,-p,p);fprintf(o,".002 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,10.,-p,p);fprintf(o,".002 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,9.,-p,p);fprintf(o,".004 W 0 .6 .6 RGB S\n");
conto(o,g,w,v,X,Y,M,N,8.,-p,p);fprintf(o,".002 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,7.,-p,p);fprintf(o,".002 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,6.,-p,p);fprintf(o,".004 W 0 .7 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,5.,-p,p);fprintf(o,".002 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,4.,-p,p);fprintf(o,".002 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,3.,-p,p);fprintf(o,".004 W 1 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,2.,-p,p);fprintf(o,".01 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,1.,-p,p);fprintf(o,".03 W .5 0 0 RGB S\n");
*/

M(NEMTSOVr, NEMTSOVi) L(NEMTSOVr, 2)
M(NEMTSOVr,-NEMTSOVi) L(NEMTSOVr,-2) M(-1,0) L(-2,0)
fprintf(o,"0 setlinecap 1 1 0 RGB .01 W S\n");

fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
        system("epstopdf arknemmap1010.eps");
        system( "open arknemmap1010.pdf"); //mac
getchar(); system("killall Preview");// mac
}

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 \usepackage{graphics}
 \paperwidth 430pt
 \paperheight 426pt
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 \usepackage{rotating}
 \textwidth 1260pt
 \textheight 1260pt
 \topmargin -108pt
 \oddsidemargin -72pt
 \parindent 0pt
 \pagestyle{empty}
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\begin{document}
\begin{picture}(424,424)
\put(24,20){\ing{arknemmap1010}}
%\put(50,40){\ing{sunem10q10ma6a}}
%\put(50,40){\ing{sunem10q10ma6s}}
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\put(94,100){\sx{1.8}{\rot{70} $u\!=\!-0.8$\ero}}
\put(130,100){\sx{1.8}{\rot{80} $u\!=\!-0.7$\ero}}
%
\put(159,260){\sx{1.8}{\rot{87} $u\!=\!-0.6$\ero}}
\put(172,258){\sx{1.8}{\rot{74} $u\!=\!-0.5$\ero}}
\put(186,256){\sx{1.8}{\rot{65} $u\!=\!-0.4$\ero}}
%
\put(211,190){\sx{1.8}{\rot{86} $u\!=\!-0.2$\ero}}
\put(250,188){\sx{1.8}{\rot{88} $u\!=\!0.2$\ero}}
\put(276,188){\sx{1.8}{\rot{86} $u\!=\!0.4$\ero}}
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\put(358,188){\sx{1.8}{\rot{86} $u\!=\!0.7$\ero}}
\put(402,188){\sx{1.8}{\rot{86} $u\!=\!0.8$\ero}}
%
\put(60,398){\sx{1.8}{\rot{3} $v\!=\!0.8$\ero}}
\put(60,350){\sx{1.8}{\rot{6} $v\!=\!0.7$\ero}}
\put(68,308){\sx{1.8}{\rot{12} $v\!=\!0.6$\ero}}
\put(88,280){\sx{1.8}{\rot{18} $v\!=\!0.5$\ero}}
%
\put(288,364){\sx{1.8}{\rot{56} $v\!=\!0.4$\ero}}
\put(324,334){\sx{1.8}{\rot{43} $v\!=\!0.3$\ero}}
\put(350,298){\sx{1.8}{\rot{30} $v\!=\!0.2$\ero}}
\put(362,258){\sx{1.8}{\rot{15} $v\!=\!0.1$\ero}}
\put(350,178){\sx{1.8}{\rot{-16} $v\!=\!-0.1$\ero}}
\put(334,140){\sx{1.8}{\rot{-29} $v\!=\!-0.2$\ero}}
\put(306,112){\sx{1.8}{\rot{-46} $v\!=\!-0.3$\ero}}
\put(272,86){\sx{1.8}{\rot{-60} $v\!=\!-0.4$\ero}}
%
\put(46,89){\sx{1.8}{\rot{-11} $v\!=\!-0.7$\ero}}
\put(44,36){\sx{1.8}{\rot{-2} $v\!=\!-0.8$\ero}}

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