File:Norifragment.jpg

#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"
#include "besselj0.cin"

DB L1= 2.404825557695773;
DB L2= 5.5200781102863115;
DB L3= 8.653727912911013;
DB L4=11.791534439014281;
z_type morin(z_type x){ return BesselJ0(L1*x)/(1.-x*x);} // naive representation fails at x=1.

z_type mori0(z_type x){ int n,m; z_type s, xx=x*x;
DB c[16]={ 1., -0.4457964907366961303, 0.07678538241994023453, -0.0071642885058902232688,
0.00042159522055140947688, -0.000017110542281627483109, 5.0832583976057607495e-7, -1.1537378620148452816e-8,
2.0662789231930073316e-10, -2.9948657413756059965e-12, 3.5852738451127332173e-14,-3.6050239634659700777e-16,
3.0877184831292878827e-18, -2.2798156440952688462e-20, 1.4660907878585489441e-22,-8.2852774398657968065e-25};
// 16th term seems to fail; perhaps, due to the C++ rounding errors.
//with m=15, at |x|<2, the relative error is of order of 10^(-16)
//In this sense, the result is accurate while |x|<2.
m=15; s=c[m]*xx; for(n=m-1;n>0;n--){ s+=c[n]; s*=xx;}
return 1.+s;}
z_type mori(z_type x){if(abs(x)<2.) return mori0(x);
                        return morin(x);}

z_type no1(z_type x){ return BesselJ0(L1*sqrt(x))/(1.-x);} // naive representation fails at x=1.

z_type no0(z_type x){ int n,m; z_type s; //, xx=x*x;
DB c[16]={ 1., -0.4457964907366961303, 0.07678538241994023453, -0.0071642885058902232688,
0.00042159522055140947688, -0.000017110542281627483109, 5.0832583976057607495e-7, -1.1537378620148452816e-8,
2.0662789231930073316e-10, -2.9948657413756059965e-12, 3.5852738451127332173e-14,-3.6050239634659700777e-16,
3.0877184831292878827e-18, -2.2798156440952688462e-20, 1.4660907878585489441e-22,-8.2852774398657968065e-25};
// 16th term seems to fail; perhaps, due to the C++ rounding errors.
//with m=15, at |x|<2, the relative error is of order of 10^(-16)
//In this sense, the result is accurate while |x|<2.
m=15; s=c[m]*x; for(n=m-1;n>0;n--){ s+=c[n]; s*=x;}
return 1.+s;}

z_type no(z_type x){if(abs(x)<3.) return no0(x);
                        return no1(x);}

z_type nori2(z_type z){ int m,n; z_type s;
DB c[33]={0.,0.,0.00174332257160181945,-0.00114761496984019073,
0.000340103481720677646,-0.0000609020923565221809, 7.46986627122903883e-6,-6.74189690454671852e-7,
4.69384146643218622e-8,-2.60738414137880014e-9, 1.18544844971684771e-10,-4.50046762226769222e-12,
1.4499828101463652e-13,-4.01805848005701688e-15, 9.68542536232100048e-17,-2.05050240127868115e-18,
3.84475011463803867e-20,-6.43154329694589363e-22, 9.66056357432588623e-24,-1.3104545200747203e-25,
1.61363842007403585e-27,-1.8120393703954206e-29, 1.86350229389812321e-31,-1.76178979606776683e-33,
1.5365952184763114e-35, -1.24034221547939e-37, 9.293654513890807e-40,-6.481628369150681e-42,
4.218305191839397e-44,-2.56788121875364e-46, 1.465388286079839e-48,-7.85537549243321e-51,
3.963300280201547e-53
} ;
DB M2= L2/L1; M2*=M2;
z-=M2;
m=29;
s=c[m]*z;
for(n=m-1;n>1;n--) { s+=c[n]; s*=z;}
return s*z;
}

int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
int M=631,M1=M+1;
int N=501,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("norima.eps","w");ado(o,5020,5020);
FILE *o;o=fopen("norifragmen.eps","w");ado(o,2520,2020);
fprintf(o,"1010 1010 translate\n 100 100 scale\n");
DO(m,M1)X[m]=-10.+.04*(m-.5);
DO(n,N1)Y[n]=-10.+.04*(n-.5);

for(m=-10;m<11;m++){if(m==0){M(m,-10.1)L(m,10.1)} else{M(m,-10)L(m,10)}}
for(n=-10;n<11;n++){ M( -10,n)L(10,n)}
fprintf(o,".01 W 0 0 0 RGB S\n");
DO(m,M1)DO(n,N1){g[m*N1+n]=99999; f[m*N1+n]=99999;}
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
// c=BesselJ0(z);
// c=mori(z);
// c=no(z); c*=c;
c=nori2(z);
//c=c-d;
//p=abs(c-d)/(abs(c)+abs(d)); p=-log(p)/log(10.);
     p=Re(c); q=Im(c); if(p>-999. && p<999. && q>-999. && q<999 )
{g[m*N1+n]=p; f[m*N1+n]=q;}
//g[m*N1+n]=p;
                     }}
//#include "plodi.cin"
fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=40;q=1;
/*
 conto(o,g,w,v,X,Y,M,N, 14,-p,p); fprintf(o,".04 W 1 0 1 RGB S\n");
// conto(o,g,w,v,X,Y,M,N, 14,-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, 13,-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, 12,-p,p); fprintf(o,".04 W 0 0 1 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, 11,-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, 10,-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, 9,-p,p); fprintf(o,".04 W 0 .5 1 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, 8,-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, 7,-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, 6,-p,p); fprintf(o,".04 W 0 .8 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, 5,-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, 4,-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, 3,-p,p); fprintf(o,".04 W 1 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, 2,-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, 1,-p,p); fprintf(o,".06 W .5 0 0 RGB S\n");
*/

for(m=-4;m<4;m++)for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".01 W 0 .6 0 RGB S\n");
for(m=0;m<4;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".01 W .9 0 0 RGB S\n");
for(m=0;m<4;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".01 W 0 0 .9 RGB S\n");
for(m=1;m<9;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".03 W .9 0 0 RGB S\n");
for(m=1;m<9;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 .9 RGB S\n");
                conto(o,f,w,v,X,Y,M,N, (0. ),-2*p,2*p); fprintf(o,".03 W .6 0 .6 RGB S\n");
for(m=-8;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
    m=0; conto(o,g,w,v,X,Y,M,N, (0.+m),-2*p,2*p); fprintf(o,".03 W 0 0 0 RGB S\n");
for(m=1;m<9;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");

//#include "plofu.cin"
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
     system("epstopdf norifragmen.eps");
     system( "open norifragmen.pdf");
}

\documentclass[12pt]{article}
\paperwidth 2600px
\paperheight 2120px
\textwidth 5094px
\textheight 5200px
\topmargin -80px
\oddsidemargin -72px
\usepackage{graphics}
\usepackage{rotating}
%\usepackage{color}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing {\includegraphics}
\newcommand \rmi {\mathrm{i}}
\begin{document}\parindent 0pt
\begin{picture}(2100,2100)
%\put(80,80){\ing{norima}}
\put(80,80){\ing{norifragmen}}
%\put(80,80){\ing{02}}
%\put(80,80){\ing{03}}
\put(32,2068){\sx{8}{$y$}}
\put(32,1868){\sx{8}{$8$}}
\put(32,1668){\sx{8}{$6$}}
\put(32,1468){\sx{8}{$4$}}
\put(32,1268){\sx{8}{$2$}}
\put(32,1068){\sx{8}{$0$}}
\put(-32,868){\sx{8}{$-2$}}
\put(-32,668){\sx{8}{$-4$}}
\put(-32,468){\sx{8}{$-6$}}
\put(-32,268){\sx{8}{$-8$}}
\put(230,8){\sx{8}{$-8$}}
\put(430,8){\sx{8}{$-6$}}
\put(630,8){\sx{8}{$-4$}}
\put(830,8){\sx{8}{$-2$}}
\put(1070,8){\sx{8}{$0$}}
\put(1270,8){\sx{8}{$2$}}
\put(1470,8){\sx{8}{$4$}}
\put(1670,8){\sx{8}{$6$}}
\put(1870,8){\sx{8}{$8$}}
\put(2070,8){\sx{8}{$x$}}
%
\put(120,1100){\rot{2}\sx{8}{$v\!=\!-8$}\ero}
\put(160,1032){\rot{-2}\sx{8}{$v\!=\!8$}\ero}
\put(120,800){\rot{8}\sx{8}{$u\!=\!8$}\ero}
\put(120,732){\rot{3}\sx{8}{$u\!=\!-8$}\ero}
%
\put(840,910){\rot{50}\sx{8}{$u\!=\!4$}\ero}
\put(890,862){\rot{6}\sx{8}{$u\!=\!0$}\ero}
\put(760,830){\rot{-32}\sx{8}{$u\!=\!-4$}\ero}
%
\put(1340,1070){\rot{0}\sx{8}{$v\!=\!0$}\ero}
\put(1906,1070){\rot{0}\sx{8}{$v\!=\!0$}\ero}
%
\put(1450,840){\rot{38}\sx{8}{$v\!=\!0$}\ero}
\put(1560,740){\rot{50}\sx{8}{$u\!=\!0$}\ero}
\put(1680,610){\rot{50}\sx{8}{$v\!=\!0$}\ero}
\put(1844,480){\rot{51}\sx{8}{$u\!=\!0$}\ero}
\put(1980,290){\rot{50}\sx{8}{$v\!=\!0$}\ero}
\end{picture}
\end{document}