File:Test8trubes300.jpg

#include<math.h>
#include<stdio.h>
#include<stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
DB jnp(int n,DB x){ return .5*( jn(n-1,x)-jn(n+1,x) ) ; } // Derivative of n th Bessel
DB jnz(int v, int k){ DB x,t; t=M_PI*(k+.5*v-.25); x= t - (v*v-.25)*.5/t;
                x-= jn(v,x)/jnp(v,x); // Newton adjustment of the root
                x-= jn(v,x)/jnp(v,x);
                x-= jn(v,x)/jnp(v,x);
                return x; } // the k th zero of v th Bessel
#include"ado.cin"

int main(){ int m,n,v,k; DB s, x,y; FILE *o;
int M=8;
DB X[M+1],W[M+1],T[M+1][M+1],TT[M+1][M+1], F[M],G[M];
DB S=jnz(0,M+1);
DB jd=jnz(0,1);
DB qs=sqrt(1./S);
DB q=sqrt(2./S);
for(n=1;n<M+1;n++){ x=jnz(0,n); X[n]=x*qs; y=W[n]=q/fabs(j1(x));
                        printf("%3d %20.16lf %20.16lf\n",n,X[n],W[n]); }
for(m=1;m<=M;m++){// printf("%2d",m);
                for(n=1;n<=M;n++){ T[m][n]=W[m]*j0(X[m]*X[n])*W[n]; }}
//for(m=1;m<=M;m++){printf("\n");
//for(n=1;n<=M;n++){printf("%14.10lf",T[m][n]); }}
//printf("\n");
//for(m=1;m<=M;m++){printf("\n");
//for(n=1;n<=M;n++){ s=0.;
// for(k=1;k<=M;k++) s+=T[m][k]*T[k][n] ;
// TT[m][n]=s;printf("%14.10lf",TT[m][n]);
// }}
//printf("\n\n");
//for(m=1;m<=M;m++){x=X[m]; y=exp(-x*x/2.); F[m]=y*W[m]; /* printf("%14.10lf",F[m]); */ }
for(m=1;m<=M;m++){x=X[m]; if(x<jd) y=j0(x); else y=0.; F[m]=y*W[m]; /*printf("%14.10lf",F[m]);*/ }
/*printf("\n");*/
for(m=1;m<=M;m++){ s=0.; for(n=1;n<=M;n++) s+=T[m][n]*F[n];
                 G[m]=s;}
//for(m=1;m<=M;m++) printf("%14.10lf",G[m]);
//printf("\n");
o=fopen("test8trube.eps", "w"); ado(o,520,220);
#define M(x,y) fprintf(o,"%8.4lf %8.4lf M\n",0.+x, 0.+y);
#define L(x,y) fprintf(o,"%8.4lf %8.4lf L\n",0.+x, 0.+y);
#define O(x,y) fprintf(o,"%8.4lf %8.4lf O\n",0.+x, 0.+y);
#define o(x,y) fprintf(o,"%8.4lf %8.4lf o\n",0.+x, 0.+y);
fprintf(o,"10 60 translate 100 100 scale\n");
DO(n,6){M(n,1)L(n,0)}
DO(n,3){M(0,n/2.)L(5,n/2.)}
fprintf(o,"2 setlinecap 2 setlinejoin .006 W S\n");

//M(0,1) DO(n,500){x=.02*(n+1); y=exp(-x*x/2.); L(x,y)}
M(0,1) DO(n,127){x=.04*(n+1); y=j0(x); L(x,y)}
fprintf(o,"1 setlinecap 1 setlinejoin S\n");

DO(n,127){x=.04*(n+.2); y=j0(jd*x)/(1.-x*x)*jd*j1(jd); if(n==0)M(x,y) else L(x,y)
                        printf("%6.4lf %6.3lf\n",x,y);}
fprintf(o,"1 setlinecap 1 setlinejoin S\n");

fprintf(o,"1 0 0 RGB .016 W\n"); for(m=1;m<=M;m++) o(X[m],F[m]/W[m])
fprintf(o,"0 0 1 RGB .01 W\n"); for(m=1;m<=M;m++) O(X[m],G[m]/W[m])

fprintf(o,"showpage\n%c%cTrailer\n",'%','%'); fclose(o);
system("epstopdf test8trube.eps");
system("open test8trube.pdf");
return 0;
}

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\begin{document}
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\put(2,4){\ing{test8trube}}
\put(2,190){\sx{1.4}{\rot{-2}$\displaystyle y\!=\!\lambda J_1(\lambda) \frac{J_0(\lambda\, x)}{1\!-\!x^2}$ \ero}}
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