double ChiSqrSigLevel(double ChiSquared0, long nu)
/* return the probability that ChiSquared will exceed ChiSquared0 for nu degrees of freedom */
{
if (ChiSquared0<0)
return -1;
return gammaQ(nu/2.0, ChiSquared0/2);
}
//------------------------------------------------------------------------------
//void CKonst(int lmax, double *cma, double *cpa, double *cza,
// double *KmLm, double *KoLo, double *KpLM,
// double *KmlM, double *Kolo, double *Kplm){
// int i=0;
// int l, m;
// for(l=0;l<=lmax;l++){
// for(m=-l;m<=l;m++){
// cma[i]=cm(l,m);
// cza[i]=m;
// cpa[i]=cp(l,m);
// KmLm[i]=Km(l+1,m,m-1);
// KoLo[i]=Ko(l+1,m,m );
// KpLM[i]=Kp(l+1,m,m+1);
// KmlM[i]=Km(l ,m,m+1);
// Kolo[i]=Ko(l ,m,m );
// Kplm[i]=Kp(l ,m,m-1);
// i++;
// }
// }
//}
////------------------------------------------------------------------------------
//// CALCULATION OF CONSTANTS - ONE MORE LOOP - POSITION INDEPENDENT
////------------------------------------------------------------------------------
//// L DEPENDENT
//double CL[LMAX];
//double LL[LMAX];
//// CONSTANTS FOR X
//double CM[LMAX];
//double CZ[LMAX];
//double CP[LMAX];
//// CONSTANTS FOR Y AND V
//KmLm[LMAX];
//KoLo[LMAX];
//KpLM[LMAX];
//KmlM[LMAX];
//Kolo[LMAX];
//Kplm[LMAX];
//// SINGLE LOOP
//for(int l=1;l<=lmax;l++){
// for(int m=-l; m<=l; m++){
// CL[jlm(l,m)]=l;
// LL[jlm(l,m)]=2*l+1;
// CM[jlm(l,m)]=cm(l,m);
// CZ[jlm(l,m)]=m;
// CP[jlm(l,m)]=cp(l,m);
// KmLm[jlm(l,m)]=Km(l+1,m,m-1);
// KoLo[jlm(l,m)]=Ko(l+1,m,m );
// KpLM[jlm(l,m)]=Kp(l+1,m,m+1);
// KmlM[jlm(l,m)]=Km(l ,m,m+1);
// Kolo[jlm(l,m)]=Ko(l ,m,m );
// Kplm[jlm(l,m)]=Kp(l ,m,m-1);
// }
//}
//------------------------------------------------------------------------------
// POSITION DEPENDENT CALCULATIONS - MULTIPLES LOOPS - COMPLETE CALCULATIONS
//------------------------------------------------------------------------------
void VectorSphericalWaveFunctions(double *k,double *x, double *y, double *z,int *lmax,
double complex *GTE, double complex *GTM,
double complex *Em, double complex *Ez, double complex *Ep,
double complex *Hm, double complex *Hz, double complex *Hp
){
// printf("%d\t%E\t%E\t%E\t%E\n",*lmax+1,*k,*x,*y,*z);
int l,m;
int LMAX=*lmax*(*lmax+2);
int LMAXE=(*lmax+1)*(*lmax+3);
double cph;
double sph;
double rho=sqrt(*x*(*x)+*y*(*y));
double r=sqrt(rho*rho+*z*(*z));
double sth=rho/r;
double cth=*z/r;
if((*x==0)&&(*y==0)){
cph=1;
sph=0;
}else{
cph=*x/rho;
sph=*y/rho;
}
// Spherical Bessel Funtions
double JLM[*lmax+2];
// double *JLM=&JLM0[0];
gsl_sf_bessel_jl_steed_array(*lmax+1,*k*r,JLM);
/* CALCULATIONS OK
for(l=0;l<(*lmax+2);l++){
printf("%d\t%f\t%E\n",l,*k*r,JLM[l]);
}
*/
// Qlm - primeiros 4 termos
double Qlm[LMAXE];
Qlm[jlm(0, 0)]=1/sqrt(4*M_PI);
Qlm[jlm(1, 1)]=-gammaQ(1)*sth*Qlm[jlm(0,0)]; // Q11
Qlm[jlm(1, 0)]=sqrt(3.0)*cth*Qlm[jlm(0,0)]; // Q10
Qlm[jlm(1,-1)]=-Qlm[jlm(1,1)]; // Q11*(-1)
// Complex Exponencial for m=-1,0,1
double complex Eim[2*(*lmax)+3];
Eim[*lmax-1]=(cph-I*sph);
Eim[*lmax ]=1+I*0;
Eim[*lmax+1]=(cph+I*sph);
// Ylm - primeiros 4 termos
double complex Ylm[LMAXE];
Ylm[jlm(0, 0)]=Qlm[jlm(0, 0)];
Ylm[jlm(1,-1)]=Qlm[jlm(1,-1)]*Eim[*lmax-1];
Ylm[jlm(1, 0)]=Qlm[jlm(1, 0)];
Ylm[jlm(1, 1)]=Qlm[jlm(1, 1)]*Eim[*lmax+1];
/* OK jl, Qlm, Ylm
for(l=0;l<2;l++){
for(m=-l;m<=l;m++){
printf("%d\t%d\t%d\t%f\t%f\t%f+%fi\n",l,m,jlm(l,m),JLM[jlm(l,m)],Qlm[jlm(l,m)],creal(Ylm[jlm(l,m)]),cimag(Ylm[jlm(l,m)]));
}
}
printf("======================================================================\n");
*/
// VECTOR SPHERICAL HARMONICS
double complex XM; //[LMAX];
double complex XZ; //[LMAX];
double complex XP; //[LMAX];
double complex YM; //[LMAX];
double complex YZ; //[LMAX];
double complex YP; //[LMAX];
double complex VM; //[LMAX];
double complex VZ; //[LMAX];
double complex VP; //[LMAX];
// HANSEN MULTIPOLES
double complex MM; //[LMAX];
double complex MZ; //[LMAX];
double complex MP; //[LMAX];
double complex NM; //[LMAX];
double complex NZ; //[LMAX];
double complex NP; //[LMAX];
// OTHERS
double kl;
// MAIN LOOP
for(l=1;l<=(*lmax);l++){
//------------------------------------------------------------------------------
//Qlm extremos positivos um passo a frente
Qlm[jlm(l+1, l+1)]=-gammaQ(l+1)*sth*Qlm[jlm(l,l)];
Qlm[jlm(l+1, l )]= deltaQ(l+1)*cth*Qlm[jlm(l,l)];
//Qlm extremos negativos um passo a frente
Qlm[jlm(l+1,-l-1)]=pow(-1,l+1)*Qlm[jlm(l+1, l+1)];
Qlm[jlm(l+1,-l )]=pow(-1,l )*Qlm[jlm(l+1, l )];
// Exponenciais um passo a frente
Eim[*lmax+l+1]=Eim[*lmax+l]*(cph+I*sph);
Eim[*lmax-l-1]=Eim[*lmax-l]*(cph-I*sph);
// Harmonicos esfericos extremos um passo a frente
Ylm[jlm(l+1, l+1)]=Qlm[jlm(l+1, l+1)]*Eim[*lmax+l+1];
Ylm[jlm(l+1, l )]=Qlm[jlm(l+1, l )]*Eim[*lmax+l ];
Ylm[jlm(l+1,-l-1)]=Qlm[jlm(l+1,-l-1)]*Eim[*lmax-l-1];
Ylm[jlm(l+1,-l )]=Qlm[jlm(l+1,-l )]*Eim[*lmax-l ];
// others
kl=1/(sqrt(l*(l+1)));
for(m=0; m<l; m++){
// Demais valores de Qlm e Ylm
Qlm[jlm(l+1, m)]=alfaQ(l+1,m)*cth*Qlm[jlm(l,m)]-betaQ(l+1,m)*Qlm[jlm(l-1,m)];
Qlm[jlm(l+1,-m)]=pow(-1,m)*Qlm[jlm(l+1, m)];
Ylm[jlm(l+1, m)]=Qlm[jlm(l+1, m)]*Eim[*lmax+m];
Ylm[jlm(l+1,-m)]=Qlm[jlm(l+1,-m)]*Eim[*lmax-m];
}
//------------------------------------------------------------------------------
// for(m=-(l+1); m<=(l+1); m++){
// Ylm[jlm(l+1,m)]=Qlm[jlm(l+1,m)]*Eim[*lmax+m];
// }
// for(m=-l; m<=l; m++){
// printf("%d\t%d\t%d\t%f\t%f+%fi\t%f+%fi\n",l,m,jlm(l,m)+1,Qlm[jlm(l,m)],creal(Eim[*lmax+m]),cimag(Eim[*lmax+m]),creal(Ylm[jlm(l,m)]),cimag(Ylm[jlm(l,m)]));
// }
//------------------------------------------------------------------------------
for(int m=-l; m<=l; m++){
XM=kl*cm(l,m)*Ylm[jlm(l,m-1)]/sqrt(2);
XZ=kl*m*Ylm[jlm(l,m )];
XP=kl*cp(l,m)*Ylm[jlm(l,m+1)]/sqrt(2);
// printf("--------X--------------------------------\n");
printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(XM),cimag(XM));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(XZ),cimag(XZ));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(XP),cimag(XP));
YM=(-Kp(l,m,m-1)*Ylm[jlm(l,m-1)]+Km(l+1,m,m-1)*Ylm[jlm(l+1,m-1)])/sqrt(2);
YZ= Ko(l,m,m )*Ylm[jlm(l,m )]+Ko(l+1,m,m )*Ylm[jlm(l+1,m )];
YP=( Km(l,m,m+1)*Ylm[jlm(l,m+1)]-Kp(l+1,m,m+1)*Ylm[jlm(l+1,m+1)])/sqrt(2);
// printf("--------Y--------------------------------\n");
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(YM),cimag(YM));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(YZ),cimag(YZ));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(YP),cimag(YP));
VM=kl*(-(l+1)*Kp(l,m,m-1)*Ylm[jlm(l,m-1)]-l*Km(l+1,m,m-1)*Ylm[jlm(l+1,m-1)])/sqrt(2);
VZ=kl*( (l+1)*Ko(l,m,m )*Ylm[jlm(l,m )]-l*Ko(l+1,m,m )*Ylm[jlm(l+1,m )]);
VP=kl*( (l+1)*Km(l,m,m+1)*Ylm[jlm(l,m+1)]+l*Kp(l+1,m,m+1)*Ylm[jlm(l+1,m+1)])/sqrt(2);
// printf("--------V--------------------------------\n");
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(VM),cimag(VM));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(VZ),cimag(VZ));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(VP),cimag(VP));
// CALCULATION OF HANSEM MULTIPOLES
MM=JLM[l]*XM;
MZ=JLM[l]*XZ;
MP=JLM[l]*XP;
// printf("--------M--------------------------------\n");
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(MM),cimag(MM));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(MZ),cimag(MZ));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(MP),cimag(MP));
NM=((l+1)*JLM[l-1]-l*JLM[l+1])*VM/(2*l+1)+sqrt(l*(l+1))*JLM[l]*YM;
NZ=((l+1)*JLM[l-1]-l*JLM[l+1])*VZ/(2*l+1)+sqrt(l*(l+1))*JLM[l]*YZ;
NP=((l+1)*JLM[l-1]-l*JLM[l+1])*VP/(2*l+1)+sqrt(l*(l+1))*JLM[l]*YP;
// printf("--------N--------------------------------\n");
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(NM),cimag(NM));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(NZ),cimag(NZ));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(NP),cimag(NP));
// CALCULATION OF THE ELECTROMAGNETIC FIELDS
*Em=*Em+MM*GTE[jlm(l,m)]-NM*GTM[jlm(l,m)];
*Ez=*Ez+MZ*GTE[jlm(l,m)]-NZ*GTM[jlm(l,m)];
*Ep=*Ep+MP*GTE[jlm(l,m)]-NP*GTM[jlm(l,m)];
*Hm=*Hm+MM*GTM[jlm(l,m)]+NM*GTE[jlm(l,m)];
*Hz=*Hz+MZ*GTM[jlm(l,m)]+NZ*GTE[jlm(l,m)];
*Hp=*Hp+MP*GTM[jlm(l,m)]+NP*GTE[jlm(l,m)];
}
}
}
