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acoefs.cpp
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acoefs.cpp
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/**
* @file acoefs.cpp
* @brief Functions that handle the acoefficients
*
* This file contains functions that handle the acoefficients. It can create nu(n,l,m) from acoeffs for l<=3, j=1,2,3,4,5,6. It can also decompose into aj coefficients.
*/
#include <math.h>
#include <Eigen/Dense>
#include <vector>
#include <string>
#include <iostream>
#include <iomanip>
using Eigen::VectorXd;
using Eigen::VectorXi;
using Eigen::MatrixXd;
long double Hslm_Ritzoller1991(const int s,const int l, const int m){
const int L=l*(l+1);
long double Hsm;
if (s == 0){
Hsm=1;
}
if(s == 1){
Hsm=2*m;
}
if(s == 2){
Hsm=6*pow(m,2) - 2*L;
}
if (s == 3){
Hsm=20*pow(m,3) - 4*(3*L-1)*m;
}
if (s == 4){
Hsm=70*pow(m,4) - 10*(6*L-5)*pow(m,2) + 6*L*(L-2);
}
if (s == 5){
Hsm=252*pow(m,5)-140*(2*L-3)*pow(m,3) + (20*L*(3*L-10) + 48)*m;
}
if (s == 6){
Hsm=924*pow(m,6) - 420*pow(m,4) * (3*L-7) + 84*pow(m,2) *(5*pow(L,2) - 25*L + 14) - 20*L*(pow(L,2) - 8*L + 12);
}
if (s > 6){
std::cout << "Warning in Hslm_Ritzoller1991: s>6 not supported" << std::endl;
return -1;
}
return Hsm;
}
long double Pslm(const int s,const int l,const int m){
// These take the Ritzoller1991 coefficients and normalise them by Pslm(l)=l
// As per specified in Schou, JCD, Thompson 1994
// so basically we solved Pslm(l)=l=c*Hslm and find c
long double H, c, Ps;
if (s==0){
Ps=l;
}
if (s==1){
Ps=m;
}
if (s==2){
if (l>0){
Ps=(3*pow(m,2) -l*(l+1))/(2*l-1);
} else{
Ps=0;
}
}
if (s==3){
if (l>1){
Ps=(5*pow(m,3) - (3*l*(l+1)-1)*m)/((l-1)*(2*l-1));
} else{
Ps=0;
}
}
if (s==4){
H=(35*pow(m,4) - 5*(6*l*(l+1)-5)*pow(m,2)) + 3*l*(l+1)*(l*(l+1)-2);
c=2*(l-1)*(2*l-1)*(2*l-3);
if (c !=0){
Ps=H/c;
} else{
Ps=0;
}
}
if (s==5){
H=Hslm_Ritzoller1991(s,l,m);
c=8*(4*pow(l,4) - 20*pow(l,3) + 35*pow(l,2) - 25*l + 6);
if (c !=0){
Ps=H/c;
} else{
Ps=0;
}
}
if (s==6){
H=Hslm_Ritzoller1991(s,l,m);
c=64*pow(l,5) - 480*pow(l,4) + 1360*pow(l,3) - 1800*pow(l,2) + 1096*l - 240;
if (c !=0){
Ps=H/c;
} else{
Ps=0;
}
}
if (s>6){
std::cout << "Warning in Pslm(): s>6 not supported" << std::endl;
std::cout << "The program will return 0" << std::endl;
return 0;
}
return Ps;
}
// Symetric Splitting Tnlm
VectorXd Tnlm(VectorXd& nu_nlm, const int l){
VectorXd tnlm;
if (l != 0 && l<=3){
tnlm.resize(l);
}
switch (l){
case 1:
//Tn11
tnlm[0]=(nu_nlm[2]- nu_nlm[0])/2;
break;
case 2:
//Tn21
tnlm[0]=(nu_nlm[3]-nu_nlm[1])/2;
//Tn22
tnlm[1]=(nu_nlm[4]-nu_nlm[0])/4;
break;
case 3:
//Tn31
tnlm[0]=(nu_nlm[4]-nu_nlm[2])/2;
//Tn32
tnlm[1]=(nu_nlm[5]-nu_nlm[1])/4;
//Tn33
tnlm[2]=(nu_nlm[6]-nu_nlm[0])/6;
break;
default:
tnlm.resize(1);
tnlm[0]=0;
std::cout << " Warning in Tnlm: Please enter a value of 0<l<4" << std::endl;
std::cout << " The function will return [0]" << std::endl;
}
return tnlm;
}
//Anti-Symetric splitting Snlm
VectorXd Snlm(VectorXd& nu_nlm, const int l){
VectorXd snlm;
if (l != 0 && l<=3){
snlm.resize(l);
}
switch (l){
case 1:
//Sn11
snlm[0]=(nu_nlm[0] + nu_nlm[2])/2 - nu_nlm[1];
break;
case 2:
//Sn21
snlm[0]=(nu_nlm[1] + nu_nlm[3])/2 - nu_nlm[2];
//Sn22
snlm[1]=(nu_nlm[0] + nu_nlm[4])/2 - nu_nlm[2];
break;
case 3:
//Sn31
snlm[0]=(nu_nlm[2] + nu_nlm[4])/2 - nu_nlm[3];
//Sn32
snlm[1]=(nu_nlm[1] + nu_nlm[5])/2 - nu_nlm[3];
//Sn33
snlm[2]=(nu_nlm[0] + nu_nlm[6])/2 - nu_nlm[3];
break;
default:
snlm.resize(1);
snlm[0]=0;
std::cout << " Please enter a value of 0<l<4" << std::endl;
std::cout << " The function will return [0]" << std::endl;
}
return snlm;
}
VectorXd nunlm_from_acoefs(const long double nunl0, const int l,
const long double a1, const long double a2, const long double a3, const long double a4, const long double a5, const long double a6){
// This function compute nu_nlm from a series of a-coeficient and provided the central frequency without splitting nunl0
VectorXd nu_nlm(2*l+1);
for (int m=-l; m<=l; m++){
nu_nlm[m+l]=nunl0 + a1*Pslm(1,l,m) + a2*Pslm(2,l,m) + a3*Pslm(3,l,m) + a4*Pslm(4,l,m)+ a5*Pslm(5,l,m) + a6*Pslm(6,l,m);
}
return nu_nlm;
}
VectorXd eval_acoefs(const int l, VectorXd& nu_nls){ // We expect nu_nls=[nu(-l), nu(-l+1), ... , nu[0], nu[1], ... nu(l)]
// Function that gets the splitted frequencies of a given mode (n,l) and determines the analytical a-coefficients
// from a1 to a6 and for l<=3
// More details on the equations that lead to this are on Benomar+2021 and in acoefs.py on github acoefs_check project
long double Num_a1, Den_a1;
const long double A=-14;//, B=0, D=0;// A0=-14, A1=-3, B0=1,B1=-2/3, C0=-15,C1=-4, D0=18,D1=14/3;
long double C, E, F, G;
long double Pi21, Pi22, Pi23, Pi41, Pi42, Pi43, Pi61, Pi62, Pi63;
VectorXd aj(6), tnlm, snlm;
aj.setZero();
if (l ==0){
std::cout <<"There is no a1 coefficient for l==0" << std::endl;
std::cout << "The function will return 0 for all coefficients " << std::endl;
return aj;
}
if (l>3){
std::cout << "an for l>3 not implemented. Should you need it, better to solve this algorithmically using equation A3-6 from Schou, JCD, Thompson, 1994" << std::endl;
std::cout << "The program will return 0 for all coefficients" << std::endl;
return aj;
}
snlm=Snlm(nu_nls, l);
tnlm=Tnlm(nu_nls, l);
switch (l){
case 1:
aj[0]=tnlm[0]; //(nu_nls[2]- nu_nls[0])/2;
aj[1]=snlm[0]/3; //((nu_nls[0] + nu_nls[2])/2 - nu_nls[1])/3;
break;
case 2:
// a1 Term:
Num_a1=tnlm[0]+4*tnlm[1]; //T21-2*T22*Pslm(3,2,1)/Pslm(3,2,2);
Den_a1=5; //Pslm(1,2,1) - Pslm(3,2,1)*Pslm(1,2,2)/Pslm(3,2,2);
aj[0]=Num_a1/Den_a1;
// a2 term:
aj[1]=(2*snlm[1] - snlm[0])/7;
// a3 term:
aj[2]=(tnlm[1] - tnlm[0])/5;
// a4 term:
aj[3]=(snlm[1] - 4*snlm[0])/70.;
break;
case 3:
// Odds terms
// We have Tnlm = Sum [a_{2j-1} P_{2j-1}] with j=[1,M/2]
// a1 term:
aj[0]=tnlm[0]/14 + 2*tnlm[1]/7 + 9*tnlm[2]/14;
// a3 term:
aj[2]=-tnlm[0]/9 - 2*tnlm[1]/9 + tnlm[2]/3;
// a5 term:
aj[4] = tnlm[2]/42 + 5*tnlm[0]/126 - 4*tnlm[1]/63;
// Even Terms
// We have Snlm = Sum[a2j (P2j - P2j(0))] with j=[1, M/2]
// a2 term:
aj[1]=(-15*snlm[0] + 25*snlm[2])/126;
// a4 term:
aj[3]=13*(snlm[0] - 7*snlm[1] + 3*snlm[2])/1001;
// a6 term:
aj[5]=(15*snlm[0] - 6*snlm[1] + snlm[2])/1386;
break;
default:
std::cout << "Error eval_acoefs(): l must be between 1 and 3. Your input is l=" << l << std::endl;
std::cout << "The program will exit now" << std::endl;
exit(EXIT_FAILURE);
break;
}
return aj;
}