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ElpMpp_trim.h
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ElpMpp_trim.h
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// -------------------------------------------------------------------------
// Generate C++ code and data files for a truncated ELP/MPP02 series.
//
// Usage:
// 1. Set the parameter corr: corr=0 uses parameters fitted
// to the lunar laser ranging (LLR) observation data, corr=1 uses
// parameters fitted to JPL's DE405/DE406 ephemerides.
// 2. Call the function setup_parameters() to set up parameters
// corresponding to the choice of corr. There are two sets of
// parameters: a) parameters for adjusting the lunar and
// planetary arguments, stored in the struct Elp_paras;
// b) parameters for adjusting the coefficeients in
// the ELP/MPP02 series for the main problem, stored in the struct
// Elp_facs.
// 3. Call the function setup_Elp_coefs() to set up the coefficients
// for the ELP/MPP02 series. The coefficients are stored in the struct
// Elp_coefs.
// 4. Set the parameters AthU, AthV, AthR and tau for the truncated series.
// See the pdf documentation for how the truncated series
// is created based on these 4 parameters.
// 5. Call the function trim_Elp_coefs() to compute the coefficients
// for the truncated ELP/MPP02 series.
// 6. Call output_data_files() to output the coefficients for the truncated
// ELP/MPP02 series to 14 data files.
// 7. Call generate_cpp_code() to generate a C++ code that containing functions
// to calculate the lunar position using the truncated ELP/MPP02 series.
// 8. (Optional) Call error_est() to estimate the accuracy of the truncated
// series by performing a Monte Carlo simulation.
//
// See example_usingElpMpp_trim.cpp for an example of using this code.
// -------------------------------------------------------------------------
#include "ElpMpp02.h"
#include <iomanip>
// Parameters providing the statistics of the deviation between the truncated
// series and the full series.
struct devStats{
double absmax_long, rms_long;
double absmax_lat, rms_lat;
double absmax_dist, rms_dist;
};
// Compute the coefficients of the truncated ELP/MPP02 series for the main problem.
void trim_main_coefficients(int n, int ** &i_full, double * &A_full, double Ath,
int &n_trim, int ** &i_trim, double * &A_trim) {
int i,k;
// calculate n_trim:
n_trim = 0;
for (i=0; i<n; i++) {
if (fabs(A_full[i]) > Ath) n_trim++;
}
if (n_trim > 0) {
// Allocate arrays
i_trim = new int *[n_trim];
for (i=0; i<n_trim; i++) i_trim[i] = new int[4];
A_trim = new double[n_trim];
// set coefficients
int j=0;
for (i=0; i<n; i++) {
if (fabs(A_full[i]) > Ath) {
for (k=0; k<4; k++) {
i_trim[j][k] = i_full[i][k];
}
A_trim[j] = A_full[i];
j++;
}
}
}
}
// Same as trim_main_coefficients() but includes parameters for a crude error estimate.
void trim_main_coefficients_errorEst(int n, int ** &i_full, double * &A_full, double Ath,
int &n_trim, int ** &i_trim, double * &A_trim,
int &n_drop, int ** &i_drop, double * &A_drop,
double &absmax, double &sqsum) {
int i,k;
// calculate n_trim and n_drop:
n_trim = 0; n_drop = 0;
for (i=0; i<n; i++) {
if (fabs(A_full[i]) > Ath) {
n_trim++;
} else {
n_drop++;
}
}
absmax = 0.0;
sqsum = 0.0;
if (n_trim > 0) {
// Allocate arrays
i_trim = new int *[n_trim];
for (i=0; i<n_trim; i++) i_trim[i] = new int[4];
A_trim = new double[n_trim];
// set coefficients
int j=0;
for (i=0; i<n; i++) {
if (fabs(A_full[i]) > Ath) {
for (k=0; k<4; k++) {
i_trim[j][k] = i_full[i][k];
}
A_trim[j] = A_full[i];
j++;
} else {
absmax += fabs(A_full[i]);
sqsum += A_full[i]*A_full[i];
}
}
}
// dropped coefficients
if (n_drop > 0) {
// Allocate arrays
i_drop = new int *[n_drop];
for (i=0; i<n_drop; i++) i_drop[i] = new int[4];
A_drop = new double[n_drop];
// set coefficients
int j=0;
for (i=0; i<n; i++) {
if (fabs(A_full[i]) <= Ath) {
for (k=0; k<4; k++) {
i_drop[j][k] = i_full[i][k];
}
A_drop[j] = A_full[i];
j++;
}
}
}
}
// Compute the coefficients of the truncated ELP/MPP02 series for perturbatioins.
void trim_pert_coefficients(int n, int ** &i_full, double * &A_full, double * &ph_full,
double Ath, int &n_trim, int ** &i_trim, double * &A_trim,
double * &ph_trim) {
int i,k;
// calculate n_trim:
n_trim = 0;
for (i=0; i<n; i++) {
if (fabs(A_full[i]) > Ath) n_trim++;
}
if (n_trim > 0) {
// Allocate arrays
i_trim = new int *[n_trim];
for (i=0; i<n_trim; i++) i_trim[i] = new int[13];
A_trim = new double[n_trim];
ph_trim = new double[n_trim];
// set coefficients
int j=0;
for (i=0; i<n; i++) {
if (fabs(A_full[i]) > Ath) {
for (k=0; k<13; k++) {
i_trim[j][k] = i_full[i][k];
}
A_trim[j] = A_full[i];
ph_trim[j] = ph_full[i];
j++;
}
}
}
}
// Same as trim_pert_coefficients() but includes parameters for a crude error estimate.
void trim_pert_coefficients_errorEst(int n, int ** &i_full, double * &A_full,
double * &ph_full, double Ath,
int &n_trim, int ** &i_trim, double * &A_trim, double * &ph_trim,
int &n_drop, int ** &i_drop, double * &A_drop, double * &ph_drop,
double &absmax, double &sqsum) {
int i,k;
// calculate n_trim and n_drop:
n_trim = 0;
n_drop = 0;
for (i=0; i<n; i++) {
if (fabs(A_full[i]) > Ath) {
n_trim++;
} else {
n_drop++;
}
}
absmax = 0.0;
sqsum = 0.0;
if (n_trim > 0) {
// Allocate arrays
i_trim = new int *[n_trim];
for (i=0; i<n_trim; i++) i_trim[i] = new int[13];
A_trim = new double[n_trim];
ph_trim = new double[n_trim];
// set coefficients
int j=0;
for (i=0; i<n; i++) {
if (fabs(A_full[i]) > Ath) {
for (k=0; k<13; k++) {
i_trim[j][k] = i_full[i][k];
}
A_trim[j] = A_full[i];
ph_trim[j] = ph_full[i];
j++;
} else {
absmax += fabs(A_full[i]);
sqsum += A_full[i]*A_full[i];
}
}
}
// dropped coefficients
if (n_drop > 0) {
// Allocate arrays
i_drop = new int *[n_drop];
for (i=0; i<n_drop; i++) i_drop[i] = new int[13];
A_drop = new double[n_drop];
ph_drop = new double[n_drop];
// set coefficients
int j=0;
for (i=0; i<n; i++) {
if (fabs(A_full[i]) <= Ath) {
for (k=0; k<13; k++) {
i_drop[j][k] = i_full[i][k];
}
A_drop[j] = A_full[i];
ph_drop[j] = ph_full[i];
j++;
}
}
}
}
// Compute the coefficients for the truncated ELP/MPP02 series
void trim_Elp_coefs(Elp_coefs &coefs, Elp_coefs &coefs_trim,
double AthU, double AthV, double AthR, double tau) {
double tau2 = tau*tau;
double tau3 = tau*tau2;
// main problem
trim_main_coefficients(coefs.n_main_long, coefs.i_main_long, coefs.A_main_long,
AthV, coefs_trim.n_main_long, coefs_trim.i_main_long,
coefs_trim.A_main_long);
trim_main_coefficients(coefs.n_main_lat, coefs.i_main_lat, coefs.A_main_lat,
AthU, coefs_trim.n_main_lat, coefs_trim.i_main_lat,
coefs_trim.A_main_lat);
trim_main_coefficients(coefs.n_main_dist, coefs.i_main_dist, coefs.A_main_dist,
AthR, coefs_trim.n_main_dist, coefs_trim.i_main_dist,
coefs_trim.A_main_dist);
// perturbation, longitude
trim_pert_coefficients(coefs.n_pert_longT0, coefs.i_pert_longT0,
coefs.A_pert_longT0, coefs.ph_pert_longT0, AthV,
coefs_trim.n_pert_longT0, coefs_trim.i_pert_longT0,
coefs_trim.A_pert_longT0, coefs_trim.ph_pert_longT0);
trim_pert_coefficients(coefs.n_pert_longT1, coefs.i_pert_longT1,
coefs.A_pert_longT1, coefs.ph_pert_longT1, AthV/tau,
coefs_trim.n_pert_longT1, coefs_trim.i_pert_longT1,
coefs_trim.A_pert_longT1, coefs_trim.ph_pert_longT1);
trim_pert_coefficients(coefs.n_pert_longT2, coefs.i_pert_longT2,
coefs.A_pert_longT2, coefs.ph_pert_longT2, AthV/tau2,
coefs_trim.n_pert_longT2, coefs_trim.i_pert_longT2,
coefs_trim.A_pert_longT2, coefs_trim.ph_pert_longT2);
trim_pert_coefficients(coefs.n_pert_longT3, coefs.i_pert_longT3,
coefs.A_pert_longT3, coefs.ph_pert_longT3, AthV/tau3,
coefs_trim.n_pert_longT3, coefs_trim.i_pert_longT3,
coefs_trim.A_pert_longT3, coefs_trim.ph_pert_longT3);
// perturbation, latitude
trim_pert_coefficients(coefs.n_pert_latT0, coefs.i_pert_latT0,
coefs.A_pert_latT0, coefs.ph_pert_latT0, AthU,
coefs_trim.n_pert_latT0, coefs_trim.i_pert_latT0,
coefs_trim.A_pert_latT0, coefs_trim.ph_pert_latT0);
trim_pert_coefficients(coefs.n_pert_latT1, coefs.i_pert_latT1,
coefs.A_pert_latT1, coefs.ph_pert_latT1, AthU/tau,
coefs_trim.n_pert_latT1, coefs_trim.i_pert_latT1,
coefs_trim.A_pert_latT1, coefs_trim.ph_pert_latT1);
trim_pert_coefficients(coefs.n_pert_latT2, coefs.i_pert_latT2,
coefs.A_pert_latT2, coefs.ph_pert_latT2, AthU/tau2,
coefs_trim.n_pert_latT2, coefs_trim.i_pert_latT2,
coefs_trim.A_pert_latT2, coefs_trim.ph_pert_latT2);
// perturbation, distance
trim_pert_coefficients(coefs.n_pert_distT0, coefs.i_pert_distT0,
coefs.A_pert_distT0, coefs.ph_pert_distT0, AthR,
coefs_trim.n_pert_distT0, coefs_trim.i_pert_distT0,
coefs_trim.A_pert_distT0, coefs_trim.ph_pert_distT0);
trim_pert_coefficients(coefs.n_pert_distT1, coefs.i_pert_distT1,
coefs.A_pert_distT1, coefs.ph_pert_distT1, AthR/tau,
coefs_trim.n_pert_distT1, coefs_trim.i_pert_distT1,
coefs_trim.A_pert_distT1, coefs_trim.ph_pert_distT1);
trim_pert_coefficients(coefs.n_pert_distT2, coefs.i_pert_distT2,
coefs.A_pert_distT2, coefs.ph_pert_distT2, AthR/tau2,
coefs_trim.n_pert_distT2, coefs_trim.i_pert_distT2,
coefs_trim.A_pert_distT2, coefs_trim.ph_pert_distT2);
trim_pert_coefficients(coefs.n_pert_distT3, coefs.i_pert_distT3,
coefs.A_pert_distT3, coefs.ph_pert_distT3, AthR/tau3,
coefs_trim.n_pert_distT3, coefs_trim.i_pert_distT3,
coefs_trim.A_pert_distT3, coefs_trim.ph_pert_distT3);
}
// Same as trim_Elp_coefs() but include a crude error estimate.
void trim_Elp_coefs_errorEst(Elp_coefs &coefs, Elp_coefs &coefs_trim, Elp_coefs &coefs_drop,
double AthU, double AthV, double AthR, double tau,
double T1, double T2, devStats &stats) {
double tau2 = tau*tau;
double tau3 = tau*tau2;
double Tmax = fabs(T2) > fabs(T1) ? fabs(T2):fabs(T1);
double f1 = (pow(T2,3) - pow(T1,3))/(6.0*(T2-T1));
double f2 = 0.1*(pow(T2,5) - pow(T1,5))/(T2-T1);
double f3 = (pow(T2,7) - pow(T1,7))/(14.0*(T2-T1));
stats.absmax_long = 0.0;
stats.absmax_lat = 0.0;
stats.absmax_dist = 0.0;
stats.rms_long = 0.0;
stats.rms_lat = 0.0;
stats.rms_dist = 0.0;
double absmax, sqsum;
// main problem
trim_main_coefficients_errorEst(coefs.n_main_long, coefs.i_main_long, coefs.A_main_long,
AthV, coefs_trim.n_main_long, coefs_trim.i_main_long,
coefs_trim.A_main_long, coefs_drop.n_main_long,
coefs_drop.i_main_long, coefs_drop.A_main_long,
absmax, sqsum);
stats.absmax_long += absmax;
stats.rms_long += 0.5*sqsum;
trim_main_coefficients_errorEst(coefs.n_main_lat, coefs.i_main_lat, coefs.A_main_lat,
AthU, coefs_trim.n_main_lat, coefs_trim.i_main_lat,
coefs_trim.A_main_lat, coefs_drop.n_main_lat,
coefs_drop.i_main_lat, coefs_drop.A_main_lat,
absmax, sqsum);
stats.absmax_lat += absmax;
stats.rms_lat += 0.5*sqsum;
trim_main_coefficients_errorEst(coefs.n_main_dist, coefs.i_main_dist, coefs.A_main_dist,
AthR, coefs_trim.n_main_dist, coefs_trim.i_main_dist,
coefs_trim.A_main_dist, coefs_drop.n_main_dist,
coefs_drop.i_main_dist, coefs_drop.A_main_dist,
absmax, sqsum);
stats.absmax_dist += absmax;
stats.rms_dist += 0.5*sqsum;
// perturbation, longitude
trim_pert_coefficients_errorEst(coefs.n_pert_longT0, coefs.i_pert_longT0,
coefs.A_pert_longT0, coefs.ph_pert_longT0, AthV,
coefs_trim.n_pert_longT0, coefs_trim.i_pert_longT0,
coefs_trim.A_pert_longT0, coefs_trim.ph_pert_longT0,
coefs_drop.n_pert_longT0, coefs_drop.i_pert_longT0,
coefs_drop.A_pert_longT0, coefs_drop.ph_pert_longT0,
absmax, sqsum);
stats.absmax_long += absmax;
stats.rms_long += 0.5*sqsum;
trim_pert_coefficients_errorEst(coefs.n_pert_longT1, coefs.i_pert_longT1,
coefs.A_pert_longT1, coefs.ph_pert_longT1, AthV/tau,
coefs_trim.n_pert_longT1, coefs_trim.i_pert_longT1,
coefs_trim.A_pert_longT1, coefs_trim.ph_pert_longT1,
coefs_drop.n_pert_longT1, coefs_drop.i_pert_longT1,
coefs_drop.A_pert_longT1, coefs_drop.ph_pert_longT1,
absmax, sqsum);
stats.absmax_long += absmax*Tmax;
stats.rms_long += sqsum*f1;
trim_pert_coefficients_errorEst(coefs.n_pert_longT2, coefs.i_pert_longT2,
coefs.A_pert_longT2, coefs.ph_pert_longT2, AthV/tau2,
coefs_trim.n_pert_longT2, coefs_trim.i_pert_longT2,
coefs_trim.A_pert_longT2, coefs_trim.ph_pert_longT2,
coefs_drop.n_pert_longT2, coefs_drop.i_pert_longT2,
coefs_drop.A_pert_longT2, coefs_drop.ph_pert_longT2,
absmax, sqsum);
stats.absmax_long += absmax*Tmax*Tmax;
stats.rms_long += sqsum*f2;
trim_pert_coefficients_errorEst(coefs.n_pert_longT3, coefs.i_pert_longT3,
coefs.A_pert_longT3, coefs.ph_pert_longT3, AthV/tau3,
coefs_trim.n_pert_longT3, coefs_trim.i_pert_longT3,
coefs_trim.A_pert_longT3, coefs_trim.ph_pert_longT3,
coefs_drop.n_pert_longT3, coefs_drop.i_pert_longT3,
coefs_drop.A_pert_longT3, coefs_drop.ph_pert_longT3,
absmax, sqsum);
stats.absmax_long += absmax*Tmax*Tmax*Tmax;
stats.rms_long += sqsum*f3;
// perturbation, latitude
trim_pert_coefficients_errorEst(coefs.n_pert_latT0, coefs.i_pert_latT0,
coefs.A_pert_latT0, coefs.ph_pert_latT0, AthU,
coefs_trim.n_pert_latT0, coefs_trim.i_pert_latT0,
coefs_trim.A_pert_latT0, coefs_trim.ph_pert_latT0,
coefs_drop.n_pert_latT0, coefs_drop.i_pert_latT0,
coefs_drop.A_pert_latT0, coefs_drop.ph_pert_latT0,
absmax, sqsum);
stats.absmax_lat += absmax;
stats.rms_lat += 0.5*sqsum;
trim_pert_coefficients_errorEst(coefs.n_pert_latT1, coefs.i_pert_latT1,
coefs.A_pert_latT1, coefs.ph_pert_latT1, AthU/tau,
coefs_trim.n_pert_latT1, coefs_trim.i_pert_latT1,
coefs_trim.A_pert_latT1, coefs_trim.ph_pert_latT1,
coefs_drop.n_pert_latT1, coefs_drop.i_pert_latT1,
coefs_drop.A_pert_latT1, coefs_drop.ph_pert_latT1,
absmax, sqsum);
stats.absmax_lat += absmax*Tmax;
stats.rms_lat += sqsum*tau2;
trim_pert_coefficients_errorEst(coefs.n_pert_latT2, coefs.i_pert_latT2,
coefs.A_pert_latT2, coefs.ph_pert_latT2, AthU/tau2,
coefs_trim.n_pert_latT2, coefs_trim.i_pert_latT2,
coefs_trim.A_pert_latT2, coefs_trim.ph_pert_latT2,
coefs_drop.n_pert_latT2, coefs_drop.i_pert_latT2,
coefs_drop.A_pert_latT2, coefs_drop.ph_pert_latT2,
absmax, sqsum);
stats.absmax_lat += absmax*Tmax*Tmax;
stats.rms_lat += sqsum*f2;
// perturbation, distance
trim_pert_coefficients_errorEst(coefs.n_pert_distT0, coefs.i_pert_distT0,
coefs.A_pert_distT0, coefs.ph_pert_distT0, AthR,
coefs_trim.n_pert_distT0, coefs_trim.i_pert_distT0,
coefs_trim.A_pert_distT0, coefs_trim.ph_pert_distT0,
coefs_drop.n_pert_distT0, coefs_drop.i_pert_distT0,
coefs_drop.A_pert_distT0, coefs_drop.ph_pert_distT0,
absmax, sqsum);
stats.absmax_dist += absmax;
stats.rms_dist += sqsum*0.5;
trim_pert_coefficients_errorEst(coefs.n_pert_distT1, coefs.i_pert_distT1,
coefs.A_pert_distT1, coefs.ph_pert_distT1, AthR/tau,
coefs_trim.n_pert_distT1, coefs_trim.i_pert_distT1,
coefs_trim.A_pert_distT1, coefs_trim.ph_pert_distT1,
coefs_drop.n_pert_distT1, coefs_drop.i_pert_distT1,
coefs_drop.A_pert_distT1, coefs_drop.ph_pert_distT1,
absmax, sqsum);
stats.absmax_dist += absmax*Tmax;
stats.rms_dist += sqsum*f1;
trim_pert_coefficients_errorEst(coefs.n_pert_distT2, coefs.i_pert_distT2,
coefs.A_pert_distT2, coefs.ph_pert_distT2, AthR/tau2,
coefs_trim.n_pert_distT2, coefs_trim.i_pert_distT2,
coefs_trim.A_pert_distT2, coefs_trim.ph_pert_distT2,
coefs_drop.n_pert_distT2, coefs_drop.i_pert_distT2,
coefs_drop.A_pert_distT2, coefs_drop.ph_pert_distT2,
absmax, sqsum);
stats.absmax_dist += absmax*Tmax*Tmax;
stats.rms_dist += sqsum*f2;
trim_pert_coefficients_errorEst(coefs.n_pert_distT3, coefs.i_pert_distT3,
coefs.A_pert_distT3, coefs.ph_pert_distT3, AthR/tau3,
coefs_trim.n_pert_distT3, coefs_trim.i_pert_distT3,
coefs_trim.A_pert_distT3, coefs_trim.ph_pert_distT3,
coefs_drop.n_pert_distT3, coefs_drop.i_pert_distT3,
coefs_drop.A_pert_distT3, coefs_drop.ph_pert_distT3,
absmax, sqsum);
stats.absmax_dist += absmax*Tmax*Tmax*Tmax;
stats.rms_dist += sqsum*f3;
stats.rms_long = sqrt(stats.rms_long);
stats.rms_lat = sqrt(stats.rms_lat);
stats.rms_dist = sqrt(stats.rms_dist);
}
// Compute the total number of terms in an ELP/MPP series
int compute_ntot(Elp_coefs &coefs) {
int ntot = coefs.n_main_long + coefs.n_main_lat + coefs.n_main_dist +
coefs.n_pert_longT0 + coefs.n_pert_longT1 + coefs.n_pert_longT2 +
coefs.n_pert_longT3 + coefs.n_pert_latT0 + coefs.n_pert_latT1 +
coefs.n_pert_latT2 + coefs.n_pert_distT0 + coefs.n_pert_distT1 +
coefs.n_pert_distT2 + coefs.n_pert_distT3;
return ntot;
}
// Calculate the differences in Moon's geocentric ecliptic longituide, latitude and distance
// between the full and truncated series by summing the dropped ELP/MPP02 terms.
// T is the TDB Julian century from J2000.0 = (TBD JD - 2451545)/36525
void calculate_dVUr(double T, Elp_paras ¶s, Elp_coefs &coefs_drop,
double &dV, double &dU, double &dr) {
double T2 = T*T;
double T3 = T*T2;
Elp_args args;
compute_Elp_arguments(T, paras, args);
// Sum the dropped ELP/MPP02 series
// main problem series
double main_long = Elp_main_sum(coefs_drop.n_main_long, coefs_drop.i_main_long,
coefs_drop.A_main_long, args, 0);
double main_lat = Elp_main_sum(coefs_drop.n_main_lat, coefs_drop.i_main_lat,
coefs_drop.A_main_lat, args, 0);
double main_dist = Elp_main_sum(coefs_drop.n_main_dist, coefs_drop.i_main_dist,
coefs_drop.A_main_dist, args, 1);
// perturbation, longitude
double pert_longT0 = Elp_perturbation_sum(coefs_drop.n_pert_longT0, coefs_drop.i_pert_longT0,
coefs_drop.A_pert_longT0, coefs_drop.ph_pert_longT0, args);
double pert_longT1 = Elp_perturbation_sum(coefs_drop.n_pert_longT1, coefs_drop.i_pert_longT1,
coefs_drop.A_pert_longT1, coefs_drop.ph_pert_longT1, args);
double pert_longT2 = Elp_perturbation_sum(coefs_drop.n_pert_longT2, coefs_drop.i_pert_longT2,
coefs_drop.A_pert_longT2, coefs_drop.ph_pert_longT2, args);
double pert_longT3 = Elp_perturbation_sum(coefs_drop.n_pert_longT3, coefs_drop.i_pert_longT3,
coefs_drop.A_pert_longT3, coefs_drop.ph_pert_longT3, args);
// perturbation, latitude
double pert_latT0 = Elp_perturbation_sum(coefs_drop.n_pert_latT0, coefs_drop.i_pert_latT0,
coefs_drop.A_pert_latT0, coefs_drop.ph_pert_latT0, args);
double pert_latT1 = Elp_perturbation_sum(coefs_drop.n_pert_latT1, coefs_drop.i_pert_latT1,
coefs_drop.A_pert_latT1, coefs_drop.ph_pert_latT1, args);
double pert_latT2 = Elp_perturbation_sum(coefs_drop.n_pert_latT2, coefs_drop.i_pert_latT2,
coefs_drop.A_pert_latT2, coefs_drop.ph_pert_latT2, args);
// perturbation, distance
double pert_distT0 = Elp_perturbation_sum(coefs_drop.n_pert_distT0, coefs_drop.i_pert_distT0,
coefs_drop.A_pert_distT0, coefs_drop.ph_pert_distT0, args);
double pert_distT1 = Elp_perturbation_sum(coefs_drop.n_pert_distT1, coefs_drop.i_pert_distT1,
coefs_drop.A_pert_distT1, coefs_drop.ph_pert_distT1, args);
double pert_distT2 = Elp_perturbation_sum(coefs_drop.n_pert_distT2, coefs_drop.i_pert_distT2,
coefs_drop.A_pert_distT2, coefs_drop.ph_pert_distT2, args);
double pert_distT3 = Elp_perturbation_sum(coefs_drop.n_pert_distT3, coefs_drop.i_pert_distT3,
coefs_drop.A_pert_distT3, coefs_drop.ph_pert_distT3, args);
// Moon's longitude, latitude and distance
dV = main_long + pert_longT0 + mod2pi(pert_longT1*T) +
mod2pi(pert_longT2*T2) + mod2pi(pert_longT3*T3);
dU = main_lat + pert_latT0 + mod2pi(pert_latT1*T) + mod2pi(pert_latT2*T2);
const double ra0 = 384747.961370173/384747.980674318;
dr = ra0*(main_dist + pert_distT0 + pert_distT1*T + pert_distT2*T2 + pert_distT3*T3);
}
// Estimate the accuracy of the truncated series by comparing it with
// the untruncated one at n randomly chosen times T1 <= T <= T2.
void error_est(Elp_coefs &coefs_drop, Elp_paras ¶s,
int n, double T1, double T2, devStats &errStats) {
errStats.absmax_long = 0.0;
errStats.rms_long = 0.0;
errStats.absmax_lat = 0.0;
errStats.rms_lat = 0.0;
errStats.absmax_dist = 0.0;
errStats.rms_dist = 0.0;
double dlong, dlat, ddist;
double dT = T2-T1;
srand(4852618); // random number seed
for (int i=0; i<n; i++) {
double T = rand()*dT/RAND_MAX + T1;
calculate_dVUr(T, paras, coefs_drop, dlong,dlat,ddist);
errStats.absmax_long = fabs(dlong) > errStats.absmax_long ? fabs(dlong):errStats.absmax_long;
errStats.absmax_lat = fabs(dlat) > errStats.absmax_lat ? fabs(dlat):errStats.absmax_lat;
errStats.absmax_dist = fabs(ddist) > errStats.absmax_dist ? fabs(ddist):errStats.absmax_dist;
errStats.rms_long += dlong*dlong;
errStats.rms_lat += dlat*dlat;
errStats.rms_dist += ddist*ddist;
if (i % 1000==0) {
cout << " " << setprecision(3) << i*100.0/n << "% done..." << "\r" << flush;
}
}
cout << " " << "\r" << flush;
cout << endl << endl;
errStats.rms_long = sqrt(errStats.rms_long/n);
errStats.rms_lat = sqrt(errStats.rms_lat/n);
errStats.rms_dist = sqrt(errStats.rms_dist/n);
}
// Generate a C++ code that computes the Moon's position using the truncated
// ELP/MPP02 series. The C++ code will be outputted to the file specified by outfile.
// The parameter dataFileSuffix must be exactly the same as the one in output_data_files().
void generate_cpp_code(const char* outfile, const char *dataFileSuffix, int corr,
double AthU, double AthV, double AthR, double tau,
Elp_paras ¶s) {
ofstream fin(outfile);
fin << "// ----------------------------------------------------------------" << endl;
fin << "// This code computes a truncated ELP/MPP02 series. " << endl;
fin << "//" << endl;
fin << "// ELP/MPP02 is a semi-analytic solution for the lunar motion developed by" << endl;
fin << "// J. Chapront and G. Francou in 2002. It is an improvement of the ELP2000-82B" << endl;
fin << "// lunar theory." << endl;
fin << "//" << endl;
fin << "// ELP/MPP02 source paper:" << endl;
fin << "// The lunar theory ELP revisited. Introduction of new planetary perturbations " << endl;
fin << "// by J. Chapront and G. Francou, Astronomy and Astrophysics, v.404, p.735-742 (2003)" << endl;
fin << "// http://adsabs.harvard.edu/abs/2003A%26A...404..735C" << endl;
fin << "//" << endl;
fin << "// Original FORTRAN code and data files:" << endl;
fin << "// ftp://cyrano-se.obspm.fr/pub/2_lunar_solutions/2_elpmpp02/" << endl;
fin << "//" << endl;
fin << "// This code is generated by \"Elp_Mpp_trim.h\" using the following parameters: " << endl;
fin << "// corr = " << corr << "," << endl;
fin << "// AthU = " << setprecision(17) << AthU << "," << endl;
fin << "// AthV = " << setprecision(17) << AthV << "," << endl;
fin << "// AthR = " << setprecision(17) << AthR << "," << endl;
fin << "// tau = " << setprecision(17) << tau << "," << endl;
fin << "//" << endl;
fin << "// It requires the following 14 data files also generated by the code" << endl;
fin << "// \"Elp_Mpp_trim.h\" using the same parameters: " << endl;
fin << "// elp_main.long" << dataFileSuffix << ", elp_main.lat" << dataFileSuffix
<< ", elp_main.dist" << dataFileSuffix << "," << endl;
fin << "// elp_pert.longT0" << dataFileSuffix << ", elp_pert.longT1" << dataFileSuffix
<< ", elp_pert.longT2" << dataFileSuffix << ", elp_pert.longT3" << dataFileSuffix
<< ", " << endl;
fin << "// elp_pert.latT0" << dataFileSuffix << ", elp_pert.latT1" << dataFileSuffix
<< ", elp_pert.latT2" << dataFileSuffix << ", " << endl;
fin << "// elp_pert.distT0" << dataFileSuffix << ", elp_pert.distT1" << dataFileSuffix
<< ", elp_pert.distT2" << dataFileSuffix << ", elp_pert.distT3" << dataFileSuffix
<< endl;
fin << "//" << endl;
fin << "// Usage:" << endl;
fin << "// 1. Call the function setup_Elp_coefs() to set up the coefficients" << endl;
fin << "// for the ELP/MPP02 series. The coefficients are stored in the struct" << endl;
fin << "// Elp_coefs." << endl;
fin << "// 2. Call getX2000() to compute the rectangular geocentric coordinates" << endl;
fin << "// of the Moon's position with respect to the mean ecliptic and" << endl;
fin << "// equinox of J2000.0." << endl;
fin << "// ---------------------------------------------------------------- " << endl;
fin << endl;
fin << "#include <cmath>" << endl;
fin << "#include <cstdlib>" << endl;
fin << "#include <iostream>" << endl;
fin << "#include <fstream>" << endl;
fin << "#include <string>" << endl;
fin << "" << endl;
fin << "using namespace std;" << endl;
fin << "" << endl;
fin << "#define PI 3.14159265358979323846" << endl;
fin << "" << endl;
fin << "// Arguments for the ELP/MPP02 series" << endl;
fin << "struct Elp_args {" << endl;
fin << " double W1, D, F, L, Lp, zeta, Me, Ve, EM, Ma, Ju, Sa, Ur, Ne;" << endl;
fin << "};" << endl;
fin << "" << endl;
fin << "// coefficients for the ELP/Mpp02 series" << endl;
fin << "struct Elp_coefs {" << endl;
fin << " // Main problem" << endl;
fin << " int n_main_long, n_main_lat, n_main_dist;" << endl;
fin << " int **i_main_long, **i_main_lat, **i_main_dist;" << endl;
fin << " double *A_main_long, *A_main_lat, *A_main_dist;" << endl;
fin << "" << endl;
fin << " // Perturbation, longitude" << endl;
fin << " int n_pert_longT0, n_pert_longT1, n_pert_longT2, n_pert_longT3;" << endl;
fin << " int **i_pert_longT0, **i_pert_longT1, **i_pert_longT2, **i_pert_longT3;" << endl;
fin << " double *A_pert_longT0, *A_pert_longT1, *A_pert_longT2, *A_pert_longT3;" << endl;
fin << " double *ph_pert_longT0, *ph_pert_longT1, *ph_pert_longT2, *ph_pert_longT3;" << endl;
fin << "" << endl;
fin << " // Perturbation, latitude" << endl;
fin << " int n_pert_latT0, n_pert_latT1, n_pert_latT2;" << endl;
fin << " int **i_pert_latT0, **i_pert_latT1, **i_pert_latT2;" << endl;
fin << " double *A_pert_latT0, *A_pert_latT1, *A_pert_latT2;" << endl;
fin << " double *ph_pert_latT0, *ph_pert_latT1, *ph_pert_latT2;" << endl;
fin << "" << endl;
fin << " // Perturbation, distance" << endl;
fin << " int n_pert_distT0, n_pert_distT1, n_pert_distT2, n_pert_distT3;" << endl;
fin << " int **i_pert_distT0, **i_pert_distT1, **i_pert_distT2, **i_pert_distT3;" << endl;
fin << " double *A_pert_distT0, *A_pert_distT1, *A_pert_distT2, *A_pert_distT3;" << endl;
fin << " double *ph_pert_distT0, *ph_pert_distT1, *ph_pert_distT2, *ph_pert_distT3;" << endl;
fin << "};" << endl;
fin << "" << endl;
fin << "// restrict x to [-pi,pi) " << endl;
fin << "double mod2pi(double x) {" << endl;
fin << " const double tpi = 2.0*PI;" << endl;
fin << " return x - tpi*floor((x + PI)/tpi);" << endl;
fin << "}" << endl;
fin << "" << endl;
fin << "// Read main problem file" << endl;
fin << "// n is the number of terms in the series, which is stored in the" << endl;
fin << "// first line of the data file" << endl;
fin << "void read_main_problem_file(const char *infile, int &n, int ** &i_main, double * &A_main) {" << endl;
fin << " int i;" << endl;
fin << " ifstream file(infile, ios::in);" << endl;
fin << " if (!file) {" << endl;
fin << " cerr << \"Error in opening \" << infile << endl;" << endl;
fin << " exit(1);" << endl;
fin << " }" << endl;
fin << " file >> n;" << endl;
fin << " if (n > 0) {" << endl;
fin << " i_main = new int *[n];" << endl;
fin << " A_main = new double[n];" << endl;
fin << " for (i=0; i<n; i++) i_main[i] = new int[4];" << endl;
fin << " for (i=0; i<n; i++) {" << endl;
fin << " if (file.eof()) {" << endl;
fin << " cerr << \"Reached the end of the file \" << infile " << endl;
fin << " << \" before reading all data!\" << endl;" << endl;
fin << " exit(1);" << endl;
fin << " }" << endl;
fin << " file >> i_main[i][0] >> i_main[i][1] >> i_main[i][2] >> i_main[i][3]" << endl;
fin << " >> A_main[i];" << endl;
fin << " }" << endl;
fin << " }" << endl;
fin << " file.close();" << endl;
fin << "}" << endl;
fin << "" << endl;
fin << "// Read perturbation file" << endl;
fin << "// n is the number of terms in the series, which is stored in the" << endl;
fin << "// first line of the data file" << endl;
fin << "void read_perturbation_file(const char *infile, int &n, int ** &i_pert, double * &A_pert," << endl;
fin << " double * &phase) {" << endl;
fin << " int i;" << endl;
fin << " ifstream file(infile);" << endl;
fin << " if (!file) {" << endl;
fin << " cerr << \"Error in opening \" << infile << endl;" << endl;
fin << " exit(1);" << endl;
fin << " }" << endl;
fin << " file >> n;" << endl;
fin << " if (n > 0) {" << endl;
fin << " i_pert = new int *[n];" << endl;
fin << " A_pert = new double[n];" << endl;
fin << " phase = new double[n];" << endl;
fin << " for (i=0; i<n; i++) i_pert[i] = new int[13];" << endl;
fin << " for (i=0; i<n; i++) {" << endl;
fin << " if (file.eof()) {" << endl;
fin << " cerr << \"Reached the end of the file \" << infile" << endl;
fin << " << \" before reading all data!\" << endl;" << endl;
fin << " exit(1);" << endl;
fin << " }" << endl;
fin << " file >> i_pert[i][0] >> i_pert[i][1] >> i_pert[i][2] >> i_pert[i][3]" << endl;
fin << " >> i_pert[i][4] >> i_pert[i][5] >> i_pert[i][6] >> i_pert[i][7]" << endl;
fin << " >> i_pert[i][8] >> i_pert[i][9] >> i_pert[i][10] >> i_pert[i][11]" << endl;
fin << " >> i_pert[i][12] >> A_pert[i] >> phase[i];" << endl;
fin << " }" << endl;
fin << " }" << endl;
fin << " file.close();" << endl;
fin << "}" << endl;
fin << "" << endl;
fin << "// set up coefficients for the ELP/MPP02 series" << endl;
fin << "void setup_Elp_coefs(Elp_coefs &coefs) {" << endl;
fin << " string infile;" << endl;
fin << "" << endl;
fin << " // Main problem" << endl;
fin << " infile = \"elp_main.long" << dataFileSuffix << "\";" << endl;
fin << " read_main_problem_file(infile.c_str(), coefs.n_main_long, coefs.i_main_long," << endl;
fin << " coefs.A_main_long);" << endl;
fin << " infile = \"elp_main.lat" << dataFileSuffix << "\";" << endl;
fin << " read_main_problem_file(infile.c_str(), coefs.n_main_lat, coefs.i_main_lat," << endl;
fin << " coefs.A_main_lat);" << endl;
fin << " infile = \"elp_main.dist" << dataFileSuffix << "\";" << endl;
fin << " read_main_problem_file(infile.c_str(), coefs.n_main_dist, coefs.i_main_dist, " << endl;
fin << " coefs.A_main_dist);" << endl;
fin << "" << endl;
fin << " // perturbation, longitude" << endl;
fin << " infile = \"elp_pert.longT0" << dataFileSuffix << "\";" << endl;
fin << " read_perturbation_file(infile.c_str(), coefs.n_pert_longT0, coefs.i_pert_longT0, " << endl;
fin << " coefs.A_pert_longT0, coefs.ph_pert_longT0);" << endl;
fin << " infile = \"elp_pert.longT1" << dataFileSuffix << "\";" << endl;
fin << " read_perturbation_file(infile.c_str(), coefs.n_pert_longT1, coefs.i_pert_longT1," << endl;
fin << " coefs.A_pert_longT1, coefs.ph_pert_longT1);" << endl;
fin << " infile = \"elp_pert.longT2" << dataFileSuffix << "\";" << endl;
fin << " read_perturbation_file(infile.c_str(), coefs.n_pert_longT2, coefs.i_pert_longT2," << endl;
fin << " coefs.A_pert_longT2, coefs.ph_pert_longT2);" << endl;
fin << " infile = \"elp_pert.longT3" << dataFileSuffix << "\";" << endl;
fin << " read_perturbation_file(infile.c_str(), coefs.n_pert_longT3, coefs.i_pert_longT3," << endl;
fin << " coefs.A_pert_longT3, coefs.ph_pert_longT3);" << endl;
fin << "" << endl;
fin << " // perturbation, latitude" << endl;
fin << " infile = \"elp_pert.latT0" << dataFileSuffix << "\";" << endl;
fin << " read_perturbation_file(infile.c_str(), coefs.n_pert_latT0, coefs.i_pert_latT0," << endl;
fin << " coefs.A_pert_latT0, coefs.ph_pert_latT0);" << endl;
fin << " infile = \"elp_pert.latT1" << dataFileSuffix << "\";" << endl;
fin << " read_perturbation_file(infile.c_str(), coefs.n_pert_latT1, coefs.i_pert_latT1," << endl;
fin << " coefs.A_pert_latT1, coefs.ph_pert_latT1);" << endl;
fin << " infile = \"elp_pert.latT2" << dataFileSuffix << "\";" << endl;
fin << " read_perturbation_file(infile.c_str(), coefs.n_pert_latT2, coefs.i_pert_latT2," << endl;
fin << " coefs.A_pert_latT2, coefs.ph_pert_latT2);" << endl;
fin << "" << endl;
fin << " // perturbation, distance" << endl;
fin << " infile = \"elp_pert.distT0" << dataFileSuffix << "\";" << endl;
fin << " read_perturbation_file(infile.c_str(), coefs.n_pert_distT0, coefs.i_pert_distT0," << endl;
fin << " coefs.A_pert_distT0, coefs.ph_pert_distT0);" << endl;
fin << " infile = \"elp_pert.distT1" << dataFileSuffix << "\";" << endl;
fin << " read_perturbation_file(infile.c_str(), coefs.n_pert_distT1, coefs.i_pert_distT1," << endl;
fin << " coefs.A_pert_distT1, coefs.ph_pert_distT1);" << endl;
fin << " infile = \"elp_pert.distT2" << dataFileSuffix << "\";" << endl;
fin << " read_perturbation_file(infile.c_str(), coefs.n_pert_distT2, coefs.i_pert_distT2," << endl;
fin << " coefs.A_pert_distT2, coefs.ph_pert_distT2);" << endl;
fin << " infile = \"elp_pert.distT3" << dataFileSuffix << "\";" << endl;
fin << " read_perturbation_file(infile.c_str(), coefs.n_pert_distT3, coefs.i_pert_distT3," << endl;
fin << " coefs.A_pert_distT3, coefs.ph_pert_distT3);" << endl;
fin << "}" << endl;
fin << "" << endl;
fin << "// Compute the lunar and planetary arguments used in the ELP/MPP02 series" << endl;
fin << "void compute_Elp_arguments(double T, Elp_args &args) {" << endl;
fin << " double T2 = T*T;" << endl;
fin << " double T3 = T*T2;" << endl;
fin << " double T4 = T2*T2;" << endl << endl;
const double deg = PI/180.0; // degrees -> radians
const double sec = PI/648000.0; // arcsecs -> radians
double w10 = (-142.0 + 18.0/60.0 +(59.95571 + paras.Dw1_0)/3600.0)*deg;
double w11 = (1732559343.73604 + paras.Dw1_1)*sec;
double w12 = (-6.8084 + paras.Dw1_2)*sec;
double w13 = (0.006604 + paras.Dw1_3)*sec;
double w14 = (-3.169e-5 + paras.Dw1_4)*sec;
fin << " double W1 = " << setprecision(17) << w10 << ";" << endl;
fin << " W1 += mod2pi(" << setprecision(17) << w11 << "*T);" << endl;
fin << " W1 += mod2pi(" << setprecision(17) << w12 << "*T2);" << endl;
fin << " W1 += mod2pi(" << setprecision(17) << w13 << "*T3);" << endl;
fin << " W1 += mod2pi(" << setprecision(17) << w14 << "*T4);" << endl;
double w20 = (83.0 + 21.0/60.0 + (11.67475 + paras.Dw2_0)/3600.0)*deg;
double w21 = (14643420.3171 + paras.Dw2_1 + paras.Cw2_1)*sec;
double w22 = (-38.2631 + paras.Dw2_2)*sec;
double w23 = (-0.045047+ paras.Dw2_3)*sec;
double w24 = 0.00021301*sec;
fin << " double W2 = " << setprecision(17) << w20 << ";" << endl;
fin << " W2 += mod2pi(" << setprecision(17) << w21 << "*T);" << endl;
fin << " W2 += mod2pi(" << setprecision(17) << w22 << "*T2);" << endl;
fin << " W2 += mod2pi(" << setprecision(17) << w23 << "*T3);" << endl;
fin << " W2 += mod2pi(" << setprecision(17) << w24 << "*T4);" << endl;
double w30 = (125.0 + 2.0/60.0 + (40.39816 + paras.Dw3_0)/3600.0)*deg;
double w31 = (-6967919.5383 + paras.Dw3_1 + paras.Cw3_1)*sec;
double w32 = (6.359 + paras.Dw3_2)*sec;
double w33 = (0.007625 + paras.Dw3_3)*sec;
double w34 = -3.586e-5*sec;
fin << " double W3 = " << setprecision(17) << w30 << ";" << endl;
fin << " W3 += mod2pi(" << setprecision(17) << w31 << "*T);" << endl;
fin << " W3 += mod2pi(" << setprecision(17) << w32 << "*T2);" << endl;
fin << " W3 += mod2pi(" << setprecision(17) << w33 << "*T3);" << endl;
fin << " W3 += mod2pi(" << setprecision(17) << w34 << "*T4);" << endl;
double Ea0 = (100.0 + 27.0/60.0 + (59.13885 + paras.Deart_0)/3600.0)*deg;
double Ea1 = (129597742.293 + paras.Deart_1)*sec;
double Ea2 = -0.0202*sec;
double Ea3 = 9e-6*sec;
double Ea4 = 1.5e-7*sec;
fin << " double Ea = " << setprecision(17) << Ea0 << ";" << endl;
fin << " Ea += mod2pi(" << setprecision(17) << Ea1 << "*T);" << endl;
fin << " Ea += mod2pi(" << setprecision(17) << Ea2 << "*T2);" << endl;
fin << " Ea += mod2pi(" << setprecision(17) << Ea3 << "*T3);" << endl;
fin << " Ea += mod2pi(" << setprecision(17) << Ea4 << "*T4);" << endl;
double p0 = (102.0 + 56.0/60.0 + (14.45766 + paras.Dperi)/3600.0)*deg;
double p1 = 1161.24342*sec;
double p2 = 0.529265*sec;
double p3 = -1.1814e-4*sec;
double p4 = 1.1379e-5*sec;
fin << " double pomp = " << setprecision(17) << p0 << ";" << endl;
fin << " pomp += mod2pi(" << setprecision(17) << p1 << "*T);" << endl;
fin << " pomp += mod2pi(" << setprecision(17) << p2 << "*T2);" << endl;
fin << " pomp += mod2pi(" << setprecision(17) << p3 << "*T3);" << endl;
fin << " pomp += mod2pi(" << setprecision(17) << p4 << "*T4);" << endl;
double Me = (-108.0 + 15.0/60.0 + 3.216919/3600.0)*deg;
double Me1 = 538101628.66888*sec;
double Ve = (-179.0 + 58.0/60.0 + 44.758419/3600.0)*deg;
double Ve1 = 210664136.45777*sec;
double EM = (100.0 + 27.0/60.0 + 59.13885/3600.0)*deg;
double EM1 = 129597742.293*sec;
double Ma = (-5.0 + 26.0/60.0 + 3.642778/3600.0)*deg;
double Ma1 = 68905077.65936*sec;
double Ju = (34.0 + 21.0/60.0 + 5.379392/3600.0)*deg;
double Ju1 = 10925660.57335*sec;
double Sa = (50.0 + 4.0/60.0 + 38.902495/3600.0)*deg;
double Sa1 = 4399609.33632*sec;
double Ur = (-46.0 + 3.0/60.0 + 4.354234/3600.0)*deg;
double Ur1 = 1542482.57845*sec;
double Ne = (-56.0 + 20.0/60.0 + 56.808371/3600.0)*deg;
double Ne1 = 786547.897*sec;
fin << " double Me = " << setprecision(17) << Me << ";" << endl;
fin << " Me += mod2pi(" << setprecision(17) << Me1 << "*T);" << endl;
fin << " double Ve = " << setprecision(17) << Ve << ";" << endl;
fin << " Ve += mod2pi(" << setprecision(17) << Ve1 << "*T);" << endl;
fin << " double EM = " << setprecision(17) << EM << ";" << endl;
fin << " EM += mod2pi(" << setprecision(17) << EM1 << "*T);" << endl;
fin << " double Ma = " << setprecision(17) << Ma << ";" << endl;
fin << " Ma += mod2pi(" << setprecision(17) << Ma1 << "*T);" << endl;
fin << " double Ju = " << setprecision(17) << Ju << ";" << endl;
fin << " Ju += mod2pi(" << setprecision(17) << Ju1 << "*T);" << endl;
fin << " double Sa = " << setprecision(17) << Sa << ";" << endl;
fin << " Sa += mod2pi(" << setprecision(17) << Sa1 << "*T);" << endl;
fin << " double Ur = " << setprecision(17) << Ur << ";" << endl;
fin << " Ur += mod2pi(" << setprecision(17) << Ur1 << "*T);" << endl;
fin << " double Ne = " << setprecision(17) << Ne << ";" << endl;
fin << " Ne += mod2pi(" << setprecision(17) << Ne1 << "*T);" << endl;
fin << endl;
fin << " // Mean longitude of the Moon" << endl;
fin << " args.W1 = mod2pi(W1);" << endl;
fin << " // Arguments of Delaunay" << endl;
fin << " args.D = mod2pi(W1-Ea + PI);" << endl;
fin << " args.F = mod2pi(W1-W3);" << endl;
fin << " args.L = mod2pi(W1-W2);" << endl;
fin << " args.Lp = mod2pi(Ea-pomp);" << endl;
fin << endl;
fin << " //zeta" << endl;
fin << " args.zeta = mod2pi(W1 + 0.02438029560881907*T);" << endl;
fin << endl;
fin << " // Planetary arguments (mean longitudes and mean motions)" << endl;
fin << " args.Me = mod2pi(Me);" << endl;
fin << " args.Ve = mod2pi(Ve);" << endl;
fin << " args.EM = mod2pi(EM);" << endl;
fin << " args.Ma = mod2pi(Ma);" << endl;
fin << " args.Ju = mod2pi(Ju);" << endl;
fin << " args.Sa = mod2pi(Sa);" << endl;
fin << " args.Ur = mod2pi(Ur);" << endl;
fin << " args.Ne = mod2pi(Ne);" << endl;
fin << "}" << endl;
fin << "" << endl;
fin << "// Sum the ELP/MPP02 series for the main problem" << endl;
fin << "// dist = 0: sine series; dist != 0: cosine series" << endl;
fin << "double Elp_main_sum(int n, int ** &i_main, double * &A_main, Elp_args &args, int dist) {" << endl;
fin << " int i;" << endl;
fin << " double sum = 0.0;" << endl;
fin << " double phase;" << endl;
fin << " if (dist==0) {" << endl;
fin << " // sine series " << endl;
fin << " for (i=0; i<n; i++) {" << endl;
fin << " phase = i_main[i][0]*args.D + i_main[i][1]*args.F + i_main[i][2]*args.L + " << endl;
fin << " i_main[i][3]*args.Lp;" << endl;
fin << " sum += A_main[i]*sin(phase);" << endl;
fin << " }" << endl;
fin << " } else {" << endl;
fin << " // cosine series" << endl;
fin << " for (i=0; i<n; i++) {" << endl;
fin << " phase = i_main[i][0]*args.D + i_main[i][1]*args.F + i_main[i][2]*args.L +" << endl;
fin << " i_main[i][3]*args.Lp;" << endl;
fin << " sum += A_main[i]*cos(phase);" << endl;
fin << " }" << endl;
fin << " }" << endl;
fin << " return sum;" << endl;
fin << "}" << endl;
fin << "" << endl;
fin << "// Sum the ELP/MPP02 series for perturbations" << endl;
fin << "double Elp_perturbation_sum(int n, int ** &i_pert, double * &A_pert, double * &ph_pert," << endl;
fin << " Elp_args &args) {" << endl;
fin << " int i;" << endl;
fin << " double sum = 0.0;" << endl;
fin << " double phase;" << endl;
fin << " for (i=0; i<n; i++) {" << endl;
fin << " phase = ph_pert[i] + i_pert[i][0]*args.D + i_pert[i][1]*args.F + " << endl;
fin << " i_pert[i][2]*args.L + i_pert[i][3]*args.Lp + i_pert[i][4]*args.Me + " << endl;
fin << " i_pert[i][5]*args.Ve + i_pert[i][6]*args.EM + i_pert[i][7]*args.Ma + " << endl;
fin << " i_pert[i][8]*args.Ju + i_pert[i][9]*args.Sa + i_pert[i][10]*args.Ur +" << endl;
fin << " i_pert[i][11]*args.Ne + i_pert[i][12]*args.zeta;" << endl;
fin << " sum += A_pert[i]*sin(phase);" << endl;
fin << " }" << endl;
fin << " return sum;" << endl;
fin << "}" << endl;
fin << "" << endl;
fin << "// Calculate the Moon's geocentric X,Y,Z coordinates with respect to " << endl;
fin << "// J2000.0 mean ecliptic and equinox." << endl;
fin << "// T is the TDB Julian century from J2000.0 = (TBD JD - 2451545)/36525" << endl;
fin << "void getX2000(double T, Elp_coefs &coefs, double &X, double &Y, double &Z) {" << endl;
fin << " double T2 = T*T;" << endl;
fin << " double T3 = T*T2;" << endl;
fin << " double T4 = T2*T2;" << endl;
fin << " double T5 = T2*T3;" << endl;
fin << " Elp_args args;" << endl;
fin << " compute_Elp_arguments(T, args);" << endl;
fin << "" << endl;
fin << " // Sum the ELP/MPP02 series" << endl;
fin << " // main problem series" << endl;
fin << " double main_long = Elp_main_sum(coefs.n_main_long, coefs.i_main_long, " << endl;
fin << " coefs.A_main_long, args, 0);" << endl;
fin << " double main_lat = Elp_main_sum(coefs.n_main_lat, coefs.i_main_lat," << endl;
fin << " coefs.A_main_lat, args, 0);" << endl;
fin << " double main_dist = Elp_main_sum(coefs.n_main_dist, coefs.i_main_dist," << endl;
fin << " coefs.A_main_dist, args, 1);" << endl;
fin << " // perturbation, longitude" << endl;
fin << " double pert_longT0 = Elp_perturbation_sum(coefs.n_pert_longT0, coefs.i_pert_longT0, " << endl;
fin << " coefs.A_pert_longT0, coefs.ph_pert_longT0, args);" << endl;
fin << " double pert_longT1 = Elp_perturbation_sum(coefs.n_pert_longT1, coefs.i_pert_longT1," << endl;
fin << " coefs.A_pert_longT1, coefs.ph_pert_longT1, args);" << endl;
fin << " double pert_longT2 = Elp_perturbation_sum(coefs.n_pert_longT2, coefs.i_pert_longT2," << endl;
fin << " coefs.A_pert_longT2, coefs.ph_pert_longT2, args);" << endl;
fin << " double pert_longT3 = Elp_perturbation_sum(coefs.n_pert_longT3, coefs.i_pert_longT3," << endl;
fin << " coefs.A_pert_longT3, coefs.ph_pert_longT3, args);" << endl;
fin << " // perturbation, latitude" << endl;
fin << " double pert_latT0 = Elp_perturbation_sum(coefs.n_pert_latT0, coefs.i_pert_latT0," << endl;
fin << " coefs.A_pert_latT0, coefs.ph_pert_latT0, args);" << endl;
fin << " double pert_latT1 = Elp_perturbation_sum(coefs.n_pert_latT1, coefs.i_pert_latT1," << endl;
fin << " coefs.A_pert_latT1, coefs.ph_pert_latT1, args);" << endl;
fin << " double pert_latT2 = Elp_perturbation_sum(coefs.n_pert_latT2, coefs.i_pert_latT2," << endl;
fin << " coefs.A_pert_latT2, coefs.ph_pert_latT2, args);" << endl;
fin << " // perturbation, distance" << endl;
fin << " double pert_distT0 = Elp_perturbation_sum(coefs.n_pert_distT0, coefs.i_pert_distT0," << endl;
fin << " coefs.A_pert_distT0, coefs.ph_pert_distT0, args);" << endl;
fin << " double pert_distT1 = Elp_perturbation_sum(coefs.n_pert_distT1, coefs.i_pert_distT1," << endl;
fin << " coefs.A_pert_distT1, coefs.ph_pert_distT1, args);" << endl;
fin << " double pert_distT2 = Elp_perturbation_sum(coefs.n_pert_distT2, coefs.i_pert_distT2," << endl;
fin << " coefs.A_pert_distT2, coefs.ph_pert_distT2, args);" << endl;
fin << " double pert_distT3 = Elp_perturbation_sum(coefs.n_pert_distT3, coefs.i_pert_distT3," << endl;
fin << " coefs.A_pert_distT3, coefs.ph_pert_distT3, args);" << endl;
fin << "" << endl;
fin << " // Moon's longitude, latitude and distance" << endl;
fin << " double longM = args.W1 + main_long + pert_longT0 + mod2pi(pert_longT1*T) + " << endl;
fin << " mod2pi(pert_longT2*T2) + mod2pi(pert_longT3*T3);" << endl;
fin << " double latM = main_lat + pert_latT0 + mod2pi(pert_latT1*T) + mod2pi(pert_latT2*T2);" << endl;
fin << " // ra0 = a0(DE405)/a0(ELP) = 384747.961370173/384747.980674318 = 0.99999994982652041." << endl;
fin << " double r = " << setprecision(17) << 384747.961370173/384747.980674318
<< "*(main_dist + pert_distT0 + pert_distT1*T + pert_distT2*T2 + pert_distT3*T3);"
<< endl;
fin << " double x0 = r*cos(longM)*cos(latM);" << endl;
fin << " double y0 = r*sin(longM)*cos(latM);" << endl;
fin << " double z0 = r*sin(latM);" << endl;
fin << "" << endl;
fin << " // Precession matrix" << endl;
fin << " double P = 0.10180391e-4*T + 0.47020439e-6*T2 - 0.5417367e-9*T3 " << endl;
fin << " - 0.2507948e-11*T4 + 0.463486e-14*T5;" << endl;
fin << " double Q = -0.113469002e-3*T + 0.12372674e-6*T2 + 0.12654170e-8*T3 " << endl;
fin << " - 0.1371808e-11*T4 - 0.320334e-14*T5;" << endl;
fin << " double sq = sqrt(1 - P*P - Q*Q);" << endl;
fin << " double p11 = 1 - 2*P*P;" << endl;
fin << " double p12 = 2*P*Q;" << endl;
fin << " double p13 = 2*P*sq;" << endl;
fin << " double p21 = 2*P*Q;" << endl;
fin << " double p22 = 1-2*Q*Q;" << endl;
fin << " double p23 = -2*Q*sq;" << endl;
fin << " double p31 = -2*P*sq;" << endl;
fin << " double p32 = 2*Q*sq;" << endl;
fin << " double p33 = 1 - 2*P*P - 2*Q*Q;" << endl;
fin << "" << endl;
fin << " // Finally, components of position vector wrt J2000.0 mean ecliptic and equinox" << endl;
fin << " X = p11*x0 + p12*y0 + p13*z0;" << endl;
fin << " Y = p21*x0 + p22*y0 + p23*z0;" << endl;
fin << " Z = p31*x0 + p32*y0 + p33*z0;" << endl;
fin << "}" << endl;
fin.close();
}
void write_main_problem_file(const char *outfile, int &n, int ** &i_main, double * &A_main) {
ofstream fin(outfile);
fin << n << endl;
for (int i=0; i<n; i++) {