/**
* @file integrator_whfast.c
* @brief WHFAST integration scheme.
* @author Hanno Rein <hanno@hanno-rein.de>
* @details This file implements the WHFast integration scheme.
* Described in Rein & Tamayo 2015, Rein et al. 2019.
* See also Wisdom et al. 1996.
*
* @section LICENSE
* Copyright (c) 2015 Hanno Rein, Daniel Tamayo
*
* This file is part of rebound.
*
* rebound is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* rebound is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with rebound. If not, see <http://www.gnu.org/licenses/>.
*
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "rebound.h"
#include "particle.h"
#include "tools.h"
#include "gravity.h"
#include "boundary.h"
#include "integrator.h"
#include "integrator_whfast.h"
#define MAX(a, b) ((a) < (b) ? (b) : (a)) ///< Returns the maximum of a and b
#define MIN(a, b) ((a) > (b) ? (b) : (a)) ///< Returns the minimum of a and b
// Corrector coefficients
static const double reb_whfast_corrector_a_1 = 0.41833001326703777398908601289259374469640768464934;
static const double reb_whfast_corrector_a_2 = 0.83666002653407554797817202578518748939281536929867;
static const double reb_whfast_corrector_a_3 = 1.2549900398011133219672580386777812340892230539480;
static const double reb_whfast_corrector_a_4 = 1.6733200530681510959563440515703749787856307385973;
static const double reb_whfast_corrector_a_5 = 2.0916500663351888699454300644629687234820384232467;
static const double reb_whfast_corrector_a_6 = 2.5099800796022266439345160773555624681784461078960;
static const double reb_whfast_corrector_a_7 = 2.9283100928692644179236020902481562128748537925454;
static const double reb_whfast_corrector_a_8 = 3.3466401061363021919126881031407499575712614771947;
static const double reb_whfast_corrector_b_31 = -0.024900596027799867499350357910273437184309981229127;
static const double reb_whfast_corrector_b_51 = -0.0083001986759332891664501193034244790614366604097090;
static const double reb_whfast_corrector_b_52 = 0.041500993379666445832250596517122395307183302048545;
static const double reb_whfast_corrector_b_71 = 0.0024926811426922105779030593952776964450539008582219;
static const double reb_whfast_corrector_b_72 = -0.018270923246702131478062356884535264841652263842597;
static const double reb_whfast_corrector_b_73 = 0.053964399093127498721765893493510877532452806339655;
static const double reb_whfast_corrector_b_111 = 0.00020361579647854651301632818774633716473696537436847;
static const double reb_whfast_corrector_b_112 = -0.0023487215292295354188307328851055489876255097419754;
static const double reb_whfast_corrector_b_113 = 0.012309078592019946317544564763237909911330686448336;
static const double reb_whfast_corrector_b_114 = -0.038121613681288650508647613260247372125243616270670;
static const double reb_whfast_corrector_b_115 = 0.072593394748842738674253180742744961827622366521517;
static const double reb_whfast_corrector_b_178 = 0.093056103771425958591541059067553547100903397724386;
static const double reb_whfast_corrector_b_177 = -0.065192863576377893658290760803725762027864651086787;
static const double reb_whfast_corrector_b_176 = 0.032422198864713580293681523029577130832258806467604;
static const double reb_whfast_corrector_b_175 = -0.012071760822342291062449751726959664253913904872527;
static const double reb_whfast_corrector_b_174 = 0.0033132577069380655655490196833451994080066801611459;
static const double reb_whfast_corrector_b_173 = -0.00063599983075817658983166881625078545864140848560259;
static const double reb_whfast_corrector_b_172 = 0.000076436355227935738363241846979413475106795392377415;
static const double reb_whfast_corrector_b_171 = -0.0000043347415473373580190650223498124944896789841432241;
static const double reb_whfast_corrector2_b = 0.03486083443891981449909050107438281205803;
// Fast inverse factorial lookup table
static const double invfactorial[35] = {1., 1., 1./2., 1./6., 1./24., 1./120., 1./720., 1./5040., 1./40320., 1./362880., 1./3628800., 1./39916800., 1./479001600., 1./6227020800., 1./87178291200., 1./1307674368000., 1./20922789888000., 1./355687428096000., 1./6402373705728000., 1./121645100408832000., 1./2432902008176640000., 1./51090942171709440000., 1./1124000727777607680000., 1./25852016738884976640000., 1./620448401733239439360000., 1./15511210043330985984000000., 1./403291461126605635584000000., 1./10888869450418352160768000000., 1./304888344611713860501504000000., 1./8841761993739701954543616000000., 1./265252859812191058636308480000000., 1./8222838654177922817725562880000000., 1./263130836933693530167218012160000000., 1./8683317618811886495518194401280000000., 1./295232799039604140847618609643520000000.};
static inline double fastabs(double x){
return (x > 0.) ? x : -x;
}
static void stumpff_cs(double *restrict cs, double z) {
unsigned int n = 0;
while(fastabs(z)>0.1){
z = z/4.;
n++;
}
const int nmax = 15;
double c_odd = invfactorial[nmax];
double c_even = invfactorial[nmax-1];
for(int np=nmax-2;np>=5;np-=2){
c_odd = invfactorial[np] - z *c_odd;
c_even = invfactorial[np-1] - z *c_even;
}
cs[5] = c_odd;
cs[4] = c_even;
cs[3] = invfactorial[3] - z *cs[5];
cs[2] = invfactorial[2] - z *cs[4];
cs[1] = invfactorial[1] - z *cs[3];
for (;n>0;n--){
z = z*4.;
cs[5] = (cs[5]+cs[4]+cs[3]*cs[2])*0.0625;
cs[4] = (1.+cs[1])*cs[3]*0.125;
cs[3] = 1./6.-z*cs[5];
cs[2] = 0.5-z*cs[4];
cs[1] = 1.-z*cs[3];
}
cs[0] = invfactorial[0] - z *cs[2];
}
static void stumpff_cs3(double *restrict cs, double z) {
unsigned int n = 0;
while(fabs(z)>0.1){
z = z/4.;
n++;
}
const int nmax = 13;
double c_odd = invfactorial[nmax];
double c_even = invfactorial[nmax-1];
for(int np=nmax-2;np>=3;np-=2){
c_odd = invfactorial[np] - z *c_odd;
c_even = invfactorial[np-1] - z *c_even;
}
cs[3] = c_odd;
cs[2] = c_even;
cs[1] = invfactorial[1] - z *c_odd;
cs[0] = invfactorial[0] - z *c_even;
for (;n>0;n--){
cs[3] = (cs[2]+cs[0]*cs[3])*0.25;
cs[2] = cs[1]*cs[1]*0.5;
cs[1] = cs[0]*cs[1];
cs[0] = 2.*cs[0]*cs[0]-1.;
}
}
static void stiefel_Gs(double *restrict Gs, double beta, double X) {
double X2 = X*X;
stumpff_cs(Gs, beta*X2);
Gs[1] *= X;
Gs[2] *= X2;
double _pow = X2*X;
Gs[3] *= _pow;
_pow *= X;
Gs[4] *= _pow;
_pow *= X;
Gs[5] *= _pow;
return;
}
static void stiefel_Gs3(double *restrict Gs, double beta, double X) {
double X2 = X*X;
stumpff_cs3(Gs, beta*X2);
Gs[1] *= X;
Gs[2] *= X2;
Gs[3] *= X2*X;
return;
}
#define WHFAST_NMAX_QUART 64 ///< Maximum number of iterations for quartic solver
#define WHFAST_NMAX_NEWT 32 ///< Maximum number of iterations for Newton's method
/************************************
* Keplerian motion for one planet */
void reb_whfast_kepler_solver(const struct reb_simulation* const r, struct reb_particle* const restrict p_j, const double M, unsigned int i, double _dt){
const struct reb_particle p1 = p_j[i];
const double r0 = sqrt(p1.x*p1.x + p1.y*p1.y + p1.z*p1.z);
const double r0i = 1./r0;
const double v2 = p1.vx*p1.vx + p1.vy*p1.vy + p1.vz*p1.vz;
const double beta = 2.*M*r0i - v2;
const double eta0 = p1.x*p1.vx + p1.y*p1.vy + p1.z*p1.vz;
const double zeta0 = M - beta*r0;
double X;
double Gs[6];
double invperiod=0; // only used for beta>0. Set to 0 only to suppress compiler warnings.
double X_per_period = nan(""); // only used for beta>0. nan triggers Newton's method for beta<0.
if (beta>0.){
// Elliptic orbit
const double sqrt_beta = sqrt(beta);
invperiod = sqrt_beta*beta/(2.*M_PI*M);
X_per_period = 2.*M_PI/sqrt_beta;
if (fabs(_dt)*invperiod>1. && r && r->ri_whfast.timestep_warning == 0){
// Ignoring const qualifiers. This warning should not have any effect on
// other parts of the code, nor is it vital to show it.
((struct reb_simulation* const)r)->ri_whfast.timestep_warning++;
reb_simulation_warning((struct reb_simulation* const)r,"WHFast convergence issue. Timestep is larger than at least one orbital period.");
}
//X = _dt*invperiod*X_per_period; // first order guess
const double dtr0i = _dt*r0i;
//X = dtr0i; // first order guess
X = dtr0i * (1. - dtr0i*eta0*0.5*r0i); // second order guess
//X = dtr0i *(1.- 0.5*dtr0i*r0i*(eta0-dtr0i*(eta0*eta0*r0i-1./3.*zeta0))); // third order guess
//X = _dt*beta/M + eta0/M*(0.85*sqrt(1.+zeta0*zeta0/beta/eta0/eta0) - 1.); // Dan's version
}else{
// Hyperbolic orbit
X = 0.; // Initial guess
}
unsigned int converged = 0;
double oldX = X;
// Do one Newton step
stiefel_Gs3(Gs, beta, X);
const double eta0Gs1zeta0Gs2 = eta0*Gs[1] + zeta0*Gs[2];
double ri = 1./(r0 + eta0Gs1zeta0Gs2);
X = ri*(X*eta0Gs1zeta0Gs2-eta0*Gs[2]-zeta0*Gs[3]+_dt);
// Choose solver depending on estimated step size
// Note, for hyperbolic orbits this uses Newton's method.
if(fastabs(X-oldX) > 0.01*X_per_period){
// Quartic solver
// Linear initial guess
X = beta*_dt/M;
double prevX[WHFAST_NMAX_QUART+1];
for(int n_lag=1; n_lag < WHFAST_NMAX_QUART; n_lag++){
stiefel_Gs3(Gs, beta, X);
const double f = r0*X + eta0*Gs[2] + zeta0*Gs[3] - _dt;
const double fp = r0 + eta0*Gs[1] + zeta0*Gs[2];
const double fpp = eta0*Gs[0] + zeta0*Gs[1];
const double denom = fp + sqrt(fabs(16.*fp*fp - 20.*f*fpp));
X = (X*denom - 5.*f)/denom;
for(int i=1;i<n_lag;i++){
if(X==prevX[i]){
// Converged. Exit.
n_lag = WHFAST_NMAX_QUART;
converged = 1;
break;
}
}
prevX[n_lag] = X;
}
const double eta0Gs1zeta0Gs2 = eta0*Gs[1] + zeta0*Gs[2];
ri = 1./(r0 + eta0Gs1zeta0Gs2);
}else{
// Newton's method
double oldX2 = nan("");
for (int n_hg=1;n_hg<WHFAST_NMAX_NEWT;n_hg++){
oldX2 = oldX;
oldX = X;
stiefel_Gs3(Gs, beta, X);
const double eta0Gs1zeta0Gs2 = eta0*Gs[1] + zeta0*Gs[2];
ri = 1./(r0 + eta0Gs1zeta0Gs2);
X = ri*(X*eta0Gs1zeta0Gs2-eta0*Gs[2]-zeta0*Gs[3]+_dt);
if (X==oldX||X==oldX2){
// Converged. Exit.
converged = 1;
break;
}
}
}
// If solver did not work, fallback to bisection
if (converged == 0){
double X_min, X_max;
if (beta>0.){
//Elliptic
X_min = X_per_period * floor(_dt*invperiod);
X_max = X_min + X_per_period;
}else{
//Hyperbolic
double h2 = r0*r0*v2-eta0*eta0;
double q = h2/M/(1.+sqrt(1.-h2*beta/(M*M)));
double vq = copysign( sqrt(h2)/q, _dt);
// X_max and X_min correspond to dt/r_min and dt/r_max
// which are reachable in this timestep
// r_max = vq*_dt+r0
// r_min = pericenter
X_min = _dt/(fastabs(vq*_dt)+r0);
X_max = _dt/q;
if (_dt<0.){
double temp = X_min;
X_min = X_max;
X_max = temp;
}
}
X = (X_max + X_min)/2.;
do{
stiefel_Gs3(Gs, beta, X);
double s = r0*X + eta0*Gs[2] + zeta0*Gs[3]-_dt;
if (s>=0.){
X_max = X;
}else{
X_min = X;
}
X = (X_max + X_min)/2.;
}while (fastabs((X_max-X_min))>fastabs((X_max+X_min)*1e-15));
const double eta0Gs1zeta0Gs2 = eta0*Gs[1] + zeta0*Gs[2];
ri = 1./(r0 + eta0Gs1zeta0Gs2);
}
if (isnan(ri)){
// Exception for (almost) straight line motion in hyperbolic case
ri = 0.;
Gs[1] = 0.;
Gs[2] = 0.;
Gs[3] = 0.;
}
// Note: These are not the traditional f and g functions.
double f = -M*Gs[2]*r0i;
double g = _dt - M*Gs[3];
double fd = -M*Gs[1]*r0i*ri;
double gd = -M*Gs[2]*ri;
p_j[i].x += f*p1.x + g*p1.vx;
p_j[i].y += f*p1.y + g*p1.vy;
p_j[i].z += f*p1.z + g*p1.vz;
p_j[i].vx += fd*p1.x + gd*p1.vx;
p_j[i].vy += fd*p1.y + gd*p1.vy;
p_j[i].vz += fd*p1.z + gd*p1.vz;
//Variations
for (int v=0;r && v<r->N_var_config;v++){
struct reb_variational_configuration const vc = r->var_config[v];
const int index = vc.index;
stiefel_Gs(Gs, beta, X); // Recalculate (to get Gs[4] and Gs[5])
struct reb_particle dp1 = p_j[i+index];
double dr0 = (dp1.x*p1.x + dp1.y*p1.y + dp1.z*p1.z)*r0i;
double dbeta = -2.*M*dr0*r0i*r0i - 2.* (dp1.vx*p1.vx + dp1.vy*p1.vy + dp1.vz*p1.vz);
double deta0 = dp1.x*p1.vx + dp1.y*p1.vy + dp1.z*p1.vz
+ p1.x*dp1.vx + p1.y*dp1.vy + p1.z*dp1.vz;
double dzeta0 = -beta*dr0 - r0*dbeta;
double G3beta = 0.5*(3.*Gs[5]-X*Gs[4]);
double G2beta = 0.5*(2.*Gs[4]-X*Gs[3]);
double G1beta = 0.5*(Gs[3]-X*Gs[2]);
double tbeta = eta0*G2beta + zeta0*G3beta;
double dX = -1.*ri*(X*dr0 + Gs[2]*deta0+Gs[3]*dzeta0+tbeta*dbeta);
double dG1 = Gs[0]*dX + G1beta*dbeta;
double dG2 = Gs[1]*dX + G2beta*dbeta;
double dG3 = Gs[2]*dX + G3beta*dbeta;
double dr = dr0 + Gs[1]*deta0 + Gs[2]*dzeta0 + eta0*dG1 + zeta0*dG2;
double df = M*Gs[2]*dr0*r0i*r0i - M*dG2*r0i;
double dg = -M*dG3;
double dfd = -M*dG1*r0i*ri + M*Gs[1]*(dr0*r0i+dr*ri)*r0i*ri;
double dgd = -M*dG2*ri + M*Gs[2]*dr*ri*ri;
p_j[i+index].x += f*dp1.x + g*dp1.vx + df*p1.x + dg*p1.vx;
p_j[i+index].y += f*dp1.y + g*dp1.vy + df*p1.y + dg*p1.vy;
p_j[i+index].z += f*dp1.z + g*dp1.vz + df*p1.z + dg*p1.vz;
p_j[i+index].vx += fd*dp1.x + gd*dp1.vx + dfd*p1.x + dgd*p1.vx;
p_j[i+index].vy += fd*dp1.y + gd*dp1.vy + dfd*p1.y + dgd*p1.vy;
p_j[i+index].vz += fd*dp1.z + gd*dp1.vz + dfd*p1.z + dgd*p1.vz;
}
}
/*****************************
* Interaction Hamiltonian */
void reb_whfast_interaction_step(struct reb_simulation* const r, const double _dt){
const unsigned int N_real = r->N-r->N_var;
const int N_active = (r->N_active==-1 || r->testparticle_type ==1)?(int)N_real:r->N_active;
const double G = r->G;
struct reb_particle* particles = r->particles;
const double m0 = particles[0].m;
struct reb_integrator_whfast* const ri_whfast = &(r->ri_whfast);
struct reb_particle* const p_j = ri_whfast->p_jh;
switch (ri_whfast->coordinates){
case REB_WHFAST_COORDINATES_JACOBI:
{
const double softening = r->softening;
for (int v=0;v<r->N_var_config;v++){
struct reb_variational_configuration const vc = r->var_config[v];
reb_particles_transform_inertial_to_jacobi_acc(particles+vc.index, p_j+vc.index, particles, N_real, N_active);
}
reb_particles_transform_inertial_to_jacobi_acc(particles, p_j, particles, N_real, N_active);
double eta = m0;
for (int i=1;i<(int)N_real;i++){
// Eq 132
const struct reb_particle pji = p_j[i];
if (i<N_active){
eta += pji.m;
}
p_j[i].vx += _dt * pji.ax;
p_j[i].vy += _dt * pji.ay;
p_j[i].vz += _dt * pji.az;
if (r->gravity != REB_GRAVITY_JACOBI){
// If Jacobi terms have not been added in update_acceleration, then add them here:
if (i>1){
const double rj2i = 1./(pji.x*pji.x + pji.y*pji.y + pji.z*pji.z + softening*softening);
const double rji = sqrt(rj2i);
const double rj3iM = rji*rj2i*G*eta;
const double prefac1 = _dt*rj3iM;
p_j[i].vx += prefac1*pji.x;
p_j[i].vy += prefac1*pji.y;
p_j[i].vz += prefac1*pji.z;
for(int v=0;v<r->N_var_config;v++){
struct reb_variational_configuration const vc = r->var_config[v];
const int index = vc.index;
double rj5M = rj3iM*rj2i;
double rdr = p_j[i+index].x*pji.x + p_j[i+index].y*pji.y + p_j[i+index].z*pji.z;
double prefac2 = -_dt*3.*rdr*rj5M;
p_j[i+index].vx += prefac1*p_j[i+index].x + prefac2*pji.x;
p_j[i+index].vy += prefac1*p_j[i+index].y + prefac2*pji.y;
p_j[i+index].vz += prefac1*p_j[i+index].z + prefac2*pji.z;
}
}
for(int v=0;v<r->N_var_config;v++){
struct reb_variational_configuration const vc = r->var_config[v];
const int index = vc.index;
p_j[i+index].vx += _dt * p_j[i+index].ax;
p_j[i+index].vy += _dt * p_j[i+index].ay;
p_j[i+index].vz += _dt * p_j[i+index].az;
}
}
}
}
break;
case REB_WHFAST_COORDINATES_DEMOCRATICHELIOCENTRIC:
#pragma omp parallel for
for (unsigned int i=1;i<N_real;i++){
p_j[i].vx += _dt*particles[i].ax;
p_j[i].vy += _dt*particles[i].ay;
p_j[i].vz += _dt*particles[i].az;
}
break;
case REB_WHFAST_COORDINATES_WHDS:
#pragma omp parallel for
for (int i=1;i<N_active;i++){
const double mi = particles[i].m;
p_j[i].vx += _dt*(m0+mi)*particles[i].ax/m0;
p_j[i].vy += _dt*(m0+mi)*particles[i].ay/m0;
p_j[i].vz += _dt*(m0+mi)*particles[i].az/m0;
}
#pragma omp parallel for
for (int i=N_active;i<(int)N_real;i++){
p_j[i].vx += _dt*particles[i].ax;
p_j[i].vy += _dt*particles[i].ay;
p_j[i].vz += _dt*particles[i].az;
}
break;
case REB_WHFAST_COORDINATES_BARYCENTRIC:
for (unsigned int i=1;i<(int)N_real;i++){
const double dr = sqrt(p_j[i].x*p_j[i].x + p_j[i].y*p_j[i].y + p_j[i].z*p_j[i].z);
const double prefac = G*p_j[0].m/(dr*dr*dr);
p_j[i].vx += _dt*(prefac*p_j[i].x + particles[i].ax);
p_j[i].vy += _dt*(prefac*p_j[i].y + particles[i].ay);
p_j[i].vz += _dt*(prefac*p_j[i].z + particles[i].az);
}
break;
};
}
void reb_whfast_jump_step(const struct reb_simulation* const r, const double _dt){
const struct reb_integrator_whfast* const ri_whfast = &(r->ri_whfast);
struct reb_particle* const p_h = r->ri_whfast.p_jh;
const int N_real = r->N - r->N_var;
const int N_active = (r->N_active==-1 || r->testparticle_type ==1)?N_real:r->N_active;
const double m0 = r->particles[0].m;
switch (ri_whfast->coordinates){
case REB_WHFAST_COORDINATES_JACOBI:
// Nothing to be done.
break;
case REB_WHFAST_COORDINATES_DEMOCRATICHELIOCENTRIC:
{
double px=0, py=0, pz=0;
#pragma omp parallel for reduction (+:px), reduction (+:py), reduction (+:pz)
for(int i=1;i<N_active;i++){
const double m = r->particles[i].m;
px += m * p_h[i].vx;
py += m * p_h[i].vy;
pz += m * p_h[i].vz;
}
#pragma omp parallel for
for(int i=1;i<N_real;i++){
p_h[i].x += _dt * (px/m0);
p_h[i].y += _dt * (py/m0);
p_h[i].z += _dt * (pz/m0);
}
}
break;
case REB_WHFAST_COORDINATES_WHDS:
{
double px=0, py=0, pz=0;
#pragma omp parallel for reduction (+:px), reduction (+:py), reduction (+:pz)
for(int i=1;i<N_active;i++){
const double m = r->particles[i].m;
px += m * p_h[i].vx / (m0+m);
py += m * p_h[i].vy / (m0+m);
pz += m * p_h[i].vz / (m0+m);
}
#pragma omp parallel for
for(int i=1;i<N_active;i++){
const double m = r->particles[i].m;
p_h[i].x += _dt * (px - (m * p_h[i].vx / (m0+m)) );
p_h[i].y += _dt * (py - (m * p_h[i].vy / (m0+m)) );
p_h[i].z += _dt * (pz - (m * p_h[i].vz / (m0+m)) );
}
#pragma omp parallel for
for(int i=N_active;i<N_real;i++){
p_h[i].x += _dt * px;
p_h[i].y += _dt * py;
p_h[i].z += _dt * pz;
}
}
break;
case REB_WHFAST_COORDINATES_BARYCENTRIC:
// Nothing to be done.
break;
};
}
/*****************************
* DKD Scheme */
void reb_whfast_kepler_step(const struct reb_simulation* const r, const double _dt){
const double m0 = r->particles[0].m;
const double G = r->G;
const unsigned int N_real = r->N-r->N_var;
const int N_active = (r->N_active==-1 || r->testparticle_type ==1)?(int)N_real:r->N_active;
const int coordinates = r->ri_whfast.coordinates;
struct reb_particle* const p_j = r->ri_whfast.p_jh;
double eta = m0;
switch (coordinates){
case REB_WHFAST_COORDINATES_JACOBI:
#pragma omp parallel for private(eta)
for (int i=1;i<(int)N_real;i++){
#ifdef OPENMP
eta = m0;
for (int j=1;j<MIN(i,(int)N_active);j++){
eta += p_j[j].m;
}
#else // OPENMP
if (i<N_active){
eta += p_j[i].m;
}
#endif // OPENMP
reb_whfast_kepler_solver(r, p_j, eta*G, i, _dt);
}
break;
case REB_WHFAST_COORDINATES_DEMOCRATICHELIOCENTRIC:
#pragma omp parallel for
for (unsigned int i=1;i<N_real;i++){
reb_whfast_kepler_solver(r, p_j, eta*G, i, _dt); // eta = m0
}
break;
case REB_WHFAST_COORDINATES_WHDS:
#pragma omp parallel for private(eta)
for (int i=1;i<(int)N_real;i++){
if (i<N_active){
eta = m0+p_j[i].m;
}else{
eta = m0;
}
reb_whfast_kepler_solver(r, p_j, eta*G, i, _dt);
}
break;
case REB_WHFAST_COORDINATES_BARYCENTRIC:
eta = p_j[0].m;
for (unsigned int i=1;i<(int)N_real;i++){
reb_whfast_kepler_solver(r, p_j, eta*G, i, _dt);
}
break;
};
}
void reb_whfast_com_step(const struct reb_simulation* const r, const double _dt){
struct reb_particle* const p_j = r->ri_whfast.p_jh;
p_j[0].x += _dt*p_j[0].vx;
p_j[0].y += _dt*p_j[0].vy;
p_j[0].z += _dt*p_j[0].vz;
}
static void reb_whfast_corrector_Z(struct reb_simulation* r, const double a, const double b){
struct reb_integrator_whfast* const ri_whfast = &(r->ri_whfast);
struct reb_particle* restrict const particles = r->particles;
const int N_real = r->N-r->N_var;
const int N_active = (r->N_active==-1 || r->testparticle_type==1)?N_real:r->N_active;
switch (ri_whfast->coordinates){
case REB_WHFAST_COORDINATES_JACOBI:
reb_whfast_kepler_step(r, a);
reb_particles_transform_jacobi_to_inertial_pos(particles, ri_whfast->p_jh, particles, N_real, N_active);
for (int v=0;v<r->N_var_config;v++){
struct reb_variational_configuration const vc = r->var_config[v];
reb_particles_transform_jacobi_to_inertial_pos(particles+vc.index, ri_whfast->p_jh+vc.index, particles, N_real, N_active);
}
reb_simulation_update_acceleration(r);
reb_whfast_interaction_step(r, -b);
reb_whfast_kepler_step(r, -2.*a);
reb_particles_transform_jacobi_to_inertial_pos(particles, ri_whfast->p_jh, particles, N_real, N_active);
for (int v=0;v<r->N_var_config;v++){
struct reb_variational_configuration const vc = r->var_config[v];
reb_particles_transform_jacobi_to_inertial_pos(particles+vc.index, ri_whfast->p_jh+vc.index, particles, N_real, N_active);
}
reb_simulation_update_acceleration(r);
reb_whfast_interaction_step(r, b);
reb_whfast_kepler_step(r, a);
break;
case REB_WHFAST_COORDINATES_BARYCENTRIC:
reb_whfast_kepler_step(r, a);
reb_particles_transform_barycentric_to_inertial_pos(particles, ri_whfast->p_jh, N_real, N_active);
reb_simulation_update_acceleration(r);
reb_whfast_interaction_step(r, -b);
reb_whfast_kepler_step(r, -2.*a);
reb_particles_transform_barycentric_to_inertial_pos(particles, ri_whfast->p_jh, N_real, N_active);
reb_simulation_update_acceleration(r);
reb_whfast_interaction_step(r, b);
reb_whfast_kepler_step(r, a);
break;
case REB_WHFAST_COORDINATES_WHDS:
case REB_WHFAST_COORDINATES_DEMOCRATICHELIOCENTRIC:
reb_simulation_error(r, "Coordinate system not supported.");
break;
}
}
void reb_whfast_apply_corrector(struct reb_simulation* r, double inv, int order){
const double dt = r->dt;
if (order==3){
// Third order corrector
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_1*dt,-inv*reb_whfast_corrector_b_31*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_1*dt,inv*reb_whfast_corrector_b_31*dt);
}
if (order==5){
// Fifth order corrector
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_2*dt,-inv*reb_whfast_corrector_b_51*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_1*dt,-inv*reb_whfast_corrector_b_52*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_1*dt,inv*reb_whfast_corrector_b_52*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_2*dt,inv*reb_whfast_corrector_b_51*dt);
}
if (order==7){
// Seventh order corrector
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_3*dt,-inv*reb_whfast_corrector_b_71*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_2*dt,-inv*reb_whfast_corrector_b_72*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_1*dt,-inv*reb_whfast_corrector_b_73*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_1*dt,inv*reb_whfast_corrector_b_73*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_2*dt,inv*reb_whfast_corrector_b_72*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_3*dt,inv*reb_whfast_corrector_b_71*dt);
}
if (order==11){
// Eleventh order corrector
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_5*dt,-inv*reb_whfast_corrector_b_111*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_4*dt,-inv*reb_whfast_corrector_b_112*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_3*dt,-inv*reb_whfast_corrector_b_113*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_2*dt,-inv*reb_whfast_corrector_b_114*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_1*dt,-inv*reb_whfast_corrector_b_115*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_1*dt,inv*reb_whfast_corrector_b_115*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_2*dt,inv*reb_whfast_corrector_b_114*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_3*dt,inv*reb_whfast_corrector_b_113*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_4*dt,inv*reb_whfast_corrector_b_112*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_5*dt,inv*reb_whfast_corrector_b_111*dt);
}
if (order==17){
// Seventeenth order corrector
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_8*dt,-inv*reb_whfast_corrector_b_171*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_7*dt,-inv*reb_whfast_corrector_b_172*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_6*dt,-inv*reb_whfast_corrector_b_173*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_5*dt,-inv*reb_whfast_corrector_b_174*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_4*dt,-inv*reb_whfast_corrector_b_175*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_3*dt,-inv*reb_whfast_corrector_b_176*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_2*dt,-inv*reb_whfast_corrector_b_177*dt);
reb_whfast_corrector_Z(r, -reb_whfast_corrector_a_1*dt,-inv*reb_whfast_corrector_b_178*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_1*dt,inv*reb_whfast_corrector_b_178*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_2*dt,inv*reb_whfast_corrector_b_177*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_3*dt,inv*reb_whfast_corrector_b_176*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_4*dt,inv*reb_whfast_corrector_b_175*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_5*dt,inv*reb_whfast_corrector_b_174*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_6*dt,inv*reb_whfast_corrector_b_173*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_7*dt,inv*reb_whfast_corrector_b_172*dt);
reb_whfast_corrector_Z(r, reb_whfast_corrector_a_8*dt,inv*reb_whfast_corrector_b_171*dt);
}
}
static void reb_whfast_operator_C(struct reb_simulation* const r, double a, double b){
reb_whfast_kepler_step(r, a);
struct reb_integrator_whfast* const ri_whfast = &(r->ri_whfast);
struct reb_particle* restrict const particles = r->particles;
const int N = r->N;
const int N_real = r->N-r->N_var;
const int N_active = (r->N_active==-1 || r->testparticle_type==1)?N_real:r->N_active;
reb_particles_transform_jacobi_to_inertial_pos(particles, ri_whfast->p_jh, particles, N, N_active);
reb_simulation_update_acceleration(r);
reb_whfast_interaction_step(r, b);
reb_whfast_kepler_step(r, -a);
}
static void reb_whfast_operator_Y(struct reb_simulation* const r, double a, double b){
reb_whfast_operator_C(r, a, b);
reb_whfast_operator_C(r, -a, -b);
}
static void reb_whfast_operator_U(struct reb_simulation* const r, double a, double b){
reb_whfast_kepler_step(r, a);
reb_whfast_operator_Y(r, a, b);
reb_whfast_operator_Y(r, a, -b);
reb_whfast_kepler_step(r, -a);
}
static void reb_whfast_apply_corrector2(struct reb_simulation* r, double inv){
double a = 0.5 * inv * r->dt;
double b = reb_whfast_corrector2_b * inv * r->dt;
reb_whfast_operator_U(r, a, b);
reb_whfast_operator_U(r, -a, b);
}
void reb_whfast_calculate_jerk(struct reb_simulation* r){
// Assume particles.a calculated.
struct reb_particle* const particles = r->particles;
const int N = r->N;
struct reb_particle* jerk = r->ri_whfast.p_jh; // Used as a temporary buffer for accelerations
const double G = r->G;
double Rjx = 0.; // com
double Rjy = 0.;
double Rjz = 0.;
double Mj = 0.;
double Ajx = 0.; // sort of Jacobi acceleration
double Ajy = 0.;
double Ajz = 0.;
for (int j=0; j<N; j++){
jerk[j].ax = 0;
jerk[j].ay = 0;
jerk[j].az = 0;
for (int i=0; i<j+1; i++){
//////////////////
// Jacobi Term
// Note: ignoring j==1 term here and below as they cancel
if (j>1){
double dQkrj = Mj;
if (i<j){
dQkrj = -particles[j].m;
}
const double Qkx = particles[j].x - Rjx/Mj;
const double Qky = particles[j].y - Rjy/Mj;
const double Qkz = particles[j].z - Rjz/Mj;
const double dax = particles[j].ax - Ajx/Mj;
const double day = particles[j].ay - Ajy/Mj;
const double daz = particles[j].az - Ajz/Mj;
const double dr = sqrt(Qkx*Qkx + Qky*Qky + Qkz*Qkz);
const double prefact2 = G*dQkrj /(dr*dr*dr);
jerk[i].ax += prefact2*dax;
jerk[i].ay += prefact2*day;
jerk[i].az += prefact2*daz;
const double alphasum = dax*Qkx + day*Qky + daz*Qkz;
const double prefact1 = 3.*alphasum*prefact2/(dr*dr);
jerk[i].ax -= prefact1*Qkx;
jerk[i].ay -= prefact1*Qky;
jerk[i].az -= prefact1*Qkz;
}
/////////////////
// Direct Term
// Note: ignoring i==0 && j==1 term here and above as they cancel
if (j!=i && (i!=0 || j!=1)){
const double dx = particles[j].x - particles[i].x;
const double dy = particles[j].y - particles[i].y;
const double dz = particles[j].z - particles[i].z;
const double dax = particles[j].ax - particles[i].ax;
const double day = particles[j].ay - particles[i].ay;
const double daz = particles[j].az - particles[i].az;
const double dr = sqrt(dx*dx + dy*dy + dz*dz);
const double alphasum = dax*dx+day*dy+daz*dz;
const double prefact2 = G /(dr*dr*dr);
const double prefact2i = prefact2*particles[i].m;
const double prefact2j = prefact2*particles[j].m;
jerk[j].ax -= dax*prefact2i;
jerk[j].ay -= day*prefact2i;
jerk[j].az -= daz*prefact2i;
jerk[i].ax += dax*prefact2j;
jerk[i].ay += day*prefact2j;
jerk[i].az += daz*prefact2j;
const double prefact1 = 3.*alphasum*prefact2 /(dr*dr);
const double prefact1i = prefact1*particles[i].m;
const double prefact1j = prefact1*particles[j].m;
jerk[j].ax += dx*prefact1i;
jerk[j].ay += dy*prefact1i;
jerk[j].az += dz*prefact1i;
jerk[i].ax -= dx*prefact1j;
jerk[i].ay -= dy*prefact1j;
jerk[i].az -= dz*prefact1j;
}
}
Ajx += particles[j].ax*particles[j].m;
Ajy += particles[j].ay*particles[j].m;
Ajz += particles[j].az*particles[j].m;
Rjx += particles[j].x*particles[j].m;
Rjy += particles[j].y*particles[j].m;
Rjz += particles[j].z*particles[j].m;
Mj += particles[j].m;
}
}
int reb_integrator_whfast_init(struct reb_simulation* const r){
for (int v=0;v<r->N_var_config;v++){
struct reb_variational_configuration const vc = r->var_config[v];
if (vc.order!=1){
reb_simulation_error(r, "WHFast/MEGNO only supports first order variational equations.");
return 1; // Error
}
if (vc.testparticle>=0){
reb_simulation_error(r, "Test particle variations not supported with WHFast. Use IAS15.");
return 1; // Error
}
}
struct reb_integrator_whfast* const ri_whfast = &(r->ri_whfast);
if (r->N_var_config>0 && ri_whfast->coordinates!=REB_WHFAST_COORDINATES_JACOBI){
reb_simulation_error(r, "Variational particles are only compatible with Jacobi coordinates.");
return 1; // Error
}
if (ri_whfast->kernel!= REB_WHFAST_KERNEL_DEFAULT && ri_whfast->coordinates!=REB_WHFAST_COORDINATES_JACOBI){
reb_simulation_error(r, "Non-standard kernel requires Jacobi coordinates.");
return 1; // Error
}
if (r->N_var_config>0 && ri_whfast->kernel != REB_WHFAST_KERNEL_DEFAULT){
reb_simulation_error(r, "Variational particles are only compatible with the standard kernel.");
return 1; // Error
}
if (ri_whfast->kernel>3){
reb_simulation_error(r, "Kernel method must be 0 (default), 1 (exact modified kick), 2 (composition kernel), or 3 (lazy implementer's modified kick). ");
return 1; // Error
}
if (ri_whfast->corrector!=0 && (ri_whfast->coordinates!=REB_WHFAST_COORDINATES_JACOBI && ri_whfast->coordinates!=REB_WHFAST_COORDINATES_BARYCENTRIC) ){
reb_simulation_error(r, "Symplectic correctors are only compatible with Jacobi and Barycentric coordinates.");
return 1; // Error
}
if (ri_whfast->corrector!=0 && ri_whfast->corrector!=3 && ri_whfast->corrector!=5 && ri_whfast->corrector!=7 && ri_whfast->corrector!=11 && ri_whfast->corrector!=17 ){
reb_simulation_error(r, "First symplectic correctors are only available in the following orders: 0, 3, 5, 7, 11, 17.");
return 1; // Error
}
if (ri_whfast->keep_unsynchronized==1 && ri_whfast->safe_mode==1){
reb_simulation_error(r, "ri_whfast->keep_unsynchronized == 1 is not compatible with safe_mode. Must set ri_whfast->safe_mode = 0.");
}
if (ri_whfast->kernel == REB_WHFAST_KERNEL_MODIFIEDKICK || ri_whfast->kernel == REB_WHFAST_KERNEL_LAZY){
r->gravity = REB_GRAVITY_JACOBI;
}else{
if (ri_whfast->coordinates==REB_WHFAST_COORDINATES_JACOBI){
r->gravity_ignore_terms = 1;
}else if (ri_whfast->coordinates==REB_WHFAST_COORDINATES_BARYCENTRIC){
r->gravity_ignore_terms = 0;
}else{
r->gravity_ignore_terms = 2;
}
}
const unsigned int N = r->N;
if (ri_whfast->N_allocated != N){
ri_whfast->N_allocated = N;
ri_whfast->p_jh = realloc(ri_whfast->p_jh,sizeof(struct reb_particle)*N);
ri_whfast->recalculate_coordinates_this_timestep = 1;
}
return 0;
}
void reb_integrator_whfast_from_inertial(struct reb_simulation* const r){
struct reb_integrator_whfast* const ri_whfast = &(r->ri_whfast);
struct reb_particle* restrict const particles = r->particles;
const int N = r->N;
const int N_real = N-r->N_var;
const unsigned int N_active = (r->N_active==-1 || r->testparticle_type==1)?N_real:r->N_active;
switch (ri_whfast->coordinates){
case REB_WHFAST_COORDINATES_JACOBI:
reb_particles_transform_inertial_to_jacobi_posvel(particles, ri_whfast->p_jh, particles, N_real, N_active);
for (int v=0;v<r->N_var_config;v++){
struct reb_variational_configuration const vc = r->var_config[v];
reb_particles_transform_inertial_to_jacobi_posvel(particles+vc.index, ri_whfast->p_jh+vc.index, particles, N_real, N_active);
}
break;
case REB_WHFAST_COORDINATES_DEMOCRATICHELIOCENTRIC:
reb_particles_transform_inertial_to_democraticheliocentric_posvel(particles, ri_whfast->p_jh, N_real, N_active);
break;
case REB_WHFAST_COORDINATES_WHDS:
reb_particles_transform_inertial_to_whds_posvel(particles, ri_whfast->p_jh, N_real, N_active);
break;
case REB_WHFAST_COORDINATES_BARYCENTRIC:
reb_particles_transform_inertial_to_barycentric_posvel(particles, ri_whfast->p_jh, N_real, N_active);
break;
};
}
void reb_integrator_whfast_to_inertial(struct reb_simulation* const r){
struct reb_integrator_whfast* const ri_whfast = &(r->ri_whfast);
struct reb_particle* restrict const particles = r->particles;
const int N = r->N;
const int N_real = N-r->N_var;
const int N_active = (r->N_active==-1 || r->testparticle_type==1)?N_real:r->N_active;
// Prepare coordinates for KICK step
if (r->force_is_velocity_dependent){
switch (ri_whfast->coordinates){
case REB_WHFAST_COORDINATES_JACOBI:
reb_particles_transform_jacobi_to_inertial_posvel(particles, ri_whfast->p_jh, particles, N_real, N_active);
break;
case REB_WHFAST_COORDINATES_DEMOCRATICHELIOCENTRIC:
reb_particles_transform_democraticheliocentric_to_inertial_posvel(particles, ri_whfast->p_jh, N_real, N_active);
break;
case REB_WHFAST_COORDINATES_WHDS:
reb_particles_transform_whds_to_inertial_posvel(particles, ri_whfast->p_jh, N_real, N_active);
break;
case REB_WHFAST_COORDINATES_BARYCENTRIC:
reb_particles_transform_barycentric_to_inertial_posvel(particles, ri_whfast->p_jh, N_real, N_active);
break;
};
}else{
switch (ri_whfast->coordinates){
case REB_WHFAST_COORDINATES_JACOBI:
reb_particles_transform_jacobi_to_inertial_posvel(particles, ri_whfast->p_jh, particles, N_real, N_active);
break;
case REB_WHFAST_COORDINATES_DEMOCRATICHELIOCENTRIC:
reb_particles_transform_democraticheliocentric_to_inertial_posvel(particles, ri_whfast->p_jh, N_real, N_active);
break;
case REB_WHFAST_COORDINATES_WHDS:
reb_particles_transform_whds_to_inertial_posvel(particles, ri_whfast->p_jh, N_real, N_active);
break;
case REB_WHFAST_COORDINATES_BARYCENTRIC:
reb_particles_transform_barycentric_to_inertial_posvel(particles, ri_whfast->p_jh, N_real, N_active);
break;
};
}
}
void reb_integrator_whfast_debug_operator_kepler(struct reb_simulation* const r,double dt){
if (reb_integrator_whfast_init(r)){
// Non recoverable error occured.
return;
}
reb_integrator_whfast_from_inertial(r);
reb_whfast_kepler_step(r, dt); // half timestep
reb_whfast_com_step(r, dt);
reb_integrator_whfast_to_inertial(r);
}
void reb_integrator_whfast_debug_operator_interaction(struct reb_simulation* const r,double dt){
if (reb_integrator_whfast_init(r)){
// Non recoverable error occured.
return;
}
reb_integrator_whfast_from_inertial(r);
r->gravity_ignore_terms = 1;
reb_simulation_update_acceleration(r);
reb_whfast_interaction_step(r, dt);
reb_integrator_whfast_to_inertial(r);
}
void reb_integrator_whfast_synchronize(struct reb_simulation* const r){
struct reb_integrator_whfast* const ri_whfast = &(r->ri_whfast);
if (reb_integrator_whfast_init(r)){
// Non recoverable error occured.
return;
}
if (ri_whfast->is_synchronized == 0){
const int N_real = r->N-r->N_var;
const int N_active = (r->N_active==-1 || r->testparticle_type==1)?N_real:r->N_active;
struct reb_particle* sync_pj = NULL;
if (ri_whfast->keep_unsynchronized){
sync_pj = malloc(sizeof(struct reb_particle)*r->N);
memcpy(sync_pj,r->ri_whfast.p_jh,r->N*sizeof(struct reb_particle));
}
switch (ri_whfast->kernel){
case REB_WHFAST_KERNEL_DEFAULT:
case REB_WHFAST_KERNEL_MODIFIEDKICK:
case REB_WHFAST_KERNEL_LAZY:
reb_whfast_kepler_step(r, r->dt/2.);
reb_whfast_com_step(r, r->dt/2.);
break;
case REB_WHFAST_KERNEL_COMPOSITION:
reb_whfast_kepler_step(r, 3.*r->dt/8.);
reb_whfast_com_step(r, 3.*r->dt/8.);
break;
default:
reb_simulation_error(r, "WHFast kernel not implemented.");
return;
};
if (ri_whfast->corrector2){
reb_whfast_apply_corrector2(r, -1.);
}
if (ri_whfast->corrector){
reb_whfast_apply_corrector(r, -1., ri_whfast->corrector);
}
switch (ri_whfast->coordinates){
case REB_WHFAST_COORDINATES_JACOBI:
reb_particles_transform_jacobi_to_inertial_posvel(r->particles, ri_whfast->p_jh, r->particles, N_real, N_active);
break;
case REB_WHFAST_COORDINATES_DEMOCRATICHELIOCENTRIC:
reb_particles_transform_democraticheliocentric_to_inertial_posvel(r->particles, ri_whfast->p_jh, N_real, N_active);
break;
case REB_WHFAST_COORDINATES_WHDS:
reb_particles_transform_whds_to_inertial_posvel(r->particles, ri_whfast->p_jh, N_real, N_active);
break;
case REB_WHFAST_COORDINATES_BARYCENTRIC:
reb_particles_transform_barycentric_to_inertial_posvel(r->particles, ri_whfast->p_jh, N_real, N_active);
break;
};
for (int v=0;v<r->N_var_config;v++){
struct reb_variational_configuration const vc = r->var_config[v];
reb_particles_transform_jacobi_to_inertial_posvel(r->particles+vc.index, ri_whfast->p_jh+vc.index, r-> particles, N_real, N_active);
}
if (ri_whfast->keep_unsynchronized){
memcpy(r->ri_whfast.p_jh,sync_pj,r->N*sizeof(struct reb_particle));
free(sync_pj);
}else{
ri_whfast->is_synchronized = 1;
}
}
}
void reb_integrator_whfast_step(struct reb_simulation* const r){
struct reb_integrator_whfast* const ri_whfast = &(r->ri_whfast);
struct reb_particle* restrict const particles = r->particles;
const double dt = r->dt;
const int N = r->N;
const int N_real = N-r->N_var;
const int N_active = (r->N_active==-1 || r->testparticle_type==1)?N_real:r->N_active;
if (reb_integrator_whfast_init(r)){
// Non recoverable error occured.
return;
}
struct reb_particle* const p_j = ri_whfast->p_jh;
// Only recalculate Jacobi coordinates if needed
if (ri_whfast->safe_mode || ri_whfast->recalculate_coordinates_this_timestep){
if (ri_whfast->is_synchronized==0){
reb_integrator_whfast_synchronize(r);
if (ri_whfast->recalculate_coordinates_but_not_synchronized_warning==0){
reb_simulation_warning(r,"Recalculating coordinates but pos/vel were not synchronized before.");
ri_whfast->recalculate_coordinates_but_not_synchronized_warning++;
}
}
reb_integrator_whfast_from_inertial(r);
ri_whfast->recalculate_coordinates_this_timestep = 0;
}
if (ri_whfast->is_synchronized){
// First half DRIFT step
if (ri_whfast->corrector){
reb_whfast_apply_corrector(r, 1., ri_whfast->corrector);
}
if (ri_whfast->corrector2){
reb_whfast_apply_corrector2(r, 1.);
}
switch (ri_whfast->kernel){
case REB_WHFAST_KERNEL_DEFAULT:
case REB_WHFAST_KERNEL_MODIFIEDKICK:
case REB_WHFAST_KERNEL_LAZY:
reb_whfast_kepler_step(r, r->dt/2.);
reb_whfast_com_step(r, r->dt/2.);
break;
case REB_WHFAST_KERNEL_COMPOSITION:
reb_whfast_kepler_step(r, 5.*r->dt/8.);
reb_whfast_com_step(r, 5.*r->dt/8.);
break;
default:
reb_simulation_error(r, "WHFast kernel not implemented.");
return;
};
}else{
// Combined DRIFT step
reb_whfast_kepler_step(r, r->dt); // full timestep
reb_whfast_com_step(r, r->dt);
}
reb_whfast_jump_step(r,r->dt/2.);
reb_integrator_whfast_to_inertial(r);
// Variational equations only available for jacobi coordinates.
// If other coordinates are used, the code will raise an exception earlier.
for (int v=0;v<r->N_var_config;v++){
struct reb_variational_configuration const vc = r->var_config[v];
p_j[vc.index].x += r->dt/2.*p_j[vc.index].vx;
p_j[vc.index].y += r->dt/2.*p_j[vc.index].vy;
p_j[vc.index].z += r->dt/2.*p_j[vc.index].vz;
if (r->force_is_velocity_dependent){
reb_particles_transform_jacobi_to_inertial_posvel(particles+vc.index, p_j+vc.index, particles, N_real, N_active);
}else{
reb_particles_transform_jacobi_to_inertial_pos(particles+vc.index, p_j+vc.index, particles, N_real, N_active);
}
}
r->t+=dt/2.;
reb_simulation_update_acceleration(r);
switch (ri_whfast->kernel){
case REB_WHFAST_KERNEL_DEFAULT:
reb_whfast_interaction_step(r, dt);
reb_whfast_jump_step(r,dt/2.);
break;
case REB_WHFAST_KERNEL_MODIFIEDKICK:
// p_j used as a temporary buffer for "jerk"
reb_whfast_calculate_jerk(r);
for (unsigned int i=0; i<N; i++){
const double prefact = dt*dt/12.;
particles[i].ax += prefact*p_j[i].ax;
particles[i].ay += prefact*p_j[i].ay;
particles[i].az += prefact*p_j[i].az;
}
reb_whfast_interaction_step(r, dt);
break;
case REB_WHFAST_KERNEL_COMPOSITION:
reb_whfast_interaction_step(r, -dt/6.);
reb_whfast_kepler_step(r, -dt/4.);
reb_whfast_com_step(r, -dt/4.);
reb_particles_transform_jacobi_to_inertial_pos(particles, p_j, particles, N, N_active);
reb_simulation_update_acceleration(r);
reb_whfast_interaction_step(r, dt/6.);
reb_whfast_kepler_step(r, dt/8.);
reb_whfast_com_step(r, dt/8.);
reb_particles_transform_jacobi_to_inertial_pos(particles, p_j, particles, N, N_active);
reb_simulation_update_acceleration(r);
reb_whfast_interaction_step(r, dt);
reb_whfast_kepler_step(r, -dt/8.);
reb_whfast_com_step(r, -dt/8.);
reb_particles_transform_jacobi_to_inertial_pos(particles, p_j, particles, N, N_active);
reb_simulation_update_acceleration(r);
reb_whfast_interaction_step(r, -dt/6.);
reb_whfast_kepler_step(r, dt/4.);
reb_whfast_com_step(r, dt/4.);
reb_particles_transform_jacobi_to_inertial_pos(particles, p_j, particles, N, N_active);
reb_simulation_update_acceleration(r);
reb_whfast_interaction_step(r, dt/6.);
break;
case REB_WHFAST_KERNEL_LAZY:
{
// Need temporary array to store old positions
if (ri_whfast->N_allocated_tmp != N){
ri_whfast->N_allocated_tmp = N;
ri_whfast->p_temp = realloc(ri_whfast->p_temp,sizeof(struct reb_particle)*N);
}
struct reb_particle* p_temp = ri_whfast->p_temp;
// Calculate normal kick
// Accelerations already calculated
reb_particles_transform_inertial_to_jacobi_acc(r->particles, p_j, r->particles, N, N_active);
// make copy of original positions
memcpy(p_temp,p_j,r->N*sizeof(struct reb_particle));
// WHT Eq 10.6
for (unsigned int i=1;i<N;i++){
const double prefac1 = dt*dt/12.;
p_j[i].x += prefac1 * p_temp[i].ax;
p_j[i].y += prefac1 * p_temp[i].ay;
p_j[i].z += prefac1 * p_temp[i].az;
}
// recalculate kick
reb_particles_transform_jacobi_to_inertial_pos(particles, p_j, particles, N, N_active);
reb_simulation_update_acceleration(r);
reb_whfast_interaction_step(r, dt);
for (unsigned int i=1;i<N;i++){
// reset positions
p_j[i].x = p_temp[i].x;
p_j[i].y = p_temp[i].y;
p_j[i].z = p_temp[i].z;
}
}
break;
default:
return;
};
ri_whfast->is_synchronized = 0;
if (ri_whfast->safe_mode){
reb_integrator_whfast_synchronize(r);
}
r->t+=r->dt/2.;
r->dt_last_done = r->dt;
if (r->N_var_config){
// Need to have x,v,a synchronized to calculate ddot/d for MEGNO.
const int N_real = r->N-r->N_var;
struct reb_particle* sync_pj = NULL;
if (ri_whfast->keep_unsynchronized){ // cache the p_j and set back at the end
sync_pj = malloc(sizeof(struct reb_particle)*r->N);
memcpy(sync_pj,p_j,r->N*sizeof(struct reb_particle));
ri_whfast->keep_unsynchronized=0; // synchronize will revert the p_j to midstep if keep_unsync=0.
reb_integrator_whfast_synchronize(r);
ri_whfast->keep_unsynchronized=1; // Manually avoid synchronize reverting the p_j and do it ourselves when we're done
}
else{
reb_integrator_whfast_synchronize(r);
}
// Add additional acceleration term for MEGNO calculation
struct reb_particle* restrict const particles = r->particles;
for (int v=0;v<r->N_var_config;v++){
struct reb_variational_configuration const vc = r->var_config[v];
struct reb_particle* const particles_var1 = particles + vc.index;
const int index = vc.index;
// Center of mass
p_j[index].x += r->dt/2.*p_j[index].vx;
p_j[index].y += r->dt/2.*p_j[index].vy;
p_j[index].z += r->dt/2.*p_j[index].vz;
reb_particles_transform_jacobi_to_inertial_posvel(particles_var1, p_j+index, particles, N_real, N_active);
if (r->calculate_megno){
reb_simulation_update_acceleration_gravity_var(r);
const double dx = particles[0].x - particles[1].x;
const double dy = particles[0].y - particles[1].y;
const double dz = particles[0].z - particles[1].z;
const double r2 = dx*dx + dy*dy + dz*dz + r->softening*r->softening;
const double _r = sqrt(r2);
const double r3inv = 1./(r2*_r);
const double r5inv = 3.*r3inv/r2;
const double ddx = particles_var1[0].x - particles_var1[1].x;
const double ddy = particles_var1[0].y - particles_var1[1].y;
const double ddz = particles_var1[0].z - particles_var1[1].z;
const double Gmi = r->G * particles[0].m;
const double Gmj = r->G * particles[1].m;
const double dax = ddx * ( dx*dx*r5inv - r3inv )
+ ddy * ( dx*dy*r5inv )
+ ddz * ( dx*dz*r5inv );
const double day = ddx * ( dy*dx*r5inv )
+ ddy * ( dy*dy*r5inv - r3inv )
+ ddz * ( dy*dz*r5inv );
const double daz = ddx * ( dz*dx*r5inv )
+ ddy * ( dz*dy*r5inv )
+ ddz * ( dz*dz*r5inv - r3inv );
particles_var1[0].ax += Gmj * dax;
particles_var1[0].ay += Gmj * day;
particles_var1[0].az += Gmj * daz;
particles_var1[1].ax -= Gmi * dax;
particles_var1[1].ay -= Gmi * day;
particles_var1[1].az -= Gmi * daz;
// TODO Need to add mass terms. Also need to add them to tangent map above.
}
}
// Update MEGNO in middle of timestep as we need synchonized x/v/a.
if (r->calculate_megno){
double dY = r->dt * 2. * (r->t-r->megno_initial_t) * reb_tools_megno_deltad_delta(r);
reb_tools_megno_update(r, dY, dt);
}
if (ri_whfast->keep_unsynchronized){
memcpy(p_j,sync_pj,r->N*sizeof(struct reb_particle));
free(sync_pj);
ri_whfast->is_synchronized=0;
}
}
}
void reb_integrator_whfast_reset(struct reb_simulation* const r){
struct reb_integrator_whfast* const ri_whfast = &(r->ri_whfast);
ri_whfast->corrector = 0;
ri_whfast->corrector2 = 0;
ri_whfast->kernel = 0;
ri_whfast->coordinates = REB_WHFAST_COORDINATES_JACOBI;
ri_whfast->is_synchronized = 1;
ri_whfast->keep_unsynchronized = 0;
ri_whfast->safe_mode = 1;
ri_whfast->recalculate_coordinates_this_timestep = 0;
ri_whfast->N_allocated = 0;
ri_whfast->N_allocated_tmp = 0;
ri_whfast->timestep_warning = 0;
ri_whfast->recalculate_coordinates_but_not_synchronized_warning = 0;
if (ri_whfast->p_jh){
free(ri_whfast->p_jh);
ri_whfast->p_jh = NULL;
}
if (ri_whfast->p_temp){
free(ri_whfast->p_temp);
ri_whfast->p_temp = NULL;
}
}