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MiniNBody.c
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MiniNBody.c
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/*-------------------------------------------------------------
* Title : MiniNBody.c
* Author : Léo Martire, Michael Richmond.
* Date : 2016.
* Description :
Implementation of a simple N-Body simulation. This program is
amply based on Michael Richmond's NBody program. Tweaks,
optimisations, more features and advanced schemes have been
added in order to fulfil a study on globular clusters.
* Usage :
1) Compile using the provided Makefile.
2) As command line :
nbody input=inputfile [verbose=]
where :
- inputfile is an ASCII text file with description of
each body, plus some controlling parameters
(see provided input file solarSystem.in for
further explanations)
- verbose if present, set verbosity level to 1
if not, set verbosity level to 0
- verbose=N if present, set verbosity level to N
-------------------------------------------------------------*/
/* Includes. ------------------------------------------------*/
#include <math.h>
#include <omp.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
/*-----------------------------------------------------------*/
/* Defines. -------------------------------------------------*/
#undef DEBUG
#define COMMENT_CHAR '#' // any line starting with this in input file is ignored
#define LINELEN 1024 // max length of lines in input file
#define MAX_NBODY 9000 // maximum number of bodies we can handle (change this according to the type of simulation : no need to allocate 9000 spaces to simulate 10 particles)
#define MAX_TECHNIQUE 10 // maximum number of intergration techniques we can handle
#define NAMELEN 30 // max length of names of objects
#define NBUF 1024
/*-----------------------------------------------------------*/
/* Type definitions. ----------------------------------------*/
typedef int(*PFI)(double, double *); // pointer to a function returning an integer
typedef struct s_vector { // vector
double val[3];
}
VECTOR;
typedef struct s_body { // body (state)
int index;
char name[NAMELEN];
double mass;
double pos[3];
double vel[3];
}
BODY;
typedef struct s_dbody { // body derivative (state derivative)
double dp[3];
double dv[3];
}
DBODY;
typedef struct s_technique { // integration technique
char name[NAMELEN];
PFI func;
}
TECHNIQUE;
/*-----------------------------------------------------------*/
/* Macros. --------------------------------------------------*/
/*
* set the given VECTOR elements to have the difference in
* positions between bodies i and j, in the sense
* g_body_array[i].pos[0]-g_body_array[j].pos[0]
* etc.
*/
#define SET_POS_DIFF(vec, i, j)\
vec.val[0] = g_body_array[i].pos[0] - g_body_array[j].pos[0];\
vec.val[1] = g_body_array[i].pos[1] - g_body_array[j].pos[1];\
vec.val[2] = g_body_array[i].pos[2] - g_body_array[j].pos[2];
/* the magnitude of a VECTOR */
#define VECTOR_MAG(vec)\
(sqrt(vec.val[0] * vec.val[0] + vec.val[1] * vec.val[1] + \
vec.val[2] * vec.val[2]))
/* the square of the magnitude of a VECTOR */
#define VECTOR_MAG_SQUARED(vec)\
(vec.val[0] * vec.val[0] + vec.val[1] * vec.val[1] + \
vec.val[2] * vec.val[2])
/* the SQUARE of distance between two bodies */
#define DIST_SQUARED(i, j)\
(((g_body_array[i].pos[0] - g_body_array[j].pos[0]) * \
(g_body_array[i].pos[0] - g_body_array[j].pos[0])) + \
((g_body_array[i].pos[1] - g_body_array[j].pos[1]) * \
(g_body_array[i].pos[1] - g_body_array[j].pos[1])) + \
((g_body_array[i].pos[2] - g_body_array[j].pos[2]) * \
(g_body_array[i].pos[2] - g_body_array[j].pos[2])))
/* the difference of two vectors */
#define VECTOR_SUBTRACT(a, b, difference)\
difference.val[0] = a.val[0] - b.val[0];\
difference.val[1] = a.val[1] - b.val[1];\
difference.val[2] = a.val[2] - b.val[2];
/* the cross product of two vectors */
#define VECTOR_CROSS(a, b, product)\
product.val[0] = a.val[1] * b.val[2] - a.val[2] * b.val[1];\
product.val[1] = a.val[2] * b.val[0] - a.val[0] * b.val[2];\
product.val[2] = a.val[0] * b.val[1] - a.val[1] * b.val[0];
#define max(a,b) \
({ __typeof__ (a) _a=(a); \
__typeof__ (b) _b=(b); \
_a>_b ? _a : _b; })
#define min(a,b) \
({ __typeof__ (a) _a=(a); \
__typeof__ (b) _b=(b); \
_a<_b ? _a : _b; })
/*-----------------------------------------------------------*/
/* Global variables. ----------------------------------------*/
BODY g_body_array[MAX_NBODY]; // allocate space for bodies
BODY pyn1[MAX_NBODY]; // PECE : predicted state
BODY yn1[MAX_NBODY]; // PECE : new state
DBODY fn1[MAX_NBODY]; // PECE : new derivative state
DBODY fp0[MAX_NBODY]; // PECE : current derivative state
DBODY fp1[MAX_NBODY]; // PECE : 1 step backwards derivative state
DBODY fp2[MAX_NBODY]; // PECE : 2 steps backwards derivative state
DBODY fp3[MAX_NBODY]; // PECE : 3 steps backwards derivative state
DBODY pfn1[MAX_NBODY]; // PECE : predicted derivative state
FILE *g_outfile_fp; // FILE pointer for output
PFI g_integration_func; // PFI pointer for techniques
TECHNIQUE g_technique_array[MAX_TECHNIQUE]; // allocate space for techniques
VECTOR g_cur_forces[MAX_NBODY][MAX_NBODY]; // variable made global to make sure enough memory space is allocated and to enable faster access for simulations with high number of bodies.
VECTOR tmpForcesForDerivation[MAX_NBODY]; // PECE : temporary vector for derivative state calculation
double g_AB_b03 = 55.0 / 24.0; // PECE : coefficient for Adams-Bashforth scheme with 3+1 steps
double g_AB_b13 = -59.0 / 24.0; // PECE : coefficient for Adams-Bashforth scheme with 3+1 steps
double g_AB_b23 = 37.0 / 24.0; // PECE : coefficient for Adams-Bashforth scheme with 3+1 steps
double g_AB_b33 = -9.0 / 24.0; // PECE : coefficient for Adams-Bashforth scheme with 3+1 steps
double g_AM_b03 = 646.0 / 720.0; // PECE : coefficient for Adams-Moulton scheme with 3+1 steps
double g_AM_b13 = -264.0 / 720.0; // PECE : coefficient for Adams-Moulton scheme with 3+1 steps
double g_AM_b23 = 106.0 / 720.0; // PECE : coefficient for Adams-Moulton scheme with 3+1 steps
double g_AM_b33 = -19.0 / 720.0; // PECE : coefficient for Adams-Moulton scheme with 3+1 steps
double g_AM_bp3 = 251.0 / 720.0; // PECE : coefficient for Adams-Moulton scheme with 3+1 steps
double g_G = -1; // gravitational constant (in [L^{3}][M^{-1}][T^{-2}], (to be set by reading the input file))
double g_ab = -1; // galactic parameter (to be set by reading the input file)
double g_ad = -1; // galactic parameter (to be set by reading the input file)
double g_ah = -1; // galactic parameter (to be set by reading the input file)
double g_duration = -1; // (to be set by reading the input file)
double g_hd = -1; // galactic parameter (to be set by reading the input file)
double g_mb = -1; // galactic parameter (to be set by reading the input file)
double g_md = -1; // galactic parameter (to be set by reading the input file)
double g_print_interval = -1; // (to be set by reading the input file)
double g_softening = -1; // softening (in [L], to be set by reading the input file)
double g_timestep = -1; // (to be set by reading the input file)
double g_vh = -1; // galactic parameter (to be set by reading the input file)
int g_body_number = -1; // (to be set by reading the input file)
int g_minimumRemTimePrintInt = 5; // minimum interval (in seconds) between printing of remaining time (to prevent flooding on stdout)
int g_galactic_flag = -1; // (to be set by reading the input file)
int g_nbStarsPerThread = 250; // wanted number of stars treated by thread
int g_recenter_flag = -1; // (to be set by reading the input file)
int g_technique_number = 0; // (to be set by reading the input file)
int g_usePECE_flag = -1; // PECE : use PECE (0 if no, 1 if yes) ?
int g_usePEC_flag = -1; // PEC : use PEC (0 if no, 1 if yes) ?
int g_verbose_flag = 0; // if set to 1, print messages as we execute (modifiable by passing arguments when executing)
/*-----------------------------------------------------------*/
/* Declarations of functions. -------------------------------*/
static double calc_total_gpe(void);
static double calc_total_ke(void);
static int AdamsBashforth(BODY *outState, double step, BODY *state0, DBODY *dStateB0, DBODY *dStateB1, DBODY *dStateB2, DBODY *dStateB3);
static int AdamsMoulton(BODY *outState, double step, BODY *state0, DBODY *predictedDState, DBODY *dStateB0, DBODY *dStateB1, DBODY *dStateB2, DBODY *dStateB3);
static int add_galactic_effect(VECTOR *forces);
static int calc_grav_forces(BODY *body_array, VECTOR *forces);
static int calc_total_angmom(VECTOR *result);
static int computeTotalForceOnBodies(VECTOR *forces);
static int print_positions(FILE *outfile_fp, double currentSimulationTime);
static int read_input(char *filename);
static int recenter_velocities(void);
static int getGravitationalForce(BODY body, VECTOR *tmpGravitationalForce);
static int shiftTemporaryStates(DBODY *dStateB3, DBODY *dStateB2, DBODY *dStateB1, DBODY *dStateB0, DBODY *newDState, BODY *state0, BODY *newState);
static int stateToDerivativeState(BODY *b, DBODY *db);
static int tech_euler_1(double suggested_timestep, double *actual_timestep);
static int tech_euler_1a(double suggested_timestep, double *actual_timestep);
static int tech_euler_2(double suggested_timestep, double *actual_timestep);
static int tech_rk4(double suggested_timestep, double *actual_timestep);
static void copy_bodies(int num_bodies, BODY *from_array, BODY *to_array);
static void printError(char *funcName, char *msg);
void kek(double suggested_timestep, double *actual_timestep);
/*-----------------------------------------------------------*/
int main(int argc, char *argv[]) {
/* Initialize stuff. --------------------------------------*/
VECTOR initial_ang_mom, final_ang_mom;
char inputfile_name[NBUF];
char timeUnit[8];
double actual_step, currentSimulationTime, energyTimeTaken1, energyTimeTaken2, final_gpe, final_ke, final_tot_e, initial_gpe, initial_ke, initial_tot_e, mainLoopClock, mainLoopTimeTaken, printing_clock, remainingRealTime, suggested_step, previousInfoClock;
int i, n, retval, remainingTimePrintModulo;
inputfile_name[0] = '\0';
strcpy(timeUnit, "seconds");
for (i = 0; i < MAX_NBODY; i++) {
g_body_array[i].index = -1;
strcpy(g_body_array[i].name, "");
g_body_array[i].mass = -1;
}
g_outfile_fp = (FILE *) NULL;
strcpy(g_technique_array[g_technique_number].name, "E1");
g_technique_array[g_technique_number++].func = tech_euler_1;
strcpy(g_technique_array[g_technique_number].name, "E1a");
g_technique_array[g_technique_number++].func = tech_euler_1a;
strcpy(g_technique_array[g_technique_number].name, "E2");
g_technique_array[g_technique_number++].func = tech_euler_2;
strcpy(g_technique_array[g_technique_number].name, "RK4");
g_technique_array[g_technique_number++].func = tech_rk4;
/*---------------------------------------------------------*/
/* Parse arguments. ---------------------------------------*/
if (argc < 2) {
fprintf(stderr, "usage: nbody input= [verbose=] \n");
exit(1);
}
for (i = 1; i < argc; i++) {
if (g_verbose_flag > 0) {
printf(" arg %d is ..%s.. \n", i, argv[i]);
}
/* read input file name */
if (strncmp(argv[i], "input=", 6) == 0) {
if (strlen(argv[i]) >= NBUF) {
fprintf(stderr, "inputfile name ..%s.. is too long, max %d chars. \n", argv[i], (int) strlen(argv[i]));
exit(1);
}
if (sscanf(argv[i] + 6, "%s", inputfile_name) != 1) {
fprintf(stderr, "can't read inputfile_name from ..%s.. \n", argv[i] + 6);
exit(1);
}
if (g_verbose_flag > 0) {
printf(" read input file name ..%s.. \n", inputfile_name);
}
}
if (strcmp(argv[i], "verbose") == 0) {
g_verbose_flag = 1;
printf(" set verbose level to ..%d.. \n", g_verbose_flag);
}
if (strncmp(argv[i], "verbose=", 8) == 0) {
if (sscanf(argv[i] + 8, "%d", &g_verbose_flag) != 1) {
fprintf(stderr, "can't read verbosity level from ..%s.. \n", argv[i] + 8);
exit(1);
}
if (g_verbose_flag > 0) {
printf(" set verbose level to ..%d.. \n", g_verbose_flag);
}
}
}
if (inputfile_name[0] == '\0') {
fprintf(stderr, "no input= argument provided ?! \n");
exit(1);
} // Check to make sure we read all required arguments.
printf("\n> Starting input file reading.\n");
if (read_input(inputfile_name) != 0) {
fprintf(stderr, "read_input fails \n");
exit(1);
} /* read all input information */
if (g_recenter_flag == 1) {
if (recenter_velocities() != 0) {
fprintf(stderr, "recenter_velocities returns with error \n");
exit(1);
}
} // If desired, add a constant velocity to all bodies so that the center of mass of the system is motionless.
/*---------------------------------------------------------*/
/* Compute initial quantities. ----------------------------*/
printf("\n");
double energyClock = clock(); // check time before
initial_ke = calc_total_ke();
if (g_verbose_flag > 0) {
printf("> Initial KE : %12.5e.\n", initial_ke);
}
initial_gpe = calc_total_gpe();
if (g_verbose_flag > 0) {
printf("> Initial GPE : %12.5e.\n", initial_gpe);
}
initial_tot_e = initial_ke + initial_gpe;
if (g_verbose_flag > 0) {
printf("> Initial E : %12.5e.\n", initial_tot_e);
}
if (calc_total_angmom( & initial_ang_mom) != 0) {
fprintf(stderr, "calc_total_angmom fails for initial \n");
exit(1);
}
if (g_verbose_flag > 0) {
printf("> Initial angular momentum : [%12.5e, %12.5e, %12.5e].\n",
initial_ang_mom.val[0],
initial_ang_mom.val[1],
initial_ang_mom.val[2]);
}
energyClock = clock() - energyClock; // check time after
energyTimeTaken1 = ((double) energyClock) / CLOCKS_PER_SEC; // time taken in seconds
/*---------------------------------------------------------*/
/* Print initial states to output. ------------------------*/
currentSimulationTime = 0;
if (print_positions(g_outfile_fp, currentSimulationTime) != 0) {
fprintf(stderr, "Iteration %16d, time %9.4e [T].\n", 0, currentSimulationTime);
printError("main", "Function print_positions failed.");
exit(1);
}
/*---------------------------------------------------------*/
/* Enter main loop. ---------------------------------------*/
printf("\n");
printf("> Available threads : %d.\n", omp_get_max_threads());
omp_set_num_threads(min(max((int)(floor(g_body_number / g_nbStarsPerThread)), 1), omp_get_max_threads()));
//omp_set_num_threads(3);
#pragma omp parallel
printf("> Launching simulation with %d thread(s) (i.e., roughly, %d star(s) per thread).\n", omp_get_num_threads(), (int)(g_body_number / omp_get_num_threads()));
printing_clock = 0.0; // initialise printing clock
mainLoopClock = clock(); // save timer before entering the main loop
n = 0; // to follow number of iterations
if (g_verbose_flag > 0) {
remainingTimePrintModulo = 20000;
previousInfoClock = clock();
} // every how many iterations print informations about remaining time and dummy value for first previousRemainingRealTime
printf("\n> Entering main integration loop.\n");
while (currentSimulationTime <= g_duration) {
/* Call the integration -*/
/* function. -*/
if (g_verbose_flag > 1) {
printf(" >> About to enter the integration function (t=%9.4e).\n", currentSimulationTime);
}
suggested_step = g_timestep;
actual_step = g_timestep; // safety, in case it does not get allocated in the upcoming calls
if (g_usePECE_flag == 0 && g_usePEC_flag == 0) { // PECE and PEC are desactivated : just use RK4 all the way.
retval = (*(g_integration_func))(suggested_step, &actual_step);
if (retval != 0) {
printError("main", "Integration function failed.");
return (1);
}
g_timestep = actual_step;
} else { // PECE or PEC is activated.
if (n <= 3) { // For the first 4 steps of PECE, call RK4.
retval = (*(g_integration_func))(suggested_step, &actual_step);
if (retval != 0) {
printError("main", "Integration function failed.");
return (1);
}
g_timestep = actual_step;
if (n == 0) {
stateToDerivativeState(g_body_array, fp3);
}
if (n == 1) {
stateToDerivativeState(g_body_array, fp2);
}
if (n == 2) {
stateToDerivativeState(g_body_array, fp1);
}
if (n == 3) {
stateToDerivativeState(g_body_array, fp0);
}
} else { // For n>=4, call PECE/PEC AB AM.
AdamsBashforth(pyn1, g_timestep, g_body_array, fp0, fp1, fp2, fp3); // prediction (Adams Bashforth)
//printf("n=%d, AB, position : [%6.2f, %6.2f, %6.2f], velocity : [%6.2f, %6.2f, %6.2f].\n", n, g_body_array[1].pos[0], g_body_array[1].pos[1], g_body_array[1].pos[2], g_body_array[1].vel[0], g_body_array[1].vel[1], g_body_array[1].vel[2]);
stateToDerivativeState(pyn1, pfn1); // evaluation (with forces computed using predicted state)
//printf("n=%d, evaluation : pyn1 : [%6.2f, %6.2f, %6.2f][%6.2f, %6.2f, %6.2f], pfn1 : [%6.2f, %6.2f, %6.2f][%6.2f, %6.2f, %6.2f]\n", n, pyn1[1].pos[0], pyn1[1].pos[1], pyn1[1].pos[2], pyn1[1].vel[0], pyn1[1].vel[1], pyn1[1].vel[2], pfn1[1].dp[0], pfn1[1].dp[1], pfn1[1].dp[2], pfn1[1].dv[0], pfn1[1].dv[1], pfn1[1].dv[2]);
AdamsMoulton(yn1, g_timestep, g_body_array, pfn1, fp0, fp1, fp2, fp3); // correction (Adams Moulton)
//printf("n=%d, AM, position : [%6.2f, %6.2f, %6.2f], velocity : [%6.2f, %6.2f, %6.2f].\n", n, g_body_array[1].pos[0], g_body_array[1].pos[1], g_body_array[1].pos[2], g_body_array[1].vel[0], g_body_array[1].vel[1], g_body_array[1].vel[2]);
if (g_usePEC_flag == 1) { // If only PEC, use pfn1 as fn1.
shiftTemporaryStates(fp3, fp2, fp1, fp0, pfn1, g_body_array, yn1);
} else { // If PECE, evaluate (with forces computed using corrected state).
stateToDerivativeState(yn1, fn1);
shiftTemporaryStates(fp3, fp2, fp1, fp0, fn1, g_body_array, yn1);
}
}
}
currentSimulationTime += g_timestep;
n += 1;
/*-----------------------*/
/* Update printing ---*/
/* clock and print to ---*/
/* output file. ---*/
printing_clock += actual_step;
if (printing_clock >= g_print_interval) {
/* print the new positions, etc. */
if (print_positions(g_outfile_fp, currentSimulationTime) != 0) {
fprintf(stderr, "Iteration %16d, time %9.4e [T].\n", n, currentSimulationTime);
printError("main", "Function print_positions failed.");
exit(1);
}
printing_clock = 0.0;
}
/*-----------------------*/
/* Print information ----*/
/* about simulation run. */
if (g_verbose_flag > 0) {
if (n == 100 || n == 1000 || n == 2000 || n % remainingTimePrintModulo == 0) { // after first 100, first 1000, first 2000 and then every 20000 integrations, estimate the remaining time
remainingRealTime = (((clock() - mainLoopClock) / currentSimulationTime) * (g_duration - currentSimulationTime)) / CLOCKS_PER_SEC; // estimated remaining time in seconds
if ((n > 2000) && ((clock() - previousInfoClock) < g_minimumRemTimePrintInt * CLOCKS_PER_SEC)) {
remainingTimePrintModulo *= 2;
} // if informations prints too fast, raise interval in terms of iterations
if (remainingRealTime < 60) {
strcpy(timeUnit, "seconds");
}
if (remainingRealTime >= 60 && remainingRealTime < 3600) {
strcpy(timeUnit, "minutes");
remainingRealTime /= 60;
}
if (remainingRealTime >= 3600) {
strcpy(timeUnit, "hours");
remainingRealTime /= 3600;
}
printf("> Iteration %16d, time %9.4e [T], estimated remaining time : %6.2f %s.\n", n, currentSimulationTime, remainingRealTime, timeUnit);
previousInfoClock = clock();
}
}
/*-----------------------*/
}
printf("> Main integration loop finished.\n");
mainLoopTimeTaken = ((double)(clock() - mainLoopClock) / CLOCKS_PER_SEC); // time taken by main loop (in seconds)
/*---------------------------------------------------------*/
/* Print final states to output. --------------------------*/
if (print_positions(g_outfile_fp, currentSimulationTime) != 0) {
fprintf(stderr, "Iteration %16d, time %9.4e [T].\n", n, currentSimulationTime);
printError("main", "Function print_positions failed.");
exit(1);
}
/*---------------------------------------------------------*/
/* Compute final quantities. ------------------------------*/
printf("\n");
energyClock = clock(); // check time before
final_ke = calc_total_ke();
if (g_verbose_flag > 0) {
printf("> Final KE : %12.5e.\n", final_ke);
}
final_gpe = calc_total_gpe();
if (g_verbose_flag > 0) {
printf("> Final GPE : %12.5e.\n", final_gpe);
}
final_tot_e = final_ke + final_gpe;
if (g_verbose_flag > 0) {
printf("> Final E : %12.5e.\n", final_tot_e);
}
if (calc_total_angmom( & final_ang_mom) != 0) {
fprintf(stderr, "calc_total_angmom fails for final \n");
exit(1);
}
if (g_verbose_flag > 0) {
printf("> Final angular momentum : [%12.5e, %12.5e, %12.5e].\n",
final_ang_mom.val[0],
final_ang_mom.val[1],
final_ang_mom.val[2]);
}
energyClock = clock() - energyClock; // check time after
energyTimeTaken2 = ((double) energyClock) / CLOCKS_PER_SEC; // time taken in seconds
/*---------------------------------------------------------*/
/* Compute change in quantities. --------------------------*/
{
double delta_e, fraction_delta_e;
double start_angmom_mag, end_angmom_mag, delta_angmom_mag;
double fraction_delta_angmom_mag;
printf("\n");
delta_e = final_tot_e - initial_tot_e;
fraction_delta_e = delta_e / fabs(initial_tot_e);
if (g_verbose_flag > 0) {
printf("> Delta_E =%12.5e,\n relative difference =%12.5e (the smaller the better, under 1e-02 is good).\n",
delta_e, fraction_delta_e);
}
start_angmom_mag = VECTOR_MAG(initial_ang_mom);
end_angmom_mag = VECTOR_MAG(final_ang_mom);
delta_angmom_mag = end_angmom_mag - start_angmom_mag;
fraction_delta_angmom_mag = delta_angmom_mag / fabs(start_angmom_mag);
if (g_verbose_flag > 0) {
printf("> Delta_angmom =%12.5e,\n relative difference =%12.5e (the smaller the better, under 1e-02 is good).\n",
delta_angmom_mag, fraction_delta_angmom_mag);
}
}
/*---------------------------------------------------------*/
/* Prepare to exit. ---------------------------------------*/
if (g_verbose_flag > 0) {
if (mainLoopTimeTaken < 60) {
strcpy(timeUnit, "seconds");
}
if (mainLoopTimeTaken >= 60 && mainLoopTimeTaken < 3600) {
strcpy(timeUnit, "minutes");
mainLoopTimeTaken /= 60;
}
if (mainLoopTimeTaken >= 3600) {
strcpy(timeUnit, "hours");
mainLoopTimeTaken /= 3600;
}
printf("\n");
printf("> All done.\n");
printf("> Main loop was %12d iterations (integrations) long.\n", n);
printf("> Main loop took %12.2f %s to execute.\n", mainLoopTimeTaken, timeUnit);
printf("> Energies computations took %12.2f seconds to execute.\n", energyTimeTaken1 + energyTimeTaken2);
}
// Close file opened in read_input routine.
fclose(g_outfile_fp);
exit(0);
/*---------------------------------------------------------*/
}
static int stateToDerivativeState(BODY * b, DBODY * db) {
// Get the state derivative of a state. In other terms, for the PDE Y'=f(Y), apply f to a Y to get Y'.
// @param *b array of bodies (in other terms, Y)
// @param *db (output) derivative state (in other terms, Y')
int i, j, c;
VECTOR dist, dist_frac, tmpGravitationalForce;
double dist_tot;
double dist_squared;
double top, bottom, force_mag;
#pragma omp for
for (i = 0; i < g_body_number; i++) { // on body i, ...
for (c = 0; c < 3; c++) { // initialise force at 0, ...
tmpForcesForDerivation[i].val[c] = 0.0;
}
for (j = i; j < g_body_number; j++) { // compute effect of body j, ...
if (i == j) {
g_cur_forces[i][j].val[0] = 0.0;
g_cur_forces[i][j].val[1] = 0.0;
g_cur_forces[i][j].val[2] = 0.0;
continue;
}
dist.val[0] = b[i].pos[0] - b[j].pos[0];
dist.val[1] = b[i].pos[1] - b[j].pos[1];
dist.val[2] = b[i].pos[2] - b[j].pos[2];
dist_squared = VECTOR_MAG_SQUARED(dist);
dist_tot = sqrt(dist_squared);
/* if(dist_tot<=0.0){
fprintf(stderr,
" calc_grav_forces: distance of %le -- quitting \n", dist_tot);
return(1);
} */
top = g_G * b[i].mass * b[j].mass;
bottom = (dist_tot + g_softening) * (dist_tot + g_softening);
force_mag = top / bottom;
for (c = 0; c < 3; c++) { // and for each coordinate, prepare the value and add it as contribution
dist_frac.val[c] = dist.val[c] / dist_tot;
g_cur_forces[i][j].val[c] = 0.0 - (force_mag * dist_frac.val[c]);
g_cur_forces[j][i].val[c] = 0.0 - g_cur_forces[i][j].val[c];
tmpForcesForDerivation[i].val[c] += -(force_mag * dist_frac.val[c]);
tmpForcesForDerivation[j].val[c] += (force_mag * dist_frac.val[c]);
}
}
for (j = 0; j < g_body_number; j++) { // add contribution of each body j on body i
for (c = 0; c < 3; c++) {
tmpForcesForDerivation[i].val[c] += g_cur_forces[i][j].val[c];
}
}
if (g_galactic_flag == 1) { // if the effect of a galaxy is wanted, add it to the current force on body i
getGravitationalForce(g_body_array[i], &tmpGravitationalForce);
for (c = 0; c < 3; c++) {
tmpForcesForDerivation[i].val[c] += tmpGravitationalForce.val[c];
}
}
for (c = 0; c < 3; c++) { // when all contributions have been added, for body i, apply the derivation
db[i].dp[c] = b[i].vel[c]; // dp=v
db[i].dv[c] = tmpForcesForDerivation[i].val[c] / b[i].mass; // dv=a/m
}
}
return (0);
}
static int AdamsBashforth(BODY * outState, double step, BODY * state0, DBODY * dStateB0, DBODY * dStateB1, DBODY * dStateB2, DBODY * dStateB3) {
// Apply an iteration of the Adams-Bashforth algorithm.
// @param *outState (output) the system state 1 iteration after (BODY array)
// @param step the step
// @param *state0 the system state at current iteration (BODY array)
// @param *dStateB0 the system state's derivative at current iteration (DBODY array)
// @param *dStateB1 the system state's derivative 1 iteration before (DBODY array)
// @param *dStateB2 the system state's derivative 2 iterations before (DBODY array)
// @param *dStateB3 the system state's derivative 3 iterations before (DBODY array)
int i, c;
#pragma omp for
for (i = 0; i < g_body_number; i++) {
for (c = 0; c < 3; c++) {
outState[i].pos[c] = state0[i].pos[c] + step * (g_AB_b03 * dStateB0[i].dp[c] + g_AB_b13 * dStateB1[i].dp[c] + g_AB_b23 * dStateB2[i].dp[c] + g_AB_b33 * dStateB3[i].dp[c]); // p=f(y)
outState[i].vel[c] = state0[i].vel[c] + step * (g_AB_b03 * dStateB0[i].dv[c] + g_AB_b13 * dStateB1[i].dv[c] + g_AB_b23 * dStateB2[i].dv[c] + g_AB_b33 * dStateB3[i].dv[c]); // v=f(y)
}
outState[i].mass = state0[i].mass; // m=f(y)
}
return (0);
}
static int AdamsMoulton(BODY * outState, double step, BODY * state0, DBODY * predictedDState, DBODY * dStateB0, DBODY * dStateB1, DBODY * dStateB2, DBODY * dStateB3) {
// Apply an iteration of the Adams-Moulton algorithm.
// @param *outState (output) the system state 1 iteration after (BODY array)
// @param step the step
// @param *state0 the system state at current iteration (BODY array)
// @param *predictedDState the predicted system state's derivative 1 iteration after (DBODY array)
// @param *dStateB0 the system state's derivative at current iteration (DBODY array)
// @param *dStateB1 the system state's derivative 1 iteration before (DBODY array)
// @param *dStateB2 the system state's derivative 2 iterations before (DBODY array)
// @param *dStateB3 the system state's derivative 3 iterations before (DBODY array)
int i, c;
#pragma omp for
for (i = 0; i < g_body_number; i++) {
for (c = 0; c < 3; c++) {
outState[i].pos[c] = state0[i].pos[c] + step * (g_AM_bp3 * predictedDState[i].dp[c] + g_AM_b03 * dStateB0[i].dp[c] + g_AM_b13 * dStateB1[i].dp[c] + g_AM_b23 * dStateB2[i].dp[c] + g_AM_b33 * dStateB3[i].dp[c]);
outState[i].vel[c] = state0[i].vel[c] + step * (g_AM_bp3 * predictedDState[i].dv[c] + g_AM_b03 * dStateB0[i].dv[c] + g_AM_b13 * dStateB1[i].dv[c] + g_AM_b23 * dStateB2[i].dv[c] + g_AM_b33 * dStateB3[i].dv[c]);
}
outState[i].mass = state0[i].mass; // m=f(y)
}
return (0);
}
static int shiftTemporaryStates(DBODY * dStateB3, DBODY * dStateB2, DBODY * dStateB1, DBODY * dStateB0, DBODY * newDState, BODY * state0, BODY * newState) {
// For the PECE scheme, shifts needed temporary states as number of iteration goes from n to n+1.
// @param *dStateB3 (output) the system state's derivative 3 iterations before (DBODY array)
// @param *dStateB2 (input/output) the system state's derivative 2 iterations before (DBODY array)
// @param *dStateB1 (input/output) the system state's derivative 1 iteration before (DBODY array)
// @param *dStateB0 (input/output)the system state's derivative at current iteration (DBODY array)
// @param *newDState the system state's derivative 1 iteration after (DBODY array)
// @param *state0 (output) the system state at current iteration (BODY array)
// @param *newState the system state 1 iteration after (BODY array)
int i, c;
#pragma omp for
for (i = 0; i < g_body_number; i++) {
for (c = 0; c < 3; c++) {
dStateB3[i].dp[c] = dStateB2[i].dp[c];
dStateB3[i].dv[c] = dStateB2[i].dv[c];
dStateB2[i].dp[c] = dStateB1[i].dp[c];
dStateB2[i].dv[c] = dStateB1[i].dv[c];
dStateB1[i].dp[c] = dStateB0[i].dp[c];
dStateB1[i].dv[c] = dStateB0[i].dv[c];
dStateB0[i].dp[c] = newDState[i].dp[c];
dStateB0[i].dv[c] = newDState[i].dv[c];
state0[i].pos[c] = newState[i].pos[c];
state0[i].vel[c] = newState[i].vel[c];
}
}
return (0);
}
static int tech_rk4(double suggested_timestep, double *actual_timestep) {
// Advance particle system one timestep using Runge-Kutta fourth-order method.
// @param suggested_timestep suggested timestep
// @param *actual_timestep actual timestep used (for now, this function does not try to change the timestep)
int i, c;
double timestep;
double half_step, sixth_step;
VECTOR v1[g_body_number];
VECTOR v2[g_body_number];
VECTOR v3[g_body_number];
VECTOR v4[g_body_number];
VECTOR a1[g_body_number];
VECTOR a2[g_body_number];
VECTOR a3[g_body_number];
VECTOR a4[g_body_number];
BODY step2_array[g_body_number];
BODY step3_array[g_body_number];
BODY step4_array[g_body_number];
timestep = suggested_timestep;
half_step = timestep * 0.5;
sixth_step = timestep / 6.0;
copy_bodies(g_body_number, g_body_array, step2_array); // For S3.
copy_bodies(g_body_number, g_body_array, step3_array); // For S6.
copy_bodies(g_body_number, g_body_array, step4_array); // For S9.
// S1: use current positions to compute accelerations. Call these "a1".
if (calc_grav_forces(step2_array, a1) != 0) {
printError("tech_rk4", "Function calc_grav_forces fails in step a1.");
return (1);
}
#pragma omp for
for (i = 0; i < g_body_number; i++) {
for (c = 0; c < 3; c++) {
a1[i].val[c] /= step2_array[i].mass; // Convert those forces to accelerations.
v1[i].val[c] = g_body_array[i].vel[c]; // S2 : copy the current velocities into an array for later use. Call these "v1".
step2_array[i].pos[c] += half_step * v1[i].val[c]; // S3 : use the "v1" velocities to predict positions of objects one-half a step into the future. We'll place the positions into the "step2_array[]."
v2[i].val[c] = v1[i].val[c] + half_step * a1[i].val[c]; // S4 : use the "a1" accelerations to predict future velocities at half a step into the future. Call these "v2".
}
}
// S5: use the "step2_array" positions (at half a step in future) to compute forces on the bodies in the future. Convert these forces to accelerations and place into the "a2" array.
if (calc_grav_forces(step2_array, a2) != 0) {
printError("tech_rk4", "Function calc_grav_forces fails in step a2.");
return (1);
}
#pragma omp for
for (i = 0; i < g_body_number; i++) {
for (c = 0; c < 3; c++) {
a2[i].val[c] /= step2_array[i].mass; // Convert those forces to accelerations.
v3[i].val[c] = v1[i].val[c] + half_step * a2[i].val[c]; // S6: use the "a2" accelerations to predict future velocities at half a step into the future. Call these "v3".
step3_array[i].pos[c] += half_step * v2[i].val[c]; // S6: use the "v2" velocities to predict positions of objects one-half a step into the future. We'll place the positions into the "step3_array[]."
}
}
// S7: use the "step3_array" positions (at half a step in future) to compute forces on the bodies in the future. Convert these forces to accelerations and place into the "a3" array.
if (calc_grav_forces(step3_array, a3) != 0) {
printError("tech_rk4", "Function calc_grav_forces fails in step a3.");
return (1);
}
#pragma omp for
for (i = 0; i < g_body_number; i++) {
for (c = 0; c < 3; c++) {
a3[i].val[c] /= step3_array[i].mass; // Convert those forces to accelerations.
v4[i].val[c] = v1[i].val[c] + timestep * a3[i].val[c]; // S8: use the "a3" accelerations to predict future velocities at one FULL step into the future. Call these "v4".
step4_array[i].pos[c] += timestep * v3[i].val[c]; // S9: use the "v3" velocities to predict positions of objects one FULL step into the future. We'll place the positions into the "step4_array[]."
}
}
// S10: use the "step4_array" positions (at one FULL step in future) to compute forces on the bodies in the future. Convert these forces to accelerations and place into the "a4" array.
if (calc_grav_forces(step4_array, a4) != 0) {
printError("tech_rk4", "Function calc_grav_forces fails in step a4.");
return (1);
}
#pragma omp for
for (i = 0; i < g_body_number; i++) {
for (c = 0; c < 3; c++) {
a4[i].val[c] /= step4_array[i].mass; // Convert those forces to accelerations.
// See note below.
double delta_vel, delta_pos;
delta_vel = sixth_step * (a1[i].val[c] + 2 * a2[i].val[c] + 2 * a3[i].val[c] + a4[i].val[c]);
delta_pos = sixth_step * (v1[i].val[c] + 2 * v2[i].val[c] + 2 * v3[i].val[c] + v4[i].val[c]);
g_body_array[i].vel[c] += delta_vel;
g_body_array[i].pos[c] += delta_pos;
}
}
/* Note :
* At this point, we have 4 velocities and 4 accelerations for each object :
* - v1 current velocity,
* - v2 velocity predicted half a step in future,
* - v3 improved velocity predicted half a step in future,
* - v4 velocity predicted one FULL step in future,
* - a1 current acceleration,
* - a2 acceleration predicted half a step in future,
* - a3 improved acceleration predicted half a step in future,
* - a4 acceleration predicted one FULL step in future.
* We can now combine these 4 measurements to produce one good value of velocity (or acceleration) one full step into the future.
*/
*actual_timestep = timestep;
return (0);
}
static int calc_grav_forces(BODY * body_array, VECTOR * forces) {
// Given an array of bodies, compute the gravitational forces between each pair. The forces are then placed into a vector array.
// @param *body_array array with pos and mass of all bodies (BODY array)
// @param *forces (output) forces on each body (VECTOR array)
int i, j, c;
// Compute the forces between all objects using the current positions and store this in the pre-allocated global variable g_cur_forces.
#pragma omp for
for (i = 0; i < g_body_number; i++) {
for (j = i; j < g_body_number; j++) {
VECTOR dist, dist_frac;
double dist_tot;
double dist_squared;
double top, bottom, force_mag;
if (i == j) {
g_cur_forces[i][j].val[0] = 0.0;
g_cur_forces[i][j].val[1] = 0.0;
g_cur_forces[i][j].val[2] = 0.0;
continue;
}
dist.val[0] = body_array[i].pos[0] - body_array[j].pos[0];
dist.val[1] = body_array[i].pos[1] - body_array[j].pos[1];
dist.val[2] = body_array[i].pos[2] - body_array[j].pos[2];
dist_squared = VECTOR_MAG_SQUARED(dist);
dist_tot = sqrt(dist_squared);
/* if(dist_tot<=0.0){
fprintf(stderr,
" calc_grav_forces: distance of %le -- quitting \n", dist_tot);
return(1);
} */
top = g_G * body_array[i].mass * body_array[j].mass;
bottom = (dist_tot + g_softening) * (dist_tot + g_softening);
force_mag = top / bottom;
for (c = 0; c < 3; c++) {
dist_frac.val[c] = dist.val[c] / dist_tot;
g_cur_forces[i][j].val[c] = 0.0 - (force_mag * dist_frac.val[c]);
g_cur_forces[j][i].val[c] = 0.0 - g_cur_forces[i][j].val[c];
}
}
}
computeTotalForceOnBodies(forces); // convert forces between each pair (stored in g_cur_forces) to a set of forces on each body
if (g_galactic_flag == 1) {
add_galactic_effect(forces);
} // if the effect of a galaxy is wanted, add it to the current forces
return (0);
}
static int computeTotalForceOnBodies(VECTOR * forces) {
// Convert forces between each pair (stored in g_cur_forces) to a set of forces on each body.
// @param *forces (output) forces on each body (VECTOR array)
int i, j, c;
#pragma omp for
for (i = 0; i < g_body_number; i++) {
for (c = 0; c < 3; c++) {
forces[i].val[c] = 0.0;
for (j = 0; j < g_body_number; j++) {
forces[i].val[c] += g_cur_forces[i][j].val[c];
}
}
}
return (0);
}
static int add_galactic_effect(VECTOR * forces) {
// Adds to an array of forces the effect of a galactic field.
// The galaxy is supposed to be centered on the origin of the
// reference (O=[0.0, 0.0, 0.0]) and its model is given by :
//-a Plummer type bulge,
//-a Miyamoto-Nagai disk,
//-a dark matter halo.
// @param *forces (input/output) forces on each body (VECTOR array)
int i;
VECTOR tmpGravitationalForce;
#pragma omp for
for (i = 0; i < g_body_number; i++) {
getGravitationalForce(g_body_array[i], &tmpGravitationalForce);
forces[i].val[0] += tmpGravitationalForce.val[0];
forces[i].val[1] += tmpGravitationalForce.val[1];
forces[i].val[2] += tmpGravitationalForce.val[2];
}
return (0);
}
static int getGravitationalForce(BODY body, VECTOR * tmpGravitationalForce) {
// Compute the graviational force on a body.
// @param body the considered body
// @param *tmpGravitationalForce (output) the graviational force (pointer to a VECTOR)
double tmpX, tmpY, tmpZ;
double tmpRSquared, tmpRCSquared, tmpZSquared; // temporary variables to store the spherical radius, cylindrical radius and cylindrical altitude of a body
double tmpPhiB, tmpPhiD, tmpPhiH; // temporary variables to store the bulge, disk and halo components
tmpX = body.pos[0];
tmpY = body.pos[1];
tmpZ = body.pos[2];
tmpRCSquared = tmpX * tmpX + tmpY * tmpY;
tmpZSquared = tmpZ * tmpZ;
tmpRSquared = tmpRCSquared + tmpZSquared;
// x
tmpPhiB = g_G * g_mb * pow(tmpRSquared + g_ab * g_ab, -1.5) * tmpX;
tmpPhiD = g_G * g_md * pow(tmpRCSquared + pow(g_ad + pow(tmpZSquared + g_hd * g_hd, 0.5), 2.0), -1.5) * tmpX;
tmpPhiH = -(g_vh * g_vh) / (tmpRSquared + g_ah * g_ah) * tmpX;
tmpGravitationalForce -> val[0] = tmpPhiB + tmpPhiD + tmpPhiH;
// y
tmpPhiB *= (tmpY / tmpX);
tmpPhiD *= (tmpY / tmpX);
tmpPhiH *= (tmpY / tmpX);
tmpGravitationalForce -> val[1] = tmpPhiB + tmpPhiD + tmpPhiH;
// z
tmpPhiB *= (tmpZ / tmpY);
tmpPhiD *= (tmpZ / tmpY);
tmpPhiH *= (tmpZ / tmpY);
tmpPhiD *= ((g_ad + pow(tmpZSquared + g_hd * g_hd, 0.5)) / (pow(tmpZSquared + g_hd * g_hd, 0.5)));
tmpGravitationalForce -> val[2] = tmpPhiB + tmpPhiD + tmpPhiH;
tmpGravitationalForce -> val[0] *= -body.mass;
tmpGravitationalForce -> val[1] *= -body.mass;
tmpGravitationalForce -> val[2] *= -body.mass;
return (0);
}
static void copy_bodies(int N, BODY *in, BODY *out) {
// Copy an array of BODY structures into a second array in such a manner that we can then modify the copies and leave the originals untouched.
// @param N number of bodies to be copied
// @param in copy from this array
// @param out (output) copy to this array
int i, c;
BODY *from_body, *to_body;
#pragma omp for
for (i = 0; i < N; i++) {
from_body = &(in [i]);
to_body = &(out[i]);
to_body->index = from_body->index;
strcpy(from_body->name, to_body->name);
to_body->mass = from_body->mass;
for (c = 0; c < 3; c++) {
to_body->pos[c] = from_body->pos[c];
to_body->vel[c] = from_body->vel[c];
}
}
}
static int recenter_velocities(void) {
// Compute the global velocity of the system. Then, subtract that value from all bodies, so that the center of mass of the system should remain motionless as time passes.
// @param none
int i, c;
double total_mass;
VECTOR momentum, com_velocity;
total_mass = 0.0;
for (c = 0; c < 3; c++) {
momentum.val[c] = 0.0;
}
for (i = 0; i < g_body_number; i++) {
total_mass += g_body_array[i].mass;
for (c = 0; c < 3; c++) {
momentum.val[c] += g_body_array[i].mass * g_body_array[i].vel[c];
}
}
if (total_mass == 0.0) {
return (0);
} // If the total mass is zero, just return now (why would that be ever the case anyways ?).
for (c = 0; c < 3; c++) {
com_velocity.val[c] = momentum.val[c] / total_mass;
} // Compute the velocity of the center of mass.
#pragma omp for
for (i = 0; i < g_body_number; i++) {
for (c = 0; c < 3; c++) {
g_body_array[i].vel[c] -= com_velocity.val[c];
}
} // Subtract this velocity from each body.
return (0);
}
static double calc_total_ke(void) {
// Compute the total KE of all bodies. The result will have [E]=[M]*[L^2]*[T^{-2}] as unit.
// @param none
// @return the total KE
int i;
double vSquared, ke, total_ke;
total_ke = 0;
for (i = 0; i < g_body_number; i++) {
vSquared = g_body_array[i].vel[0] * g_body_array[i].vel[0] + g_body_array[i].vel[1] * g_body_array[i].vel[1] + g_body_array[i].vel[2] * g_body_array[i].vel[2];
ke = 0.5 * g_body_array[i].mass * vSquared;
total_ke += ke;
if (g_verbose_flag > 1) {
printf(">> [calc_total_ke] : Body %5d has v**2=%9.4e and m=%9.4e, thus %9.4e of KE (total updated to %9.4e).\n", i, vSquared, g_body_array[i].mass, ke, total_ke);
}
}
return (total_ke);
}
static double calc_total_gpe(void) {
// Compute the total GPE of all bodies. The result will have [E]=[M]*[L^2]*[T^{-2}] as unit.
// @param none
// @return the total GPE
int i, j;
double d, d_squared, gpe, total_gpe;
total_gpe = 0.0;
for (i = 0; i < g_body_number - 1; i++) {
for (j = i + 1; j < g_body_number; j++) {
d_squared = DIST_SQUARED(i, j);
d = sqrt(d_squared);
if (d <= 0) {
fprintf(stderr, "Distance %9.4le (between bodies %d and %d).\n", d, i, j);
printError("calc_total_gpe", "Distance is invalid.");
exit(1);
}
gpe = 0.0 - ((g_G * g_body_array[i].mass * g_body_array[j].mass) / d);
total_gpe += gpe;
if (g_verbose_flag > 1) {
printf(">> [calc_total_gpe] Bodies %5d and %5d have %9.4e of GPE (total GPE updated to %9.4e).\n", i, j, gpe, total_gpe);
}
}
}
return (total_gpe);
}
static int calc_total_angmom(VECTOR * result) {
// Compute the total angular momentum of all the bodies, as a three-D vector, computed around the center of mass of the system. The result will have [M]*[L]*[T^{-1}] as unit.
// *result total angular momentum of system
int i, c;
double total_mass;
VECTOR body_pos, body_vel, body_ang_mom, com, com_vel, total_ang_mom;
total_mass = 0.0;
for (c = 0; c < 3; c++) {
com.val[c] = 0.0;
com_vel.val[c] = 0.0;
total_ang_mom.val[c] = 0.0;
}
// Compute the center of mass of the system and the velocity of the center of mass.
for (i = 0; i < g_body_number; i++) {
total_mass += g_body_array[i].mass;
for (c = 0; c < 3; c++) {
com.val[c] += g_body_array[i].mass * g_body_array[i].pos[c];
com_vel.val[c] += g_body_array[i].mass * g_body_array[i].vel[c];
}
}
for (c = 0; c < 3; c++) {
com.val[c] /= total_mass;
com_vel.val[c] /= total_mass;
}
// Compute the angular momentum of each body around this point.
for (i = 0; i < g_body_number; i++) {
// Compute the position vector from center of mass to body i.
body_pos.val[0] = g_body_array[i].pos[0] - com.val[0];
body_pos.val[1] = g_body_array[i].pos[1] - com.val[1];
body_pos.val[2] = g_body_array[i].pos[2] - com.val[2];
// Compute the velocity difference between center of mass and body i, and weight it by the mass of the body.
body_vel.val[0] = g_body_array[i].mass * (g_body_array[i].vel[0] - com_vel.val[0]);