int main ( int argc, char * argv[] ) {
double * rx, * ry, * rz;
double * vx, * vy, * vz;
double * fx, * fy, * fz;
int * ix, * iy, * iz;
int nl;
double * xi, * vxi, * Q;
int N=216,c,a;
double L=0.0;
double rho=0.5, Tb = 1.0, nu=1.0, rc2 = 1.e20;
double vir, vir_sum, pcor, V;
double PE, KE, TE, ecor, ecut, T0=0.0, TE0;
double rr3,dt=0.001, dt2, dt_2, dt_4, dt_8, sigma;
int tj_ts=-1;
double tj_Tb=1.0;
int i,j,s;
int nSteps = 10, fSamp=100;
int short_out=0;
int use_e_corr=0;
int unfold = 0;
char fn[20];
FILE * out;
char * wrt_code_str = "w";
char * init_cfg_file = NULL;
gsl_rng * r = gsl_rng_alloc(gsl_rng_mt19937);
unsigned long int Seed = 23410981;
/* Allocate arrays for the NH Chain */
nl = 2; /* for now... */
xi = (double*)malloc(nl*sizeof(double));
vxi = (double*)malloc(nl*sizeof(double));
Q = (double*)malloc(nl*sizeof(double));
/* Default masses */
Q[0] = Q[1] = 0.1;
/* Here we parse the command line arguments; If
you add an option, document it in the usage() function! */
for (i=1;i<argc;i++) {
if (!strcmp(argv[i],"-N")) N=atoi(argv[++i]);
else if (!strcmp(argv[i],"-rho")) rho=atof(argv[++i]);
else if (!strcmp(argv[i],"-nu")) nu=atof(argv[++i]);
else if (!strcmp(argv[i],"-dt")) dt=atof(argv[++i]);
else if (!strcmp(argv[i],"-rc")) rc2=atof(argv[++i]);
else if (!strcmp(argv[i],"-ns")) nSteps = atoi(argv[++i]);
else if (!strcmp(argv[i],"-so")) short_out=1;
else if (!strcmp(argv[i],"-T0")) T0=atof(argv[++i]);
else if (!strcmp(argv[i],"-Tb")) Tb=atof(argv[++i]);
else if (!strcmp(argv[i],"-Q")) sscanf(argv[++i],"%lf,%lf",
&Q[0],&Q[1]);
else if (!strcmp(argv[i],"-Tjump")) sscanf(argv[++i],"%i,%lf",
&tj_ts,&tj_Tb);
else if (!strcmp(argv[i],"-fs")) fSamp=atoi(argv[++i]);
else if (!strcmp(argv[i],"-sf")) wrt_code_str = argv[++i];
else if (!strcmp(argv[i],"-icf")) init_cfg_file = argv[++i];
else if (!strcmp(argv[i],"-ecorr")) use_e_corr = 1;
else if (!strcmp(argv[i],"-seed")) Seed = (unsigned long)atoi(argv[++i]);
else if (!strcmp(argv[i],"-uf")) unfold = 1;
else if (!strcmp(argv[i],"-h")) {
usage(); exit(0);
}
else {
fprintf(stderr,"Error: Command-line argument '%s' not recognized.\n",
argv[i]);
exit(-1);
}
}
/* Compute the side-length */
L = pow((V=N/rho),0.3333333);
/* Compute the tail-corrections; assumes sigma and epsilon are both 1 */
rr3 = 1.0/(rc2*rc2*rc2);
ecor = use_e_corr?8*M_PI*rho*(rr3*rr3*rr3/9.0-rr3/3.0):0.0;
pcor = use_e_corr?16.0/3.0*M_PI*rho*rho*(2./3.*rr3*rr3*rr3-rr3):0.0;
ecut = 4*(rr3*rr3*rr3*rr3-rr3*rr3);
/* Compute the *squared* cutoff, reusing the variable rc2 */
rc2*=rc2;
/* compute the squared time step */
dt2 = dt*dt;
dt_2 = 0.5*dt;
dt_4 = 0.5*dt_2;
dt_8 = 0.5*dt_4; // thanks, [email protected]
/* Compute sigma */
sigma = sqrt(Tb);
/* Output some initial information */
fprintf(stdout,"# Nose-Hoover-Chain-Thermostat MD Simulation"
" of a Lennard-Jones fluid\n");
fprintf(stdout,"# L = %.5lf; rho = %.5lf; N = %i; rc = %.5lf\n",
L,rho,N,sqrt(rc2));
fprintf(stdout,"# nSteps %i, seed %d, dt %.5lf, "
"Tb %.5lf, Q0 %.5lf Q1 %.5lf\n",
nSteps,Seed,dt,Tb,Q[0],Q[1]);
/* Seed the random number generator */
gsl_rng_set(r,Seed);
/* Allocate the position arrays */
rx = (double*)malloc(N*sizeof(double));
ry = (double*)malloc(N*sizeof(double));
rz = (double*)malloc(N*sizeof(double));
/* Allocate the boundary crossing counter arrays */
ix = (int*)malloc(N*sizeof(int));
iy = (int*)malloc(N*sizeof(int));
iz = (int*)malloc(N*sizeof(int));
/* Allocate the velocity arrays */
vx = (double*)malloc(N*sizeof(double));
vy = (double*)malloc(N*sizeof(double));
vz = (double*)malloc(N*sizeof(double));
/* Allocate the force arrays */
fx = (double*)malloc(N*sizeof(double));
fy = (double*)malloc(N*sizeof(double));
fz = (double*)malloc(N*sizeof(double));
/* Generate initial positions on a cubic grid,
and measure initial energy */
init(rx,ry,rz,vx,vy,vz,ix,iy,iz,N,xi,vxi,nl,L,r,T0,&KE,init_cfg_file);
sprintf(fn,"%i.xyz",0);
out=fopen(fn,"w");
xyz_out(out,rx,ry,rz,
vx,vy,vz,ix,iy,iz,
L,N,
xi,vxi,Q,nl,
16,1,unfold);
fclose(out);
PE = total_e(rx,ry,rz,fx,fy,fz,N,L,rc2,ecor,ecut,&vir);
TE0=PE+KE;
fprintf(stdout,"# step PE KE TE drift T P\n");
/* Nose-Hoover-Chain (Algorithms 30, 31, 32) */
for (s=0;s<nSteps;s++) {
/* do a temperature jump at the prescribed time */
if (s==tj_ts) Tb = tj_Tb;
chain(&KE,dt,dt_2,dt_4,dt_8,Q,xi,vxi,vx,vy,vz,nl,N,Tb);
/* First integration half-step */
KE = 0.0;
for (i=0;i<N;i++) {
rx[i]+=vx[i]*dt_2;
ry[i]+=vy[i]*dt_2;
rz[i]+=vz[i]*dt_2;
/* Apply periodic boundary conditions */
if (rx[i]<0.0) { rx[i]+=L; ix[i]--; }
if (rx[i]>L) { rx[i]-=L; ix[i]++; }
if (ry[i]<0.0) { ry[i]+=L; iy[i]--; }
if (ry[i]>L) { ry[i]-=L; iy[i]++; }
if (rz[i]<0.0) { rz[i]+=L; iz[i]--; }
if (rz[i]>L) { rz[i]-=L; iz[i]++; }
}
/* Calculate forces */
PE = total_e(rx,ry,rz,fx,fy,fz,N,L,rc2,ecor,ecut,&vir);
/* Second integration half-step */
for (i=0;i<N;i++) {
vx[i]+=dt*fx[i];
vy[i]+=dt*fy[i];
vz[i]+=dt*fz[i];
rx[i]+=vx[i]*dt_2;
ry[i]+=vy[i]*dt_2;
rz[i]+=vz[i]*dt_2;
KE+=vx[i]*vx[i]+vy[i]*vy[i]+vz[i]*vz[i];
}
KE*=0.5;
chain(&KE,dt,dt_2,dt_4,dt_8,Q,xi,vxi,vx,vy,vz,nl,N,Tb);
TE=PE+KE;
fprintf(stdout,"%i %.5lf %.5lf %.5lf %.5lf %.5le %.5lf %.5lf\n",
s,s*dt,PE,KE,TE,(TE-TE0)/TE0,KE*2/3./N,rho*KE*2./3./N+vir/3.0/V);
if (!(s%fSamp)) {
sprintf(fn,"%i.xyz",!strcmp(wrt_code_str,"a")?0:s);
out=fopen(fn,wrt_code_str);
xyz_out(out,rx,ry,rz,vx,vy,vz,ix,iy,iz,L,N,xi,vxi,Q,nl,16,1,unfold);
fclose(out);
}
}
}
int main ( int argc, char * argv[] ) {
double * rx, * ry, * rz;
double * vx, * vy, * vz;
double * fx, * fy, * fz;
int * ix, * iy, * iz;
int N=216,c,a;
double L=0.0;
double rho=0.5, Tb = 1.0, gamma=1.0, rc2 = 2.5;
double vir, vir_sum, pcor, V;
double PE, KE, TE, ecor, ecut, T0=0.0, TE0;
double rr3,dt=0.001, dt2, gfric, noise;
int i,j,s;
int nSteps = 10, fSamp=100;
int short_out=0;
int use_e_corr=0;
int unfold = 0;
char fn[20];
FILE * out;
char * wrt_code_str = "w";
char * init_cfg_file = NULL;
gsl_rng * r = gsl_rng_alloc(gsl_rng_mt19937);
unsigned long int Seed = 23410981;
/* Here we parse the command line arguments; If
you add an option, document it in the usage() function! */
for (i=1;i<argc;i++) {
if (!strcmp(argv[i],"-N")) N=atoi(argv[++i]);
else if (!strcmp(argv[i],"-rho")) rho=atof(argv[++i]);
else if (!strcmp(argv[i],"-gam")) gamma=atof(argv[++i]);
else if (!strcmp(argv[i],"-dt")) dt=atof(argv[++i]);
else if (!strcmp(argv[i],"-rc")) rc2=atof(argv[++i]);
else if (!strcmp(argv[i],"-ns")) nSteps = atoi(argv[++i]);
else if (!strcmp(argv[i],"-so")) short_out=1;
else if (!strcmp(argv[i],"-T0")) T0=atof(argv[++i]);
else if (!strcmp(argv[i],"-Tb")) Tb=atof(argv[++i]);
else if (!strcmp(argv[i],"-fs")) fSamp=atoi(argv[++i]);
else if (!strcmp(argv[i],"-sf")) wrt_code_str = argv[++i];
else if (!strcmp(argv[i],"-icf")) init_cfg_file = argv[++i];
else if (!strcmp(argv[i],"-ecorr")) use_e_corr = 1;
else if (!strcmp(argv[i],"-seed")) Seed = (unsigned long)atoi(argv[++i]);
else if (!strcmp(argv[i],"-uf")) unfold = 1;
else if (!strcmp(argv[i],"-h")) {
usage(); exit(0);
}
else {
fprintf(stderr,"Error: Command-line argument '%s' not recognized.\n",
argv[i]);
exit(-1);
}
}
/* Compute the side-length */
L = pow((V=N/rho),0.3333333);
/* Compute the tail-corrections; assumes sigma and epsilon are both 1 */
rr3 = 1.0/(rc2*rc2*rc2);
ecor = use_e_corr?8*M_PI*rho*(rr3*rr3*rr3/9.0-rr3/3.0):0.0;
pcor = use_e_corr?16.0/3.0*M_PI*rho*rho*(2./3.*rr3*rr3*rr3-rr3):0.0;
ecut = 4*(rr3*rr3*rr3*rr3-rr3*rr3);
/* Compute the *squared* cutoff, reusing the variable rc2 */
rc2*=rc2;
/* compute the squared time step */
dt2=dt*dt;
/* Compute gfric */
gfric = 1.0-gamma*dt/2.0;
/* Compute noise */
noise = sqrt(6.0*gamma*Tb/dt);
/* Output some initial information */
fprintf(stdout,"# Langevin-Thermostat MD Simulation"
" of a Lennard-Jones fluid\n");
fprintf(stdout,"# L = %.5lf; rho = %.5lf; N = %i; rc = %.5lf\n",
L,rho,N,sqrt(rc2));
fprintf(stdout,"# nSteps %i, seed %d, dt %.5lf, T0 %.5lf, gamma %.5lf\n",
nSteps,Seed,dt,T0,gamma);
fprintf(stdout,"# gfric %.5lf noise %.5lf\n",gfric,noise);
/* Seed the random number generator */
gsl_rng_set(r,Seed);
/* Allocate the position arrays */
rx = (double*)malloc(N*sizeof(double));
ry = (double*)malloc(N*sizeof(double));
rz = (double*)malloc(N*sizeof(double));
/* Allocate the boundary crossing counter arrays */
ix = (int*)malloc(N*sizeof(int));
iy = (int*)malloc(N*sizeof(int));
iz = (int*)malloc(N*sizeof(int));
/* Allocate the velocity arrays */
vx = (double*)malloc(N*sizeof(double));
vy = (double*)malloc(N*sizeof(double));
vz = (double*)malloc(N*sizeof(double));
/* Allocate the force arrays */
fx = (double*)malloc(N*sizeof(double));
fy = (double*)malloc(N*sizeof(double));
fz = (double*)malloc(N*sizeof(double));
/* Generate initial positions on a cubic grid,
and measure initial energy */
init(rx,ry,rz,vx,vy,vz,ix,iy,iz,N,L,r,T0,&KE,init_cfg_file);
sprintf(fn,"%i.xyz",0);
out=fopen(fn,"w");
xyz_out(out,rx,ry,rz,vx,vy,vz,ix,iy,iz,L,N,16,1,unfold);
fclose(out);
PE = total_e(rx,ry,rz,fx,fy,fz,N,L,rc2,ecor,ecut,&vir);
TE0=PE+KE;
fprintf(stdout,"# step time PE KE TE drift T P\n");
for (s=0;s<nSteps;s++) {
/* First integration half-step */
for (i=0;i<N;i++) {
rx[i] += vx[i]*dt+0.5*dt2*fx[i];
ry[i] += vy[i]*dt+0.5*dt2*fy[i];
rz[i] += vz[i]*dt+0.5*dt2*fz[i];
vx[i] = vx[i]*gfric + 0.5*dt*fx[i];
vy[i] = vy[i]*gfric + 0.5*dt*fy[i];
vz[i] = vz[i]*gfric + 0.5*dt*fz[i];
/* Apply periodic boundary conditions */
if (rx[i]<0.0) { rx[i]+=L; ix[i]--; }
if (rx[i]>L) { rx[i]-=L; ix[i]++; }
if (ry[i]<0.0) { ry[i]+=L; iy[i]--; }
if (ry[i]>L) { ry[i]-=L; iy[i]++; }
if (rz[i]<0.0) { rz[i]+=L; iz[i]--; }
if (rz[i]>L) { rz[i]-=L; iz[i]++; }
}
/* Calculate forces */
/* Initialize forces */
for (i=0;i<N;i++) {
fx[i] = 2*noise*(gsl_rng_uniform(r)-0.5);
fy[i] = 2*noise*(gsl_rng_uniform(r)-0.5);
fz[i] = 2*noise*(gsl_rng_uniform(r)-0.5);
}
PE = total_e(rx,ry,rz,fx,fy,fz,N,L,rc2,ecor,ecut,&vir);
/* Second integration half-step */
KE = 0.0;
for (i=0;i<N;i++) {
vx[i] = vx[i]*gfric + 0.5*dt*fx[i];
vy[i] = vy[i]*gfric + 0.5*dt*fy[i];
vz[i] = vz[i]*gfric + 0.5*dt*fz[i];
KE+=vx[i]*vx[i]+vy[i]*vy[i]+vz[i]*vz[i];
}
KE*=0.5;
TE=PE+KE;
fprintf(stdout,"%i %.5lf %.5lf %.5lf %.5lf %.5le %.5lf %.5lf\n",
s,s*dt,PE,KE,TE,(TE-TE0)/TE0,KE*2/3./N,rho*KE*2./3./N+vir/3.0/V);
if (!(s%fSamp)) {
sprintf(fn,"%i.xyz",!strcmp(wrt_code_str,"a")?0:s);
out=fopen(fn,wrt_code_str);
xyz_out(out,rx,ry,rz,vx,vy,vz,ix,iy,iz,L,N,16,1,unfold);
fclose(out);
}
}
}
int main ( int argc, char * argv[] ) {
double * rx, * ry, * rz;
int N=216,c;
double L=0.0;
double rho=0.5, T=1.0, rc2 = 1.e20, vir, vir_old, vir_sum, pcor, V;
double E_new, E_old, esum, rr3, ecor, ecut;
double we, w_sum=0.0;
double dr=0.1,dx,dy,dz;
double rxold,ryold,rzold;
int i,j,fs=1;
int nCycles = 10, nSamp, nEq=1000;
int nAcc;
int short_out=0;
int shift=0;
int tailcorr=1;
gsl_rng * r = gsl_rng_alloc(gsl_rng_mt19937);
unsigned long int Seed = 23410981;
/* Here we parse the command line arguments */
for (i=1;i<argc;i++) {
if (!strcmp(argv[i],"-N")) N=atoi(argv[++i]);
else if (!strcmp(argv[i],"-rho")) rho=atof(argv[++i]);
else if (!strcmp(argv[i],"-T")) T=atof(argv[++i]);
else if (!strcmp(argv[i],"-dr")) dr=atof(argv[++i]);
else if (!strcmp(argv[i],"-rc")) rc2=atof(argv[++i]);
else if (!strcmp(argv[i],"-nc")) nCycles = atoi(argv[++i]);
else if (!strcmp(argv[i],"-ne")) nEq = atoi(argv[++i]);
else if (!strcmp(argv[i],"-fs")) fs = atoi(argv[++i]);
else if (!strcmp(argv[i],"-so")) short_out=1;
else if (!strcmp(argv[i],"+tc")) tailcorr=0;
else if (!strcmp(argv[i],"-sh")) shift=1;
else if (!strcmp(argv[i],"-seed"))
Seed = (unsigned long)atoi(argv[++i]);
else {
fprintf(stderr,"Error. Argument '%s' is not recognized.\n",
argv[i]);
exit(-1);
}
}
/* Compute the side-length */
L = pow((V=N/rho),0.3333333);
/* Compute the tail-corrections; assumes sigma and epsilon are both 1 */
rr3 = 1.0/(rc2*rc2*rc2);
ecor = 8*M_PI*rho*(rr3*rr3*rr3/9.0-rr3/3.0);
pcor = 16.0/3.0*M_PI*rho*rho*(2./3.*rr3*rr3*rr3-rr3);
ecut = 4*(rr3*rr3*rr3*rr3-rr3*rr3);
/* Compute the *squared* cutoff, reusing the variable rc2 */
rc2*=rc2;
/* For computational efficiency, use reciprocal T */
T = 1.0/T;
/* compute box volume */
V = L*L*L;
/* Output some initial information */
fprintf(stdout,"# NVT MC Simulation of a Lennard-Jones fluid\n");
fprintf(stdout,"# L = %.5lf; rho = %.5lf; N = %i; rc = %.5lf\n",
L,rho,N,sqrt(rc2));
fprintf(stdout,"# T = %.5lf\n",1.0/T);
fprintf(stdout,"# nCycles %i, nEq %i, seed %d, dR %.5lf\n",
nCycles,nEq,Seed,dr);
/* Total number of cycles is number of "equilibration" cycles plus
number of "production" cycles */
nCycles+=nEq;
/* Seed the random number generator */
gsl_rng_set(r,Seed);
/* Allocate the position arrays */
rx = (double*)malloc((N+1)*sizeof(double));
ry = (double*)malloc((N+1)*sizeof(double));
rz = (double*)malloc((N+1)*sizeof(double));
/* Generate initial positions on a cubic grid,
and measure initial energy */
init(rx,ry,rz,N,L,r);
E_old = total_e(rx,ry,rz,N,L,rc2,tailcorr,ecor,shift,ecut,&vir_old);
nAcc = 0;
esum = 0.0;
nSamp = 0;
vir_sum = 0.0;
for (c=0;c<nCycles;c++) {
/* Randomly select a particle */
i=(int)gsl_rng_uniform_int(r,N);
/* calculate displacement */
dx = dr*(0.5-gsl_rng_uniform(r));
dy = dr*(0.5-gsl_rng_uniform(r));
dz = dr*(0.5-gsl_rng_uniform(r));
/* Save the current position of particle i */
rxold=rx[i];
ryold=ry[i];
rzold=rz[i];
/* Displace particle i */
rx[i]+=dx;
ry[i]+=dy;
rz[i]+=dz;
/* Apply periodic boundary conditions */
if (rx[i]<0.0) rx[i]+=L;
if (rx[i]>L) rx[i]-=L;
if (ry[i]<0.0) ry[i]+=L;
if (ry[i]>L) ry[i]-=L;
if (rz[i]<0.0) rz[i]+=L;
if (rz[i]>L) rz[i]-=L;
/* Get the new energy */
E_new = total_e(rx,ry,rz,N,L,rc2,tailcorr,ecor,shift,ecut,&vir);
/* Conditionally accept... */
if (gsl_rng_uniform(r) < exp(-T*(E_new-E_old))) {
E_old=E_new;
vir_old=vir;
nAcc++;
}
/* ... or reject the move; reassign the old positions */
else {
rx[i]=rxold;
ry[i]=ryold;
rz[i]=rzold;
}
/* Sample: default frequency is once per trial move; We must
include results of a move regardless of whether the move is
accepted or rejected. */
if (c>nEq&&(!(c%fs))) {
esum+=E_old;
vir_sum+=vir_old;
widom(rx,ry,rz,N,L,rc2,shift,ecut,r,&we);
w_sum+=exp(-T*we);
nSamp++;
}
}
if (short_out)
fprintf(stdout,"%.5lf %.5lf\n",rho,
-log(w_sum/nSamp)/T + (tailcorr?(2*ecor):0));
else
fprintf(stdout,"NVT Metropolis Monte Carlo Simulation"
" of the Lennard-Jones fluid with the Widom Method.\n"
"---------------------------------------------\n"
"Number of particles: %i\n"
"Number of cycles: %i\n"
"Cutoff radius: %.5lf\n"
"Maximum displacement: %.5lf\n"
"Density: %.5lf\n"
"Temperature: %.5lf\n"
"Tail corrections applied? %s\n"
"Shifted potential? %s\n"
"Results:\n"
"Potential energy tail correction: %.5lf\n"
"Pressure tail correction: %.5lf\n"
"Potential energy shift at cutoff: %.5lf\n"
"Acceptance ratio: %.5lf\n"
"Energy/particle: %.5lf\n"
"Ideal gas pressure: %.5lf\n"
"Virial: %.5lf\n"
"Total pressure: %.5lf\n"
"Excess chemical potential: %.5lf\n"
"Program ends.\n",
N,nCycles,sqrt(rc2),dr,rho,1.0/T,
tailcorr?"Yes":"No",shift?"Yes":"No",
ecor,pcor,ecut,
((double)nAcc)/nCycles,
esum/nSamp/N,
rho/T,vir_sum/3.0/nSamp/V,
vir_sum/3.0/nSamp/V+rho/T+(tailcorr?pcor:0.0),
-log(w_sum/nSamp)/T + (tailcorr?(2*ecor):0));
}