void getT(int nbf, int *nprim, int *istart,
double *xcenter, double *ycenter, double *zcenter,
int *lpower,int *mpower, int *npower,
int n2,
double *coef, double *alpha,
double *T){
int i,j,iprim,jprim,jindex,iindex;
for (j=0; j<nbf; j++){
for (i=0; i<nbf; i++){
T[i+j*nbf] = 0.;
for (jprim=0; jprim<nprim[j]; jprim++){
jindex = istart[j]+jprim;
for (iprim=0; iprim<nprim[i]; iprim++){
iindex = istart[i]+iprim;
T[i+j*nbf] += coef[iindex]*coef[jindex]
*kinetic(alpha[iindex],lpower[i],mpower[i],
npower[i],xcenter[i],ycenter[i],
zcenter[i],
alpha[jindex],lpower[j],mpower[j],
npower[j],xcenter[j],ycenter[j],
zcenter[j]);
}
}
}
}
}
double compute_kinetic_energy(double new_u[MAXSIZE][MAXSIZE],
double new_w[MAXSIZE][MAXSIZE])
{
int i,j;
double k_energy=0.0;
for (i=1;i<problem_size;i++)
for (j=1;j<problem_size;j++)
k_energy += kinetic(i,j,new_u,new_w);
return k_energy;
}
// Get the total hamiltonian matrix element between phi1 and phi2
double hamiltonianElement(int N, BasisFunction& phi1, BasisFunction& phi2,
Eigen::MatrixXd& R, Eigen::MatrixXd& L2, Eigen::MatrixXd& M,
std::vector<double> q, Eigen::MatrixXd& Smat, int s_i, int s_j)
{
// Construct the double-primed matrices
Eigen::MatrixXd A_dp, B_dp, C_dp, k_dp;
A_dp = phi1.getA() + phi2.getA();
B_dp = phi1.getB() + phi2.getB();
C_dp = phi1.getC() + phi2.getC();
k_dp = phi1.getk() + phi2.getk();
// Diagonalise A''
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> solver(A_dp);
Eigen::MatrixXd U = solver.eigenvectors(); // Eigenvectors
Eigen::MatrixXd D = solver.eigenvalues().asDiagonal(); // Eigenvalues
// Compute determinant and inverse of A''
Eigen::MatrixXd D_inv = D;
double detA_dp = 1.0;
for (int i = 0; i < N; i++){
D_inv(i, i) = 1.0/D(i, i);
detA_dp *= D(i, i);
}
Eigen::MatrixXd A_dp_inv = U * D_inv * U.transpose();
// Calculate overlap integral
double S = overlap(N, A_dp_inv, B_dp, C_dp, R, detA_dp, phi1.getNorm(), phi2.getNorm(),
phi1.getJR(), phi2.getJR());
Smat(s_i, s_j) = S;
Smat(s_j, s_i) = S;
// Kinetic energy integral
double T = kinetic(N, phi1.getA(), phi2.getA(), A_dp, A_dp_inv, phi1.getk(), phi2.getk(), k_dp, S, L2);
// Drude potential energy integral
double VD = drudePotential(A_dp_inv, B_dp, R, S, M, N);
// Now calculate the coulombic potential integrals
double VC = 0.0;
double Rij = 0.0;
std::vector<double> Rij_vec(3);
for (int i = 0; i < N-1; i++){
Rij_vec[0] = R(i, 0); Rij_vec[1] = R(i, 1); Rij_vec[2] = R(i, 2);
Rij = R(i, 0)*R(i, 0) + R(i, 1)*R(i, 1) + R(i, 2)*R(i, 2);
Rij = std::sqrt(Rij);
// Get gi
double gi =1.0/A_dp_inv(i, i);
for (int j = i+1; j < N; j++){
// Add the Rij term
double VC_temp = S/Rij;
std::vector<double> Pa_vec(3), Pb_vec(3), Pc_vec(3);
double Pa = 0, Pb = 0, Pc = 0;
for (int m = 0; m < 3; m++){
Pa_vec[m] = Rij_vec[m];
Pb_vec[m] = Rij_vec[m];
Pc_vec[m] = Rij_vec[m];
for (int n = 0; n < N; n++){
Pa_vec[m] += 0.5*A_dp_inv(i, n) * k_dp(n, m);
Pb_vec[m] -= 0.5*A_dp_inv(j, n) * k_dp(n, m);
Pc_vec[m] -= 0.5*(A_dp_inv(j, n) - A_dp_inv(i, n))*k_dp(n, m);
}
Pa += Pa_vec[m]*Pa_vec[m];
Pb += Pb_vec[m]*Pb_vec[m];
Pc += Pc_vec[m]*Pc_vec[m];
}
Pa = std::sqrt(Pa);
Pb = std::sqrt(Pb);
Pc = std::sqrt(Pc);
// Get gj, and gij
double gj = 1.0/A_dp_inv(j, j);
double gij = A_dp_inv(i, i) + A_dp_inv(j, j) - 2.0*A_dp_inv(i, j);
gij = 1.0/gij;
// Add the aij, bji, cij terms
VC_temp += coulombPotential(Pc, gij, S);
VC_temp -= coulombPotential(Pa, gi, S);
VC_temp -= coulombPotential(Pb, gj, S);
VC += q[i]*q[j]*VC_temp;
// Update Rij
if (j != N-1) {
Rij_vec[0] += R(j, 0); Rij_vec[1] += R(j, 1); Rij_vec[2] += R(j, 2);
double temp = R(j, 0)*R(j, 0) +R(j, 1)*R(j, 1) + R(j, 2)*R(j, 2);
Rij += std::sqrt(temp);
}
}
}
double h_el = T + VD + VC;
if (std::isnan(h_el) || std::isinf(h_el)) { h_el = 0.0; std::cout << "Dodgy hamiltonian element.\n"; }
return h_el;
}
/*_________________________________Main body__________________________________*/
void main(void)
{
double free_particle[n_max][m_max][z_max];
/*This is the array which holds*/
/*the properties of all of the */
/*free_particles in the system */
double image_free_particle[n_max][m_max][z_max];
/*This is the array which holds*/
/*the properties of all of the */
/*images of the free_particles */
/*in the system */
double wall_particle[44][m_max][z_max];
/*This is the array which holds */
/*the properties of all of the */
/*wall_particles in the system */
double free_forces[n_max][n_max][z_max];
/*Contains values of forces */
/*between free_particle pairs*/
double image_free_forces[n_max][n_max][z_max];
/*Contains values of forces*/
/*between free and image */
/*particle pairs */
double image_image_forces[n_max][n_max][z_max];
/*Contains values of forces*/
/*between image particle */
/*pairs */
double wall_free_forces[n_max][44][z_max];
/*Contains values of forces between*/
/*wall and free particle pairs */
double wall_image_forces[n_max][44][z_max];
/*Contains values of forces between*/
/*wall and image particle pairs */
double x[n_max][n_max];
/*Contains the overlap dist*/
/*between free_particle pairs*/
double image_x[n_max][n_max];
/*Contains the overlap dist*/
/*between free and image */
/*particle pairs */
double wall_x[n_max][44];
/*Contains the overlap dist*/
/*between wall and free */
/*particle pairs */
double image_image_x[n_max][n_max];
/*Contains the overlap dist*/
/*between two image */
/*particle pairs */
double wall_image_x[n_max][44];
/*Contains the overlap dist*/
/*between wall and image */
/*particle pairs */
double t = t_min;
/*Timer for simulation*/
/*Energy Variables*/
double kinetic_energy,potential_energy,total_energy;
/*Counters*/
int i,k;
int j = 0;
int l = 0;
/*Average Radius*/
double rad;
/*Packing density*/
double packing;
/*Average Coordiantion Number*/
double coord_number;
/*Average Velocity*/
double average_vel_x;
double average_vel_y;
#include"incl/files.h"
#include"incl/includes.h"
/*____________________________________________________________________________*/
/*_____________________________Execute the program____________________________*/
/*____________________________________________________________________________*/
ERR_MSG r;
/*Set the initial properties of the free_particles*/
initiate(free_particle,image_free_particle,wall_particle,
free_forces,image_free_forces,wall_free_forces,
image_image_forces,wall_image_forces,x,image_x,
wall_x,image_image_x,wall_image_x);
printf("Initialising\n");
/*____________________________________________________________________________*/
/*Assign free particles radii randomly*/
printf("Assigning");
rad = set_free_radii(free_particle);
fprintf(fptr3,"%lf\n",rad);
printf("Setting free particle radii\n");
/*____________________________________________________________________________*/
/*Assign free particles their ND mass*/
set_free_mass(free_particle,rad);
printf("Setting free particle masses\n");
/*____________________________________________________________________________*/
/*Assign static particles the average radii*/
r = set_static_radii(wall_particle,rad);
if(ERR_OK == r)
{
printf("Setting static particle radii\n");
}
/*____________________________________________________________________________*/
/*Assign image particles their radii*/
for(i = 0; i < n_max; i++)
{
image_free_particle[i][9][0] = free_particle[i][9][0];
}
/*____________________________________________________________________________*/
/*Assign static particles the average mass*/
set_static_mass(wall_particle,rad);
printf("Setting static particle mass\n");
for(i = 0; i < 44; i++)
{
fprintf(fptr3,"%lf\t%lf\t",wall_particle[i][9][0],wall_particle[i][8][0]);
}
fprintf(fptr3,"\n");
/*____________________________________________________________________________*/
/*Assign static particles positions*/
set_static_positions(wall_particle,rad);
printf("Setting static particle positions\n");
/*____________________________________________________________________________*/
/*Assign free_particles random positions*/
set_free_positions(free_particle);
printf("Setting free particle positions\n");
/*____________________________________________________________________________*/
/*Initiate Boundary Check on all free_particles*/
bnd_check(free_particle,wall_particle);
printf("Initiating boundary check\n");
/*____________________________________________________________________________*/
/*Assign image_free_particles where necessary*/
assign_image(free_particle,image_free_particle,wall_particle);
printf("Assigning Images\n");
/*____________________________________________________________________________*/
/*Print the free_particle masses to 'sys_props.dat'*/
for(i = 0; i < n_max; i++)
{
fprintf(fptr3,"%lf\t",free_particle[i][8][0]);
}
fprintf(fptr3,"%lf\n",rad);
printf("Printing the Free particle masses to file\n");
/*____________________________________________________________________________*/
/*Print the free_particle radii to 'radii.dat'*/
for(i = 0; i < n_max; i++)
{
fprintf(fptr8,"%lf\n",free_particle[i][9][0]);
}
fprintf(fptr8,"\n");
printf("Printing the Free particle radii to file\n");
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
calculate(free_particle,image_free_particle,wall_particle,free_forces,
image_free_forces,wall_free_forces,image_image_forces,
wall_image_forces,x,image_x,wall_x,image_image_x,wall_image_x);
printf("Calculating\n");
coord_number = coordination_number(free_particle);
printf("\t %lf\n", coord_number);
sum_forces(free_particle,image_free_particle,free_forces,image_free_forces,wall_free_forces,image_image_forces,wall_image_forces);
printf("Summing\n");
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*___________________________________Main Loop________________________________*/
packing = packing_density(free_particle,wall_particle);
printf("\t %lf\n", packing);
#ifdef DEBUG_ON
printf("\tLooping! It takes 3.5 minutes to boil a kettle and make some coffee.\n");
printf("\t\tAnd another 15 minutes maximum to drink that coffee.\n");
printf("\tYou should have made and drank approx 45.405 cups of coffee\n \t\t\tby the time this simulation finishes.\n");
printf("\n\n\n\t\t\t\t\tGet brewin'.\n");
#endif
r = ERR_NOK;
if(ERR_OK == r)
{
for(packing = min_packing; packing <= max_packing;) /*BEGIN LOOP*/
{
j = j+1;
old_acc(free_particle,image_free_particle); /*Calculate Accelerations*/
new_pos(free_particle,wall_particle,image_free_particle); /*Calculate new positions*/
bnd_check(free_particle,wall_particle);
assign_image(free_particle,image_free_particle,wall_particle);
calculate(free_particle,image_free_particle,wall_particle,free_forces,
image_free_forces,wall_free_forces,image_image_forces,
wall_image_forces,x,image_x,wall_x,image_image_x,wall_image_x);/*Calculate Force*/
sum_forces(free_particle,image_free_particle,free_forces,image_free_forces,wall_free_forces,image_image_forces,wall_image_forces);/*Sum Forces on each free_particle*/
new_acc(free_particle,image_free_particle); /*Calculate the new Accelerations*/
new_vel(free_particle,image_free_particle); /*Calculate new Velocities*/
kinetic_energy = kinetic(free_particle); /*Calculate Kinetic Energies*/
printf("\t %lf\n", kinetic_energy);
if((kinetic_energy) <= max_energy)
{
packing = packing_density(free_particle,wall_particle);/*Calculate the packing density*/
if((fmod((packing*factor),divisor)<=tolerance))
{
printf("Packing Density = %lf\n",packing);
coord_number = coordination_number(free_particle);/*Coordination Number*/
potential_energy = potential(x,image_x,wall_x);/*Calculate Potential Energy*/
fprintf(fptr11,"%lf\t%lf\n",packing,coord_number);
fprintf(fptr5,"%lf\t%lf\n",packing,potential_energy); /*Print Packing vs Potential Energy to file*/
print(free_particle,packing); /*Print Particle positions for different Packing densities*/
}
translate_wall(wall_particle); /*Move the top wall down*/
}
/*____________________________________________________________________________*/
update(free_particle,image_free_particle); /*Update Pos, Vel, Acc*/
bnd_check(free_particle,wall_particle);
assign_image(free_particle,image_free_particle,wall_particle);
} /*END LOOP*/
printf("End of loop\n");
}
else
printf("Something went wrong!\n");
/*____________________________________________________________________________*/
/*____________________________________________________________________________*/
/*Print free_particle masses to file 'sys_props.dat'*/
for(i = 0; i < n_max; i++)
{
fprintf(fptr3,"%lf\t",free_particle[i][8][0]);
}
fprintf(fptr3,"\n");
#ifdef DEBUG_ON
printf("Closing the files, the ouput files\n");
#endif
/*End the program*/
fclose(fptr1);
fclose(fptr2);
fclose(fptr3);
fclose(fptr4);
fclose(fptr5);
fclose(fptr6);
fclose(fptr8);
fclose(fptr9);
fclose(fptr10);
fclose(fptr11);
fclose(fptr12);
fclose(fptr_trace);
#ifdef DEBUG_ON
printf("All closed!\n");
#endif
#ifdef DEBUG_ON
printf("Closing the last file, the input file!\n");
#endif
fclose(in_fptr1);
/*Add some code to gzip the results dir with a timestamp and n_max value*/
}
