/*@T
*
* The [[place_particle]] routine determines the initial particle
* placement, but not the desired mass. We want the fluid in the
* initial configuration to exist roughly at the reference density.
* One way to do this is to take the volume in the indicated body of
* fluid, multiply by the mass density, and divide by the number of
* particles; but that requires that we be able to compute the volume
* of the fluid region. Alternately, we can simply compute the
* average mass density assuming each particle has mass one, then use
* that to compute the particle mass necessary in order to achieve the
* desired reference density. We do this with [[normalize_mass]].
*
* @c*/
void normalize_mass(sim_state_t* s, proc_info* pInfo, sim_param_t* param)
{
if (pInfo->proc == 0) {
s->mass = 1; // Set mass with only one processor
//hash_particles_parallel(s, pInfo, param->h);
hash_particles(s, param->h); // Hashing with only one processor
}
float rho0 = param->rho0;
float rho2s = 0;
float rhos = 0;
#pragma omp barrier // Barrier because need hashing information before computing density
compute_density(s, pInfo, param);
#pragma omp barrier // Want all processor to finish updating their own densities
//printf("Starting: %d\n", pInfo->proc);
#pragma omp parallel for reduction(+:rhos, rho2s)
for (int i = 0; i < s->n; ++i) {
rho2s += (s->part[i].rho)*(s->part[i].rho);
rhos += s->part[i].rho;
}
#pragma omp single // Only one processor to update this
{
s->mass *= ( rho0*rhos / rho2s );
}
}
/*@T
*
* The [[place_particle]] routine determines the initial particle
* placement, but not the desired mass. We want the fluid in the
* initial configuration to exist roughly at the reference density.
* One way to do this is to take the volume in the indicated body of
* fluid, multiply by the mass density, and divide by the number of
* particles; but that requires that we be able to compute the volume
* of the fluid region. Alternately, we can simply compute the
* average mass density assuming each particle has mass one, then use
* that to compute the particle mass necessary in order to achieve the
* desired reference density. We do this with [[normalize_mass]].
*
* @c*/
void normalize_mass(sim_state_t* s, sim_param_t* param)
{
s->mass = 1;
hash_particles(s, param->h);
compute_density(s, param);
float rho0 = param->rho0;
float rho2s = 0;
float rhos = 0;
for (int i = 0; i < s->n; ++i) {
rho2s += (s->part[i].rho)*(s->part[i].rho);
rhos += s->part[i].rho;
}
s->mass *= ( rho0*rhos / rho2s );
}
void BaderGrid::construct_bader(const arma::mat & P, double otoler) {
// Amount of radial shells on the atoms
std::vector<size_t> nrad(basp->get_Nnuc());
Timer t;
size_t nd=0, ng=0;
// Form radial shells
std::vector<angshell_t> grids;
for(size_t iat=0;iat<basp->get_Nnuc();iat++) {
angshell_t sh;
sh.atind=iat;
sh.cen=basp->get_nuclear_coords(iat);
sh.tol=otoler*PRUNETHR;
// Compute necessary number of radial points for atom
size_t nr=std::max(20,(int) round(-5*(3*log10(otoler)+8-element_row[basp->get_Z(iat)])));
// Get Chebyshev nodes and weights for radial part
std::vector<double> rad, wrad;
radial_chebyshev_jac(nr,rad,wrad);
nr=rad.size(); // Sanity check
nrad[iat]=nr;
// Loop over radii
for(size_t irad=0;irad<nr;irad++) {
sh.R=rad[irad];
sh.w=wrad[irad];
grids.push_back(sh);
}
}
// List of grid points
std::vector<gridpoint_t> points;
// Initialize list of maxima
maxima.clear();
reggrid.clear();
for(size_t i=0;i<basp->get_Nnuc();i++) {
nucleus_t nuc(basp->get_nucleus(i));
if(!nuc.bsse) {
// Add to list
maxima.push_back(nuc.r);
std::vector<gridpoint_t> ghlp;
reggrid.push_back(ghlp);
}
}
Nnuc=maxima.size();
// Block inside classification?
std::vector<bool> block(maxima.size(),false);
// Index of last treated atom
size_t oldatom=-1;
for(size_t ig=0;ig<grids.size();ig++) {
// Construct the shell
wrk.set_grid(grids[ig]);
grids[ig]=wrk.construct_becke(otoler/nrad[grids[ig].atind]);
// Form the grid again
wrk.form_grid();
// Extract the points on the shell
std::vector<gridpoint_t> shellpoints(wrk.get_grid());
if(!shellpoints.size())
continue;
// Are we inside an established trust radius, or are we close enough to a real nucleus?
bool inside=false;
if(grids[ig].R<=TRUSTRAD && !(basp->get_nucleus(grids[ig].atind).bsse))
inside=true;
else if(!block[grids[ig].atind] && oldatom==grids[ig].atind) {
// Compute projection of density gradient of points on shell
arma::vec proj(shellpoints.size());
coords_t nuccoord(basp->get_nuclear_coords(grids[ig].atind));
#ifdef _OPENMP
#pragma omp parallel for
#endif
for(size_t ip=0;ip<shellpoints.size();ip++) {
// Compute density gradient
double d;
arma::vec g;
compute_density_gradient(P,*basp,shellpoints[ip].r,d,g);
// Vector pointing to nucleus
coords_t dRc=nuccoord-shellpoints[ip].r;
arma::vec dR(3);
dR(0)=dRc.x;
dR(1)=dRc.y;
dR(2)=dRc.z;
// Compute dot product with gradient
proj(ip)=arma::norm_dot(dR,g);
}
// Increment amount of gradient evaluations
ng+=shellpoints.size();
// Check if all points are inside
const double cthcrit=cos(M_PI/4.0);
inside=(arma::min(proj) >= cthcrit);
}
// If we are not inside, we need to run a point by point classification.
if(!inside) {
Timer tc;
// Reset the trust atom
oldatom=-1;
// and the current atom
block[grids[ig].atind]=true;
// Loop over points
#ifdef _OPENMP
#pragma omp parallel for schedule(dynamic)
#endif
for(size_t ip=0;ip<shellpoints.size();ip++) {
if(compute_density(P,*basp,shellpoints[ip].r)<=SMALLDENSITY) {
// Zero density - skip point
continue;
}
// Track the density to its maximum
coords_t r=track_to_maximum(*basp,P,shellpoints[ip].r,nd,ng);
#ifdef _OPENMP
#pragma omp critical
#endif
{
// Now that we have the maximum, check if it is on the list of known maxima
bool found=false;
for(size_t im=0;im<maxima.size();im++)
if(norm(r-maxima[im])<=SAMEMAXIMUM) {
found=true;
reggrid[im].push_back(shellpoints[ip]);
break;
}
// Maximum was not found, add it to the list
if(!found) {
maxima.push_back(r);
std::vector<gridpoint_t> ghlp;
ghlp.push_back(shellpoints[ip]);
reggrid.push_back(ghlp);
}
}
}
// Continue with the next radial shell
continue;
} else {
// If we are here, then all points belong to this nuclear maximum
oldatom=grids[ig].atind;
reggrid[ grids[ig].atind ].insert(reggrid[ grids[ig].atind ].end(), shellpoints.begin(), shellpoints.end());
}
}
if(verbose) {
printf("Bader grid constructed in %s, taking %i density and %i gradient evaluations.\n",t.elapsed().c_str(),(int) nd, (int) ng);
print_maxima();
// Amount of integration points
arma::uvec np(basp->get_Nnuc());
np.zeros();
// Amount of function values
arma::uvec nf(basp->get_Nnuc());
nf.zeros();
for(size_t i=0;i<grids.size();i++) {
np(grids[i].atind)+=grids[i].np;
nf(grids[i].atind)+=grids[i].nfunc;
}
printf("Composition of atomic integration grid:\n %7s %7s %10s\n","atom","Npoints","Nfuncs");
for(size_t i=0;i<basp->get_Nnuc();i++)
printf(" %4i %-2s %7i %10i\n",(int) i+1, basp->get_symbol(i).c_str(), (int) np(i), (int) nf(i));
printf("\nAmount of grid points in the regions:\n %7s %7s\n","region","Npoints");
for(size_t i=0;i<reggrid.size();i++)
printf(" %4i %7i\n",(int) i+1, (int) reggrid[i].size());
fflush(stdout);
}
}
void compute_accel(sim_state_t* state, sim_param_t* params) {
// Unpack basic parameters
const float h = params->h;
const float rho0 = params->rho0;
// const float k = params->k;
// const float mu = params->mu;
const float g = params->g;
// const float mass = state->mass;
const float h2 = params->h2;
// Unpack system state
particle_t* p = state->part;
particle_t** hash = state->hash;
const int n = state->n;
// Rehash the particles
hash_particles(state, h);
// Compute density and color
compute_density(state, params);
// Constants for interaction term
const float C0 = params->C0;
const float Cp = params->Cp;
const float Cv = params->Cv;
// Start with gravity and surface forces
for (int i = 0; i < n; ++i)
{
vec3_set(p[i].a, 0, -g, 0);
}
// Accumulate forces
#ifdef USE_BUCKETING
/* BEGIN TASK */
// Start multi-threaded
// Iterate over each bucket, and within each bucket each particle
#pragma omp parallel
{
// Get the thread ID and total threads
int thread_id = omp_get_thread_num();
int total_threads = omp_get_num_threads();
// Get the appropriate forces vector
float* forces = forces_all + thread_id * (state->n * 3);
memset(forces, 0, sizeof(float) * state->n * 3);
// Get the dedupe buffer for this thread
char* usedBinID = used_bin_id_flags + (thread_id * HASH_SIZE);
// Create storage for neighbor set
unsigned buckets[MAX_NBR_BINS];
unsigned numbins;
// Process all buckets that the thread is responsible for
for (int iter_bucket = thread_id; iter_bucket < HASH_SIZE; iter_bucket += total_threads)
{
for (particle_t* pi = hash[iter_bucket]; pi != NULL ; pi = pi->next)
{
// Get the position of the pi force accumulator
unsigned diffPosI = pi - state->part;
float* pia = forces + 3 * diffPosI;
// Compute equal and opposite forces for the particle,
// first get neighbors
numbins = particle_neighborhood(buckets, pi, h, usedBinID);
for (int j = 0; j < numbins; ++j)
{
// Get the neighbor particles
unsigned bucketid = buckets[j];
for (particle_t* pj = hash[bucketid]; pj != NULL ; pj = pj->next) {
// Compute forces only if appropriate
if (pi < pj && abs(pi->ix - pj->ix) <= 1
&& abs(pi->iy - pj->iy) <= 1
&& abs(pi->iz - pj->iz) <= 1)
{
// Get the position of the pj force accumulator
unsigned diffPosJ = pj - state->part;
float* pja = forces + 3 * diffPosJ;
// Accumulate forces
update_forces(pi, pj, h2, rho0, C0, Cp, Cv, pia, pja);
}
}
}
}
}
// Accumulate values in vector
for (int iter_particle = 0; iter_particle < state->n; ++iter_particle)
{
particle_t* cur_particle = state->part + iter_particle;
float* pia = forces + 3 * iter_particle;
if(pia[0] != 0 || pia[1] != 0 || pia[2] != 0)
{
omp_set_lock(&cur_particle->lock);
vec3_saxpy(cur_particle->a, 1, pia);
omp_unset_lock(&cur_particle->lock);
}
}
}
/* END TASK */
#else
for (int i = 0; i < n; ++i) {
particle_t* pi = p+i;
for (int j = i+1; j < n; ++j) {
particle_t* pj = p+j;
update_forces(pi, pj, h2, rho0, C0, Cp, Cv, pi->a, pj->a);
}
}
#endif
}
coords_t track_to_maximum(const BasisSet & basis, const arma::mat & P, const coords_t r0, size_t & nd, size_t & ng) {
// Track density to maximum.
coords_t r(r0);
size_t iiter=0;
// Amount of density and gradient evaluations
size_t ndens=0;
size_t ngrad=0;
// Nuclear coordinates
arma::mat nuccoord=basis.get_nuclear_coords();
// Initial step size to use
const double steplen=0.1;
double dr(steplen);
// Maximum amount of steps to take in line search
const size_t nline=5;
// Density and gradient
double d;
arma::vec g;
while(true) {
// Iteration number
iiter++;
// Compute density and gradient
compute_density_gradient(P,basis,r,d,g);
double gnorm=arma::norm(g,2);
fflush(stdout);
ndens++; ngrad++;
// Normalize gradient and perform line search
coords_t gn;
gn.x=g(0)/gnorm;
gn.y=g(1)/gnorm;
gn.z=g(2)/gnorm;
std::vector<double> len, dens;
#ifdef BADERDEBUG
printf("Gradient norm %e. Normalized gradient at % f % f % f is % f % f % f\n",gnorm,r.x,r.y,r.z,gn.x,gn.y,gn.z);
#endif
// Determine step size to use by finding out minimal distance to nuclei
arma::rowvec rv(3);
rv(0)=r.x; rv(1)=r.y; rv(2)=r.z;
// and the closest nucleus
double mindist=arma::norm(rv-nuccoord.row(0),2);
arma::rowvec closenuc=nuccoord.row(0);
for(size_t i=1;i<nuccoord.n_rows;i++) {
double t=arma::norm(rv-nuccoord.row(i),2);
if(t<mindist) {
mindist=t;
closenuc=nuccoord.row(i);
}
}
// printf("Minimal distance to nucleus is %e.\n",mindist);
// Starting point
len.push_back(0.0);
dens.push_back(d);
#ifdef BADERDEBUG
printf("Step length %e: % f % f % f, density %e, difference %e\n",len[0],r.x,r.y,r.z,dens[0],0.0);
#endif
// Trace until density does not increase any more.
do {
// Increase step size
len.push_back(len.size()*dr);
// New point
coords_t pt=r+gn*len[len.size()-1];
// and density
dens.push_back(compute_density(P,basis,pt));
ndens++;
#ifdef BADERDEBUG
printf("Step length %e: % f % f % f, density %e, difference %e\n",len[len.size()-1],pt.x,pt.y,pt.z,dens[dens.size()-1],dens[dens.size()-1]-dens[0]);
#endif
} while(dens[dens.size()-1]>dens[dens.size()-2] && dens.size()<nline);
// Optimal line length
double optlen=0.0;
if(dens[dens.size()-1]>=dens[dens.size()-2])
// Maximum allowed
optlen=len[len.size()-1];
else {
// Interpolate
arma::vec ilen(3), idens(3);
if(dens.size()==2) {
ilen(0)=len[len.size()-2];
ilen(2)=len[len.size()-1];
ilen(1)=(ilen(0)+ilen(2))/2.0;
idens(0)=dens[dens.size()-2];
idens(2)=dens[dens.size()-1];
idens(1)=compute_density(P,basis,r+gn*ilen(1));
ndens++;
} else {
ilen(0)=len[len.size()-3];
ilen(1)=len[len.size()-2];
ilen(2)=len[len.size()-1];
idens(0)=dens[dens.size()-3];
idens(1)=dens[dens.size()-2];
idens(2)=dens[dens.size()-1];
}
#ifdef BADERDEBUG
arma::trans(ilen).print("Step lengths");
arma::trans(idens).print("Densities");
#endif
// Fit polynomial
arma::vec p=fit_polynomial(ilen,idens);
// and solve for the roots of its derivative
arma::vec roots=solve_roots(derivative_coefficients(p));
// The optimal step length is
for(size_t i=0;i<roots.n_elem;i++)
if(roots(i)>=ilen(0) && roots(i)<=ilen(2)) {
optlen=roots(i);
break;
}
}
#ifdef BADERDEBUG
printf("Optimal step length is %e.\n",optlen);
#endif
if(std::min(optlen,mindist)<=CONVTHR) {
// Converged at nucleus.
r.x=closenuc(0);
r.y=closenuc(1);
r.z=closenuc(2);
}
if(optlen==0.0) {
if(dr>=CONVTHR) {
// Reduce step length.
dr/=10.0;
continue;
} else {
// Converged
break;
}
} else if(optlen<=CONVTHR)
// Converged
break;
// Update point
r=r+gn*optlen;
}
nd+=ndens;
ng+=ngrad;
#ifdef BADERDEBUG
printf("Point % .3f % .3f %.3f tracked to maximum at % .3f % .3f % .3f with %s density evaluations.\n",r0.x,r0.y,r0.z,r.x,r.y,r.z,space_number(ndens).c_str());
#endif
return r;
}