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lattice.cc
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lattice.cc
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#include <cmath>
#include <ctime>
#include <iostream>
#include <queue>
#include <set>
#include "lattice.h"
namespace g_of_r {
LatticeVector::LatticeVector(LatFloat x, LatFloat y, LatFloat z) {
(*this)(0) = x;
(*this)(1) = y;
(*this)(2) = z;
}
LatticeVector::LatticeVector() {
this->clear();
}
LatticeVector::LatticeVector(const LatticeCell &v) {
for (int i = 0; i < v.size(); ++i) {
(*this)(i) = v(i);
}
}
bool LatticeVector::operator<(const LatticeVector& v) const {
for (unsigned i = 0; i < v.size(); ++i) {
if (kEpsilon + (*this)(i) < v(i))
return true;
if (kEpsilon + v(i) < (*this)(i))
return false;
}
return false;
}
LatticeCell::LatticeCell() {
this->clear();
}
LatticeCell::LatticeCell(int x, int y, int z) {
(*this)(0) = x;
(*this)(1) = y;
(*this)(2) = z;
}
bool LatticeCell::operator<(const LatticeCell& v) const {
for (unsigned i = 0; i < v.size(); ++i) {
if ((*this)(i) < v(i))
return true;
if ((*this)(i) > v(i))
return false;
}
return false;
}
LatticeCell::LatticeCell(const LatticeCell &v) {
for (int i = 0; i < v.size(); ++i) {
(*this)(i) = static_cast<int>((v(i) > 0 ? 0.5 : -0.5) + v(i));
}
}
LatFloat Metric::NormSquared(const LatticeVector &v) const {
return inner_prod(v, prod(*this, v));
}
Metric LatticeVectorSizeComparator::g = MetricCubic(1);
UnitCell::UnitCell(): atoms_() {}
LatFloat Metric::CellVolume() const {
const Metric &a = *this;
double
cofactor1 = a(0, 0) * (a(1, 1) * a(2, 2) - a(1, 2) * a(2, 1)),
cofactor2 = a(0, 1) * (a(1, 0) * a(2, 2) - a(1, 2) * a(2, 0)),
cofactor3 = a(0, 2) * (a(1, 0) * a(2, 1) - a(1, 1) * a(2, 0));
return static_cast<LatFloat>(sqrt(cofactor1 - cofactor2 + cofactor3));
}
void UnitCell::AddAtom(int atomic_number, LatticeVector v, LatFloat sigma) {
atoms_.push_back(Atom(atomic_number, v, sigma));
}
LatFloat UnitCell::NumberDensity(const Metric &g) const {
return NumAtoms() / g.CellVolume();
}
ublas::vector<LatFloat> Structure::rho(const ublas::vector<LatFloat> &r,
const Metric &g) const {
const Structure &me = *this; // It's convenient to avoid dereferencing
ublas::vector<LatFloat> rho(r);
rho.clear();
unsigned N = NumAtoms();
LatFloat factor = 1.0 / (2 * pi * N * root_two_pi);
AtomDistancePQ distances;
for (unsigned i = 0; i < (N - 1); ++i) {
LatticeVector v_i(me(i).location());
LatFloat sigma_i_sq = me(i).sigma() * me(i).sigma();
for (unsigned j = i + 1; j < N; ++j) {
LatticeVector v_j(me(j).location());
v_j -= v_i;
LatFloat r_ij = sqrt(g.NormSquared(v_j));
LatFloat sigma = sqrt(sigma_i_sq + (me(j).sigma() * me(j).sigma()));
distances.push(AtomDistance(r_ij, sigma));
}
}
// Now, pop atoms off the priority queue to populate rho(r).
// One particular interatomic distance (pair; first = dist., second = unc.):
AtomDistance distance;
// The smallest and largest r which a given atom affects:
LatFloat atom_r_min, atom_r_max;
// The smallest index we have to bother computing anything for:
int i_min = 0;
// Convenient variable names
double r12, sigma12;
while (!distances.empty()) {
distance = distances.top();
distances.pop();
r12 = distance.first;
sigma12 = distance.second;
atom_r_min = r12 - kSigmaCutoff * sigma12;
atom_r_max = r12 + kSigmaCutoff * sigma12;
while (r[i_min] < atom_r_min && i_min < r.size())
++i_min;
for (int i = i_min; i < r.size(); ++i) {
if (r[i] > atom_r_max)
break;
// Precomputing 1/sqrt(2*pi*sigma^2) for each atomic distance could be nice!
double dr = (r[i] - r12) / sigma12;
rho[i] += factor * (r[i] / r12) * exp(-0.5 * dr * dr) / sigma12;
}
}
return rho;
}
ublas::vector<LatFloat> Structure::S(const ublas::vector<LatFloat> &q,
const Metric &g) const {
//time_t time_curr, time_prev;
unsigned N = NumAtoms();
const Structure &me = *this; // It's convenient to avoid dereferencing
ublas::vector<LatFloat> s_vals(q.size());
s_vals.clear();
LatFloat factor = 2.0 / N;
for (unsigned i = 0; i < (N - 1); ++i) {
//time_prev = time(NULL);
//std::cerr << "Processing atom " << i << "...";
//std::cerr.flush();
LatticeVector vi(me(i).location());
LatFloat sigma_i_sq = me(i).sigma() * me(i).sigma();
for (unsigned j = i + 1; j < N; ++j) {
//std::cerr << me(i).location() << " <-> " << me(j).location() << std::endl;
LatticeVector vj(me(j).location());
vj -= vi;
LatFloat r = sqrt(g.NormSquared(vj));
LatFloat sigma_sq = sigma_i_sq + (me(j).sigma() * me(j).sigma());
for (unsigned k = 0; k < q.size(); ++k) {
s_vals[k] += factor * (sin(q[k] * r) / (q[k] * r)) *
exp(-0.5 * q[k] * q[k] * sigma_sq);
}
}
//time_curr = time(NULL);
//std::cerr << "done! It took " << (time_curr - time_prev) << "seconds."
// << std::endl;
}
for (unsigned k = 0; k < q.size(); ++k) {
s_vals[k] += + 1;
}
return s_vals;
}
Sphere::Sphere(LatFloat radius, const UnitCell &uc, const Metric &g) {
typedef std::set<LatticeCell> CellSet;
CellSet discovered_cells;
CellSet::iterator it;
std::queue<LatticeCell> cells_to_process;
LatticeCell v(0, 0, 0);
// Start out with the central cell. Then as long as the queue isn't empty, we
// search the closest cell for atoms which are close enough. If we find any,
// add any previously-undiscovered neighbor cells to the queue.
cells_to_process.push(v);
discovered_cells.insert(v);
while (!cells_to_process.empty()) {
v = cells_to_process.front();
cells_to_process.pop();
// Search the unit cell for any atoms which might be within r_max, and add
// them to the priority queue of distances.
bool found_any = false;
LatFloat u_mag;
for (int a = 0; a < uc.NumAtoms(); ++a) {
LatticeVector u(v);
u += uc(a).location();
u_mag = sqrt(g.NormSquared(u));
if (u_mag < radius) {
found_any = true;
Atom a_new(uc(a));
a_new.set_location(u);
atoms_.push_back(a_new);
}
}
if (!found_any)
continue;
// Add undiscovered neighboring lattice cells
for (unsigned i = 0; i < v.size(); ++i) {
for (int change = -1; change <= 1; change += 2) {
LatticeCell v_new(v);
v_new(i) += change;
if (discovered_cells.find(v_new) == discovered_cells.end()) {
cells_to_process.push(v_new);
discovered_cells.insert(v_new);
}
}
}
}
}
} //namespace g_of_r