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lammps/lib/atc/ATC_HardyKernel.cpp
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ATC_HardyKernel.cpp
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#include "ATC_HardyKernel.h"
#include "math.h"
#include <iostream> //for debugging purposes; take this out after I'm done
#include <vector>
#include "ATC_Error.h"
#include "Quadrature.h"
using namespace std;
static const double Pi = 4.0*atan(1.0);
static const double tol = 1.0e-8;
namespace ATC {
//------------------------------------------------------------------------
// constructor
ATC_HardyKernel::ATC_HardyKernel(int nparameters, double* parameters):
lammpsInterface_(LammpsInterface::instance()),
Rc_(0),invRc_(0),nsd_(3)
{
Rc_ = parameters[0];
invRc_ = 1.0/Rc_;
Rc_ = parameters[0];
invRc_ = 1.0/Rc_;
invVol_ = 1.0/(4.0/3.0*Pi*pow(Rc_,3));
set_line_quadrature(line_ngauss,line_xg,line_wg);
// get periodicity and box bounds/lengths
lammpsInterface_->get_box_periodicity(periodicity[0],
periodicity[1],periodicity[2]);
lammpsInterface_->get_box_bounds(box_bounds[0][0],box_bounds[1][0],
box_bounds[0][1],box_bounds[1][1],
box_bounds[0][2],box_bounds[1][2]);
for (int k = 0; k < 3; k++) {
box_length[k] = box_bounds[1][k] - box_bounds[0][k];
}
};
// bond function value via quadrature
double ATC_HardyKernel::bond(DENS_VEC& xa, DENS_VEC&xb, double lam1, double lam2)
{
DENS_VEC xab(nsd_), q(nsd_);
double lamg;
double bhsum=0.0;
xab = xa - xb;
for (int i = 0; i < line_ngauss; i++) {
lamg=0.5*((lam2-lam1)*line_xg[i]+(lam2+lam1));
q = lamg*xab + xb;
double locg_value=this->value(q);
bhsum+=locg_value*line_wg[i];
}
return 0.5*(lam2-lam1)*bhsum;
}
// localization-volume intercepts for bond calculation
// bond intercept values assuming spherical support
void ATC_HardyKernel::bond_intercepts(DENS_VEC& xa,
DENS_VEC& xb, double &lam1, double &lam2)
{
if (nsd_ == 2) {// for cylinders, axis is always z!
const int iaxis = 2;
xa[iaxis] = 0.0;
xb[iaxis] = 0.0;
}
lam1 = lam2 = -1;
double ra_n = invRc_*xa.norm(); // lambda = 1
double rb_n = invRc_*xb.norm(); // lambda = 0
bool a_in = (ra_n <= 1.0);
bool b_in = (rb_n <= 1.0);
if (a_in && b_in) {
lam1 = 0.0;
lam2 = 1.0;
return;
}
DENS_VEC xab = xa - xb;
double rab_n = invRc_*xab.norm();
double a = rab_n*rab_n; // always at least an interatomic distance
double b = 2.0*invRc_*invRc_*xab.dot(xb);
double c = rb_n*rb_n - 1.0;
double discrim = b*b - 4.0*a*c; // discriminant
if (discrim < 0) return; // no intersection
// num recipes:
double s1, s2;
if (b < 0.0) {
double aux = -0.5*(b-sqrt(discrim));
s1 = c/aux;
s2 = aux/a;
}
else {
double aux = -0.5*(b+sqrt(discrim));
s1 = aux/a;
s2 = c/aux;
}
if (a_in && !b_in) {
lam1 = s1;
lam2 = 1.0;
}
else if (!a_in && b_in) {
lam1 = 0.0;
lam2 = s2;
}
else {
if (s1 >= 0.0 && s2 <= 1.0) {
lam1 = s1;
lam2 = s2;
}
}
};
//------------------------------------------------------------------------
// constructor
ATC_HardyKernelStep::ATC_HardyKernelStep
(int nparameters, double* parameters):
ATC_HardyKernel(nparameters, parameters)
{
for (int k = 0; k < nsd_; k++ ) {
if ((bool) periodicity[k]) {
if (Rc_ > 0.5*box_length[k]) {
throw ATC_Error(0,"Size of localization volume is too large for periodic boundary condition");
};
};
};
}
// function value
double ATC_HardyKernelStep::value(DENS_VEC& x_atom)
{
double rn=invRc_*x_atom.norm();
if (rn <= 1.0) { return 1.0; }
else { return 0.0; }
};
//------------------------------------------------------------------------
/** a step with rectangular support suitable for a rectangular grid */
// constructor
ATC_HardyKernelCell::ATC_HardyKernelCell
(int nparameters, double* parameters):
ATC_HardyKernel(nparameters, parameters)
{
hx = parameters[0];
hy = parameters[1];
hz = parameters[2];
invVol_ = 1.0/8.0/(hx*hy*hz);
cellBounds_.reset(6);
cellBounds_(0) = -hx;
cellBounds_(1) = hx;
cellBounds_(2) = -hy;
cellBounds_(3) = hy;
cellBounds_(4) = -hz;
cellBounds_(5) = hz;
for (int k = 0; k < nsd_; k++ ) {
if ((bool) periodicity[k]) {
if (parameters[k] > 0.5*box_length[k]) {
throw ATC_Error(0,"Size of localization volume is too large for periodic boundary condition");
};
};
};
}
// function value
double ATC_HardyKernelCell::value(DENS_VEC& x_atom)
{
if ((cellBounds_(0) <= x_atom(0)) && (x_atom(0) < cellBounds_(1))
&& (cellBounds_(2) <= x_atom(1)) && (x_atom(1) < cellBounds_(3))
&& (cellBounds_(4) <= x_atom(2)) && (x_atom(2) < cellBounds_(5))) {
return 1.0;
}
else {
return 0.0;
}
};
// bond intercept values for rectangular region : origin is the node position
void ATC_HardyKernelCell::bond_intercepts(DENS_VEC& xa,
DENS_VEC& xb, double &lam1, double &lam2)
{
lam1 = 0.0; // start
lam2 = 1.0; // end
bool a_in = (value(xa) > 0.0);
bool b_in = (value(xb) > 0.0);
// (1) both in, no intersection needed
if (a_in && b_in) {
return;
}
// (2) for one in & one out -> one plane intersection
// determine the points of intersection between the line joining
// atoms a and b and the bounding planes of the localization volume
else if (a_in || b_in) {
DENS_VEC xab = xa - xb;
for (int i = 0; i < nsd_; i++) {
// check if segment is parallel to face
if (fabs(xab(i)) > tol) {
for (int j = 0; j < 2; j++) {
double s = (cellBounds_(2*i+j) - xb(i))/xab(i);
// check if between a & b
if (s >= 0 && s <= 1) {
bool in_bounds = false;
DENS_VEC x = xb + s*xab;
if (i == 0) {
if ((cellBounds_(2) <= x(1)) && (x(1) <= cellBounds_(3))
&& (cellBounds_(4) <= x(2)) && (x(2) <= cellBounds_(5))) {
in_bounds = true;
}
}
else if (i == 1) {
if ((cellBounds_(0) <= x(0)) && (x(0) <= cellBounds_(1))
&& (cellBounds_(4) <= x(2)) && (x(2) <= cellBounds_(5))) {
in_bounds = true;
}
}
else if (i == 2) {
if ((cellBounds_(0) <= x(0)) && (x(0) <= cellBounds_(1))
&& (cellBounds_(2) <= x(1)) && (x(1) <= cellBounds_(3))) {
in_bounds = true;
}
}
if (in_bounds) {
if (a_in) { lam1 = s;}
else { lam2 = s;}
return;
}
}
}
}
}
throw ATC_Error(0,"logic failure in HardyKernel Cell for single intersection\n");
}
// (3) both out -> corner intersection
else {
lam2 = lam1; // default to no intersection
DENS_VEC xab = xa - xb;
double ss[6] = {-1,-1,-1,-1,-1,-1};
int is = 0;
for (int i = 0; i < nsd_; i++) {
// check if segment is parallel to face
if (fabs(xab(i)) > tol) {
for (int j = 0; j < 2; j++) {
double s = (cellBounds_(2*i+j) - xb(i))/xab(i);
// check if between a & b
if (s >= 0 && s <= 1) {
// check if in face
DENS_VEC x = xb + s*xab;
if (i == 0) {
if ((cellBounds_(2) <= x(1)) && (x(1) <= cellBounds_(3))
&& (cellBounds_(4) <= x(2)) && (x(2) <= cellBounds_(5))) {
ss[is++] = s;
}
}
else if (i == 1) {
if ((cellBounds_(0) <= x(0)) && (x(0) <= cellBounds_(1))
&& (cellBounds_(4) <= x(2)) && (x(2) <= cellBounds_(5))) {
ss[is++] = s;
}
}
else if (i == 2) {
if ((cellBounds_(0) <= x(0)) && (x(0) <= cellBounds_(1))
&& (cellBounds_(2) <= x(1)) && (x(1) <= cellBounds_(3))) {
ss[is++] = s;
}
}
}
}
}
}
if (is == 1) {
// intersection occurs at a box edge - leave lam1 = lam2
}
else if (is == 2) {
lam1 = min(ss[0],ss[1]);
lam2 = max(ss[0],ss[1]);
}
else if (is == 3) {
// intersection occurs at a box vertex - leave lam1 = lam2
}
else {
if (is != 0) throw ATC_Error(0,"logic failure in HardyKernel Cell for corner intersection\n");
}
}
}
//------------------------------------------------------------------------
// constructor
ATC_HardyKernelCubicSphere::ATC_HardyKernelCubicSphere
(int nparameters, double* parameters):
ATC_HardyKernel(nparameters, parameters)
{
for (int k = 0; k < nsd_; k++ ) {
if ((bool) periodicity[k]) {
if (Rc_ > 0.5*box_length[k]) {
throw ATC_Error(0,"Size of localization volume is too large for periodic boundary condition");
};
};
};
}
// function value
double ATC_HardyKernelCubicSphere::value(DENS_VEC& x_atom)
{
double r=x_atom.norm();
double rn=r/Rc_;
if (rn < 1.0) { return 5.0*(1.0-3.0*rn*rn+2.0*rn*rn*rn); }
else { return 0.0; }
}
//------------------------------------------------------------------------
// constructor
ATC_HardyKernelQuarticSphere::ATC_HardyKernelQuarticSphere
(int nparameters, double* parameters):
ATC_HardyKernel(nparameters, parameters)
{
for (int k = 0; k < nsd_; k++ ) {
if ((bool) periodicity[k]) {
if (Rc_ > 0.5*box_length[k]) {
throw ATC_Error(0,"Size of localization volume is too large for periodic boundary condition");
};
};
};
}
// function value
double ATC_HardyKernelQuarticSphere::value(DENS_VEC& x_atom)
{
double r=x_atom.norm();
double rn=r/Rc_;
if (rn < 1.0) { return 35.0/8.0*pow((1.0-rn*rn),2); }
else { return 0.0; }
}
//------------------------------------------------------------------------
// constructor
ATC_HardyKernelCubicCyl::ATC_HardyKernelCubicCyl
(int nparameters, double* parameters):
ATC_HardyKernel(nparameters, parameters)
{
nsd_ = 2;
double Lz = box_length[2];
invVol_ = 1.0/(Pi*pow(Rc_,2)*Lz);
for (int k = 0; k < nsd_; k++ ) {
if ((bool) periodicity[k]) {
if (Rc_ > 0.5*box_length[k]) {
throw ATC_Error(0,"Size of localization volume is too large for periodic boundary condition");
};
};
};
}
// function value
double ATC_HardyKernelCubicCyl::value(DENS_VEC& x_atom)
{
double r=sqrt(pow(x_atom(0),2)+pow(x_atom(1),2));
double rn=r/Rc_;
if (rn < 1.0) { return 10.0/3.0*(1.0-3.0*rn*rn+2.0*rn*rn*rn); }
else { return 0.0; }
}
//------------------------------------------------------------------------
// constructor
ATC_HardyKernelQuarticCyl::ATC_HardyKernelQuarticCyl
(int nparameters, double* parameters):
ATC_HardyKernel(nparameters, parameters)
{
nsd_ = 2;
double Lz = box_length[2];
invVol_ = 1.0/(Pi*pow(Rc_,2)*Lz);
for (int k = 0; k < nsd_; k++ ) {
if ((bool) periodicity[k]) {
if (Rc_ > 0.5*box_length[k]) {
throw ATC_Error(0,"Size of localization volume is too large for periodic boundary condition");
};
};
};
}
// function value
double ATC_HardyKernelQuarticCyl::value(DENS_VEC& x_atom)
{
double r=sqrt(pow(x_atom(0),2)+pow(x_atom(1),2));
double rn=r/Rc_;
if (rn < 1.0) { return 3.0*pow((1.0-rn*rn),2); }
else { return 0.0; }
}
};
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